# Fibonacci Life

September 20, 2010 | Posted by Robert Sheldon under Intelligent Design |

The Fibonacci sequence is one of those math marvels that even elementary students can appreciate. Like the discovery of the √2, it possesses this element of mystery that makes Pythagoras‘ harmonic series look like a rubber-band shoe-box next to a concert grand. Pythagoras famously drowned the fellow who discovered that √2 was neither even nor odd. It went against his religion. Fortunately for Gödel, the Pythagoreans did not control peer review when he demonstrated that unprovability was a whole lot worse than irrational numbers, but all math was “incomplete” and unable to exclude ambiguous theorems. But if we don’t demand that math obey our ideas of God, we can sit back an enjoy it. Here’s a YouTube video marvelling at the ubiquity of Fibonacci, calling it the fingerprint of God.

It is a well-worn metaphor, which other mathematicians might reserve for the Mandelbrot set. Physicists, on the other hand, prefer to see this in things like cosmology. Which raises the question, is the Fibonacci series merely a mathematician’s trick, or is there something hiding in the physics? Do the sunflower whorls contain a physical necessity, or merely an aesthetic necessity to match Fibonacci? And if so, then what about the spirals of galaxies? Surely we can say more about Fibonacci than mathematical aesthetics!

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A good ID question would be to see how difficult this pattern would be to emerge under a purely unguided physical universe- with only stochastic physical reaction and redundant laws to lean on.

Methinks this is a true sign of an intelligent designer who transcends the terrestrial.

However while this pattern is neat I must say that Descartes’ little known discovery of the Platonic Topological Invariant is much more interesting to me. If your interested please check out the book that gets into it- which is about how Descartes hid it in his secret notebook until years later Leibniz came and discovered it.

http://www.amazon.com/Descarte.....038;sr=8-1

A real pleasure to read- and used is less than a buck.

Descartes is btw one of the most underrated mathematicians in history. He is the originator of the Descartes Coordinate system the X Y axis T graph used in all basic algebra classes today- a very spiritual man too who started his secret notebooks with the line

“All wisdom begins with fear of God”

Truly well written Dr. Sheldon. I think that is about as close as I’ve seen someone come to making the wonder of mathematics a spiritual experience.

My mathematically oriented interests — software engineering in general, computational number theory, and artificial intelligence — were major factors in convincing me that Darwinian chance-and-necessity orthodoxy is an irrational, totally unsupported, Himalayan-sized dung heap of hopeless speculation.

He forgot to mention how the Fibonacci sequence can give you the golden ratio and can be found in Pascal’s triangle. Or the original rabbit breeding story problem Fibonacci proposed.

There is a mathematical journal, The Fibonacci Quarterly, dedicated to this and similar sequences.

I do believe that the importance of the Fibonacci series in nature is a good argument in the cintext of cosmological ID.

Cosmological ID is a valid part of ID, but it is methodologically separated from biological ID. The reasoning and the arguments are different, even if the conclusions are similar.

While I prefer to reason about biological ID, because I feel that the arguments are at present more detailed, and that reductionists and darwinists really cannot counter them in any way, I do believe that cosmological ID is true: the non living world and its laws are no less designed than biological realities. Only, the ways to demonstrate those two aspect of design are different.

ellazimm:

I hope you had a very fine celebration of your birthday. My best wishes to you!

Pythagoras famously drowned the fellow who discovered that ?2 was neither even nor odd.?2 can’t be expressed as the ratio of two integers – I don’t think that anyone discussed the problem whether it was even or odd….

gpuccio: Yeah, had a great time and even won some money!! Thanks!

I gotta admit, the ways the Fibonacci sequence keeps coming up in nature is kind of creepy! When I was sure God was trying to send me messages it was things like that (and lots of what I thought of as highly improbably coincidences) that made me feel like I was tapping into something bigger and greater. I hope you explore the sequence more if you haven’t already. I love teaching about; even kids of age 10 or 11 can see some of the ‘magic’.

Thanks for being patient with me and polite and respectful. Be sure and let me know if I ever fail to respond in kind.

Getting close to 8am in England so I’ve got to get ready for work. Thanks again to everyone; I know I’m an erratic and stubborn contributor but I’m here ’cause I want to hear what y’all think. And I do that by asking lots of questions and I try to be honest without, hopefully, being strident.

See yah later!!

Fibs have fascinating applications outside of nature. As one who trades the stock market I use them all the time as one of my technical indicators to predict future market movements.

Vivid

ellazimm:

You ask whatever you want: I appreciate that.

One of the things that is interesting is that the integral values appear to be exact locations on what must essentially be a continuous function. The arcs we see drawn in each segment are just approximations to the “true” spiral since the curvature decreases smoothly in natural form as the radius increases.

Hello Everybody,

I’m not an english native guy and my language is not english, then it’s possible that I can’t express some ideas (“hard” ideas, of course), very well. My apologies if this is the case…

I’m very familiar with all that is said in this web because I’ve read many threads during last years and I think that the ID proposition is a good one but it need even another step in the theory to make it more understable to the science comunity.

I like very much the gpuccio position in all his participation because I think that in this time we need a constructive stand and is needed a dialog attitude and not a debate attitude, understanding dialog as a position that allow other people express his ideas, even when they are strong against ours, take the good of them and then posit own ideas on the table in order to build a greater idea…Inteligent & constructive evolution, can be named, nor destructive devolution, as in the debate position.

Now in the question, Fibonacci & Nature, what says to me?

If I write from a metaphysical point of view, this say for me that there be a hyper-intelligent-designer that can create a so beautiful universe from NOTHING. Once I can see it, it’s no dificoult for me to make a similar thing, but from SOMETHING.

But, from the scientific position, that I think we must have ever live in this site, I can see 4 great evidences:

1) The Universe we see is

quantified. Fibonacci series are a property of cardinals.2) The Universe we see has a universal

cohesionbetween his “quantos” of particles. This can be a evidence of the reality of gravity.3) The Universe we see is

fourth dimensional.and 4)

The Big-Bang theory is falsified. There must be a new theory to explain better what we see.The two last points are hard to explain well here, but the two first I think that are easyly understood for everybody.

That’s all for now, sorry if I don’t express well my thinking, but I wish that it have been enough understable.

Thanks for read me,

Obriton

Welcome Obriton, you seem to do very well expressing yourself with what English you now know.

Of related interest to The Fibonacci sequence,,, we were discussing Euler’s number yesterday, right before you posted this thread Dr. Sheldon,,, and it to seemed to take on almost a ‘spiritual’ tone as your thread currently does:

starting from this post on Human Consciousness:

http://www.uncommondescent.com.....ent-364226

it went somewhat as follows:

kf:

And as to the reality or not of numbers, I note just one little equation:

0 = 1 + e ^(i*pi) — Euler

Believe it or not, the five most important numbers in mathematics are tied together, through the complex domain.,,,,,,,,,And that points, ever so subtly but strongly, to a world of reality beyond the immediately physical.,,,,,You may resist it, but there the compass needle points.

ba77:

As well Euler’s number finds striking correlation to reality,,,

The following image, Bible verse and video are very interesting since, with the discovery of the Cosmic Microwave Background Radiation (CMBR), the universe is found to actually be a circular sphere:

3D image of CMBR

http://www.google.com/imgres?i.....9,r:3,s:12

Proverbs 8:26-27

While as yet He had not made the earth or the fields, or the primeval dust of the world. When He prepared the heavens, I was there, when He drew a circle on the face of the deep,

The Known Universe by AMNH – video

http://www.youtube.com/watch?v=17jymDn0W6U

The flatness of the ‘entire’ universe, which is necessary to correspond to pi in Euler’s is found here:

Did the Universe Hyperinflate? – Hugh Ross – April 2010

Excerpt: Perfect geometric flatness is where the space-time surface of the universe exhibits zero curvature (see figure 3). Two meaningful measurements of the universe’s curvature parameter, ½k, exist. Analysis of the 5-year database from WMAP establishes that -0.0170 < ½k < 0.0068.4 Weak gravitational lensing of distant quasars by intervening galaxies places -0.031 < ½k < 0.009.5 Both measurements confirm the universe indeed manifests zero or very close to zero geometric curvature,,,

http://www.reasons.org/did-universe-hyperinflate

This following video shows that the universe also has a primary characteristic of expanding/growing equally in all places which strongly corresponds to e in Euler's number:

Every 3D Place Is Center In This Universe – 4D space/time – video

http://www.metacafe.com/watch/3991873/

Towards the end of the following video, Michael Denton speaks of the square root of negative 1 is necessary to explain the actions of quantum mechanics in this universe:

Michael Denton – Mathematical Truths Are Transcendent And Beautiful – Square root of -1 is built into the fabric of reality – video

http://www.metacafe.com/watch/4003918

I find it extremely strange that the enigmatic Euler's number would find such striking correlation to reality. In pi we have correlation to the 'sphere of the universe' as revealed by the Cosmic Background radiation, as well pi correlates to the finely-tuned 'geometric flatness' within the 'sphere of the universe' that has now been found. In e we have the fundamental constant that is used for ascertaining exponential growth in math that strongly correlates to the fact that space time is 'expanding/growing equally' in all places of the universe. In the square root of -1 we have what is termed a 'imaginary number', which was proposed to help solve equations like x2+ 1 = 0 back in the 17th century, yet now, as Michael Denton pointed out in the preceding video, it is found that the square root of -1 is required to explain the behavior of quantum mechanics in this universe. The correlation of Euler's number, to the foundational characteristics of how this universe is constructed and operates, points overwhelmingly to a transcendent Intelligence, with a capital I, which created this universe! It should also be noted that these universal constants, pi,e, and square root -1, were at first thought to be completely transcendent of any material basis, to find that these transcendent constants of Euler's number in fact 'govern' material reality, in such a fundamental way, should be enough to send shivers down any mathematicians spine.

If that was not enough, this following video shows how pi and e are found in Genesis 1:1 and John 1:1

Euler’s Number – God Created Mathematics – video

http://www.metacafe.com/watch/4003905

This following website has the complete working out of the math of Pi and e in the Bible, in the Hebrew and Greek languages respectively, for Genesis 1:1 and John 1:1:

http://www.biblemaths.com/pag03_pie/

This following article also reminded me of your post Dr. Sheldon:

God by the Numbers

Excerpt: The final number comes from theoretical mathematics. It is Euler's (pronounced "Oiler's") number: e?i. This number is equal to -1, so when the formula is written e?i+1 = 0, it connects the five most important constants in mathematics (e, ?, i, 0, and 1) along with three of the most important mathematical operations (addition, multiplication, and exponentiation).

These five constants symbolize the four major branches of classical mathematics: arithmetic, represented by 1 and 0; algebra, by i; geometry, by ?; and analysis, by e, the base of the natural log. e?i+1 = 0 has been called "the most famous of all formulas," because, as one textbook says, "It appeals equally to the mystic, the scientist, the philosopher, and the mathematician."

http://www.christianitytoday.c.....ml?start=3

kairosfocus added this to the discussion on Euler's number:

The Euler equation is hands down the most beautiful equation in all mathematics.

And, it is so utterly astonishing, a surprise that comes out of nowhere, almost.

Zero, the empty space on the abacus

1 the first number and the number of identity

e, which governs so many kinds of growth and decay

i, the strangest number of all: the “imaginary” root of a negative number.

pi, the ratio of circumference to diameter of the “perfect” geometrical figure.

All of them, tied up in one equation.

If you needed a signature of the Ultimate Mathematician who built a world that embeds mathematics and number, here it is.

Welcome aboard Orbitron.

I enjoyed you post very much.

correction: the ? means pi in the last referenced article.

you = your

Thanks, very much UB & BA for your welcome.

I’ve learned many things here from many people, pro and against the ID bases, with very good arguments that I think are to be taken into account and I’ll would like to make my own contribution, on my possibilities, as a way of gratitude to all the people that had participated here from the beginning until now.

I want to explain the second point of my statements a little more, because I think it can be interesting for ID thinking.

I think it is impossible a coherent (understable) universe if there no be cohesion inside it. The first thing for a understable entity (universe in a local sense), functional or not, is to have some type of coherence.

Our universe posses this characteristic: one material point is connected attractively to another material point, for more and more away that it could be, with more intensity as more is the quantity of matter that is far from the original point, and more intensity as less the other point is far to the first. That is the universal gravity law. By necessity, the matter of one point in the universe is less than the rest of mass of the universe. And this cause a permanent and coherent equilibrium among all the material “pieces” of the universe because when a huge ammount of matter is accumulated in a zone the rest of the universe “reacts” attracting this huge mass and so maintains the cohesion.

Think for a moment a more or less spherical and homogeneus universe of many, many particles with a cohesion force of that sort. The interior particles tend to stand in his original position because the symetric forces of both sides (more equilibrated as more near to the center)makes a neutralization, But the outside particles are disequilibrated and tends to join.

The first time that “want” to join one outermost particle (in a spherical surface) must connect with the immediately particle forward the inner and this makes a first group near the surface of particles of 1 element and of 2 elements.

The next step, the double particles are more attracted to single particles that sigle-single connection, ant then the main joining will be 2-1, some 1-1 and a minor 2-2, that is converted in a disequilebrated point and tends to create its own dynamic. The rest of the surface goes then to a connection of 2-1 with the 1-1 to form a 5 multiparticle (his atraction is 3×2 = 6 strongest that a 1-1 connection. The five elements particle has “afinity” to the three elements particle and joins in aa eight elements particle. Then the process would be on and on in a secuence of 1-2-3-5-8-13… WOOOAAA… the Fibonacci serie.

That is then a more or less common process in a universe that is coherently and quantizied concibed, and it is in the outermost part of the same, his surface, where we can see it.

In conclusion, to see a Fibonacci serie formation in our universe is a good evidence for us that we are in a coherent and understable universe.

Thanks again for the welcome and thanks again for read my comments.

Until the next

Obriton

Is the Fibonacci any better evidence of ID than a circle? I understand it is a series, but so is the depth of sand piled up along the side of cliff side as a function of distance from the base of the cliff.

By the way, another Fibonacci series is the distance of the planted from the sun. Well, maybe not exactly a Fib. seq. but similar. As I understand it, the distance of any one planet to the sun is generally equal to the sum of the distances of the planets closer to the sun. Fibonacci-esque 😛

JGuy

“Is the Fibonacci any better evidence of ID than a circle? I understand it is a series, but so is the depth of sand piled up along the side of cliff side as a function of distance from the base of the cliff.”

My opinion:

Circles (natural circles, I understand, not artificial them), are also a consequence of a cohesive universe but a flat universe, that is, attractive conexion is only in two dimensions. When I refer “universe” I’m saying not The Universe, but a little universe within another Universe.

When we see a natural circle within a cohesive flat universe, we are seeing a design that is “forced” by the laws (natural laws) of this universe. For example, when a drop of rain fall over the surface of a lake, we are seeing the cohesión attraction inside this particular flat universe in action. They are the famous circular waves that travel over the water (really the effect is three dimensional, but the particles out in the third dimension, are those that allow see a real circle into the plane of the surface).

In the other hand, if we see a circle in a heterogeneous flat and deconexed universe, we are certain that it is an artificial circle all the way, because a no cohesive universe cannot produce by itself a circle (chance does not acts so, chance has his own laws). This circle must be designed well by an external agent, either by an internal agent that is constrained to “the law of a circle”, that is, that his distance to a point is the same for all the points of his circumpherence, or that is a inteligent agent that knows how to make a circle. For example,a circle in a grass field… ¡artificial! definitely. Can be caused, well by a circular external agent, as a metheorite or another object that leaves his footprint, or can be caused by an internal agent, as a cow that is tied to a rope that is subject to a point, the center of this circle.

From the ID perspective, I think it is very important in the first place to know the universe (little universe, of course) where a design is inserted inside. If this design is homogeneous in a heterogeneous universe, it is artificial for sure, and then we can affirm without any doubt that is a agent in action.

If the action (the design) is a instant action then, it is a external action, a footprint of the external agent. If the desig needs a continued process then it needs a internal agent capable of realize this design “without inteligence”, that is, forced by some algorithm that defines the design (in the exapmple of the circle -> x^2+y^2<=r^2).

If the design is complex enough to cannot be materialized by a single algorithm, then the agent is a

inteligent agent. I think that two or three unrelated geometric shapes (for example a circular sector and a pentagon)can be enough to considere a design within a limited heterogeneous “mini-universe”,Inteligent Designed, if the agent is a single agent. But it is the question here, and in my opinion, all it is needed is a good standard to determine if a design is inteligent, natural or circumstantial forced. I think the actual method (probabilistic method) is good for a negative background but is hard to measure in very complex designs. A analytical method would be the correct way to convince the scientific comunity. I’m working in this area and I consider that could be a way to build a theory from the analytical perspective.Sorry for the lenght of the post, although I believe it is necessary for a good understand of the question.

Regards,

Obriton

gpuccio,

“I do believe that the importance of the Fibonacci series in nature is a good argument in the cintext of cosmological ID.

Cosmological ID is a valid part of ID, but it is methodologically separated from biological ID. The reasoning and the arguments are different, even if the conclusions are similar.”

After just some cursory research on the Fibonacci Sequence, one discovers that there are patterns in nature, such as the center of the sunflower, and other flower petals, as well as marine shells, , pineapples and pine cones, which appear to follow the Fibonacci Sequence in their design. While I find it interesting, and perhaps more research on my part is required; don’t you think that a biological design argument could also be made in that regard, as opposed to just the pattern (golden rectangle, divided by a square repeatedly, finding curves, representing a spiral through all the squares) being apparent in galaxies? I also found an article, which suggests that the sequence is present in the Mandelbrot set, but I’m a little confused as to how. I suspect that much of this may be merely speculation, and people forcing evidence to match a hypothesis, but it looks intriguing.

I’m not so much intrigued by the spiral in galaxies, because there are physical explanations; however, it is interesting that the shape should follow so exactly in accord with a certain set of numbers. I don’t know how to explain it. Any thoughts?

Off-topic,

Researchers find parting of Red Sea (sort of) possible.

http://news.blogs.cnn.com/2010.....k/?hpt=Mid

Collin, I don’t know if you remember this, but a documentary was done on the Red Sea Exodus a few years back,,,:

The Exodus Decoded – Part – 1/4

http://www.youtube.com/watch?v=AjKyRoyIjjw

The documentary was done by Simcha Jacobovici and he indeed uncovered much evidence that the Exodus did indeed occur,,, volcanic ash was dated to the proper time,,, archaeological markers were dated at appropriate places before and after the Exodus,,, there may be more evidence but that is all I can recall off the top of my head,,, I gained much respect for Simcha Jacobovici and his scholarship in that documentary,, yet,,, unfortunately he lost that respect fairly quickly with his next documentary,,,

The Lost Tomb of Jesus

http://en.wikipedia.org/wiki/T.....b_of_Jesus

,,, in which he tried to use probability calculations to say that the remains of Jesus was in a tomb, along with his family members,,, yet, as you might well know, Dr. Dembski has a PhD. in mathematics in which his expertise is precisely in probability calculations,,, and Dr. Dembski wrote this following paper, in conjunction with Dr. Marks, in refutation to the later Jacobovici documentary,,,,

The Jesus Tomb Math

http://www.designinference.com.....b_Math.pdf

,,, also of note, and I don’t know if it really matters,, but Jacobovici is of Jewish heritage and may explain a little of the reason why he balanced the evidence so unevenly in the two different documentaries that he did.

Hi all. I’ve been abstaining from philosophical discussions, especially of the argumentative kind, but I saw this post about math, so I’d like to comment.

1. In the opening post, the statement, “Pythagoras famously drowned the fellow who discovered that ?2 was neither even nor odd” is quite wrong. The fact that ?2 is not odd or even is trivially true because ?2 is not an integer. Pythagorus (not someone else) proved that ?2 is

irrational, which is a considerably more significant finding, and was somewhat earth-shattering (at least to Pythagorus and his follows) at the time.The proof usually taught in high school is a proof by contradiction, and it does involve some number theory about the properties of odd and even numbers – perhaps that is what confused Sheldon.

2. To bornagain at 14: Euler’s identity does not “come out of nowhere.” It follows pretty straightforwardly from the Taylor series for sin x, cos x, e^x, and is best understood in terms of vectors in the complex plane. I teach all this to high school beginning calculus students.

It certainly is a lovely result – there is no doubt about that, and Euler et al are to be congratulated for the work they did to bring it to light.

3. To JGuy at 19: You write, “By the way, another Fibonacci series is the distance of the planted from the sun. Well, maybe not exactly a Fib. seq. but similar. As I understand it, the distance of any one planet to the sun is generally equal to the sum of the distances of the planets closer to the sun. Fibonacci-esque .”

No, the orbits aren’t close to being a Fibonacci series. Also, “the distance of any one planet to the sun is generally equal to the sum of the distances of the planets closer to the sun” is not an accurate statement of the rule that describes a Fibonacci series. You might look up the distances from the sun for each planet and see for yourself.

4. To Obitron at 20: you write, “In conclusion, to see a Fibonacci serie formation in our universe is a good evidence for us that we are in a coherent and understable universe.”

We obviously live in a coherent and understandable world. I don’t think anyone seriously doubts that.

Oops – above ?2 is really “square root of 2”. My character didn’t render the same online as it did in my word processor.

Aleta you state:

To bornagain at 14: Euler’s identity does not “come out of nowhere.”

Actually I never implied that the equation ‘came out of nowhere’. I thought I had made the corresponding physical evidence to the foundational, and the overarching, characteristics of the universe more than clear enough to illustrate that the equation has a transcendent origin from God! Sure I used broad measures to roughly fit the equation to physical characteristics, yet, despite my somewhat brute manner in my coarse fit of physical evidence to the equation, the fit has an utter serendipity that I consider a ‘beautiful thought’ pointing very strongly to truth. You see my wonder stems from the physical correspondence. And though the equation may flow some other method of math, I firmly believe you have cheated yourself of the wonder inherent in the correspondence between the physicality and the ‘transcendent equation, by fooling yourself into thinking ‘you have it all figured out’ when clearly you have missed the forest for the trees,,, Furthermore, That the default hypothesis of materialism is that such correspondence is purely, and ultimately, the result of ‘chance’ only firmly solidifies my conviction that such ‘coincidence’ is the handiwork of God.

Of note:

“The Word” in John 1-1 is called “Logos” in Greek and is the root word from which we get the word “Logic”.

Hi bornagain,

You write, “Actually I never implied that the equation ‘came out of nowhere’”

Looking back at 14, I now see, I think, that it was kairosfocus that said “And, it is so utterly astonishing, a surprise that comes out of nowhere, almost.” Since you didn’t actually show quotes, however, I read it as if those were your words – reading your post, it’s a bit hard to follow what are you words and what are quotes and excerpts from others. My apologies for mis-attributing that sentence to you.

You write, “You see my wonder stems from the physical correspondence. And though the equation may flow some other method of math, I firmly believe you have cheated yourself of the wonder inherent in the correspondence between the physicality and the ‘transcendent equation, by fooling yourself into thinking ‘you have it all figured out’ when clearly you have missed the forest for the trees.”

I think you are jumping to some unwarranted assumptions here. I believe that my wonder about both mathematics in general and Euler’s identity in particular, is enhanced, not diminished, by understanding the mathematics that produces it. “Figuring out” why it is true in terms of more basic mathematical ideas makes my understanding and appreciation more richer and deeper, I think, than the person who just contemplates the identity as a fact divorced from understanding.

Furthermore, when I teach math, I emphasize the ways in which math can be applied to the real world – I consider that a key part of my teaching. I explicitly teach the theory of mathematical modeling, and the practice of applying and testing those models in the real world. I teach the ways, for instance, that imaginary numbers can be applied to the real world, and explain how misleading it is to consider them any more or less “imaginary” than any other kind of number.

So you are wrong to think (based on what evidence I do not know) that somehow I’ve cheated myself out of something, or that I don’t understand the forest just because I also understand the individual trees. If we followed your reasoning, it seems, I wouldn’t bother to teach my students why the math they learn is true – I’d just ask them to bask in its wonder. As a teacher, I think that would very much be the wrong thing to do.

To ba77:

the equation has a transcendent origin from God!Really ? And the area of a rectangle = LxB. Does this also come from god ?

I dont remember this from school.

Aleta,

“I believe that my wonder about both mathematics in general and Euler’s identity in particular, is enhanced, not diminished, by understanding the mathematics that produces it.”

Now let’s take this statement, you say,,, “understanding mathematics that produces it” (Euler’s number)

I’m trying to make it clear to you that God mind produces it not mathematics,,, You are looking at the equation from one direction from one direction I’m looking at it from the other!

Clearly since Euler’s number is overarching and foundational in mathematics, as well as in the physical reality of the geometric structure of this universe, then all other ‘lesser’ mathematics will be derived off of, or be somehow dependent on, Euler’s number, and though you may build your way from that ‘derived, lesser’ mathematics to that equation which supplies the stable geometric structure of this universe, Namely build your way from underlying mathematical geometric principles to the main ‘blueprint’ principle of Euler’s number, that in no way gives you any right to say that the ‘lesser’ mathematics has ‘produced’ Euler’s number, for without that stable geometric structure, within this vibrantly dynamic space-time in the first place, then that ‘lesser’ mathematics would not even be able to be consistently true in the first place. i.e. Your ‘lesser’ Math is dependent on the stability of Euler’s being true in the first place… I commend you on your understanding of math, but please give credit where credit is due, the foundational equation of Euler’s number and the correspondence it has to physical reality is ‘produced’ by God not by ‘derived’ mathematics.

Hi ba.

Let’s first clear up an inaccuracy. An article you quote writes, “The final number comes from theoretical mathematics. It is Euler’s (pronounced “Oiler’s”) number: e^?i. This number is equal to -1.”

This is incorrect. e itself is Euler’s number, not e^?i.

I am a bit puzzled by the philosophy you are espousing. You write, “Clearly since Euler’s number is overarching and foundational in mathematics, as well as in the physical reality of the geometric structure of this universe, then all other ‘lesser’ mathematics will be derived off of, or be somehow dependent on, Euler’s number.”

But Euler’s number is not the endpoint of math, anymore than 1 is, or ?, or a straight line, or any number of other concepts. In some sense, math (and not its manifestation in reality) is all of a piece. We, as humans, both historically and conceptually, have build our understanding of math, and the notational systems we use to express that understanding, from the bottom up, so to speak, starting with the simplest ideas. But all of mathematics is implicitly present in the system: for instance, Mandelbrot’s set (which is far more amazing than Euler’s identity, to my mind) existed, in some sense, as a mathematical structure irrespective of whether anyone had “discovered” it, and I am sure that there are mathematical structures we have not figured out yet that are yet to be discovered.

So I don’t think one can say that we could start with e and derive the foundations backwards, and I don’t think it’s correct to say that those foundations are dependent on e. The fact that an even number squared is even, for instance ( a basic fact of number theory) is not dependent on the existence and nature of e, even though the two are entangled together by the vast web of relationships that tie all of mathematics together.

I will grant that the language that a certain chain of explanations “produces” the number e, or the larger fact that e^i pi = -1, is misleading. The chain of explanations is just that – explanations that satisfy us because we can follow the reasoning to see how e is related back to earlier concepts in a logical way. But, as I said earlier, the math itself is a holistic whole – however, but we as human beings have to approach it as building from the more basic to the less basic.

You also write, I’m trying to make it clear to you that God mind produces it not mathematics,,, You are looking at the equation from one direction from one direction I’m looking at it from the other! … I commend you on your understanding of math, but please give credit where credit is due, the foundational equation of Euler’s number and the correspondence it has to physical reality is ‘produced’ by God not by ‘derived’ mathematics.”

I don’t believe in God, as you do, so this is not very relevant to me. Also, I didn’t say that the “correspondence it has to physical reality is‘produced’ by … ‘derived’ mathematics.” The correspondence that math has to the physical world is a separate issue from the issue of how, within the logical world of math, e is related to other parts of math. I’ve been primarily discussing the former, not the latter, although I did point out that I do teach, strongly, about applying math to the real world in my classes.

Aleta

Hi, Aleta. I like you participate here with your opinion and I agree, in first instance, but I need to explain what I’m refering when I said “understandable” in that context to see why it’s not so obvious my sentence.

For understandable I mean that it’s possible, in any level of detail, explain using logic any determined phenomenon (of our universe). I think it is true but it’s not obvious.

For example, can you or anybody explain me, that is, make understandable to me, the life phenomenon?, is obvious that is understandable?

Many, many, many phenomena that we see all the days and everywhere are evident (we can see them) but not obviuosly understandable. If you see yourself walking over the sea you can’t say that it is not possible, because you are walking “naturally” over the sea, but, in my sense of understandable, you must think that it is understandable even if you can’t understand why it happen in that moment. Not so obvious, don’t?

And in the Fibonacci serie, when we can see it in our universe, I think that it can help me to see that all in the universe is understandable (life included).

Sorry if I dont explain it very well, but english is’nt my native languaje.

Thanks Aleta for your opinion and good day for everybody.

Sorry, but in the previous post I have quoted the following from Aleta, but doesn’t appears (I must have made something wrong):

“We obviously live in a coherent and understandable world. I don’t think anyone seriously doubts that.”

All that I’ve writed is about this quote.

My apologies.

Another point.

The relevance of the quantification.Many people thinks that continuity is possible. In fact, Science apply continuity to many phenomena -> the movement of the planets, the sound, the surface of a sphere, etc…

But if we try, for example, to make a single circle, with whatever or in wichever mean, we see that it is

materiallyimpossible, that is, we can’t produce with material means,finitemeans, ainfinitereality (here the question is: is circle reality?).You can say: “There be 10^10^10^10^10, that is, 10^10000 elements in our universe! Such elements are not sufficient to construct a circle?”. An the answer ever will be: No. Never. It is not a circle, it is “almost” a circle but it is a circle with 10^1000 elements which, of course, are all in a circle, but they are not a circle! A circle has…

infinite elements.That is another way, in my opinion, of stablishing the Heidenberg Principle, if you understand well which are the limits of a quantizied universe. And that is also the false, but understandable dylemma of Pytagorus with SQR2: a logic reality can’t be materialized. Where is the error?, in the logic reality or in the material reality?. I think that there isn’t error in any of the two realities, but we need to understand better what each thing is. (Off topic: I think that Pythagorus was a usurper, that he learn many things of the egyptians “doctors” who then presented as discovered by him, and he didn’t understand well many things. But this is clear off topic, and is only as a little polemic anecdote).

Thats all for now. I’ll see you later.

Lets see Aleta where do I start??? first I am not talking solely of e, (as if you really thought I was; the equation was wrote out for pete’s sake), further,,, reflecting on the ‘equation’..

e^pi*i + 1 = 0

,,, we find that,,,

pi is required here:

General Relativity (Einstein’s Equation)

https://docs.google.com/File?id=dc8z67wz_52c9nxpz2h_b

square root of negative 1 is required here:

Quantum Mechanics (Schrödinger’s Equations)

https://docs.google.com/File?id=dc8z67wz_51ck47zff3_b

and here for more detail:

http://en.wikipedia.org/wiki/S.....r_equation

e is required here in wave equations, in finding the distribution of prime numbers, in electrical theory, and is also found to be foundational to trigonometry at the bottom of the page here,,, which you referenced earlier as ‘producing’ the equation,,,:

http://www.biblemaths.com/pag03_pie/img0.gif

,,, which I now see more clearly was a false assertion of yours,,,,

Thus Aleta all this foundational math I referenced is dependent on the constants of Euler’s number being true,,, (If you want to call the equation Euler’s identity instead of Euler’s number so you don’t confuse it with the ‘exponential constant”, e, I don’t care, but I will use the common name if you don’t mind),,,

,,,That you find the mandelbrot set more ‘pleasing’, or ‘interesting’, really is uninteresting to me for I don’t see the Mandelbrot set being absolutely essential for these foundational equations we use to understand the universe,,,,.

That General Relativity would require pi, and that the Shroedinger equation would require the square root of negative 1 (i), is very interesting to me since the ‘unification’ of General Relativity and Quantum mechanics remains elusive despite decades of work by brilliant minds trying to unify them. Moreover, That pi and i would ‘unify’ so easily within Euler’s number as the exponent of e should be of no less wonder to you than it is to myself.

Further notes:

I find it extremely interesting, and strange, that quantum mechanics tells us that instantaneous quantum wave collapse to its ‘uncertain’ 3-D state is centered on each individual observer in the universe, whereas, 4-D space-time cosmology tells us each 3-D point in the universe is central to the expansion of the universe. These findings of modern science are pretty much exactly what we would expect to see if this universe were indeed created from a higher dimension by a omniscient, omnipotent, omnipresent, eternal Being who knows everything that is happening everywhere in the universe at the same time. These findings certainly seem to go to the very heart of the old question asked of many parents by their children, “How can God hear everybody’s prayers at the same time?”,,, i.e. Why should the expansion of the universe, or the quantum wave collapse of the entire universe, even care that you or I exist? Only Theism offers a rational explanation as to why you or I, or anyone else, should have such undeserved significance in such a vast universe:

Psalm 33:13-15

The LORD looks from heaven; He sees all the sons of men. From the place of His dwelling He looks on all the inhabitants of the earth; He fashions their hearts individually; He considers all their works.

Though mathematicians seem to be having a extremely difficult time ‘unifying’ QM and Relativity, this unification, into a ‘theory of everything’, between what is in essence the ‘infinite world of Quantum Mechanics’ and the ‘finite world of the space-time of General Relativity’ seems to be directly related to what Jesus apparently joined together with His resurrection, i.e. related to the unification of infinite God with finite man:

The Center Of The Universe Is Life – General Relativity, Quantum Mechanics and The Shroud Of Turin – video

http://www.metacafe.com/w/5070355

The End Of Christianity – Finding a Good God in an Evil World – Pg.31

William Dembski PhD. Mathematics

Excerpt: “In mathematics there are two ways to go to infinity. One is to grow large without measure. The other is to form a fraction in which the denominator goes to zero. The Cross is a path of humility in which the infinite God becomes finite and then contracts to zero, only to resurrect and thereby unite a finite humanity within a newfound infinity.” http://www.designinference.com.....of_xty.pdf

Philippians 2: 5-11

Let this mind be in you, which was also in Christ Jesus: Who, being in the form of God, thought it not robbery to be equal with God: But made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of men: And being found in fashion as a man, he humbled himself, and became obedient unto death, even the death of the cross. Wherefore God also hath highly exalted him, and given him a name which is above every name: That at the name of Jesus every knee should bow, of things in heaven, and things in earth, and things under the earth; And that every tongue should confess that Jesus Christ is Lord, to the glory of God the Father.

“Miracles do not happen in contradiction to nature, but only in contradiction to that which is known to us of nature.”

St. Augustine

further note:

This following site is a easy to use, and understand, interactive website that takes the user through what is termed ‘Presuppositional apologetics’. The website clearly shows that our use of the laws of logic, mathematics, science and morality cannot be accounted for unless we believe in a God who guarantees our perceptions and reasoning are trustworthy in the first place.

Proof That God Exists – easy to use interactive website

http://www.proofthatgodexists.org/index.php

Mathematics is the language with which God has written the universe.

Galileo Galilei

The Unreasonable Effectiveness of Mathematics in the Natural Sciences – Eugene Wigner

Excerpt: The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

http://www.dartmouth.edu/~matc.....igner.html

Aleta I’m sorry if I didn’t address all your points, but as to the overall point I think I have been abundantly clear that Mathematics does indeed come from God

ba writes, “Thus Aleta all this foundational math I referenced is dependent on the constants of Euler’s number being true,,, (If you want to call the equation Euler’s identity instead of Euler’s number so you don’t confuse it with the ‘exponential constant”, e, I don’t care, but I will use the common name if you don’t mind),,,”

I’m not interested in discussing whether God is the source of mathematics or not, and I’m quite familiar with the important ways in which e, i and pi can be applied to understanding our world.

But I also think proper vocabulary is important:

e is Euler’s number

e^i pi + 1 = 0 is Euler’s identity.

“Euler’s number” is NOT the common name for e^i pi + 1 = 0

Google the two phrases and compare the first 10 hits of so.

Aleta, I appreciate your concern, but as I have found the preponderance of my references to refer to the equation as Euler’s number, and I cannot change the sites on the web, then the only change I can make is to my notes with this appended note… Euler’s Number (properly called Euler’s Identity),,, Happy/// 8) ,,,

One other thing that struck a note of deep concern in me is this statement of yours,,,

‘I’m not interested in discussing whether God is the source of mathematics or not,’

Please tell me exactly why not Aleta,,, Aleta since I have in fact laid out some very compelling evidence that God is indeed the source of Mathematics,,, and as Richard Dawkins has himself stated,,,

“The presence of a creative deity in the universe is clearly a scientific hypothesis. Indeed, it is hard to imagine a more momentous hypothesis in all of science.” — Richard Dawkins.

Then why in blue blazes does this ‘not interest’ you in the least,,, Do you have perhaps some other plan than facing your Creator when you die???? I believe that plan has been put on hold Aleta!!! Ignoring the elephant in the living room, as you are treating the overwhelming evidence for God right now, certainly will not make the elephant go away! Perhaps someday when you are not so busy with all the other things in your life that seem to take precedence over what should be your primary concern about your relationship with God, you may feel differently than just ignoring this area of your life. I certainly pray so. Myself I find a hard time Imagining anything that would take such importance as to make God ‘uninteresting’ to you.

Further notes:

“The equations of physics have in them incredible simplicity, elegance, and beauty. That in itself is sufficient to prove to me that there must be a God who is responsible for these laws and responsible for the universe,”

said astrophysicist Paul Davies in his book Superforce (1984). The famous Russian physicist, Alexander Polyakov put it this way in Fortune magazine (October, 1986),

“We know that nature is described by the best of all possible mathematics because God created it.”

The best data we have [concerning the Big Bang] are exactly what I would have predicted, had I nothing to go on but the five books of Moses, the Psalms, the bible as a whole.

Dr. Arno Penzias, Nobel Laureate in Physics – co-discoverer of the Cosmic Background Radiation – as stated to the New York Times on March 12, 1978

The Underlying Mathematical Foundation Of The Universe -Walter Bradley – video

http://www.metacafe.com/watch/4491491

The Five Foundational Equations of the Universe and Brief Descriptions of Each:

http://docs.google.com/Doc?doc.....#038;hl=en

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? — Albert Einstein

“… if nature is really structured with a mathematical language and mathematics invented by man can manage to understand it, this demonstrates something extraordinary. The objective structure of the universe and the intellectual structure of the human being coincide.” – Pope Benedict XVI

The Origin of Science

Excerpt: Modern science is not only compatible with Christianity, it in fact finds its origins in Christianity.

http://www.columbia.edu/cu/aug.....rigin.html

Christianity and The Birth of Science – Michael Bumbulis, Ph.D

Excerpt: Furthermore, many of these founders of science lived at a time when others publicly expressed views quite contrary to Christianity – Hume, Hobbes, Darwin, etc. When Boyle argues against Hobbe’s materialism or Kelvin argues against Darwin’s assumptions, you don’t have a case of “closet atheists.”

http://ldolphin.org/bumbulis/

As well, ‘pure transcendent information’ is now shown to be ‘conserved’. (i.e. it is shown that all transcendent information which can possibly exist, for all possible physical/material events, past, present, and future, already must exist.) This is since transcendent information exercises direct dominion of the foundational ‘material’ entity of this universe, energy, which cannot be created or destroyed by any known ‘material’ means. i.e. First Law of Thermodynamics.

Conservation Of Transcendent Information – 2007 – video

http://www.metacafe.com/watch/3995275

Scientific Evidence For God (Logos) Creating The Universe – 2008 – video

http://www.metacafe.com/watch/3995300

Light and Quantum Entanglement Reflect Some Characteristics Of God – video

http://www.metacafe.com/watch/4102182

primary reference: Let There Be Light

http://lettherebelight-77.blog.....is_19.html

ba writes, “Aleta, I appreciate your concern, but as I have found the preponderance of my references to refer to the equation as Euler’s number, and I cannot change the sites on the web.”

Could you show me a few? If I’m wrong, I’ll change my mind. When I Google the two phrases, my point is confirmed. The one site you linked to was the one I think is wrong. Can you show me some of this preponderance of sites?

More on God later!

Aleta, I conceded your point and corrected my notes to reflect that point for Euler’s Identity being correct rather than Euler’s number. The one reference is the primary one that threw me off but I was also led off track by a Missler video. As for a partial defense to the mistake I did reference in my video that I had made a few years back that the number is also referred to Euler’ Identity. Now that the proper name is emphasized in all the proper places I feel comfortable, and more to the point whatever the proper name of the equation it still does not detract one iota from the overwhelming Theistic implications from Euler’s number (identity) that I listed here:

http://www.uncommondescent.com.....ent-364379

and here:

http://www.uncommondescent.com.....ent-364392

Of what use is it to you to be more ‘pleased’ with the LSD like mandelbrot sets than the concrete enigma that Euler’s identity, general relativity, quantum mechanics, places right in front of you for discerning reality?

Aleta:

More on God later!

Well, that’s a statement! 😉

Aleta:

More seriously, thank you for your very precise mathemathical explanations.

My personal thoughts about mathematics in general could be summed up as a double sense of wonder:

1) I find that many intrinsic aspects of mathematics are specially beautiful and in a way surprising (that could be the case for Euler identity).

2) I find really amazing that mathematics explains so well physical reality.

I am not a mathematician at all, so I would really appreciate your thoughts on those two points from the point of view of philosophy of science. Thank you in advance.

BA:

Indeed, the five constants in Euler’s eqn are foundational in a lot of math, science and engineering.

The sixth is implicit, as e^i*pi = -1 [which is why adding that result to 1 gives 0 . . . ], and that too is foundational. The operations of addition, multiplication and exponentiation, with their converses, are also key. And, of course equality.

[BTW what does it mean to raise something to an imaginary power? Hint: think of rotation in the complex plane, hence every thing that has oscillations in it . . . e^i*w*t, where w is angular velocity, w = 2 * pi*f, f the frequency. Using j as an operator defined as rotate 90 degrees anticlockwise, I would make students look at j[1], then do j[j[1]], a double rotation. this yielded -1, and bang a light would go off, we now have a way to see what sqrt[-1] is about. And on to AC theory . . . ]

You are right that key trig functions are exponential in character [and can be reduced as power series too, indeed that is a part of the Euler identity’s derivation, in at least some approaches].

Bottomline is, lo and behold these absolutely core expressions, bingo, are locked together inextricably in this one amazing and beautiful unexpected equation.

If you wanted a signature of the greatest mathematician of all, the one who is Reason Himself [LOGOS], there it is.

And if you doubted the reality of numbers and mathematical operations, here is something to give you pause. Sobering pause.

For, the depth of unity of truth that this reveals in mathematics is almost impossible to exaggerate. If we were just arbitrarily making up things as we go, there is no good reason why they should come back together into something so profound.

Talk about thinking the thoughts of the Creator after him!

GEM of TKI

Thanks, ba, about the identity vs number thing. I appreciate it that you did some research and answered the question to your own satisfaction. Clarity about vocabulary helps people communicate better, so I get a little picky about it – my students certainly think so!

ba, you write,

Well first of all, I didn’t say that the subject of God doesn’t interest me in the least, or that it was uninteresting. What I said was ,”I’m not interested in discussing whether God is the source of mathematics or not”, which is a very different statement than what you attributed to me.

But to address the topic anyway, I have been interested in religion and metaphysical philosophy since I was a teenager 45 years ago (giving my approximate age away), and have explored the topic both academically and personally. My conclusion is that even though I am a strong agnostic (we can’t really know the nature of metaphysical reality, if there is one), I have absolutely no belief in a personal God in general and the dogma of Christianity in particular. Therefore, the issues of “facing my Creator when I die” and my “relationship with God” are irrelevant to me. I know you believe whole-heartedly in the Christian God, and you think you have compelling reasons, but I also know that there are other ways to look at the world that are just as compelling to their adherents. My search, which I assure you has been long and deep, has led me to different conclusions than you have reached.

Aleta, as you probably well know, I have defended the Christian position for a few years, and much contrary to the conclusion of your deep search that has led you away from the risen Christ, I find that my personal ‘deep search’ as well as debates with hard core atheists have only strengthened my faith in Theism in particular as well as made me acutely aware of the need for the Christ that we all have in general.

We could go through the apologetics in detail if you want for each of our positions. In fact I would like very much to see what you consider your best and strongest pieces of evidence to be taken completely apart on this website,,, as I have seen countless other arguments against God be taken apart by the able and knowledgeable readers of UD.

But of more to the point on what you have addressed me on earlier, I feel completely confident that you have not accomplished in the least what you set out to do when you stated this earlier in this thread:

“Euler’s identity does not “come out of nowhere.” It follows pretty straightforwardly from the Taylor series for sin x, cos x, e^x, and is best understood in terms of vectors in the complex plane.”

Yet, Euler’s identity is not ‘produced’ by the Taylor series, as I think you hoped to convey, but is instead as kairosfocus stated:

“You are right that key trig functions are exponential in character [and can be reduced as power series too, indeed that is a part of the Euler identity’s derivation, in at least some approaches.”

In fact, in this following video, trig. is used to verify the validity of Euler’s Identity, not the other way around of Euler verifying trig., as would be required for you to successfully dodge the Theistic implication of Euler’s Identity, as clearly you were trying to do (and yet even if you were successful in your endeavor, I would have just turned right around and used trig. against your position by the way since you must ultimately give a satisfactory account of origination):

Euler’s identity

http://www.youtube.com/watch?v=zApx1UlkpNs

Thus Aleta, as far as the argument which you brought to this thread is concerned, you have not made your case in the least, in fact when looked at honestly you have made my case stronger since you are in fact trained in math and have failed to give a satisfactory account for the origination for Euler’s Identity. That you would simply brush off the stunning correspondence I noted of Euler’s Identity to this physical universe here,,,

http://www.uncommondescent.com.....ent-364305

,,, and to then ‘hide in the ‘interesting’ Mandelbrot sets’ does not impress me in the least with your claim that you have ‘searched these things out deeply’. In fact Aleta, it all honesty it seems very peculiar to me that you would choose the LSD-like Mandelbrot sets as more ‘interesting,,,

Mandelbrot Set Zoom – video

http://www.youtube.com/watch?v=gEw8xpb1aRA

,,, than choosing the sheer wonder that Euler’s Identity, and its correspondence with physical reality as more ‘interesting’. In fact I firmly believe that it is a very telling sign that you would probably much rather hide in your ‘imagination’ than to honestly consider any compelling evidence for the reality of God (of which there is plenty; Romans 1:20).

Imagine – John Lennon

http://www.youtube.com/watch?v=okd3hLlvvLw

To ba:

You write,

Ba, you are quite confused, I think. First, kf and I are saying the exact same thing: that one way to prove the Euler identity is through the Taylor series. As is often the case with math, you can prove things in different ways (because it’s all interconnected), so I’m sure there are other ways to prove it also – the Taylor series method is what I use in class because it relates to what the students have learned about derivatives and curves. Why you think what kf said somehow contradicts what I said is beyond me.

And second, my discussion about all this has nothing to do with God. Whether you believe in God or not, if you want to know why Euler’s identity is true, I’m going to show you mathematically. One person may believe that math is a manifestation of the mind of God and another may not, but that doesn’t change one bit the math we would use to prove the identity. If someone walks in and says, “This is really neat – why is it true”, saying that it is that way because God made it so isn’t going to be helpful, even to a Christian.

Question: do you have any idea why the Euler identity is true? Do you know anything about the Taylor series for sin x, cos x, and e^x, and more importantly, do you know how to derive them? Do you know about the mathematics of the complex plane? Don’t answer with links to videos: do you know the math?

You also write, “We could go through the apologetics in detail if you want for each of our positions. In fact I would like very much to see what you consider your best and strongest pieces of evidence to be taken completely apart on this website,,, as I have seen countless other arguments against God be taken apart by the able and knowledgeable readers of UD.”

Sorry, not interested. Been there, done that.

You write, “Thus Aleta, as far as the argument which you brought to this thread is concerned, you have not made your case in the least, in fact when looked at honestly you have made my case stronger since you are in fact trained in math and have failed to give a satisfactory account for the origination for Euler’s Identity. That you would simply brush off the stunning correspondence I noted of Euler’s Identity to this physical universe here,,,”

You seem to be asking me to show how math in general exists and leads to such intricate results, and why it can apply so well to the world. That is a philosophical question that is not what I have been discussing. I’ve just been discussing Euler’s identity in terms of the math itself.

Also, although I know that e (Euler’s number) shows up in many important places in applied mathematics, I am not sure that Euler’s Identity has much practical application itself: the general formula e^ix = cos x + i sin x is very important, but the particular fact that results when x = pi may be more of a neat fact without direct practical use. (I may be wrong about this – perhaps x = pi shows up often.)

And last, you write, ” and to then ‘hide in the ‘interesting’ Mandelbrot sets’ does not impress me in the least with your claim that you have ‘searched these things out deeply’. In fact Aleta, it all honesty it seems very peculiar to me that you would choose the LSD-like Mandelbrot sets as more ‘interesting,,,”

Man, I have no idea what I am “hiding” by being interested in the Mandelbrot set. However, I finally figured out that by LSD-like you are referring to psychedelics – wow, that’s weird. The Mandelbrot set is fascinating because of the math that produces it (do you know anything about that?), because of its fractal nature, and because of some of its philosophical implications. My interest in it has absolutely nothing to do with psychedelics.

… and because I find it fascinating that a mathematical procedure involving the infinite iteration of complex numbers can produce such beautiful geometric patterns. For the believer in God, I would think that the Mandelbrot set would be a marvelous example of the beauty of mathematics.

Aleta, I am not trained in the details of math, but I do have a overall picture and appreciation of why Euler’s is true and why it inspires such wonder,,,, I find it disingenuous of you asking me if I know ‘why’ Euler’s is true when the fact is, though you know all the intricacies of the proofs, as outlined in this video,,

Euler’s identity

http://www.youtube.com/watch?v=zApx1UlkpNs

,,, the plain truth is that you don’t even know ‘why’ Euler’s is true though you know the proofs,,, i.e. why this particular equation and not some other equation Aleta of which there could be multitudes??? Please tell me why this equation is true from that perspective Aleta???

As well the primary point of this post is in the first place is,,,

the ubiquity of Fibonacci,,,,

and the the lead off post even states this in its writing,,,

“calling it the fingerprint of God”.

Thus the point of this post is in fact looking beyond the mere internal consistency of mathematics, as you are trying to do, but is instead focusing on the mystery of why math should correspond to physical reality so beautifully, and even to the point of acknowledging the necessity of God to explain that correspondence!

Thus in keeping with the main point of this post, I pointed out how physical reality and Euler’s Identity have ‘the fingerprint of God’ also in their correspondence,,,

http://www.uncommondescent.com.....ent-364305

Do you deny the correspondence? No, instead of denying the correspondence I pointed out, you play the ‘mathematical authority’ card, and basically say that the correspondence is meaningless for Euler’s is internally consistent mathematically with other math that it is proved by,, and furthermore you rub it in that I just don’t understand what is going on because I am not as smart as you are mathematically. Excuse me Aleta, my point was not to prove Euler’s true mathematically, that has been done,, My point was solely to point out the stunning correspondence!

Clearly You tried to evade the clear correspondence I have roughly highlighted,,, in fact you state,,,

‘Euler’s identity does not “come out of nowhere.” It follows pretty straightforwardly from the Taylor series for sin x, cos x, e^x, and is best understood in terms of vectors in the complex plane.’

Yet I disagreed that what you state ‘produces’ Euler’s number but is merely a proof that verifies the validity of Euler’s, which I firmly believe kairosfocus will confirm is true,,,

,,, that you would so blatantly ignore that the physical/transcendent correspondence and its spiritual implications, which is the point of this post, I believe flows directly from ‘philosophical implications’ that you find distasteful,,, much like you find the mandelbrot set’s philosophical implications ‘tasteful’. Tasteful since they seem to give you a loop hole for your atheistic leanings, though I also hold that loop hole is surely illusory as to coherently explaining reality though you will surely disrespect my ‘novice’ opinion in the matter,,,.

Clearly you are trying your best to avoid what is so clear to so many,,

Namely that there is a powerful ‘spiritual connection’ between the physical reality we see around us and the transcendent nature of the equations which give us such deep understanding of that reality!

@ba

http://www.biblemaths.com/pag03_pie/

Have we not been there before? This is absolutely not convincing: God needs 111 bits to encode 13 bits of information on pi – in a way that couldn’t be found until pi is given in decimal representation? Frankly, I would be more impressed if the fraction 22/7 – or 355/113 popped up somewhere….

Finely Tuned Big Bang, Elvis In The Multiverse, and the Schroedinger Equation – Granville Sewell – video

http://www.metacafe.com/watch/4233012

To solidify Dr. Sewell’s observation that transcendent ‘math’ is found to be foundational to reality, I note just one little equation:

0 = 1 + e ^(i*pi) — Euler

Believe it or not, the five most important numbers in mathematics are tied together, through the complex domain in Euler’s number, And that points, ever so subtly but strongly, to a world of reality beyond the immediately physical. Many people resist the implications, but there the compass needle points to a transcendent reality that governs our 3D ‘physical’ reality.

God by the Numbers – Connecting the constants

Excerpt: The final number comes from theoretical mathematics. It is Euler’s (pronounced “Oiler’s”) number: e*pi*i. This number is equal to -1, so when the formula is written e*pi*i+1 = 0, it connects the five most important constants in mathematics (e, pi, i, 0, and 1) along with three of the most important mathematical operations (addition, multiplication, and exponentiation). These five constants symbolize the four major branches of classical mathematics: arithmetic, represented by 1 and 0; algebra, by i; geometry, by pi; and analysis, by e, the base of the natural log. e*pi*i+1 = 0 has been called “the most famous of all formulas,” because, as one textbook says, “It appeals equally to the mystic, the scientist, the philosopher, and the mathematician.”

http://www.christianitytoday.c.....ml?start=3

(of note; Euler’s Number (equation) is more properly called Euler’s Identity in math circles.)

Moreover Euler’s Identity, rather than just being the most enigmatic equation in math, finds striking correlation to how our 3D reality is actually structured,,,

The following picture, Bible verse, and video are very interesting since, with the discovery of the Cosmic Microwave Background Radiation (CMBR), the universe is found to actually be a circular sphere which ‘coincidentally’ corresponds to the circle of pi within Euler’s identity:

Picture of CMBR

3D picture of Cosmic Microwave Background Radiation

Proverbs 8:26-27

While as yet He had not made the earth or the fields, or the primeval dust of the world. When He prepared the heavens, I was there, when He drew a circle on the face of the deep,

The Known Universe by AMNH – video – (please note the ‘centrality’ of the Earth in the universe in the video)

http://www.youtube.com/watch?v=17jymDn0W6U

The flatness of the ‘entire’ universe, which ‘coincidentally’ corresponds to the diameter of pi in Euler’s identity, is found on this following site; (of note this flatness of the universe is an extremely finely tuned condition for the universe that could have, in reality, been a multitude of different values than ‘flat’):

Did the Universe Hyperinflate? – Hugh Ross – April 2010

Excerpt: Perfect geometric flatness is where the space-time surface of the universe exhibits zero curvature (see figure 3). Two meaningful measurements of the universe’s curvature parameter, ½k, exist. Analysis of the 5-year database from WMAP establishes that -0.0170 < ½k < 0.0068.4 Weak gravitational lensing of distant quasars by intervening galaxies places -0.031 < ½k < 0.009.5 Both measurements confirm the universe indeed manifests zero or very close to zero geometric curvature,,,

http://www.reasons.org/did-universe-hyperinflate

This following video shows that the universe also has a primary characteristic of expanding/growing equally in all places,, which 'coincidentally' strongly corresponds to e in Euler's identity. e is the constant used in all sorts of equations of math for finding what the true rates of growth and decay are for any given problem trying to find as such:

Every 3D Place Is Center In This Universe – 4D space/time – video

http://www.metacafe.com/watch/3991873/

Towards the end of the following video, Michael Denton speaks of the square root of negative 1 being necessary to understand the foundational quantum behavior of this universe. The square root of -1 is 'coincidentally' found in Euler's identity:

Michael Denton – Mathematical Truths Are Transcendent And Beautiful – Square root of -1 is built into the fabric of reality – video

http://www.metacafe.com/watch/4003918"

I find it extremely strange that the enigmatic Euler's identity would find such striking correlation to reality. In pi we have correlation to the 'sphere of the universe' as revealed by the Cosmic Background radiation, as well pi correlates to the finely-tuned 'geometric flatness' within the 'sphere of the universe' that has now been found. In e we have the fundamental constant that is used for ascertaining exponential growth in math that strongly correlates to the fact that space-time is 'expanding/growing equally' in all places of the universe. In the square root of -1 we have what is termed a 'imaginary number', which was first proposed to help solve equations like x2+ 1 = 0 back in the 17th century, yet now, as Michael Denton pointed out in the preceding video, it is found that the square root of -1 is required to explain the behavior of quantum mechanics in this universe. The correlation of Euler's identity, to the foundational characteristics of how this universe is constructed and operates, points overwhelmingly to a transcendent Intelligence, with a capital I, which created this universe! It should also be noted that these universal constants, pi,e, and square root -1, were at first thought by many to be completely transcendent of any material basis, to find that these transcendent constants of Euler's identity in fact 'govern' material reality, in such a foundational way, should be enough to send shivers down any mathematicians spine. Further discussion can be found here relating Euler's identity to General Relativity and Quantum Mechanics:

http://www.uncommondescent.com.....ent-364379

Here is a very well done video, showing the stringent 'mathematical proofs' of Euler's Identity:

Euler's identity – video

http://www.youtube.com/watch?v=zApx1UlkpNs

The mystery doesn't stop there, this following video shows how pi and e are found in Genesis 1:1 and John 1:1

Euler's Identity – God Created Mathematics – video

http://www.metacafe.com/watch/4003905

This following website has the complete working out of the math of Pi and e in the Bible, in the Hebrew and Greek languages respectively, for Genesis 1:1 and John 1:1:

http://www.biblemaths.com/pag03_pie/

Finely Tuned Big Bang, Elvis In The Multiverse, and the Schroedinger Equation – Granville Sewell – video

http://www.metacafe.com/watch/4233012

To solidify Dr. Sewell’s observation that transcendent ‘math’ is found to be foundational to reality, I note just one little equation:

0 = 1 + e ^(i*pi) — Euler

Believe it or not, the five most important numbers in mathematics are tied together, through the complex domain in Euler’s number, And that points, ever so subtly but strongly, to a world of reality beyond the immediately physical. Many people resist the implications, but there the compass needle points to a transcendent reality that governs our 3D ‘physical’ reality.

God by the Numbers – Connecting the constants

Excerpt: The final number comes from theoretical mathematics. It is Euler’s (pronounced “Oiler’s”) number: e*pi*i. This number is equal to -1, so when the formula is written e*pi*i+1 = 0, it connects the five most important constants in mathematics (e, pi, i, 0, and 1) along with three of the most important mathematical operations (addition, multiplication, and exponentiation). These five constants symbolize the four major branches of classical mathematics: arithmetic, represented by 1 and 0; algebra, by i; geometry, by pi; and analysis, by e, the base of the natural log. e*pi*i+1 = 0 has been called “the most famous of all formulas,” because, as one textbook says, “It appeals equally to the mystic, the scientist, the philosopher, and the mathematician.”

(of note; Euler’s Number (equation) is more properly called Euler’s Identity in math circles.)

Moreover Euler’s Identity, rather than just being the most enigmatic equation in math, finds striking correlation to how our 3D reality is actually structured,,,

The following picture, Bible verse, and video are very interesting since, with the discovery of the Cosmic Microwave Background Radiation (CMBR), the universe is found to actually be a circular sphere which ‘coincidentally’ corresponds to the circle of pi within Euler’s identity:

Picture of CMBR

3D picture of Cosmic Microwave Background Radiation

Proverbs 8:26-27

While as yet He had not made the earth or the fields, or the primeval dust of the world. When He prepared the heavens, I was there, when He drew a circle on the face of the deep,

The Known Universe by AMNH – video – (please note the ‘centrality’ of the Earth in the universe in the video)

http://www.youtube.com/watch?v=17jymDn0W6U

The flatness of the ‘entire’ universe, which ‘coincidentally’ corresponds to the diameter of pi in Euler’s identity, is found on this following site; (of note this flatness of the universe is an extremely finely tuned condition for the universe that could have, in reality, been a multitude of different values than ‘flat’):

Did the Universe Hyperinflate? – Hugh Ross – April 2010

Excerpt: Perfect geometric flatness is where the space-time surface of the universe exhibits zero curvature (see figure 3). Two meaningful measurements of the universe’s curvature parameter, ½k, exist. Analysis of the 5-year database from WMAP establishes that -0.0170 < ½k < 0.0068.4 Weak gravitational lensing of distant quasars by intervening galaxies places -0.031 < ½k < 0.009.5 Both measurements confirm the universe indeed manifests zero or very close to zero geometric curvature,,,

This following video shows that the universe also has a primary characteristic of expanding/growing equally in all places,, which 'coincidentally' strongly corresponds to e in Euler's identity. e is the constant used in all sorts of equations of math for finding what the true rates of growth and decay are for any given problem trying to find as such:

Every 3D Place Is Center In This Universe – 4D space/time – video

http://www.metacafe.com/watch/3991873/

Towards the end of the following video, Michael Denton speaks of the square root of negative 1 being necessary to understand the foundational quantum behavior of this universe. The square root of -1 is 'coincidentally' found in Euler's identity:

Michael Denton – Mathematical Truths Are Transcendent And Beautiful – Square root of -1 is built into the fabric of reality – video

http://www.metacafe.com/watch/4003918"

I find it extremely strange that the enigmatic Euler's identity would find such striking correlation to reality. In pi we have correlation to the 'sphere of the universe' as revealed by the Cosmic Background radiation, as well pi correlates to the finely-tuned 'geometric flatness' within the 'sphere of the universe' that has now been found. In e we have the fundamental constant that is used for ascertaining exponential growth in math that strongly correlates to the fact that space-time is 'expanding/growing equally' in all places of the universe. In the square root of -1 we have what is termed a 'imaginary number', which was first proposed to help solve equations like x2+ 1 = 0 back in the 17th century, yet now, as Michael Denton pointed out in the preceding video, it is found that the square root of -1 is required to explain the behavior of quantum mechanics in this universe. The correlation of Euler's identity, to the foundational characteristics of how this universe is constructed and operates, points overwhelmingly to a transcendent Intelligence, with a capital I, which created this universe! It should also be noted that these universal constants, pi,e, and square root -1, were at first thought by many to be completely transcendent of any material basis, to find that these transcendent constants of Euler's identity in fact 'govern' material reality, in such a foundational way, should be enough to send shivers down any mathematicians spine. Further discussion can be found here relating Euler's identity to General Relativity and Quantum Mechanics:

http://www.uncommondescent.com.....ent-364379

Here is a very well done video, showing the stringent 'mathematical proofs' of Euler's Identity:

Euler's identity – video

http://www.youtube.com/watch?v=zApx1UlkpNs

The mystery doesn't stop there, this following video shows how pi and e are found in Genesis 1:1 and John 1:1

Euler's Identity – God Created Mathematics – video

http://www.metacafe.com/watch/4003905

This following website has the complete working out of the math of Pi and e in the Bible, in the Hebrew and Greek languages respectively, for Genesis 1:1 and John 1:1:

http://www.biblemaths.com/pag03_pie/

Aleta, the preceding post is a ‘cleaned up’ version of 14

BA:

The Euler identity indeed is most easily demonstrated through using power series expansions.

But that has little to do with its significance.

For, what it toes is to unite the five or six most significant numbers in mathematics, showing the sort of unexpected coherence that testifies to the unity of truth and reason. If these numbers and their reasons for being were merely arbitrary, they would not be expected to come together like that.

That is why this equation is so astonishing.

And you have rightly pointed out that these same numbers are right there in the heart of key equations in so many vital fields of physics.

Such things are like a compass-needle, pointing to the reality of numbers, which are of course utterly abstract entities.

Which brings into serious question the claims of the materialists, in the heart of a domain they thought they had under their control. (In fact, such materialism, on independent grounds, is utterly self-referentially incoherent and cannot stand.)

GEM of TKI

@Kairosfocus

-“Such things are like a compass-needle, pointing to the reality of numbers, which are of course utterly abstract entities.

Which brings into serious question the claims of the materialists, in the heart of a domain they thought they had under their control. (In fact, such materialism, on independent grounds, is utterly self-referentially incoherent and cannot stand.)”

Interestingly enough I run into this article only a few days ago. Mathematics may just well prove to be the Trojan Horse sitting in the materialistic castle. I think you and BA will enjoy reading it:

http://www.lastseminary.com/ag.....Naturalism Reconsidered.pdf

Weir, Alan

“Naturalism Reconsidered”, Chapter 14 in The Oxford Handbook of Philosophy of Mathematics and Logic

Excerpt:

“…[A] naturalistic attitude predominates among “analytic” philosophers. This is why philosophy of mathematics, quite apart from its intrinsic interest, is of such importance in contemporary philosophy. For, on the face of it, mathematics is an enormous Trojan Horse sitting firmly in the centre of the citadel of naturalism. Modern natural science is mathematical through and through: it is impossible to do physics, chemistry, molecular biology and so forth without a very thorough and quite extensive knowledge of modern mathematics (indeed this is true to an increasing extent of social sciences such as psychology and economics). Yet, prima facie, mathematics provides a counter-example both to methodological and to ontological naturalism.”

For some reason the link got cut off. Reposting it:

http://www.lastseminary.com/ag.....idered.pdf

ba, you write, “Here is a very well done video, showing the stringent ‘mathematical proofs’ of Euler’s Identity: http://www.youtube.com/watch?v=zApx1UlkpNs”

That is exactly the approach I use. However, it just assumes that you know that the Taylor series are true, so for that you would have to back up several steps and discuss the derivatives of sin x, cos x, and e^x.

You write, “…much like you find the mandelbrot set’s philosophical implications ‘tasteful’. Tasteful since they seem to give you a loop hole for your atheistic leanings,”

Ba, how does the Mandelbrot set differ from Euler’s Identity in respect to theism and atheism? That makes no sense. They both are mathematical facts. I love Euler’s Identity, and make a big deal of it in my classes, and I likewise am fascinated by the Mandelbrot set. How does the Mandelbrot set “seem to give [me] a loop hole for [my] atheistic leanings”? It is no more atheistic or theistic than any other part of math.

You write, “,,, the plain truth is that you don’t even know ‘why’ Euler’s is true though you know the proofs,,, i.e. why this particular equation and not some other equation Aleta of which there could be multitudes??? Please tell me why this equation is true from that perspective Aleta???”

Well, it’s true because it follows logically from more fundamental math – that’s why. It’s that simple. Some other equation, such as, for instance, e ^ 2i = 17 is false because there is no math that leads to it. There are multitudes of false mathematical statements – those that are true are the ones that can be proven. This seems obvious, so I don’t understand your point.

to gpuccio at 40

You summarize well the two mysteries of mathematics:

Although I am a mathematician (among other things), and deal with both of these aspects of math in some detail at times, I don’t think I have any privileged insight into why those two things are true.

In respect to 2), from a metaphysical point of view, as I have stated, I am a strong agnostic. I am aware of various common perspectives as to why our universe can be described so well with mathematics (theism, various forms of Platonism, various forms of deism, Taoism, various forms of materialism, etc.), but I don’t think we can know which of those, if any, are true.

So, as a strong agnostic, I live with the uncertainty of not knowing. That doesn’t stop me, however, from appreciating deeply the way the world is or from loving to explore it.

As to 1), we have discovered that any set of simple rules (Conway’s game of Life is an example, or chess) can lead to unexpected results as the rules play out, and can lead to unexpected complexity that goes far beyond the simplicity of the fundamental rules. In fact, as you probably know, if you change just one of the beginning “rules” (such as the parallel postulate in geometry), you can get a new mathematical system, different than the first one, with different results. Then the question becomes which of the system best fits with reality, and that becomes an empirically testable question.

Aleta you state:

Ba, how does the Mandelbrot set differ from Euler’s Identity in respect to theism and atheism? That makes no sense.

I can find a direct correspondence of Euler’s Identity to the structure and function of this universe, as I amply re-illustrated in 48, I find no such striking correlation of the universe’s overall physical reality to Mandelbrot sets, thus my less than enthusiastic response to it, being the practical man I am.

In fact I have seen a few hard-core atheists try to invoke Mandelbrot sets to explain the generation of functional information, universes,,, etc..,,, thus maybe you can see a little clearer the reason why I showed the only practical application that I’ve seen of Mandelbrots are those LSD-like images,,, perhaps I am wrong on Mandelbrot insignificance,, I really don’t care at this point,,, The main and primary point, as I have said for about the tenth time now Aleta, is the striking correlation of the universe’s physical structure and function to Euler’s Identity, which is indeed complementary to it’s stunning mathematical uniqueness, indeed I would even go so far as to say the Universe’s physical correlation to the equation is a more excellent proof of the equation’s validity than the proofs you have offered, but perhaps that is just my severe prejudice towards actual empirical evidence speaking, none-the-less,,, in keeping with the topic,, I find ‘the fingerprint of God’ all over the equation!

Aleta such correlations are the whole point of this post!

Note the following, from the opening post:

Looks like Sheldon isn’t too worried about that atheistic Mandelbrot set!

Well Aleta score one for your pet branch of math, alhough if you could actually show me a place where it has a physical correspondence to the universe it might awaken my interest in the subject and find relevance to the post.

What has struck me as funny about your position is that you say you are a ‘strong agnostic’ as opposed to a atheistic materialist, or a Theist, I guess, but it would be easier for me if you were just a plain atheistic materialist for then I could just falsify materialism:

The Failure Of Local Realism – Materialism – Alain Aspect – video

http://www.metacafe.com/w/4744145

What blows most people away, when they first encounter quantum mechanics, is the quantum foundation of our material reality blatantly defies our concepts of time and space. Most people consider defying time and space to be a ‘miraculous & supernatural’ event. I know I certainly do! This ‘miraculous & supernatural’ foundation for our physical reality can easily be illuminated by the famous ‘double slit’ experiment. (It should be noted the double slit experiment was originally devised, in 1801, by a Christian named Thomas Young). Though I’ve listed this preceding video before, it is well worth revisiting it here:

Dr. Quantum – Double Slit Experiment & Entanglement – video

http://www.metacafe.com/watch/4096579

This following site offers more of a formal refutation of materialism:

Why Quantum Theory Does Not Support Materialism – By Bruce L Gordon:

Excerpt: Because quantum theory is thought to provide the bedrock for our scientific understanding of physical reality, it is to this theory that the materialist inevitably appeals in support of his worldview. But having fled to science in search of a safe haven for his doctrines, the materialist instead finds that quantum theory in fact dissolves and defeats his materialist understanding of the world.

http://www.4truth.net/site/c.h.....ialism.htm

,,, Yet with you Aleta the problem is more subtle than falsifying materialism, or at least just falsifying the classical form of materialism, for you yourself work with mathematics, and mathematics are in themselves transcendent. And you know very well that these transcendent equations can be formulated as you so desire so as to be put in a computer so as to have the computer do your beck and call, so you are already well aware of the dominion that logical transcendent information exercises over the material realm, thus I would say it is a pretty safe bet to say that you are not a hard-core materialist. If so there would have to be a severe disconnect in your worldview. So I guess the question I have for you Aleta, is what do you believe to be the foundational entity of reality if you are not a hard core materialist?

OK, I’ve been thinking about ba’s statement that

Eulers Identity itself, e^i pi + 1 = 0, does not itself have a “striking correlation of the universe’s physical structure,” but the constants in it are certainly of primary significance, which is, I think, ba’s point.

However, simpler ideas also have a striking correlation, such as inverse square laws k/(d^2) (gravity and electromagnetic attraction), parabolas and ellipses (paths of objects), and so on. In fact ultimately the simplest numbers of all (1, -1, and 0) are manifested in the charges carried by the proton, electron and neutron. So even though we may be most amazed at things that are most sophisticated, I think all of math deserves the same sense of wonder – if Euler’s identity is the fingerprint of God to the believer, I don’t think the parabola or the integers are any less so.

Also, ba says, “indeed I would even go so far as to say the Universe’s physical correlation to the equation is a more excellent proof of the equation’s validity than the proofs you have offered.”

But, if a long succession of people had not invented, over the centuries, the mathematical symbols and notations that we subsequently used to prove Euler’s identity, we wouldn’t even know it existed. You can’t just look at the universe and see e, i and pi, much less the meaning of e^ix. So without the mathematical proof we wouldn’t even have the mathematical ideas to then apply to the world. The application is a confirmation that world is susceptible to mathematical description, but the application doesn’t prove that the identity is true in the same way that the math proves it is true.

That is, if someone didn’t know all that stuff about e, sin x, cos x, derivatives, Taylor series, the complex plane, etc, and how it all tied together mathematically, there would be no Euler’s identity for ba to marvel at.

This all goes back to the points that gpuccio made. The are two facets to this topic: the math itself, which as a self contained logical system can start with a few simple rules and lead to fascinating and complex interrelationships, and the application of mathematical models to the real world. The latter is both wonderful and useful, but until people have done the work to do the former we don’t even have the tools to use to study the world.

The whole history of mathematics illustrates this back-and-forth interaction between the development of pure mathematics and the increasingly more sophisticated application of that math to the real world.

Let’s try this again Aleta,

the constant of e correlates to the finely tuned 4-D space-time expansion/growth of the universe which is remarkably consistent throughout the entire universe, the constant of pi correlates to the sphere of the universe, as well as to the finely-tuned flatness of the universe, the constant of the square root of negative one correlates to how foundational quantum actions will behave in this universe. In fact these constants are absolutely necessary for all the equations describing their respective areas of influence within this universe, which when there respective equations are taken together provide a complete picture of the foundational characteristics of this universe (General Relativity, Quantum Mechanics, wave theory etc.. etc..), moreover a-priori, from a atheistic/materialistic perspective, we have absolutely no reason to presuppose that there would be such coherence between these ‘transcendent constants’ in Euler’s Identity and to physical characteristics of the universe. That there actually is a correspondence is a compass needle, as kairosfocus has said, strongly pointing us to the fact that a Mind, with a capital M, planned this universe and that this universe is not an accident.

This statement of yours makes absolutely no sense Aleta:

‘You can’t just look at the universe and see e, i and pi,’

For e,i, and pi are in fact the language in which God has written this universe, to paraphrase Galileo.

Since we are on Euler’s Identity so much this story may amuse you,,,

Personal philosophy and religious beliefs

Euler and his friend Daniel Bernoulli were opponents of Leibniz’s monadism and the philosophy of Christian Wolff. Euler insisted that knowledge is founded in part on the basis of precise quantitative laws, something that monadism and Wolffian science were unable to provide. Euler’s religious leanings might also have had a bearing on his dislike of the doctrine; he went so far as to label Wolff’s ideas as “heathen and atheistic”.[40]

Much of what is known of Euler’s religious beliefs can be deduced from his Letters to a German Princess and an earlier work, Rettung der Göttlichen Offenbahrung Gegen die Einwürfe der Freygeister (Defense of the Divine Revelation against the Objections of the Freethinkers). These works show that Euler was a devout Christian who believed the Bible to be inspired; the Rettung was primarily an argument for the divine inspiration of scripture.[5]

There is a famous anecdote inspired by Euler’s arguments with secular philosophers over religion, which is set during Euler’s second stint at the St. Petersburg academy. The French philosopher Denis Diderot was visiting Russia on Catherine the Great’s invitation. However, the Empress was alarmed that the philosopher’s arguments for atheism were influencing members of her court, and so Euler was asked to confront the Frenchman. Diderot was later informed that a learned mathematician had produced a proof of the existence of God: he agreed to view the proof as it was presented in court. Euler appeared, advanced toward Diderot, and in a tone of perfect conviction announced, “Sir, {a+b^n}{n}=x, hence God exists—reply!”. Diderot, to whom (says the story) all mathematics was gibberish, stood dumbstruck as peals of laughter erupted from the court. Embarrassed, he asked to leave Russia, a request that was graciously granted by the Empress.

ba, I am quite familiar with the time/space issues of both relativity and quantum mechanics, the double-slit experiments, etc.

Let me relate this my previous post (58). Classical Newtonian physics was based on the idea of the Cartesian coordinate plane: space existing uniformly and linearly in three dimensions, with time operating independently, also uniformly and linearly. This was a mathematical model that at the time seemed self-evident and God-given.

However, we now know that this model does not in fact represent reality accurately. Coordinate geometry is still as true as it ever was within the conext of its own self-contained system, but it is no longer considered to be universally applicable. To refer to gpuccios two points, 1) didn’t change the pure math), but 2) did (the application to the real world.)

Now our representations of reality, at the quantum level or at very high speeds, require a much more mathematically sophisticated representation – one that would be impossible if mathematicians hadn’t developed new mathematical tools that go far beyond the mathematics of Newton’s time. (For instance, Feynman’s path integrals which are used to analyze quantum interactions.)

Furthermore, while the coordinate plane corresponds well with our intuitive, experiential picture of the world (think walking around in time in a room with two walls and a floor), the modern view is impossible to visualize. All we can do is manipulate the mathematics – we can’t really “understand” it by analogy to anything in our everyday experience.

Ba writes that this model defies space and time, and that “most people consider defying time and space to be a ‘miraculous & supernatural’ event. I know I certainly do!”

This is part of ba’s “problem”, in my opinion. The new model of space and time defies the old model, but that is because the old model we now understand is only true (approximately) when applied to an everyday scale. The new model isn’t any more supernatural than the old model – it’s just that we had to change our understanding of what is natural to accomodate the new evidence. Nature is not the way we once thought it was – that’s all.

So once again, the interplay of pure and applied math has played out. We had a mathematical system, coordinate geometry, that was wonderfully true, and full of delightful results. We applied that model to the real world, and by golly it worked! However, as time went by, new evidence started to show places where the Cartesian model didn’t work anymore. Therefore, new mathematics was developed, or mathematics that had been developed but not applied was brought into the picture. The new models were then applied to the new evidence, and they worked better. Nature didn’t change, but with the help of new mathematical tools our understanding of nature changed. Nothing supernatural came into the situation – our understanding of nature just broadened.

And last, and on a different topic, ba writes, “So I guess the question I have for you Aleta, is what do you believe to be the foundational entity of reality if you are not a hard core materialist?”

I repeat: I am a strong agnostic. I don’t think it is possible for us to know what metaphysical reality, if any, is “behind”, in whatever way that may be, our universe.

Aleta, despite all your assurances that all is fine and well in math-land, I ask just one question,, you have unified General Relativity and Quantum Mechanics exactly how?

ba writes,

Let’s try this again: I know you think that math reflects the Mind of God, and so do all other theists, I would imagine. But there are other, non-theistic, ways of understanding the mathematical nature of the world. I

1) don’t believe that the we can actually know which, if any, are true, but

2) I don’t believe at all that the Christian God is the explanation

Just accept that – it does not add anything to the discussion to repeat endlessly that you think math is from the mind of God. I accept that you believe that. I ask that you accept that I don’t.

ba writes, “Aleta, despite all your assurances that all is fine and well in math-land, I ask just one question,, you have unified General Relativity and Quantum Mechanics exactly how?”

ba, I thinking you are just trolling now – there is absolutely nothing in what I wrote that says either that “that all is fine and well in math-land” or that I “have unified General Relativity and Quantum Mechanics.”

I’m trying to describe (more for gpuccio than you, I think) some elements of the interplay between pure and applied math. It’s an interesting topic. You don’t seem to be interested in actually paying attention to what I write, though, so I will quit addressing myself to you, and quit writing unless someone else (gpuccio, perhaps) wants to continue the discussion.

Perhaps we should look at how reality is actually constructed from a empirical point of view Aleta instead of looking from the somewhat esoteric mathematical view:

,,,,But to reflect just a bit more on the teleportation experiment itself, is interesting to note that scientists can only ‘destroy’ a photon in these quantum teleportation experiments. No one has ‘created’ a photon as of yet. I firmly believe man shall never do as such, since I hold only God is infinite, and perfect, in information/knowledge.

Job 38:19-20

“What is the way to the abode of light? And where does darkness reside? Can you take them to their places? Do you know the paths to their dwellings?”

Further reflection on the quantum teleportation experiment:

That a photon would actually be destroyed upon the teleportation (separation) of its ‘infinite’ information to another photon is a direct controlled violation of the first law of thermodynamics. (i.e. a photon ‘disappeared’ from the ‘material’ universe when the entire information content of a photon was ‘transcendently displaced’ from the material universe by the experiment, when photon “c” transcendently became transmitted photon “a”). Thus, Quantum teleportation is direct empirical validation for the primary tenet of the Law of Conservation of Information (i.e. ‘transcendent’ information cannot be created or destroyed). This conclusion is warranted because information exercises direct dominion of energy, telling energy exactly what to be and do in the experiment. Thus, this experiment provides a direct line of logic that transcendent information cannot be created or destroyed and, in information demonstrating transcendence, and dominion, of space-time and matter-energy, becomes the only known entity that can satisfactorily explain where all energy came from as far as the origination of the universe is concerned. That is transcendent information is the only known entity which can explain where all the energy came from in the Big Bang without leaving the bounds of empirical science as the postulated multiverse does. Clearly anything that exercises dominion of the fundamental entity of this physical universe, a photon of energy, as transcendent information does in teleportation, must of necessity possess the same, as well as greater, qualities as energy does possess in the first law of thermodynamics (i.e. Energy cannot be created or destroyed by any known material means according to the first law). To reiterate, since information exercises dominion of energy in quantum teleportation then all information that can exist, for all past, present and future events of energy, already must exist.

As well, the fact that quantum teleportation shows an exact ‘location dominion’, of a photon of energy by ‘specified infinite information’, satisfies a major requirement for the entity needed to explain the missing Dark Matter. The needed transcendent explanation would have to dominate energy in a very similar ‘specified location’ fashion, as is demonstrated by the infinite information of quantum teleportation, to satisfy what is needed to explain the missing dark matter.

Colossians 1:17

He is before all things, and in Him all things hold together.

Moreover, the fact that simple quantum entanglement shows ‘coordinated universal control’ of entangled photons of energy, by transcendent information, regardless of distance, satisfies a major requirement for the entity which must explain the missing Dark Energy. i.e. The transcendent entity, needed to explain Dark Energy, must explain why the entire space of the universe is expanding in such a finely-tuned, coordinated, degree, and would have to employ a mechanism of control very similar to what we witness in the quantum entanglement experiment.

Job 9:8

He stretches out the heavens by Himself and walks on the waves of the sea.

Thus ‘infinite transcendent information’ provides a coherent picture of overarching universal control, and specificity, that could possibly unify gravity with the other forces. It very well may be possible to elucidate, mathematically, the overall pattern God has chosen to implement infinite information in this universe. The following article backs up this assertion:

Is Unknown Force In Universe Acting On Dark Matter?

Excerpt: It is possible that a non-gravitational fifth force is ruling the dark matter with an invisible hand, leaving the same fingerprints on all galaxies, irrespective of their ages, shapes and sizes.” ,,Such a force might solve an even bigger mystery, known as ‘dark energy’, which is ruling the accelerated expansion of the Universe. A more radical solution is a revision of the laws of gravity first developed by Isaac Newton in 1687 and refined by Albert Einstein’s theory of General Relativity in 1916. Einstein never fully decided whether his equation should add an omnipresent constant source, now called dark energy. ,,Dr Famaey added, “If we account for our observations with a modified law of gravity, it makes perfect sense to replace the effective action of hypothetical dark matter with a force closely related to the distribution of visible matter.”

http://www.sciencedaily.com/re.....154644.htm

“I discovered that nature was constructed in a wonderful way, and our task is to find out its mathematical structure”

Albert Einstein

Reflections on the ‘infinite transcendent information’ framework:

The weight of mass becomes infinite at the speed of light, thus mass will never go the speed of light. As well, mass would disappear from our sight if it could go the speed of light, because, from our non-speed of light perspective, distance in direction of travel will shrink to zero for the mass going the speed of light, whereas conversely, if mass could travel at the speed of light its size will stay the same while all other frames of reference not traveling the speed of light will disappear from its sight.

Special Relativity – Time Dilation and Length Contraction – video

http://www.youtube.com/watch?v=VSRIyDfo_mY

For us to hypothetically travel at the speed of light, in this universe, only gets us to first base as far as quantum entanglement, or teleportation, are concerned. That is to say, traveling at the speed of light only gets us to the place where time, as we understand it, comes to complete stop for light, i.e. gets us to the eternal, ‘past and future folding into now’, framework of time. This higher dimension ‘eternal’ inference for the time framework of light is warranted because light is not ‘frozen within time’ yet it is shown that time, as we understand it, does not pass for light.

“I’ve just developed a new theory of eternity.”

Albert Einstein

http://www.rd.com/your-america.....176-2.html

“The laws of relativity have changed timeless existence from a theological claim to a physical reality. Light, you see, is outside of time, a fact of nature proven in thousands of experiments at hundreds of universities. I don’t pretend to know how tomorrow can exist simultaneously with today and yesterday. But at the speed of light they actually and rigorously do. Time does not pass.” – Richard Swenson

Light and Quantum Entanglement Reflect Some Characteristics Of God – video

http://www.metacafe.com/watch/4102182

Also, hypothetically traveling at the speed of light in this universe would be instantaneous travel for the person going at the speed of light. This is because time does not pass for them, but, and this is a big but; this ‘timeless’ travel is still not instantaneous and transcendent to our temporal framework of time, i.e. Speed of light travel, to our temporal frame of reference, is still not completely transcendent of our framework since light appears to take time to travel from our perspective. In information teleportation though the ‘time not passing’, eternal, framework is not only achieved in the speed of light framework/dimension, but also in our temporal framework. That is to say, the instantaneous teleportation/travel of information is instantaneous to both the temporal and speed of light frameworks, not just the speed of light framework. Information teleportation/travel is not limited by time, nor space, in any way, shape or form, in any frame of reference, as light is seemingly limited to us. Thus ‘pure transcendent information’ is shown to be timeless (eternal) and completely transcendent of all material frameworks. Moreover, concluding from all lines of evidence we have now examined; transcendent, eternal, infinite information is indeed real and the framework in which ‘It’ resides is the primary reality (highest dimension) that can exist, (in so far as our limited perception of a primary reality, highest dimension, can be discerned).

“An illusion can never go faster than the speed limit of reality”

Akiane – Child Prodigy – Music video

http://www.metacafe.com/watch/4204586

Logic also dictates ‘a decision’ must have been made, by the ‘transcendent, eternal, infinite information’ from the primary timeless (eternal) reality ‘It’ inhabits, in order to purposely create a temporal reality with highly specified, irreducible complex, parameters from a infinite set of possibilities in the proper sequential order. Thus this infinite transcendent information, which is the primary reality of our reality, is shown to be alive by yet another line of evidence besides the findings of quantum mechanics.

The First Cause Must Be A Personal Being – William Lane Craig – video

http://www.metacafe.com/w/4813914

As a side light to this, leading quantum physicist Anton Zeilinger has followed in John Archibald Wheeler’s footsteps (1911-2008) by insisting reality, at its most foundational level, is ‘information’.

“It from bit symbolizes the idea that every item of the physical world has at bottom – at a very deep bottom, in most instances – an immaterial source and explanation; that which we call reality arises in the last analysis from the posing of yes-no questions and the registering of equipment-evoked responses; in short, that things physical are information-theoretic in origin.” John Archibald Wheeler

Why the Quantum? It from Bit? A Participatory Universe?

Excerpt: In conclusion, it may very well be said that information is the irreducible kernel from which everything else flows. Thence the question why nature appears quantized is simply a consequence of the fact that information itself is quantized by necessity. It might even be fair to observe that the concept that information is fundamental is very old knowledge of humanity, witness for example the beginning of gospel according to John: “In the beginning was the Word.” Anton Zeilinger – a leading expert in quantum teleportation:

http://www.metanexus.net/Magaz.....fault.aspx

The restriction imposed by our physical limitations of us ever accessing complete infinite information to our temporal space-time framework/dimension (Wheeler; Zeilinger) does not detract, in any way, from the primacy and dominion of the infinite transcendent information framework that is now established by the quantum teleportation experiment as the primary reality of our reality. Of note: All of this evidence meshes extremely well with the theistic postulation of God possessing infinite and perfect knowledge. This seems like a fitting place for this following quote and verse:

“To see the world in a grain of sand, and to see heaven in a wild flower, hold infinity in the palm of your hands, and eternity in an hour.”

William Blake

Psalm 19:1-2

The heavens declare the glory of God; the skies proclaim the work of his hands. Day after day they pour forth speech; night after night they display knowledge.

to define a photon to information Aleta:

Explaining Information Transfer in Quantum Teleportation: Armond Duwell †‡ University of Pittsburgh

Excerpt: In contrast to a classical bit, the description of a (photon) qubit requires an infinite amount of information. The amount of information is infinite because two real numbers are required in the expansion of the state vector of a two state quantum system (Jozsa 1997, 1) — Concept 2. is used by Bennett, et al. Recall that they infer that since an infinite amount of information is required to specify a (photon) qubit, an infinite amount of information must be transferred to teleport.

http://www.cas.umt.edu/phil/fa.....lPSA2K.pdf

to define an atom to information Aleta:

Atom takes a quantum leap – 2009

Excerpt: Ytterbium ions have been ‘teleported’ over a distance of a metre.,,,

“What you’re moving is information, not the actual atoms,” says Chris Monroe, from the Joint Quantum Institute at the University of Maryland in College Park and an author of the paper. But as two particles of the same type differ only in their quantum states, the transfer of quantum information is equivalent to moving the first particle to the location of the second.

http://www.freerepublic.com/fo.....1769/posts

one more note:

How Teleportation Will Work –

Excerpt: In 1993, the idea of teleportation moved out of the realm of science fiction and into the world of theoretical possibility. It was then that physicist Charles Bennett and a team of researchers at IBM confirmed that quantum teleportation was possible, but only if the original object being teleported was destroyed. — As predicted, the original photon no longer existed once the replica was made.

http://science.howstuffworks.c.....ation1.htm

Quantum Teleportation – IBM Research Page

Excerpt: “it would destroy the original (photon) in the process,,”

http://www.research.ibm.com/qu.....portation/

Unconditional Quantum Teleportation – abstract

Excerpt: This is the first realization of unconditional quantum teleportation where every state entering the device is actually teleported,,

http://www.sciencemag.org/cgi/.....2/5389/706

Hello again everyone.

First I want to spend a few friendly words to BA, which I think can help.

I appreciate very much your comments but I see that there are times when you are convinced that putting all your arguments on the table manage to convince others that your ideas or your beliefs are better. That, in one way or another we all do and I think to some extent is positive and good.

But you must understand that many times, not the number of arguments, but a good argument, a convincing argument, is the only one who can get out another one of his error. And in such case, you can just get the negative effect, ie, who may be willing to hear a good argument, given that so many of them not convinced, will eventually leave, taking the chance that maybe someone better prepared than you with the appropriate topic to draw from his error to the other person. Do you understand?

Another problem is that because we all have obligations and other persons who attend and if done too long what we suggest, many even begin to read it.

Todo esto dicho con todo mi aprecio a ti y a lo que escribes.

Y ahora sobre el tema, y parodiando la cita de BA:

“Sir, {a+b^n}{n}=x, hence God exists—reply!”

I tell Aleta:

“Sir, e^(pi)i+1=0, hence Evolution Theory is false—reply!”

(I dont know if Aleta is Sr or Mrs, but for the sake of the arguments, I assume Sir).

Aleta, I can not be shorter, the ball is on your roof.

Greetings and friendship for everyone.

Sorry, but I dont have translated some phrases before postin:

Where:

Todo esto dicho con todo mi aprecio a ti y a lo que escribes.

Y ahora sobre el tema, y parodiando la cita de BA:

Must be:

All this said with all my appreciation to you and what you write, BA.

And now on the subject, and parodying the appointment of BA:

Aleta (#54):

Thank you for your thoughtful response.

I very much agree with what you say. Regarding point 1), do you think that at least some of the wondeful results we can get, as you say, from “any set of simple rules” could be in some way attributed to the intrinsic power of our fundamental cognitive rules (whatever they are)?

It has been recently debated here, and I am aware that positions vary, but I do believe that we should recognized some shared universality (and great efficiency) to at least some cognitive principles: I am not interested in defining them (be they non contradiction, inference, or anything else), I leave that to the people who, like you, deal professionally with mathemathics, logic and some aspects of philosophy. Indeed, I believe that those fundamental principles are vastly intuitive, and rather elusive in their definition.

But, if there is some universality in human thought (be it the development of vast logical structures from some basic assumptions and rules, or the inference of vast theories about physical reality), there must be some unifying property in cognitive thought. Again, I am really interested in your position about that.

Regarding point 2), obviously, as I am a religious person, for me the most natural explanation is that an original Consciousness has structures reality, and that our personal human consciousness shares at least some properties with that original Consciousness. That is usually summed up in the concept that we are “made in His image”.

But I appreciate your position. As you define yourself as an agnostic, I would like to ask you a further specification, if you allow it.

I have always thought that the word “agnostic” is usually applied to at least two very different position (I will refer in what follows to the “major questions about reality” to signify those vast cognitive problems which are usually the foundation of general philosophical theories about it, such as “does a god exist?”, or “is there a final universal purpose to human existence?”, or “does life after death exist”?, and so on):

a) A person who has looked for an answer to the major questions about reality, and up to now has found no satisfying one. IOW, this position could be summed up as follows: “I really don’t know if credible answers of that kind exist, but certainly I have not found them up to now”. Let’s call that an “empirical agnostic”.

b) A person who believes that those answers cannot be found. IOWs, that kind of agnostic says: “I am reasonably sure that those answers don’t exist”. Let’s call that an “ideological agnostic”. That kind of agnostic is probably not a true agnostic, because he is not agnostic about the truth that answers to the major questions about reality cannot be found.

Both categories, obviously, are very different form mere materialists, reductionists and followers of scientism, who definitely have a very structures set of answers to the major questions about reality.

So, I would like to know, if you feel like answering, which kind of description you think is nearer to your position (or, if you want, you can give some completely different definition).

Hi gpuccio – I’m glad you returned to comment. Here are my thoughts, such as they are, on your questions.

You ask, “do you think that at least some of the wondeful results we can get, as you say, from “any set of simple rules” could be in some way attributed to the intrinsic power of our fundamental cognitive rules (whatever they are)?”

Hmmm, that’s a large question, and moves us to psychology as much as anything (which is a much less certain field than math!) On the one hand I certainly believe that all human beings share the same basic cognitive apparatus, in some sense, but I think the content and habits of our thinking can be strongly shaped by our culture, individual personality, and experience. Some people tend to abstract, symbolic thought easily, and some don’t. (I know there are students who just “get” math and who love manipulating the symbols to get results, and those who don’t.)

Throughout history at various times, in the major cultural traditions, there have been people who were good abstract thinkers who have invented the notions and symbols that now form the heart of our math and logic. This formalization has evolved into a tool of greater and greater power, and is part of the means by which we have created our mathematical knowledge.

So, in summary (and I’d be interested in trying to think about this some more – time is sort this morning), I think math and logic are abstract formalizations of basic human cognitive functions.

Here’s a story. A friend (who has a grey beard), playing with my granddaughter (who is learning her colors) , put a little pink piece of paper on her chin that looked like a beard. He asked her, “what color is your beard,” and she said “pink. Then he asked, “what color is my beard”. She was puzzled for a moment, because she didn’t know the color grey, and then he face brightened, and she said, “not pink.”

That’s a basic human cognitive trait – the negation which divides the world into A and ~A, yes and no, the basic binary bifurcation.

Also, you write,

I think a) is usually called weak agnoticism – it’s merely “I personally don’t know.” However, I don’t think b) is an accurate statement of it’s counterpart, strong agnosticism.

I am, to use a somewhat common term, a strong agnostic: I don’t believe we can answer the type of questions you mention. It’s not just that I personally don’t know, I don’t think that human beings can know what the “true” state of metaphysical reality is (or if there is even such a thing.)

More later, if you’d like to continue the discussion.

aleta wrote:

Don’t get so excited about a subjective comment. I did not say it was a fibonacci sequence, I intentiaonlly punctuated with a term “fibonacci-esque”. If you don’t understand the intention, it simply means there is a semblance of something. And the planets (including asteroid belt) do have a sequence reminescent of a fibonacci sequence. This is subjective, but it is not a hard to see a CLOSE comparison since it is a simple compounding addition sequence.

Do your own research on this:

“Titius-Bode Law”

…..

As a former mathematics instructor with a BS in mathematics I think Aleta has done a fine job laying out the situation from the mathematical side. When I see things like the Fibonacci sequence cropping up in the real world I tend to think there is some common structure or law. And I think it’s really important to reiterate that, from a mathematician’s point of view, while there are transcendent numbers (it’s just a word adopted by consensus) there is nothing in mathematics itself that points to anything other than a complicated axiomatic system which occasionally has a particularly beautiful result like Euler’s identity.

It’s also worth pointing out that a lot of mathematics is messy and ugly, in my mind anyway. Statistics is useful but . . . yuck. Topology is lovely to look at but I could never quite get the hang of it. Graph theory is quite nice at first anyway. (A field that Euler practically invented with his Koningsberg bridge problem.) Analysis has its breath taking moments of awe (objects with infinite surface area but finite volume) and lots and lots of grinding and crunchy slog. Non-Euclidean geometry deserves a mention for being counter-intuitive but finding application in non-Newtonian space.

I suppose, like Gauss, I find number theory the purest and most beautiful of all of mathematics with some amazing simple, pure and deep theorems that anyone can understand. BUT it took a few hundred years for someone to messily prove Fermat’s Last Theorem. And no one has yet established the Goldbach conjecture.

If you REALLY want to pursue the infinite and transcendent in mathematics you should check out set theory. Over a hundred years ago Cantor pioneered the study of different sizes of infinity (soooo cool) and got a lot of people looking at the continuum hypothesis. I still think a lot about the Axiom of Choice and it’s many versions including the marvelous Zorn’s lemma. Sigh. IF there’s something of the divine in mathematics I’d put my vote for set theory. Are there an infinite number of infinities? How many angels can dance on the head of a pin?

Ellazimm you state,

“there is nothing in mathematics itself that points to anything other than a complicated axiomatic system which occasionally has a particularly beautiful result like Euler’s identity.”

so Ellazimm do you hold that math is really just an invention of man or do you hold mathematical truths to be discovered by man?

If you hold that it is merely a useful invention of man that does not really point to anything that is transcendently real, do you then deny that absolute truth exists?

If you do so, as I think following your logic must dictate, then please visit this following web site:

This following site is a easy to use, and understand, interactive website that takes the user through what is termed ‘Presuppositional apologetics’. The website clearly shows that our use of the laws of logic, mathematics, science and morality cannot be accounted for unless we believe in a God who guarantees our perceptions and reasoning are trustworthy in the first place.

Proof That God Exists – easy to use interactive website

http://www.proofthatgodexists.org/index.php

Later on Ellazimm you mention Cantor. Have you seen this neat little film on Cantor?

Georg Cantor – The Mathematics Of Infinity – video

http://www.metacafe.com/watch/4572335

entire video: BBC-Dangerous Knowledge (Part 1-10)

http://www.youtube.com/watch?v=Cw-zNRNcF90

As you can see, somewhat from the preceding video, mathematics cannot be held to be ‘true’ unless an assumption for a highest transcendent infinity is held to be true. A highest infinity which Cantor, and even Godel, held to be God. Thus this following formal proof, which was referred to at the end of the preceding video, shows that math cannot be held to be consistently true unless the highest infinity of God is held to be consistently true as a starting assumption:

Gödel’s Incompleteness: The #1 Mathematical Breakthrough of the 20th Century

Excerpt: Gödel’s Incompleteness Theorem says:

“Anything you can draw a circle around cannot explain itself without referring to something outside the circle – something you have to assume to be true but cannot prove “mathematically” to be true.”

http://www.cosmicfingerprints......pleteness/

THE GOD OF THE MATHEMATICIANS – DAVID P. GOLDMAN – August 2010

Excerpt: we cannot construct an ontology that makes God dispensable. Secularists can dismiss this as a mere exercise within predefined rules of the game of mathematical logic, but that is sour grapes, for it was the secular side that hoped to substitute logic for God in the first place. Gödel’s critique of the continuum hypothesis has the same implication as his incompleteness theorems: Mathematics never will create the sort of closed system that sorts reality into neat boxes.

http://www.faqs.org/periodical.....27241.html

Ellazim, I know you will probably compartmentalize this away as Aleta has done, but the fact is that the math you and Aleta put so much faith is can’t be held to be true unless you in fact concede that transcendent absolute truth (God) exists in the first place.

Why does 1 + 1 = 2 depend on God? You just have to look at a thing, agree to write 1 for that thing, and then add another thing and agree to call that group 2. The truth is right in front of our eyes, and the symbols we use to write about it is an agreed-upon convention. Why is absolute transcendent truth needed to make this true?

And no videos or websites, please – what is

youranswer to that question, ba?BA77 . . . I always wonder what happened in 1977 . . . something wonderful???

Well, that is the central question isn’t it? I remember when one of my professors brought it up. I never have been able to decide for myself. And I never found it necessary to decide since I was either pursuing the mathematics for the sheer joy and pleasure, finding ways to model the real world and, finally, teaching it to students.

I will try and pursue the links you’ve provided ’cause I’m curious about the arguments employed. I really have no idea what they might be; I got through an MS degree without hearing any of them! I will admit that my first reaction is: yeah, right. But I will try and find time to look it over.

It may be that my own abilities are not up to the discussions in which case I shall admit that. Far enough?

Aleta since you do not seem to respect anything I say, I will respectfully leave you with part 6 of the video “Dangerous Knowledge” in which they actually talk about why just simply agreeing that simple math is true is not sufficient,,,, in fact they talk exactly about the huge struggle that took place just to prove 1+1=2 was true at the 4:45 minute mark

BBC-Dangerous Knowledge (Part 6-10)

http://www.youtube.com/watch?v=fqKQ0-T3swY

Hmmm. I disagree with you about the necessity of God for math, but disagreeing with someone is not the same as disrespecting them.

All I did was ask you a question, and ask you to tell me what you think rather than link to another site. Could you summarize what the BBC video says at 4:45?

BA77:

First link: Proof that God exists.

First question: I answered truthfully: I don’t know if absolute truth exists.

Second question: I don’t know if absolute truth exists, is this a) Absolutely True b) No.

I took the second absolutely true to mean TO ME and I got bounced back to the first question.

If I don’t know if absolute truth exists then I can only answer for myself and I get no where.

Do you think I proved, to myself, that God exists? I don’t think I did.

BA77: Second link, Cantor film

I watched the 8:40 (metacafe) version owing to the time I’ve got at the moment.

Nice explanation of some of what Cantor saw. His own proof that there was an infinity greater than the infinity of the natural numbers IS lovely. Turns out the infinity (aleph-naught) of the natural numbers is the same as that of the rational numbers but the infinity of the real numbers is bigger. Fascinating.

But . . . proof of God? Or just showing that our axiomatic system of mathematics throws up some pretty weird ‘truths’? I completely believe Cantor’s result but I, personally, see no evidence of the divine there. Before Cantor came along some people believed in God, some didn’t. After Cantor’s work was published some people continued to believe in God, some continued not too. I don’t personally know of anyone who really understood the mathematics who changed their mind about the existence of God after being exposed to Cantor. That may mean I just wasn’t told. I did know a mathematician who once expressed to me that things like that were indications to him of something divine BUT that he was already a believer before seeing it.

AND doing the math does not require a theistic world view. There is no faith there; just logic and working from known results.

Ellazimm, it’s “loaded” website, and that’s a generous description. (A more accurate description is “sophomorics”, or perhaps even “stupid”.) The only way you can get through it is answer “correctly” – i.e., that absolute truth exist.

I answered the first question “I don’t know whether absolute truth exists or not.”

Then it wants to know whether I consider that statement “Absolutely True” or “False”, but those two choices are a false dichotomy. The correct answer, which is not given, is simply “True” – I don’t know whether absolute truth exists. I already said that on the first screen. The statement is a true statement about what I believe.

As I said … pick whatever adjective from above that suits you.

Aleta: I’ll pick

Case unproven

I think.

I did think there’d be more to it than that. I remember reading a book by Mortimer J Adler proposing his ontological proof of the existence of God and it went on for quite a while. (It was a long time ago and I don’t remember the details.)

And, I’d like to point out to everyone else: I’m not here to debate the existence of God except . . . maybe using a mathematical justification.

The comment at 4:45 in the video was just the barest hint of what was going on in the mathematics community at the time as they struggled to attempt to justify EVERYTHING in mathematics based on the fewest possible axioms. It was a real reductionist approach which, in my mind, failed. Bertrand Russell really tried though. And some people think he pulled it off. He started with literally nothing, the empty set, and attempted to create all of mathematics from there. It was attempts like that which got Godel thinking about whether it was possible to prove everything that is demonstrably true about an axiomatic system from within the system. And, he showed (although I don’t understand the proof) that it was not possible. There will be things that are true that cannot be shown with a brick upon brick approach.

Godel is deep, deep mathematics. I’m not capable of discussing it completely and I think it takes years of study to be able to do that. I hesitate from drawing conclusions outside of mathematics using Godel’s theorem owing to it’s extreme complexity.

Very good remarks, ez. I agree with you about Russell’s reductionist program – I am more practical than that. I appreciate the deep rigor that in other places has proven very useful, but I think for basic discussions like this, especially when they are about the philosophy of math and not math itself, my statement about 1 + 1 = 2 not depending on God are perfectly adequate.

Hi, all.

A single question to ellazim & Aleta (if you want to answer, of course):

If can be mathematicaly proven that a material world needs a inmaterial (supranatural, can be named) world to exist, what would this mean for you?

If someone else wants to respond, you can do.

Thanks in advance.

Too hypothetical of a question, as I am sure that it can’t be done. There are people right here that think that a material world requires an immaterial world, but their arguments are philosophical, not mathematical.

Thanks Aleta for your answer, but I say

mathematically, using SET Theory. I would like to know what would this mean for you.But as I said, it’s too hypothetical of a question, in part because I don’t believe that you could prove that mathematically. If I thought the arguments for an immaterial world were compelling, I already would have adopted that view, but I don’t and I haven’t, and it doesn’t make sense to try to think about how I would be different if I believed differently.

Thanks, Aleta. I define then

inmaterial: entities that are mathematically proved impossible to be material. ¿Do you like this definition?Aleya:

Again, I find I agree with most of what you say.

In particular:

So, in summary (and I’d be interested in trying to think about this some more – time is sort this morning), I think math and logic are abstract formalizations of basic human cognitive functions.

That’s my opinion too. And you are right that not all human beings have the same ability for abstract thought, but still the important thing is that, where abstract thought is efficiently implemented, some common intuitions are certainly necessary to achieve an agreement (which, definitely, is achieved in most cases).

I will add here that I am a great fan of Penrose’s argument form Godel’s theorem. I know it is very controversial (all the best things are ), but I believe that it gets a point which is very important: the basic role of consciousness and representation in human knowledge.

I am a firm believer in that. While great part of human thought is certainly algorithmic, conscious representation has a crucial role which cannot be substituted by purely algorithmic processes. That is specially evident in the concept of CSI, and in the obvious empirical impotence of powerful computers to create it. But that’s another story.

So, in short, I believe that the basic cognitive functions which allow us to achieve highly efficient abstract thought (even in very complex algorithmic forms), to define foundations for logic and mathematics (whatever they are), and to have a sense of concepts like meaning and purpose, are mainly intuitive, and are tied to our conscious representations. I offer that as a proposal for further discussion.

About the second point, I would like to understand better why you say that strong agnosticism (which seems to be your position) is not well represented in my definition (I am ready to change it).

You define your position as follows:

“I am, to use a somewhat common term, a strong agnostic: I don’t believe we can answer the type of questions you mention. It’s not just that I personally don’t know, I don’t think that human beings can know what the “true” state of metaphysical reality is (or if there is even such a thing.)”

That is for me very much what I had tried to describe in what I had called “ideological agnosticism”. I meant no negative judgement about the position, just that it is a strong answer anyway.

My position is obviously different, but perhaps not completely. I will try to be more clear. If youe statement were limited to the fact that those naswers cannot be found

onlyby logic and reason, I would probably agree.And I am not saying here that some special divine grace is necessary (I believe that divine grace is necessary, obviously, but I also believe that it is always there for all, and anyway I would never use a specific belief from faith in a general discussion).

What I mean is that any final, deep and humanly certain answer to those questions implies

always, together with a correct and sincere use of reason, an involment of all our powers, both cognitive and non cognitive, including personal experience, intuition, free will, love, desire, sincerety, and so on. This is my opinion, and that’s why I never try to convince others that God exists, although I am always happy to share with them the reasons why I believe that.ellazim, Ok,,, you don’t know if absolute truth exists.,,, But in reality the only options to answer that question are that absolute truth either does exist or it does not exist. If you agree on the site, and say yes that it does exist, then the site kicks you on up to the next step, but if you say that absolute truth does not exist, then I believe, the site asks you something like this, do you believe that Absolute truth not existing is an absolute truth??? Then, it gives you a few chances to see that you are making a absolute truth claim,,, I believe,, the site has a few different paths besides the endless loop you were on,,, For instance one person told me they were on the site trying the site out, pretending to be the dogmatic atheist, just to see what would happen, and he told me after a completely series of illogical answers the site bid him ado and redirected him to the Disneyland website, with the not to subtle hint that he was living in a fantasy land.

As far as Godel goes, the incompleteness theorem was the end product of about 100 years of work which started with Cantor.

And in fact the incompleteness theorem goes directly to the heart of even such ‘taken for granted’ truths as 1+1=2,,

Here is a excerpt of Godel’s work:

Gödel is best known for his two incompleteness theorems, published in 1931 when he was 25 years of age, one year after finishing his doctorate at the University of Vienna. The more famous incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.

He also showed that the continuum hypothesis cannot be disproved from the accepted axioms of set theory, if those axioms are consistent. He made important contributions to proof theory by clarifying the connections between classical logic, intuitionistic logic, and modal logic.

http://en.wikipedia.org/wiki/Kurt_G%C3%B6del

i.e.

Gödel’s Incompleteness: The #1 Mathematical Breakthrough of the 20th Century

Excerpt: Gödel’s Incompleteness Theorem says:

“Anything you can draw a circle around cannot explain itself without referring to something outside the circle – something you have to assume to be true but cannot prove “mathematically” to be true.”

THE GOD OF THE MATHEMATICIANS – DAVID P. GOLDMAN – August 2010

Excerpt: we cannot construct an ontology that makes God dispensable. Secularists can dismiss this as a mere exercise within predefined rules of the game of mathematical logic, but that is sour grapes, for it was the secular side that hoped to substitute logic for God in the first place. Gödel’s critique of the continuum hypothesis has the same implication as his incompleteness theorems: Mathematics never will create the sort of closed system that sorts reality into neat boxes.

Obriton: I doubt that can be done (that a material world needs an immaterial world) but I’d be happy to see your argument.

But I REALLY have to deal with things at the moment.

I’ll be baaaaaaaaaaaaaaaaaaaack!! My family needs me first. Sorry.

BA77: Give me some time. I’ll be back. Sometime. Gotta eat first.

Obitron writes, “Thanks, Aleta. I define then inmaterial: entities that are mathematically proved impossible to be material. ¿Do you like this definition?”

No, that doesn’t work, because the word “entity” implies existence, and so you would need to prove that the entity existed first, before you could apply a dichotomy as to whether it was material or immaterial.

Maybe you should be more specific and just show an example of what kind of “mathematical proof” you have in mind?

Pleased to greet you ellazim.

I think that it can be proved. I’m writing now a book (not english) about a new Theory of Information, from an analytical perspective, namely to define what information is from any system using formulas and values such as being able to find how much information on a system, the complexity of this system, the complexity of language, etc. It is a difficult job, but I think eventually I managed to get published.

The point is that at any given time, trying to find a definition for the space that constitutes a data set, I saw that I had to prove a material world need another intangible to conform, to fill it with information.

The problem is that until it is published, I can not show the theorem. Hence, my question is, what do you think if this theorem is mathematically correct?

Thanks for answering and greetings to all.

Aleta @(95):

“No, that doesn’t work, because the word “entity” implies existence, and so you would need to prove that the entity existed first, before you could apply a dichotomy as to whether it was material or immaterial.”

I intend “mathematical entities”, that they are out of time, then for this entities there is not before nor after. For example, a circle, although I think that it can be defined more in abstract as a set.

Thanks, again.

Hi gpuccio.

I;ve gone back and re-read your statement b) about agnosticism, and I at first it ddin’t quite make sense to me, but now I understand. You wrote,

In comparison, I wrote,

I think I see now that perhaps what you wrote would apply to me. I do believe that we can’t answer certain kinds of questions, so to the extent that I feel certain about that, I am not agnostic about my agnosticism, so to speak.

This deepens the issue, in an interesting way.

My agnosticism, and people’s beliefs in general, exist along a spectrum of certitude. I leave open the possibility that I could be convinced that I am wrong about my agnosticism. Mine is not a so much a dogmatic position as it is a practical one, based on my experience and knowledge of the arguments used in respect to possoble metaphysical reality, on my knowledge of religion a a humen phenomena, on my knowledge of psychology, etc. I have lots of reasons to believe that the standard arguments offered are not compelling, so I consider that my agnosticism is a reasonable conclusion of which I am highly confident, but certainly not 100.00000000% certain.

You also write, “If your statement were limited to the fact that those answers cannot be found only by logic and reason, I would probably agree….What I mean is that any final, deep and humanly certain answer to those questions implies always, together with a correct and sincere use of reason, an involment of all our powers, both cognitive and non cognitive, including personal experience, intuition, free will, love, desire, sincerety, and so on..”

I agree with this. Our beliefs are formed with our whole being. Of course we bring to bear the power of logic and reason, but we also have our holistic experiences, some of which are both ineffable and subjecive, experienced only by ourself and no one else. And again, the source and validation for our beliefs are spread across a spectrum, with purely logical beliefs such as mathematics on one end, moving through empirically-based and consensually validated beliefs such as those of science on over to the more subjective beliefs of value, personal opinion, emotion, and so on.

One other point: the problem with being an agnostic, which is a position of not knowing, is that one must balance that with the need to act, and to act is to implicitly choose to believe. So even though I believe that we can’t know about metaphysical reality, I know there are some metaphysical systems that don’t appeal to me at all and some that do, and so I choose to act in accordance with the ones that do appeal to me even though I’m not attached to whether they are “really” true or not.

Bob Dylan wrote in “High Water”, ““You can’t open your mind, boys, To every conceivable point of view”. One has to have a perspective even if one is agnostic – one can’t treat all metaphysical systems equally. People have to act – can’t avoid it, and through our actions we implicitly manifest a perspective of some sort. Therefore, in my opinion, one might as well do so with as much clarity and commitment as possible.

In this sense, I am what you might call a “weak existentialist”: we can’t know, but to some extent we have to act as if we do know. So I have chosen certain ideas from the broad range of religion and philosphy as guides for my life, and rejected others, not because I think one is true and the other is not (that I cannot know), but because, taking all those things that you mention into account, they help inform my actions in what I consider to be the best possible way.

To Obitron: you write, “I intend “mathematical entities”, that they are out of time, then for this entities there is not before nor after.”

Then you have already defined them as being immaterial, so any proof that they were immaterial would be circular.

Thanks, Aleta. I can’t now show well my arguments, because for it I need to show the Theorem. I’m speaking not in a formal mathematical sintaxis, but in a plane languaje. But I try again:

Given A, a set of a space of elements that are defined

materialso and so…(this so accomplishes all we intend for a material world, intended as commonly intended), then B dont partain to A if the conditions for A are not accomplished for B. B then is namedimmaterial…And the teorem-> For A to be true, B need to be true. That’s all the hypothesis.

Do you like so?

Participants & Onlookers:

I see things got very hot in this thread overnight.

In appreciation for the Weir link, here is the Google Books link. Well worth a ponder or two.

Some of the onward remarks led me to think it would be advisable to re-post what I noted in 52 (leaving off for now the tag end on how materialism is self-referentially incoherent):

Here we go again:

0 = 1 + e^i*pi

a –> The five most important numbers in mathematics all explicitly interwoven (with the sixth, -1, implied), coming together from vastly diverse lines of inquiry.

b –> So, we are looking here at an unusual view of mathematics, a worldview perspective, and one on inference to best explanation. (The attempt to brush this aside on oh, it is the implication of a chain of argument, ho hum, misses the point.)

c –> Were these things simply diverse arbitrary human inventions with no inherent inner connexion, we would have no reason to expect such astonishing coherence.

d –> And yet, here it is. Staring us in the face and trying to evoke something.

e –> For, at the heart of scientific thought in a scientific age lies mathematics, a decidedly non-empirical, logical discipline assessing he import of certain key abstractions, starting with number itself.

f –> Number is not tangible, but is real, and is central to the operations of the world.

g –> Worse, numerical patterns and their logical implications capture such an essence of reality that scientists have had to publicly wonder on the “unreasonable” effectiveness of mathematics, that magic chalice that flows with the sweetly intoxicating wine of predictive accuracy and power to influence and control reality.

h –> Including of course, most notably, the absolutely astonishing, arcane powers of the imaginary root of -1. (My students spotting complex domain poles of dynamical systems they observe, down to the car hitting a pothole and bouncing, are only the beginning of the astonishing power of complex frequency domain analysis, as just one domain of its eldritch powers.)

i –> So, here we see the power of mind, symbol, abstract realities and abstract mental operations, logical and mathematical. And we must ask: what best explains this?

j –> That by an astonishingly lucky accident in a warm little pond or the like, a self-replicating metabolising entity came into being against all odds [well beyond astronomical], and then by chance variation and environmental culling on differential reproductive success threw up an entity capable of a brain so organised that it somehow accurately infers not only 1, 0, e and pi, but i and then reasons its way to Euler’s identity and beyond. All, programmed by lucky noise?

[ . . . ]

k –> To such a notion, we at once can rebut [cf here]:

l –> In short, evolutionary materialism is a patently self-refuting non-starter as a worldview. (It only survives as a dominant view because of ideological domination of key scientific and educational institutions as a legacy of the late C19 lingering into the early C21. Now, beginning to fade.)

m –> Instead, we should let the obvious import of a discovery like the Euler equation speak to us: numbers are real, and speak of an abstract realm of reality, a realm accessible to the mind and which is in fact the basis for the physical realm.

n –> Thus, the coherence of mathematics, its astonishing power in the physical world and our ability to use it to unlock the secrets of that physical realm are best explained on longstanding insight from the founding era of modern science: we are thinking God’s thoughts after him.

o –> Now, we may debate who or what “God” is, but the essential point stands: the observed cosmos, per its astonishing finetuning and the underlying mathematically framed order it exhibits, bespeaks its being an artifact of design by a mind with sufficient power and wisdom to create a cosmos.

p –> Similarly, when we find digitally coded information systems at the heart of the metabolic and self-replicating mechanisms of life, noting that he cosmos is finetuned in ways that support such life based on C-chemistry, this points to the design of life, and that the same designer of the cosmos is a likely candidate.

[ . . . ]

q –> Then, when we pause and explore mathematics itself, we find that amazing coherence that the Euler identity epitomises. This too bespeaks that such abstractions are real, and are integral to reality.

r –> Ultimate reality is plainly mental.

s –> Indeed, we may dare speak the word, Soul.

t –> And so — with apologies to Jastrow — after centuries of toil, the scientists and mathematicians over-top the ascent of learning, and find themselves greeted by theologians, philosophers, and even ordinary people who have known that transcendent reality through life-transforming encounter.

s –> Here is Plato, in The Laws, Bk X, 360 BC:

__________________

And so, as the Greeks were wont to say: in whatever direction we go, we meet Plato and Socrates; on the way

back. . .GEM of TKI

PS: Obriton, keep coming, I like what I am hearing.

@kairosfocus

I really enjoy reading your posts. Keep them coming :).

The form your arguments take remind me of Pascal’s Pensees.

Some random thoughts of my own.

I think BA77 has a point about missing the forest for the trees.

Its is a bit like quantum mechanics. We can’t – with high resolution – measure the properties of an individual particle but when we look at a collection of them we can. When we look at individual evidences for God we can’t quite get quite the resolution(certainty) we want, but when you look at them collectively it becomes undeniable.

Its like looking at the individual features of a face to determine if you know the person. You can’t really tell if it is the person with certainty. We need to step back and look at the whole face. Immediately the answer is obvious.

I’m going to do my best but . . . it’s late, I’m tired and I’m not really able to answer some questions. But, based on my own personal views and experience I’ll do my best.

gpuccio @91: Thank you. You speak from your heart. I won’t argue with you about these points because I have nothing to add not having thought about it on the same level. But I appreciate your approach.

BA77 @92: I don’t know why it’s not allowed to say you don’t know if absolute truth exists. Isn’t it better to admit ignorance when that’s what you think? I don’t want to be forced into an opinion that I cannot honestly support. Would you want me to?

Godel’s theorem was far from 100 years after Cantor’s work . . . but I get your implication. And hardly any major finding happens in a vacuum. I ‘think’ your summary of Godel’s theorem is good but I still don’t see what that has to do with theology. Unless you’re willing to define an axiomatic system and even then you can not anticipate what ‘truths’ will crop up without following through with things. You’ve got to be really careful in how you apply results outside of their intended field of application.

Obriton @96:

“The point is that at any given time, trying to find a definition for the space that constitutes a data set, I saw that I had to prove a material world need another intangible to conform, to fill it with information.”

I’m sorry, and I don’t mean to pick at your English but I have no idea what you’re talking about. So I can’t really comment on my reaction if it’s proven true since I don’t get what you’re proposing. Sorry. And I’m not any closer after your comments @100

“Given A, a set of a space of elements that are defined material so and so…(this so accomplishes all we intend for a material world, intended as commonly intended), then B dont partain to A if the conditions for A are not accomplished for B. B then is named immaterial…

And the teorem-> For A to be true, B need to be true. That’s all the hypothesis.”

I will wait for your completed work. Okay??

KF: I agree that Euler’s equation/identity is an amazing and beautiful congruence of important mathematical constants. I love it! I love showing to people and marvelling that it is true. But . . . it’s just an assertion that it proves anything about a deity. The point has been made on this site many times that ‘Darwinists’ are not allowed to take on faith something which has not been demonstrated. You and I can be shaken to the core that something like Euler’s equation represents a true statement utilising some of the most basic terms in mathematics but . . . is its improbability or our own inability to anticipate such a result enough to prove a greater mind behind the machinery? I’d prefer to be agnostic on that issue. It sounds like the fine tuning argument in physics.

And, to be honest, Euler’s equation, as beautiful as it is, didn’t change the mathematical landscape one jot. It didn’t force a paradigm shift. It didn’t create a legion of theistic mathematicians. It didn’t even create a new field of research unlike Euler’s examination of the Konigsburg Bridge progblem. I’m not sure it even convinced Euler of the existence of a greater mind.

I know you know that there are lots of theorems in mathematics that are surprising and beautiful and elegant. Euler’s identity may be the best but it’s pretty self evident to an undergraduate. Zorn’s lemma and the Goldbach conjecture reach much more deeply into mathematics and they are, as yet, unestablished.

Euler was a mathematical vacuum, he sucked up everything, digested it and used it all. He may be the greatest mathematician of all time and he’s certainly one of the last, great generalists. But does his identity imply divinity any more than the fundamental theory of calculus? Or the axiom of choice? Or Cantor’s work? I’m not so sure.

Anyway, it’s after 11pm here. I’m sorry that my comment are discontinuous but I have to find time when I can.

EZ:

Please, pause again, and look at the way that numbers so utterly diverse come together in an astonishing unity, in the Euler identity:

0 = 1 + e^i*pi

Then, whatever the fundamental theorem of the calculus may have to say about how rates and accumulations of change relate as mutually inverse operations, and draw in the limit and the infinitesimal as further wonders [and my favourite illustration for my students was a pipe running into a bucket, then moving on tot he bucket with an outflow . . . ], think about the revealed unexpected unity in mathematics.

Behold, and reflect.

Then, let us wonder with awe as we begin to understand that which we know and so easily pass by with a ho hum.

GEM of TKI

PS: But hen even something so “humdrum” as a simple plane mirror has behind it

a virtual half-universe, with the reflected virtual — non-material — images at definable, measurable locations that can be located through parallax!PPS: Put two such mirrors directly across form one another and we will see an infinite regress of reflections in progress. Yet another wonder in the humdrum. How blase we are!

KF: I agree, it’s very, very cool. That is NOT under dispute.

I think we’d better just leave this alone. There’s nothing else to say really. It’s fabulous whether it’s a lucky outcome or a signpost to God. Whether mathematics is invented or there to discover. If you don’t love it you don’t know mathematics; on that we can agree.

I’m also still marvelling at Goldbach’s conjecture and Fermat’s Last Theorem. Or even just prime numbers. And Pythagorean triples. And the prime number theorem. And Gabriel’s horn. And Zorn’s lemma. And the Well Ordered Principle. All epiphanies in their own way.

Ellazimm you state;

‘I don’t know why it’s not allowed to say you don’t know if absolute truth exists. Isn’t it better to admit ignorance when that’s what you think?’

‘I don’t know’ will not be an answer. The answer is only one of two possible choices,, Either absolute truth exist or it does not exist.,,, And as the site programmer wisely programmed,, if you say you don’t know then you end up in a endless loop of never being able to know any answer of any problem with certainty,,, much like Aleta’s 100.000000,,,% uncertain that God exists quip,,, Yet it dawned on me after reading that quip of Aleta’s, that, much contrary to lack of 100% certainty for her uncertainty, I am 100% certain that God does exist! One of the best ways to arrive at this 100% certainty is to use the materialists own line of reasoning for a multiverse against them,,,

if an infinite number of other possible universes must exist in order to explain the fine tuning of this one, then why is it not also infinitely possible for a infinitely powerful and transcendent Creator to exist? Using the materialist same line of reasoning for an infinity of multiverses to explain the extreme fine-tuning of this one we can surmise; If it is infinitely possible for God to exist then He, of 100% certainty, must exist no matter how small the probability is of His existence in one of these other infinity of universes, and since He certainly must exist, then all possibilities in all universes automatically become subject to Him since He is, by definition, All Powerful. To clearly illustrate the absurdity of what the materialists now consider their cutting edge science: The materialistic conjecture of an infinity of universes to explain the fine tuning of this one also insures the 100% probability of the existence of Pink Unicorns no matter how small the probability is of them existing. In fact a infinity of universes insures the existence of an infinity of Pink Unicorns an infinite number of times. Thus it is self-evident the materialists have painted themselves into a inescapable corner of logical absurdities in trying to find an escape from the Theistic implications we are finding for the fine-tuning of this universe.

This argument is actually made into a formal philosophical proof:

Ontological Argument For God From The Many Worlds Hypothesis – William Lane Craig – video

http://www.metacafe.com/watch/4784641

God Is Not Dead Yet – William Lane Craig – Page 4

The ontological argument. Anselm’s famous argument has been reformulated and defended by Alvin Plantinga, Robert Maydole, Brian Leftow, and others. God, Anselm observes, is by definition the greatest being conceivable. If you could conceive of anything greater than God, then that would be God. Thus, God is the greatest conceivable being, a maximally great being. So what would such a being be like? He would be all-powerful, all-knowing, and all-good, and he would exist in every logically possible world. But then we can argue:

1. It is possible that a maximally great being (God) exists.

2. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.

3. If a maximally great being exists in some possible world, then it exists in every possible world.

4. If a maximally great being exists in every possible world, then it exists in the actual world.

5. Therefore, a maximally great being exists in the actual world.

6. Therefore, a maximally great being exists.

7. Therefore, God exists.

Now it might be a surprise to learn that steps 2–7 of this argument are relatively uncontroversial. Most philosophers would agree that if God’s existence is even possible, then he must exist. So the whole question is: Is God’s existence possible? The atheist has to maintain that it’s impossible that God exists. He has to say that the concept of God is incoherent, like the concept of a married bachelor or a round square. But the problem is that the concept of God just doesn’t appear to be incoherent in that way. The idea of a being which is all-powerful, all knowing, and all-good in every possible world seems perfectly coherent. And so long as God’s existence is even possible, it follows that God must exist.

http://www.christianitytoday.c.....ml?start=4

,,,,Aleta’s quip also reminded me of this video,,,

Richard Dawkins Vs. Ben Stein – The UFO Interview – video

http://www.metacafe.com/watch/4134259

,,,In which Stein asked Dawkins to put a percentage on his certainty that God does not exist.,,,

The extreme, and completely unscientific, bias that Dawkins exhibits is clear for all to see in the video.

EZ:

Again, the peculiar force of the Euler equation lies in the way it unites in one such uttrerly diverse mathematical entities, showing he underlying unity of Mathematics.

Coherence.

Astonishing coherence that points to the unity of truth.

If these things were mere accidents or arbitrary inventions, they would not reasonably be expected to come together like that.

In short, this is a compass needle, and we would do well to heed where it points.

Especially given other pointers that join with it in pointing the same way.

GEM of TKI

BA77: If I don’t know is not an acceptable answer then I guess I don’t understand the question. And I AM willing to accept that all knowledge is provisional. That nothing can be known for certain. I can live with that. I can stay open to new data, new concepts, new discoveries that force me to revise my outlook.

And what happens to your proof if a maximally great being doesn’t exist? What if our limited understanding and logic is flawed? Is that not too a possibility? Do we not also have to accept the notion that we might be wrong? I could be way off the mark. What if you are? What then?

It’s almost 1am where I live. I have to stop for the night. Thanks one and all.

correction,,, much like Aleta’s

almost being100.000000,,,% uncertain that God exists quip,,,EZ, you ask:

“And what happens to your proof if a maximally great being doesn’t exist?”

That is the beauty of the ontological argument coupled with the multiverse,,, If it is even remotely possible for God to exist, however slight, then He of 100% certainty must exist,,, and as Aleta and yourself have already conceded by admitting that you are not 100% certain of your uncertainty for the existence of God, you have conceded that remote possibility to the ontological argument,,, and but yet if you try to say you are 100% certain that God does not exist then I will have you there to for I can then refer you to the site that you said ‘I don’t know’ to.

ellazim @(106)quoting me:

“The point is that

~~at any given time,~~when I wastrying to find a definition for the space that constitutes a data set, I saw that I~~had to~~needprovethata material world needsanother~~intangible~~immaterial world for~~to conform, to fill it with information~~the first could be possible.”My apologies for my bad english, but I’m used to be in my own language as short as possible, and it’s difficult for me with another languaje, because in my own one some words are intended to be, without really to be, in many phrases, and so, it is difficult to translate, sorry.

On the other hand, maybe the Theorem can be out of the book in a separate paper, before the book will be ended. But it is hypothetical for now. Althoug, just for curiosity, have you replied my first answer?

Have you a good rest!

kairofocus @104:

thank you for your kind words. I’ll try to be here with regularity, if my job allow me. Some times I’m too busy.

BA77: You are convinced God exists. I don’t know if God exists; I think s/he/it probably doesn’t exist. If the proof were as easy as you assert then why is it still disputed? Are you very sure you aren’t making a circular argument?

Obriton: are you referring to your question “If can be mathematicaly proven that a material world needs a inmaterial (supranatural, can be named) world to exist, what would this mean for you?”

IF is a might big caveat. I will read your proof when it’s available but, IF there is an immaterial world I see no evidence of it. So, without it having some effect on my life . . . it wouldn’t make much difference to me. I get by with much joy and happiness and wonder without it. My life has great meaning and purpose the way I see it. And that’s good enough for me. I don’t feel the need for outside validation of my existence or efforts. I do my best to help and understand other people and to treat them the way I want to be treated in the face of what seems to me the great indifference of heaven. I don’t expect a reward for my behaviour; I act the way I do in the hopes that after I’m gone the world is slightly a better place. I may be a dreamer but I hope I’m not the only one.

EZ::

You have put issues of truth, warrant, certainty and knowledge on the table.

It would be trivial to show that something like . . .

cannot be literally so, as it would then be self-referentially incoherent. But we will simply accept that you accept the logical possibility of error and build on that.

a –> Consider the claim C1, directly implied by the above:

b –> Now, plainly you concede its truth, as do all sane people. But if you try to deny it, for argument’s sake, something interesting happens.

c –> For, NOT-C1 => C1.

d –> That is, “Error exists,” once we understand it, is undeniably true on pain of self-referential incoherence.

e –> It is in fact something that the past 200+ years of philosophical skepticism has led many to doubt: a self-evident truth. (Not, an immediately apparent or obvious truth, but one that, once we understand what it claims based on our experience of the world, is seen to be true and to necessarily be true on pain of immediate reduction to absurdity, as we just saw with what we may now relabel Warranted, Credible Truth 1, WCT 1.)

f –> WCT 1 implies that truth exists, where truth is understood as Aristotle and Plato aptly described ever so long ago now:

that which says of what is, that it is; and of what is not, that it is not.[Cf. Metaphysics 1011b)g –> Moreover, WCT 1 is warranted beyond reasonable doubt, and more even than that: it is undeniably true on pain of reduction to absurdity.*

It is known, to demonstrative certainty.___________

h –> So, knowable truth exists, even to the point where certain things may be known beyond rational dispute.

i –> Thus, in certain restricted contexts, pure, unadulterated truth exists and is knowable to demonstrative certainty:

the truth, the whole relevant truth and nothing but the truth.(And, that is the substance of “absolute truth.”)j –> Going further, once we have a cluster of WCTs that are self-evident [cf discussion here in context], things they individually or jointly imply will also be true, as the logical implication of what is true will also be true. (This sets a sharp framework of constraints on worldview claims, i.e. it empowers and gives teeth to the process of comparative difficulties analysis across live option worldviews.)

k –> Going beyond that, other things are sufficiently well warranted as matters of fact that a reasonable person will accept them as empirically reliable or morally certain or at least reasonable; on at least a provisional basis. Scientific knowledge fits this criterion, and the sort of consequential decisions that we have to make in say a courtroom, also fit in here.

l –> In this context, the usual way the fallacy of selective hyperskepticism works is to reject what one is disinclined to believe on assertions like “extraordinary claims require extraordinary evidence.”

m –> But, as Simon Greenleaf long ago pointed out, we have no proper right to demand of a given claim a degree of warrant or certainty beyond what is adequate and reasonable for a claim of fact or the like.

n –> Especially, where on any number of similar matters, we routinely accept the degree of warrant we now wish to reject for this particular case, out of what amounts to bias.

o –> Think about the degree of warrant sufficient to drive a car down the road, or to cross a busy street; for on these degrees of warrant, you are routinely hazarding your life.

p –> Similarly, consider how you responded to the information presented in textbooks, by teachers and the like; for, on these you have built your knowledge base.

q –> So, we can see that global skepticism is futile, and that selective hyperskepticism is self-referentially incoherent. Instead, by accepting the reality of warranted, credible truth, some of which is certain, and other of which are sufficiently reliable to make momentous decisions, we can come to a much healthier view of truth, knowledge and confident action [i.e. that worldview level faith which we live by].

r –> At the same time, as error undeniably exists, we must be open to correction on credible evidence and good reason. (In that context I invite you to look here

Aleta, this also includes you.]___________________

Coming back, we here have a context in which we can look at the import of say the Euler identity, and the significance of a cosmos where phi and the Fibonnacci series or the like so often appear as design parameters.

GEM of TKI

PS: Obriton, do spare us a few moments when you can, as you plainly have some very significant things to say. As soon as you can, could you let us hear about your theorem? [Please, click on my handle “kairosfocus” in the LH column, and use the Contact me to get in touch.]

I don’t think I’m a hyper or global skeptic and I’m sorry (and wrong) if I gave that impression.

You find the beauty of Euler’s identity/equation to be indicative of great design inherent in the universe. I don’t. Given that the universe is composed of a few basic particles obeying a limited number of physical laws (not all discovered but surely not infinite) I don’t find it surprising that some patterns and congruences will arise. And that some mathematical formulations will reflect that. And that does not detract from the joy and wonder I feel when considering those things. I remember the first time I heard the four-colour theorem (graph theory). Incredible!

I also find fascinating the things that are, currently, intractable. I desperately want there to be a pattern in the prime numbers or the digits of pi. There are places where everything seems to come together and other places where it’s all seemingly disjoint and random. I try to encompass it all.

ellazim @(115)

Yes, thank you very much. I’ve made the question because for me it’s not important the actual understanding of every one over the True for me, and the true for any one. I think that we are all travellíng in the same road and there be people who use a bad map, other a better map, and many others without any road map. We can go together to some point and enjoy this moments with great pleasure and good for both. But if at any moment you need some indication to go to a route, if you dont have any map and you request me any help because you know I have a map, then I can help you and vice versa. If you see that this “map” help you well, can be that you want to have someone. If you live well without any or with your own map, then for me no problem. But if you or someother wants I go for a road that in my map is a bad road, I first try to show you my map because can be possible that your is better, and if we can not agree, then you must go by your own road and I’ll go for my own.

And it is for that that I want to know what route you wants to go if I am to go with you. The route can be logical, methodological and even physical. If we can agree on the fundamentals of any route then we can go together. If not you go for yours and I for mine, and ¡good luck for boths!

That’s all and thanks again for your answer.

KF @(116)

I’ll try to contact. Thanks. I also considered that this theorem, if it results irrefutable, can be of extraordinary significance for the understanding of the whole science, and not only of the ID theory, when formally stablished.

Ellazimm you state:

‘You are convinced God exists. I don’t know if God exists; I think s/he/it probably doesn’t exist. If the proof were as easy as you assert then why is it still disputed?’

The proof,,,

http://www.uncommondescent.com.....ent-364502

,,,, is straightforward and solid,,,

The reason why it is still disputed is because,,,,

John 1:1-5

In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning. Through him all things were made; without him nothing was made that has been made. In him was life, and that life was the light of men. The light shines in the darkness, but the darkness has not understood it.

John 3:19

This is the verdict: Light has come into the world, but men loved darkness instead of light because their deeds were evil.

EZ:

Thanks for your responses.

Admittedly, the Euler theorem is aesthetically wonderful, but that is not the core point I have observed.

The central point is that it is a case of utterly unexpected unification, that cuts across several domains in mathematical thought. That sort of coherence is a strong pointer tot he reality of these things, i.e they are not just arbitrary inventions. And so, we have to address questions of the reality of abstractions, i.e. immaterial entities apprehended by the inquiring mind. At the heart of science, which has been used as the principal point to give plausibility to materialism; which denies the reality of what is immaterial.

Now, secondly, you deny being a global or selective hyperskeptic.

That was the evident implication of the face value of your claim about knowledge as I already excerpted, but plainly you do not agree with that implication. I assume we can take it that you [now?] accept that there are some truths that are knowable and demonstrably certain, even, self-evident?

When it comes to the question of the existence of God, which you strongly doubt, in my experience, this position is generally driven by some hyperskepticism creeping in that biases how we evaluate the kind of evidence that will be accessible to us as finite, fallible, too often ill-willed mortals.

For, it can be shown that the level of evidence for the reality of God is similar to that for the existence of other minds. Also, we have millions of cases of persons whose lives have been transformed through encounter with the living God, e.g. Pascal in the context of his famous night of fire.

Finally, and as I have already linked, the prophesied and fulfilled life, death, resurrection of Jesus of Nazareth and the witness by 500+ people who could not be stopped, not even by fire sword and cross, is a powerful case in point as well.

But, that is a bit off topic for this blog.

The import of things like the Euler identity is very much within the normal ambit of this blog, though. And I think we need to look at he implications of that powerful evidence of the reality of the abstractions we meet in mathematics.

GEM of TKI

KF: you may be right . . . about being a hyper-skeptic and your other points. I shall consider it and your question (tricky one that) and get back to you when I’ve got more time. Sometimes it’s difficult to see yourself clearly and the way you appear to others. I appreciate the comments.

I agree 99.785% with what ellezim said at 114.

kf writes,

Nobody, theist or not, Platonist or not, thinks the results of math are arbitrary inventions, and I find it odd that anyone would consider this a point of contention. No matter how surprising Euler’s identity is, its truth follows, in a determined and logical fashion, from fundamental ideas that we find represented in reality: discrete things, parts of things, shapes, etc. Some of our notational systems are arbitrary conventions, but the results of math are not arbitrary. This fact, again, is as true for the non-theist as the theist: it has nothing to do with God.

It is true that Euler’s identity was unexpected, and “cuts across several domains in mathematical thought.” However, this is fairly common in math, and not unique to Euler’s identity. The fact that math produces startling results that unite what we thought were separate ideas is one of its beauties, but that doesn’t mean that those results have some different level of reality.

So, yes, the question of the nature of abstractions is relevant, but kf immediately imposes his own viewpoint on the very definition of abstraction: that they are “immaterial entities apprehended by the inquiring mind.” This Platonic view is not the only way to understand math. We have a definition of circle that is abstract: we can both think logically about further properties of circles and apply what we know to real circles. That doesn’t mean that a perfect circle exists in an immaterial world of ideas: that’s what Plato thought, and it represents one of two competing lines of thought in Western philosophy, but it is not a settled case that Plato was right.

This is in fact one of the big ideas that we disagree about (and one that I don’t think can be settled – strong agnostic, you know): do ideas (not only of math but of such things as values, emotions,morals, etc.) exist in some immaterial reality separate from the material world, or are our mental processes a local phenomena that has arisen within our universe?

Also, it is important to understand that the above is not a simple dichotomy: one might be tempted to make it a God vs. no God issue. But one can be a Platonist in respect to math and not believe in a God that has anything to do with other aspects of religious thought such as a personal investment in human beings.

EZ:

Appreciated.

It is a tough one, and certainly swims against the strong flow of this generation.

I will pray for you, and invite others to join me:

May God grant you the grace to see, to see clearly, and to have the strength to stand by what you see. AMEN.

G

Aleta:

I particularly have in mind the “invention” of i as the square root of a number that “naturally” does not have a square root, -1.

Going beyond that, we just had a pretty intense thread where some were arguing that by varying the axioms and definitions of symbols, we could equally have 2 + 2 = 4 and 2 + 2 = 147.

In short, these were exactly arguing that axiomatisation is fundamentally arbitrary; others argue that even rules of inference and logic are essentially arbitrary and pragmatic. (Cf the discussion here, as linked by someone above.)

Take in 0, originally the empty space on the abacus [the first form of full place value notation], blend in -1 [originally, what was owed in accounts], and then try to imagine what it means to raise a real but transcendent number to an imaginary and transcendent power [i*pi] and get a negative integer value: -1.

There is that strange number e, the scale point where the area under 1/x beyond x = 1 becomes unity. So, we come to natural logarithms and the weird properties of exponentials of e. Remember, we are now raising e to an IMAGINARY power.

Then add 1 to the strange result, which implies adding 1 to -1 [a strange enough action, how much is -1?], and bang — via the astonishing behaviour of power series — we have:

0 = 1 + e^ i*pi

If that eldritch result does not stop you in your tracks and give pause as you see so many key things converging in one single expression that brings together the five or six most important numbers, something is wrong.

GEM of TKI

PS: Abstraction, courtesy Collins English Dict 2003:

Someone may well be imposing a definition, but it is not me.

kf writes, “I particularly have in mind the “invention” of i as the square root of a number that “naturally” does not have a square root, -1.”

The “invention” of i to stand for the square root of -1 was no more or no less arbitrary than the invention of the negative sign to stand for the opposite of a positive number. As I have said, people have invented symbols and notational systems for thining and writing math, and those are arbitrary (although, of course, more useful systems eventually win out over less useful ones.) That doesn’t make the results of the math arbitrary. Pi is pi, irrespective of what symbol we use to represent it or what number system we use to do arithmetic with an approximation of it.

Furthermore, the words real and imaginary are very names for the numbers in question. –1 does not have a real square root, but that is only “natural” if all you know about are the real numbers. “Imaginary” numbers are no more real or imaginary than real numbers: it’s a terrible name that stuck historically and confuses students to this day. As I am sure you know, we are just talking about vectors that are perpendicular to each other, and we just as well could (and do in many situations) define two unit vectors perpendicular to each (or three) and dispense entirely with the notions of which is real and which is imaginary.

I am perfectly aware of how neat all the connections are that culminate in Euler’s identity. I also know that if you understand the relevant math (complex numbers as two dimensional vectors which can be represented with trig functions, and the patterns of the derivatives of sin x, cos x, and e^x), then it all makes sense: it’s surprising when you first see it, but it’s not mystically and mysteriously surprising once you understand why it is true.

That math results in fascinating and unexpected results, of which Euler’s identity is a prime example, is not the issue: the issue is rather whether this means that somehow God must be involved. My position is that it does not. Math works. Whether God exists is undecidable. These are two different issues.

Darn – I need to proofread. Paragraph 3 above should start: Furthermore, the words real and imaginary are very BAD names for the numbers in question.

Aleta:

Pardon a very simple exercise.

Now, of course, the Argand diagram allowed us to visualise the imaginary aspect of complex numbers as a new number line perpendicular to the real — observe the word! — number line, producing a vector pattern. [And, a 2-dimensional vector is not a number as such but an algebraic structure that links two numbers.]

Plainly, we are here dealing with abstractions that we must:

imagine, and may represent by using a drawing. (So, the hotly dismissive rhetoric about the “imaginary” part is distractive.)Yes, negative numbers are also an imaginary construct. They started with the idea of owed sums, so one had to add so many florins to clear the account. But you cannot phyically materialise “- 5” florins. (You can describe a situation in which you owe 5 florins.)

Going further, let us look at a modification of the old exercise from the previous thread:

|| + ||| –> |||||

We can concretise five matchsticks, but we cannot concretise fiveness, twoness or threeness etc.

In short, number, starting with the natural numbers, is about abstract properties tied to the cardinality of sets. (Counting is verbal matching to successive members of the set of naturals, by one to one correspondence. Addition is by abstraction form counting on, and so forth.)

Now, we take the cluster of abstractions and we put them together, after suitable manipulation, and lo and behold, we see something astonishing:

0 = 1 + e^i*pi

These increasingly strange abstractions are profoundly tied together, and in ways that are tightly integrated into the logic of how we analyse our world mathematically.

That unexpected intertwining is precisely the sort of coherence that suggests strongly — note I am not arguing a deductive proof — that the best explanation is: the lot of them are real, though not concrete, i.e. we are seeing good reason to accept the reality of such abstractions as real things.

And, as we see similar things happening with: propositions, good.evil, etc etc, where we see a consistent pattern of unity amidst the widest diversity, and associated coherence of truths, we begin to grasp that we live in a cosmos, not a chaos. A unified order that is often abstract but very real.

Too many compass needles to ignore or dismiss lightly.

(And remember, above I showed in outline why I find evolutionary materialism a non-starter as a worldview; until the past few days, I have not seriously thought on the Euler identity in literally decades. I don’t need this stuff to dismiss materialism. But, clues are clues. Including astonishing ones.)

GEM of TKI

PS; This little discussion on the reality of imaginary no’s on analogy to fractions [there considered as ordered pairs . . . ], is interesting.

I know all that math, kf. And a two-dimensional vector in the complex plane is a number – a complex number.

And, of course we live in a cosmos, not a chaos – no one believes that we live in a chaos.

But the belief in the Platonic reality of numbers (or, even more, in math being a manifestation of the mind of God), does not necessarily follow.

You write, “Too many compass needles to ignore or dismiss lightly.” I have neither ignored nor dismissed lightly the arguments for Platonism or God, but I have concluded that we can’t in fact know, and since I see that math works just as well irrespective of whether I believe in Platonism or God, it seems to me that there is no reason not to consider the issue fairly irrelevant.

As ellazim and I discussed earlier, we all make decisions about our metaphysics based on lots of factors, and I have no problem with someone taking the Platonic view as long as they don’t think that is a necessary conclusion.

And to kf’s P.S.: the way I explain the different kinds of numbers to my students is somewhat similar to kf’s link. Each kind of number that was developed (fraction, irrational, negative, complex) was developed to solve a kind of equation which gave no answers in the existing number system at the time:

x + 2 = 5 requires positive integers, the first kind of number

3x = 2 requires the invention of fractions

x^2 = 2 requires irrationals

x + 5 = 2 requires negatives

x^2 = –2 require imaginaries

However, after the invention of complex numbers, this progression stops. Any algebraic equation that we write with complex coefficients has solutions which are complex numbers.

None of these numbers are any more imaginary than any of the rest of them. Some flow more easily from common real world experience (3 people kill 2 rabbits), and some are easier to visualize (the diagonal of a unit square is quite apparent, which is why irrationals were invented before negatives), but all of them are symbols within notational systems that we have invented.

And my P.S: it’s interesting note that early number systems, such as the Egyptians, didn’t have a way of writing fractions like 2/3. They only had unit fractions (with a numerator of 1), so to them 2/3 would be written 1/2 + 1/6. The invention of writing fractions with a non-unit numerator was a useful improvement.

Aleta:

You have unfortunately begged the question on how a complex number becomes an number.

It is not a number because we tag it such.

It in fact starts life as an ordered pair, where if a in a + ib is zero, the number is purely imaginary, but still an ordered pair (a,b) with a = 0, i.e. (o, b)).

By turning the real and imaginary axis unit elements into a basis vector, we then comprise a number on the components, as a point in the defined 2-d space, i.e. we are using a 2-d vector as a number. And, of course with great success, even as the extension to 3-d vectors also works well. But, as the existence of matrices and vectors shows, a two-dimensional array is not automatically and simply a number.

Having noted that, I also note that you have not acknowledged the focal point of the little y = x^2 plotting and extracting square roots exercise. It took a creative imaginative step to define a root of -1, i, then, lo and behold it turns out to be powerfully useful, and to cohere astonishingly with other number types; as the Euler identity reflects.

It is that coherence that bespeaks its reality and power. And it points to the unity of mathematics, a coherence that points strongly to the reality of the abstract entities being discussed.

GEM of TKI

PS: With 131, we are very close to agreement on the reality of numbers of various classes, that is at the same time tied to their inherently abstract nature such that in every case, we symbolise with conventional glyphs that which does not have a concrete material existence. Even, something so apparently familiar as two-ness.

Yes, kf, at some point it became useful to define complex numbers as vectors – you can also think of them as ordered pairs, but now the complex number system is accepted as the overriding number system which includes the reals. I didn’t beg any question – I’m just outlining the points.

I also skipped over your parabola exercise because it was both simple and unnecessary. Basic number theory shows that no real number squared equals a negative.

And yes, it has taken imagination to think about defining the square root of -1, just as it took imagination to invent the square root sign, or the natural log ln, or even the negative sign to represent negative numbers. All of these things are testaments to the inventive, imaginative powers of human beings to have invented symbolic representations. I’m not sure why you appear to be lecturing me on all this.

It’s just your conclusion that this points to an immaterial reality that I disagree with.

And, in respect to your remark at 134, good. Math starts with symbolic representations of concrete reality. Two pebbles are real. The symbol 2 represent a property of the pebbles based on a single aspect of the pebble – their discreteness. It encapsulates an abstraction of part of the world – pulls it out of the unified nature of the real pebbles, so to speak.

Aleta: Only 99.785%? I won’t ask you to define your measure.

KF: I think Aleta and I have laid out our case pretty well and I think we’re all starting to repeat ourselves. And as Aleta stated: there are lots and lots of beautiful and surprising results in mathematics. e is a very useful number in modelling aspects of the world as are 0, 1 and pi. i not so obviously at first. I EXPECT there to be some cases where some of the basic building blocks come together in a clean and simple way because of the underlying structure of the system. Which is why I find the primes so vexing . . . there SHOULD be a pattern!! Which means, I WANT there to be a pattern. But, like the irrational numbers (and isn’t the most significant of those sqrt(2)? When it was ‘discovered’ there were outcries) the primes look to be intractable. If they aren’t I hope to be alive to see the reason.

I don’t know if I’m a hyper-skeptic . . . I don’t label myself. If you wish to apply that nomenclature to me that’s okay. I do tend to question most things, including my own beliefs and ‘axioms’. So maybe it IS an appropriate tag.

I certainly go through my days acting like some truths are self evident . . . but I also find myself going back and reconsidering a lot of my motivations and convictions. I suppose the only thing I find rock solid is mathematics. Only math has theorems after all! But that’s just my opinion. No matter what I think, my theories about the world don’t change the world. The world . . . reality . . . is was it is and all I can do is try to see it clearly and avoid bias and prejudgement. And, so, I don’t know if there is absolute or self evident truth. I suppose, in some ways, studying math and physics is an attempt to find absolute truth. Maybe.

I think there are things that have been so well established that it’s perverse to doubt them as Stephen Gould said about evolution. But it was only a 151 years ago that a couple of English gentlemen brought the idea out in the open so for a very long time evolution was not self-evident. I think it’s senseless to question the laws of thermodynamics, Maxwell’s equations, Newton’s laws of motion (in the right frame of reference), special and general relativity, quantum mechanics . . . maybe some day they will all be shown to be special cases of some greater unifying principle. We’ll see eh?

Okay, a footnote (or two dozen . . . ):

1 –> Complex numbers, objectively, are vectors, as are ordered pairs. That is why — circa 1600 – 1650 was it, before vectors were fully grasped? — we have to create such complex rules for working with them as though they were ordinary numbers, i.e. treat them as though they were binomial [two-part] algebraic expressions, with the added point that i^2 = -1.

2 –> So, it is understandable why they were such a hard concept to accept to begin with, especially when we can see for ourselves — that graph exercise thingie — that there is no “real” root for -1.

3 –> Then, we come back and play with them, seeing all sorts of wonders that make them useful. That makes them probably more acceptable.

4 –> Out of the blue, we can see that by applying power series to the unit circle and using pi rads,

0 = 1 + e^i*pi

5 –> Suddenly, the imaginary root of -1 [and negative numbers were themselves a bit hard to swallow at the first] takes on a very different colour, for here it is locked into a very surprising convergence of the five or six most important numbers in mathematics.

6 –> The math that got us here tells us this is true, but the expression has a worldview level significance all of its own. For, if (on the classic rule of thumb) two is coincidence and three is a plan, what are six?

7 –> In short, we are looking at the sort of convergence of apparently disparate things that points to reality. And in so pointing, it raises the further point that in the heart of the materialistic ideology is a trojan horse: the reality of numbers. Abstractions that are inherently mental are credibly real.

8 –> Mind you, as noted, we have independent grounds for rejecting evolutionary materialism; this is a wake-up and smell the coffee moment.

9–> That is why the reaction above is so trelling, like:

10 –> Similarly, note from EZ:

11 –> What is happening here is a collision between an a priori worldview level commitment and an unexpected reality — and no, the idea that the various mathematical entities and most notably i should come together like that is “expected” is simply an after the fact reconstruction. The plain truth is, given the problems with the concepts, such convergence was — and is [think about how classes of students usually respond when they first see this] — utterly unexpected.

12 –> And the problem stands out even more starkly when we see:

13 –> Evolution is of course a slippery eel of a term, ranging from small scale empirically verifiable variations in life forms on one or two base pair mutations, to the grand, deeply metaphysically tinged origins narrative sometimes called macroevolution.

14 –> But, NONE of these is ever properly self-evident: something that so soon as we understand what is being said is seen as true and as that which MUST be true on pain of reduction to absurdity. (Contrast, “error exists.”)

15 –> If the relevant type of evolution — here, presumably the grand origins narrative — is seen as so obvious and definitively established that one has to be perverse to reject it, what is happening here is ideological indoctrination and domination of a worldview.

16 –> Sadly, with a pernicious element, for he barb on such assumed perversity is Dawkins’ jibe that those who reject this account of origins are ignorant, stupid, insane or wicked.

17 –> But in fact, no-one has ever observed macroevolution, and at most a more or less arguable explanatory narrative of the unobserved deep past has been constructed and presented with evidence that makes it seem plausible. (Cf a critical short review here.)

18 –> Such a thing can at best be a provisional explanation, and must properly be seen as nowhere near as empirically well supported as thermodynamics or Newtonian dynamics, where we may routinely make direct observations. AND BOTH OF THESE, AS EXPLANATORY ACCOUNTS OF OBSERVED PHENOMENA, ARE INESCAPABLY PROVISIONAL. Quantum theory, relativity, and electromagnetism too.

19 –> Thus, we come to a key problem with our typical level of understanding of epistemology. For, we have not properly learned the limitations of the logic of inference to best explanation; the underlying logic of science.

20 –> Where a set of observations o1, o2, . . . on are to be explained, we propose possible explanations e1, e2, . . . em. They may be compared on factual adequacy, predictive power, coherence, simplicity etc. We pick the best, and if it is empirically reliable, we use it as a part of our body of empirically reliable scientific knowledge.

21 –> But Just because ej => O, the body of observations does not show ej to be true or a fact. For the direction of implication from ej to the observations O, is the opposite to the direction of he factual support: O –> ej. Facts O may well be true, but to infer form ej => O to O, so ej, is to affirm the consequent.

22 –> For instance, let ej = Tom is a cat, and O = Tom is an animal. ej ==> O, but O does not in turn imply ej at all.

23 –> That is why scientific theories are better described as empirically reliable on extensive tests, than to claim them as “true.”

24 –> When it comes to origins theories, we cannot even observe the claimed dynamical process in action, so the degree of testability is severely curtailed.

25 –> So, the perception of self-evidence we saw above is a smoking gun, highlighting a key part of what has gone wrong.

26 –> And, it is part of why it is so hard for those caught up in the system to see the worldview level issues raised by the unexpected coherence of the key numbers of mathematics shown by the Euler equation above.

________________

GEM of TKI

—ellazimm: “I don’t think I’m a hyper or global skeptic and I’m sorry (and wrong) if I gave that impression.”

After noticing your response, I developed this test for hypersketicism. OPEN TO ANYONE. [There is no pattern for yes or no answers, as hyperskepticism is sometimes indicated by a yes and sometimes with a no. It is the same with the true/false questions].

If the test is too long, just take a block of five or ten, choose randomly from different sections, and go with it.

1-4, Yes, No, or I don’t know.

[1] Can we know anything about the real world?

[2] If the answer to [1] is no, is it, under those circumstances, possible to conduct rational investigations or participate in rational discourse?

[3] Is the law of non-contradiction a self-evident truth?

[4] Is the law of causality a self-evident truth?

5 through 10, True/False.

[5] Our knowledge of the real world is reliable but imperfect.

[6] A finite whole can be less than any one of its parts.

[7] The universe is ordered?

[8] If the universe is ordered, it is syncronized with the laws of mathematics and logic?

[9] There can be more than one truth?

[10] In some cases, a cause can give more than it has to give, meaning that in some cases, there can be something in the effect that was not first in the cause.

11-20, Yes, No, or I don’t know.

[11] Does truth exist?

[12] Is there a natural moral law?

[13] Does the human conscience exist?

[14] Is design detectable?

[15] Do I consider many of these questions unanaswerable of meaningless?

[16] Does God exist?

[17] Can matter investigate itself?

[18] Evidence can speak for itself, it need not be interpreted by or mediated through the rules of right reason.

[19] Do I have free will?

[20] Can minds detect the activity of other minds?

[21] If the ordered universe is synchronized with the laws of logic, it could be a coincidence.

[22] The periodic table of elements does not necessarily indicate the presence of an intelligent agent.

[23] A universe can come into existence without a cause.

[24] Unquided evolution is a reasonable hypothesis.

[25] Cause and effect can occur without a first cause.

#139

If my ideal answer to a question begins “it depends what you mean by ….” should I respond “I don’t know?”

My answer to 15 is yes: many (most) of the questions are unanswerable for many reasons, including lack of clear definitions or meanings for the terms, or just because they are out of the scope of what human beings can know.

@140, 141: Part of the test [question #15, for example] is designed to identify the test taker’s proclivity to claim ignorance about the meaning of terms in order to avoid making and responding to arguments. Hyperskeptics specialize in the “why-whatever-do-you-mean-by-that-word” tactic. As if everyone didn’t know the meaning of the law of non-contradiction and numerous other points. Sorry, I am not buying the proposition that you don’t understand the meaning of these questions. In any case, neither of you need to take the test since you are both radical hyperskeptics.

#142

As if everyone didn’t know the meaning of the law of non-contradiction and numerous other pointsDo you want to amend this assertion slightly? If not, go out into the street and ask the first 20 passers-by to explain the meaning of the law of non-contradiction.

—mark: “Do you want to amend this assertion slightly? If not, go out into the street and ask the first 20 passers-by to explain the meaning of the law of non-contradiction.”

Well, the term “everyone” was being applied to everyone on this thread, as the context makes clear. On the other hand, if you ask any man on the street if Jupiter can exist and not exist at the same time, and he will likely provide the correct answer.

When I asked you that question, you insisted that you could never hold to such a “nonsensical” proposition. Yet, when I asked you why it was nonsensical, you grew silent. Are you now ready to answer the question?

If you ask the average man on the street if Jupiter can exist and not exist at the same time, he will likely provide the correct answer.

MF:

In this generation, where first principles of right reason are often derided and almost as often in ignorance of what is being rejected, that ignorance is itself telling.

But, I would think that most who have not been spoiled by our education systems will understand what is being claimed when one says that

something, say A, cannot both be and not be in the same sense at the same time.Ours is a saddening day.

GEM of TKI

16) “Does God exist” is outside the scope of human knowledge

13) “Does the human conscience exist?” – not clear what answering yes or no would mean to you. If you mean as some kind of separate non-material entity in a person, I would say that I personally don’t think so, but I also think the question is unanswerable in that there is no way for human beings to come to a definite answer. If you mean do I think that being concerned about doing right and wrong is a natural part of the human personality, then my answer is yes.

This is just one example of ways in which your questions are too black-and-white, and without discussion and clarification can’t be answered.

I don’t call this hyper-skepticism – I call this intellectual sophistication: being able to see the complexities of a situation and not thinking of everything as black-and-white issues.

Here are some that are realtively easy for me to answer without excessive clarification

[1] Can we know anything about the real world? Yes

[5] Our knowledge of the real world is reliable but imperfect. True

[6] A finite whole can be less than any one of its parts. No, assuming we are using the mathematical sense of parts being discrete, disjoint elements.

[7] The universe is ordered? Yes, assuming that you mean that it runs according to various laws, exhibits consistency in that similar situations generally produce similar results, is susceptible to causal explanations tying one moment to the next … Hmmm, looks like this one would need a bit of explanation as to what “ordered” means, as obviously there is great deal of disorder in the world. Scratch this one as an easy one to answer.

[9] There can be more than one truth? Of course. 2 + 2 = 4 is true. The sky is blue is true (unless you want to get pedantic.) I am typing on a computer is true. You would have to be clearer about what this question means if my obvious answer is not relevant.

[11] Does truth exist? Sure. See 1) and 9)

[12] Is there a natural moral law? outside the scope of human knoweldge

[19] Do I have free will? Here’s a question: if one assumes that every effect must have a cause except for the one first cause, does that mean all our actions must have a cause, and therefore we don’t have free will? Or, if you do think we have free will, does that mean that uncaused causes are happening every day, in every action we make, so the assumption that all effects but the first effect have a cause is wrong?

[20] Can minds detect the activity of other minds? Indirectly, by watching the actions of creations whom I assume have minds, but not directly: we can’t interact mind-to-mind. (This doesn’t affect my answer, but the word mind needs to be clarified – are we talking just consciousness here, or are we talking about our larger cognitive/emotional self?)

—Aleta: “16) “Does God exist” is outside the scope of human knowledge.”

That would be a no. One point in favor of hyperskepticism

—““Does the human conscience exist?” – not clear what answering yes or no would mean to you. If you mean as some kind of separate non-material entity in a person, I would say that I personally don’t think so, but I also think the question is unanswerable in that there is no way for human beings to come to a definite answer.”

That would be a qualified no, which would be another point for hyperskepticism.

—[1] Can we know anything about the real world? Yes

One point away from hyperskepticism.

[5] Our knowledge of the real world is reliable but imperfect. True

One point away from hyperskepticism

—[6] A finite whole can be less than any one of its parts. No, assuming we are using the mathematical sense of parts being discrete, disjoint elements.

OK. One point away from hyperskepticism.

—[7] The universe is ordered? Yes, assuming that you mean that it runs according to various laws, exhibits consistency in that similar situations generally produce similar results, is susceptible to causal explanations tying one moment to the next … Hmmm, looks like this one would need a bit of explanation as to what “ordered” means, as obviously there is great deal of disorder in the world. Scratch this one as an easy one to answer.

You avoided the question about whether it is syncronized with the laws of logic or whether the correspondence is a coincidence, or whether there are laws of logic.

That would be two points in favor of hyperskepticism.

—There can be more than one truth? Of course. 2 + 2 = 4 is true. The sky is blue is true (unless you want to get pedantic.) I am typing on a computer is true. You would have to be clearer about what this question means if my obvious answer is not relevant.”

OK. Fair enough. The issue is whether there is only one truth with many aspects or whether there can be many truths, [a truth for science, another truth for philosophy, another truth for religion etc].

—” Does truth exist? Sure. See 1) and 9)

One point away from hyperskepticism

—” Is there a natural moral law? outside the scope of human knoweldge

One point in favor of hyperskepticism.

—“Do I have free will? Here’s a question: if one assumes that every effect must have a cause except for the one first cause, does that mean all our actions must have a cause, and therefore we don’t have free will? Or, if you do think we have free will, does that mean that uncaused causes are happening every day, in every action we make, so the assumption that all effects but the first effect have a cause is wrong?”

Free will=ability to exert some control over one’s destiny, meaning that some semblance of a self directed life style is possible, meaning that psychodynamic, behavioral, and biological influences are not calling all the shots.

— Can minds detect the activity of other minds? Indirectly, by watching the actions of creations whom I assume have minds, but not directly: we can’t interact mind-to-mind. (This doesn’t affect my answer, but the word mind needs to be clarified – are we talking just consciousness here, or are we talking about our larger cognitive/emotional self?)

Mind=immaterial faculty of knowing.

If simply being a strong agnostic – we really can’t know the true nature of metahysical reality – makes me, in your words, a “hyperskeptic”, then guilty as charged, and not a bit chagrined . I think it’s the reasonable position.

Skipping over my non-hyperskeptical answers,

When I said that universe was ordered, you replied, “You avoided the question about whether it is syncronized with the laws of logic or whether the correspondence is a coincidence, or whether there are laws of logic.”

I didn’t avoid the question. I said I was answering the easy ones, and those would have taken more discussion.

On truth, you write, “OK. Fair enough. The issue is whether there is only one truth with many aspects or whether there can be many truths, [a truth for science, another truth for philosophy, another truth for religion etc].”

I think there are different kinds of truth, or perhaps truth along a spectrum based on the experiences that establish it for us, and I think truth is something relative to the capabilities of human beings.

Same issue as God – I think my position is the reasonable one – I am skeptical that human beings can know all things, but there is nothing hyper about that.

Now on free will, you write “Free will=ability to exert some control over one’s destiny, meaning that some semblance of a self directed life style is possible,” , but I would be interested in your answer to my question.

On minds, if you define them as “Mind=immaterial faculty of knowing” then I am agnostic (aka hyperskeptical) about that also. I assume the same distinction applies to conscience: I don’t think we have an immaterial conscience that knows some absolute moral law.

God, natural moral law (and absolute Truth with a capital T), immaterial mind and conscience, are all things that I don’t think we can know about. There are things that point to them as possibilities, and things that point to them as not, but we (humankind in general) don’t have the tools to actually investigate and reach a consensual decision on these matters.

If that be hyperskepticism in your eyes, then so be it. I would rather live with uncertainty than believe things that are not true, and even though I don’t have a word for it I would rather have my position than a strong but unfounded opinion that my ideas were certifiably right and everyone who disagreed with me was wrong.

Stephen, I really would like to hear your thoughts on the free will issue.

Let me outline my understanding of what might be your position.

God is the first cause. Every effect has a cause, but we can’t have an infinite regress, so there must be a first cause. God is the being who can start a chain of cause-and-effects in motion without being caused himself.

However, what goes on “inside God”, so to speak, when he acts? For instance, at some point God chose to create our universe, but it wouldn’t make sense to ask, “well, what caused God to do that?” God is never an effect – his actions are always uncaused causes. In this sense, everything God does he does through unfettered and unadulterated free will – there are no contingent causes impinging on him in the least – no outside influences on his choices.

Now what about free will in human beings.

On the one hand, if only God can create uncaused effects, then our actions, which are “downstream”, so to speak, from God are thus caused effects, and therefore we don’t have free will.

On the other hand, perhaps our will is like a little God inside us, which can initiate uncaused effects – our free will, while still entangled with our material, biological existence, can still exercise some control over what we do.

If this case, how effective is this – happening all the time with varying degrees of effectiveness, just sometimes, or what?

And if this is the case, then we constantly violate the law that every effect has a cause, or more accurately, we continually act as a first cause.

Can you elaborate or respond on this issue. Have I said things that agree with your view, and if not, what can you correct?

Aleta:

we recently had a very long (and very interesting) collective discussion about free will, where all positions were discussed in great detail.

The thread was this one:

http://www.uncommondescent.com.....n-problem/

and it is 712 comments long.

My personal discussion starts at 4, 11, 59, 64, 91, and goes on for the whole thread, which is very rich in contributions of many people with very different positions. It is really one of the best threads on UD, IMO.

In case you don’t feel like reading all the 712 posts :), I will try to summarize here for you at least part of my personal position:

1)Free will means that humans can react to circumstances in different ways, and that the way they react is at least in part not determined by the sum of the circumstamnces acting on them. Free will means that, at any moment, the behaviour of humans is not completely determined by circumstances (including one’s previous internal states), but has a “range” of variability which is determined by a free cause inherent to the conscious subject, and to nothing else.

2) That “range of freedom” can be very small, or great enough: that we really don’t know, and it probably depends on many variables. But the important concept is that it is there, and it can and does change our personal destiny.

3) Free will is the intuitive perception of agency. I believe that, without free will, we would have no concept of conscious agency. Free will is the necessary consequence of the output connection of consciousness to reality, just as perception and cognition are the necessary consequence of its input connection. Without free will there would be no non algorithmic knowledge in human mind, and no CSI could ever be produced. But free will is probably strictly connected to representations of meanings and purposes. After all, our basic choices are in the realm of cognition (true-false) and of feeling (good-bad).

4)The actual choice, in the moment it is done, utilizes all those conscious representations, at various levels of the mind, as a “substrate”. Those representations include rational elaborations of reality, past experiences, past feelings, and so on. But it is the responsibility of the agent how it reacts to that scenario, in each single case, in the range of the reactions which are possible for it in that context. That choice is not neutral, nor probabilistic: it has moral and spiritual value, because it is a choice between alternatives which have different value for the agent. So, the agent can each time choose to pursue what is best in his personal destiny, let’s say “to respond to love and God and good”, or it may choose differently.

5)Free will is all about choices. Those choices ar not purely cognitive (the problem is not: what seems more rational we do, as everybody should easily recognize). And they are nor purely choices of felling (the problem is not: what I desire I do, because otherwise everybody would be morally perfect).

The problem is: out of the few things which I can really do, because I feel I can do them, which is the one which correspond best to my highest intuition of what is good? Which is the one which is most appropriate according to God’s will, and not simply according to what I desire?

We can even think of free will in a different way: as a faculty that we can exercise or not. In that sense, if we do not exercise our free will, we will be completely determined by our previous experiences, by our desires, by our human nature. But if we choose to actively use that inner resource, we can change that. We can put our life in tune with higher values and intuitions, which are trans-personal, which are better and more pure and more powerful than what we can do by ourselves.

In other words, we can actively become receptive to good, and to God’s will. And that changes everything.

6)We cannot attribute to God the same concept of free will which is appropriate for us. In that sense, God can be said not to have free will. He simply does not need it! He is free, and He harbors no contradictions and no conflicts and no imperfections in Himself. So, He just does what He wants, and what He wants is good.

Well, I believe that our free will is a reflection of God’s freedom, in an imperfect and limited being, with conflicting desires and views, including the conflict between accepting the will of God (the good) and rebelling to it (the bad). If God had not given us that gift, that reflection if His complete freedom, we would be completely determined.

But He has. And therefore, we are strongly influenced, but partially free. That is free will: partial freedom, in a worlds of imperfection and contingency. That’s why the natural expression of that partial freedom is the power to choose, rather than the power to freely will, which is of God.

But that power to choose is no small thing. If repeatedly and patiently applied to choose good, it changes us, it changes our destiny, and it opens us to the grace of God.

Well, this is just to give you an idea. But there is much more on the thread, and there are a lot of good and deep contributions from materialists, atheists, compatibilists of various kinds, religious people for or against free will, and so on.

Stephenb

On clarifying the meaning of some of your questions

Surely some of the responses following your list make it clear that abstract concepts such as “conscience”, “free will” and “natural moral order” need clarification. This cannot just be dismissed as a tactic. I believe we have free will – but you (or it may have been a colleague) have said in the past that my concept is not the same as yours and that it is not “real” free will. How else can one resolve this but by examining the meaning of what we say? It is not just a matter of knowing what the words mean (although that is bad enough). It is sometimes the question as a whole that needs clarifying. E.g

11) Does truth exist?

I know the normal English meaing of all three words. But what is the question driving at? Are you asking if some statements are true? Or are you asking if there is some one thing called “truth”? Or what? Is it unreasonable to seek this type of clarification?

I will deal with the law of non-contradiction in the next comment.

Stephenb

On the law of non-contradictionYou ask how do I know that

Jupiter exists and does not existis nonsense.

In much the same way as I know that “green ideas sleep furiously” is nonsense. The individual words make sense. It is grammatically correct. But the statement has no function. I cannot work out what the speaker is intending to convey or do with the words. He has not told me anything about Jupiter. Imagine that someone came up to you and said “Jupiter exists and does not exist” with all the appearance of sincerity. Would you think he was misinformed, lying or speaking gobbledygook?

For fun here are my answers to the 25 questions. As you might expect, the vast majority I find I need clarification. In some cases I have tried to undertake that clarification. I cannot understand why the desire for clarification should count as a kind of scepticism. These are abstract phrases used in unusual contexts and combinations. Without examples and help it is almost impossible to be sure of what you mean.

[1] Can we know anything about the real world?

Yes of course.

[2] If the answer to [1] is no, is it, under those circumstances, possible to conduct rational investigations or participate in rational discourse?

n/a

[3] Is the law of non-contradiction a self-evident truth?

Depends on what you mean by “true” – see earlier comment.

[4] Is the law of causality a self-evident truth?

False – “cause” can mean all sorts of things but I cannot find any meaning which entails that every thing that comes into existence must have a cause.

[5] Our knowledge of the real world is reliable but imperfect.

True

[6] A finite whole can be less than any one of its parts.

Depends – “less” in what respect?

[7] The universe is ordered?

Could mean almost anything.

[8] If the universe is ordered, it is syncronized with the laws of mathematics and logic?

Could mean almost anything

[9] There can be more than one truth?

Given your clarification in #148 – true (incidentally it appears Morton Adler would agree with me!)

[10] In some cases, a cause can give more than it has to give, meaning that in some cases, there can be something in the effect that was not first in the cause.

True (I think – but could do with some clarification)

[11] Does truth exist?

Needs clarification.

[12] Is there a natural moral law?

Needs clarification.

[13] Does the human conscience exist?

Needs clarification.

[14] Is design detectable?

In sense that ID usually means it – no. Of course we detect design all the time but this relies on explicit or implicit assumptions about possible designers.

[15] Do I consider many of these questions unanaswerable of meaningless?

Yes

[16] Does God exist?

Needs clarification.

[17] Can matter investigate itself?

Needs clarification.

[18] Evidence can speak for itself, it need not be interpreted by or mediated through the rules of right reason.

Needs clarification.

[19] Do I have free will?

Needs clarification.

[20] Can minds detect the activity of other minds?

Of course. I am doing it right now.

[21] If the ordered universe is synchronized with the laws of logic, it could be a coincidence.

n/a

[22] The periodic table of elements does not necessarily indicate the presence of an intelligent agent.

True

[23] A universe can come into existence without a cause.

Yes – it is logically possible.

[24] Unquided evolution is a reasonable hypothesis.

Yes

[25] Cause and effect can occur without a first cause.

Yes

Stephen:

Your agenda of questions is certainly an interesting diagnostic on worldviews. One may debate clarity on some points [maybe, too much background context assumed, e.g. on many truths], and one may debate certain points, but overall an excellent work. Looks like an emerging diagnostic exercise to me, DSM whatever?

On cause, I note that we have sufficient factors, necessary factors, contributory factors, synergistic factors that mutually multiply on impact, sometimes a necessary and sufficient cluster of factors, and what Wiki summarises as J. L. Mackie’s argument thsat common talk of cause is a reference to ” INUS conditions (insufficient and non-redundant parts of unnecessary but sufficient causes). For example, a short circuit as a cause for a house burning down.”

In the clustered sense of cause in a given setting, I think it is reasonable to say that on our experience of the world and understanding derived therefrom, effects do not rise above their causes.

On first and final causes, I have a few notes:

1: It is a condition of events that begin to occur or may cease from being in our observed world, that there is a cosmos in which they happen.

2: So, the issue of first cause is a question of origin of a cosmos that evidently itself had a beginning and will per thermodynamics run down in a finite time, i.e. it credibly had a beginning at a finite point in the past.

3: Final cause is often used in the sense of goal or purpose. Our finely tuned cosmos, with a complex and delicately balanced adaptation to support C-chemistry cell based life, shows strong signs of purpose.

4: In that context, to baldly suggest that cause-effect chains can occur without a first cause is an expression of a worldview premise, not an observationally anchored claim. That is, it is tantamount to a declaration of materialism.

5: Going beyond that, above I cited Plato, on the issue of the nature of the first cause: the self-moved mover, the soul, whereby chains of consequential effects that are secondary, tertiary etc causes.

6: An infinite regress of effects that have finite duration is not credibly traversible by our observed, evidently finitely old cosmos. So, those who posit endless chains of effects have a serious factual adequacy problem here.

7: Of course Plato argued that the cosmos as a whole is an effect, which is still a very credible point, whatever one may wish to say about the details of Plato’s argument.

_______________

GEM of TKI

This article may be very interesting for some (gpuccio and kairosfocus):

Mere Biochemistry: Cell Division Involves Thousands of Complex, Interacting Parts

http://www.creationsafaris.com.....#20100925a

—markf: [how do you know that the statement Jupiter both exists and does not exist is nonsense]

—“In much the same way as I know that “green ideas sleep furiously” is nonsense. The individual words make sense. It is grammatically correct. But the statement has no function.”

But it does have a function. Among other things, it can serve as the starting point for a reductio ad absurdum. Also, it helps me demonstrate the absurdity of denying the law of non-contradiction.

Further, a statement cannot be non-nonsensical solely on the grounds that it doesn’t resonate with you. It can only be nonsensical if it doesn’t resonate with anyone.

–“I cannot work out what the speaker is intending to convey or do with the words.”

But the meaning is quite clear: Jupiter can exist and not exist. I know what the statement means, most readers know what it means, and I dare say you know what it means.

—“He has not told me anything about Jupiter.”

On the contrary, he has told you two things about Jupiter. Of course, those two things are contradictory, but that should be no problem for anyone who denies the law of non-contradiction as a self-evident truth.

—“Imagine that someone came up to you and said “Jupiter exists and does not exist” with all the appearance of sincerity. Would you think he was misinformed, lying or speaking gobbledygook?”

I would know that he is irrational and is likely a product of postmodernist brainwashing. I would explain to him that Jupiter cannot both exist and not exist because the law of non-contradiction that rules out the possibility that ANYTHING can exist and not exist.

In true postmodernist fashion, he would likely counter that modern science, especially quantum mechanics, has rendered the law of non-contradiction obsolete. I would then have to explain to him that science does not have the power to invalidate the laws of logic inasmuch as the latter has logical precedence over the former. He would, of course, ask me for “evidence,” and I would have to inform him that evidence doesn’t inform reason’s rules, reason’s rules inform evidence. Steeped in irrational subjectivism, he would deny the point, assert that reason has no rules, and insist that evidence can be interpreted to suit the prejudices of the investigator. In other words, he would begin making your arguments.

Hi Stephen, I know people only respond to some points, for various reasons, and that this thread is almost done (or done.) However, I’m still interested in the question of the nature of acts of human free will. Are they uncaused, because they are free, or caused? And if uncaused, does that make them examples of “first” causes, so to speak – causes of effects that have no cause themself.

I am interested in how free will fits into the theory of causality, so I would appreciate hearing your thoughts.

Hi Aleta:

I have been called away, so to speak, but I will offer an abbreviated response to your very relevant question:

I submit that we are the causes of our moral choices, but God is the cause of our capacity to make those moral choices. Insofar as God created our will, God is its cause; insofar as we have been created as causal agents, we are the causes of our actions.

Put another way, God created our will to be free (within obvious boundaries, of course) which means that he created us as moral agents capable of making moral choices.

Put yet another way, our capacity to make free choices is, in a very real sense, the effect of another cause, namely God’s creative power. All effects are accounted for, meaning there are no effects hanging out there without causes, yet our will is free.

Even our final end is the effect of a series of prior causes for which God [and we] are responsible.

Sow a thought; reap an act,

Sow an act; reap a habit,

Sow a habit; reap a character,

Sow a character; reap a destiny.

Thanks for taking the time to answer, Stephen.

I’d like to respond to three aspects of what you wrote.

First, you write, “I submit that we are the causes of our moral choices, but God is the cause of our capacity to make those moral choices.”

I assume that you are not implying that the only place we have free will is in respect to moral choices – is that correct? I am choosing to write this post, for instance, rather than go wash the dishes: this is a conscious act of free will, but not particularly a moral choice.

Then you write, “Insofar as God created our will, God is its cause; insofar as we have been created as causal agents, we are the causes of our actions. … Put yet another way, our capacity to make free choices is, in a very real sense, the effect of another cause, namely God’s creative power.”

Yes, God is the ultimate cause of our free will, as he is the ultimate cause of everything. However, is he the

proximatecause of the particular choices we make? This is the issue I am interested in: when I make a conscious decision to perform an action – an act of free will – is there any prior cause of which my decision is an effect, or is my choice an uncaused cause? Yes, God gave us this free will, but once given, do we truly have the power to initiate an action free from any prior causes?It seems to me you are perhaps not addressing this particular aspect of the situation, as you wrote, “All effects are accounted for, meaning there are no effects hanging out there without causes, yet our will is free.” I don’t think invoking God as the ultimate cause of our free will is the same as establishing that there is a direct causal chain from God to our actions, unless you mean to imply that in fact God’s will is the cause of our freely willed actions, and I don’t think that is your intent (perhaps I am wrong about that.)

You use the interesting phrase “effects hanging out there without causes”, but that phrase perhaps bypasses the issues. By definition, I think, an effect has a cause. The question is whether our freely chosen acts

areeffects (caused by prior causes), or are in fact pure uncaused causes.So the question is not whether there are “effects hanging out there without causes.” In a causal chain, every event (except the first one) is both a cause and an effect: an effect of previous causes and the cause of new effects. We assume that God is the ultimate first, uncaused cause. The question is whether our acts of free will also serve as first causes – events which cause effects but are not the effect of prior causes. That is, instead of asking if there are “effects hanging out there without causes”, I am asking if our freely chosen acts shouldn’t be described as “causes hanging out there without being an effect” – little mini first causes?

What do you think? Does the distinction, and question, that I am asking make sense?

And third, a lesser note that I don’t want to distract from the central point above, you write, “God created our will to be free (within obvious boundaries, of course) …” It seems to me that the way our free will interacts with, and is limited by, more material aspects of our biological nature, is far from obvious.

But let’s concentrate on the philosophy about the nature of our free will first: are our acts of free will uncaused proximate causes – causes which are not the effect of any immediately prior cause?

Hi Aleta. I find you a very good deeper thinker and I like very much this quality in people. Then I try to answer your request with some deep thinking. You post:

“are our acts of free will uncaused proximate causes – causes which are not the effect of any immediately prior cause?”

I answer to this YES. Absolutely YES. You can be trapped, tied, without any possibility off movement, and even so, you can see that you are able of somthing that nobody can stop until you has dead, to think (bad or good, but to think, it’s not important now).

And then you can say, if I have not free of movement, what’s matter I can think? That matters because you can see you are not only a material thing, you can continue creating information with you mind and even, in a determined instant, use it, now materialized, to go out the trap, or even if you see it as impossible, use this moments to, for example, pray for your most wanted people.

Then the cuestion could be: and when I have a normal life, free of any phisical tie (if you think it well you can see that you are from birth to dead tied to one only thing: the Universe, although withou this Universe you could not exist) for what can I use this rare ability of thinking?

Imagine you have 1000 pieces of a puzzle in front of you. All are disordered, and you may want to construct that puzzle. You are Intelligene enough to make it, but you can think: “for me it’s a waste of my time” or well “I like very much to solve puzzles”. You can do what you want, as if you want to burn this puzzle. But you only realize one. How can you know what is best for you?, if is not important a decision to another, then take your decision what you take, the final result seems dont have relevance. Then no problem: “I do what I want to do, and everybody happy”

But thinks a moment, if you decide solve the puzzle, the result is that the “mini-universe” which is surrounding you is more ordered, that is, had more information, is better. Any other decision is not so good with respect to your decision. Then when you take a good decision, is when your enviroment is better, but not only for you, but to others living with you.

Then you can see clearly that in front of a same scenario, you are free to act with free will, but if you understand that you are a information creator, and that is what is your mind, then you can put this information in place or decide to increment the disorder. And this is all God wants for you, that you do things freely, but do them as He intended better for you and for all.

You think that what you see with your mind is yourself, but you, and I and all what are seeing is not to ourselves, only, we are all seeing the Light that we are free to close our mind to It and see all with physical eyes, but you know as well as I the two eyes are not the same.

My better for you.

Obriton

RE 160 “But let’s concentrate on the philosophy about the nature of our free will first: are our acts of free will uncaused proximate causes – causes which are not the effect of any immediately prior cause?”

Aleta excellent question. I have my own thoughts on this but do not want to be a distraction. Suffice to say that to me this is a fascinating discussion.

Vivid

–Aleta: “But let’s concentrate on the philosophy about the nature of our free will first: are our acts of free will uncaused proximate causes – causes which are not the effect of any immediately prior cause?”

Time for only an abbreviated response.

I submit that any volitional act is the effect of a multiplicity of causes, including psychodynamic forces, behavioral influences, biological urges, the ravages of original sin, the fact that God continues to keep our will in existence [it wasn’t just created, it is also being sustained], and of course, the free will decision that must be made in the context of all these other limiting influences. While its range is quite limited, it does neverthess, exist.

I can influence my unconscious, or at least, my subconsious mind; I can work around many, not all, of my environmental problems; I can, with God’s help, re-direct my biological urges and command them to conform to God’s laws; I can, with the help of grace and self discipline, become closer to God and improve the psychological traits damaged by original sin. I am not required to retain the vices of lust, greed, envy, pride, and anger of my youth. I need not submit to those who would keep me in poverty, subvert my education, or take away my political freedoms, all of which, by the way, are meaningful only in the context of free will.

If, on the other hand, I do not have this power, then I have nothing at all to say about my future or my destiny, or even the kind of person I am or can become. Under the circumstances, I am no better than an animal, and I can never rise above animal status, always obeying the demands of my lower nature and never rising above it. That would also mean that I must remain a political slave to any tyrant who, himself is a slave to some other unnamed force. More important still, it means that my eternal fate was sealed before I was born and that God allowed me no options other than to play out his preliminary decision either to save me or damn me at his whim. I cannot imagine a more monstrous, or untrue, doctrine.

Thank you, Stephen. I look forward to a more extensive response.

Still my core question remains unanswered – to the extent that our free will can act in the larger context of the other causes that you list, does the action of our free will constitute an uncaused cause.

—Aleta: “Still my core question remains unanswered – to the extent that our free will can act in the larger context of the other causes that you list, does the action of our free will constitute an uncaused cause>”

Your core question has been answered several times and in several ways. You are the cause of your actions, though your freedom is limited by a number of elements that I have already alluded to.

Perhaps, it will help if I quote another authority on the matter.

From Normal Geisler: “Finite things need a cause. The person who performs the act is caused by God. The ‘power’ of freedom is caused by God, but the ‘exercise’ of freedom is caused by the person. The self is the first cause of personal actions. The principle of causality is not violated because every finite thing and every action has a cause.” [By this, he means that God, the uncaused cause, is not finite].

Aleta:

I absolutely agree with Stephen, and you can see in my 151 a detailed explanation of why I do.

I would say that free actions are, in a sense, uncaused causes, in the sense that they have no phenomenic cause. The proximate cause of free actions is the power of the transcendental self to choose among available options.

I would say, anyway, that any free action has some moral meaning. Especially writing posts here . But please, see my post 151 for the details.

Thanks, Stephen. The Geisler quote addresses my question, although it seems to be a bit inconsistent in part.

Geisler writes, “Finite things need a cause. The person who performs the act is caused by God. The ‘power’ of freedom is caused by God, but the ‘exercise’ of freedom is caused by the person. The self is the first cause of personal actions.”

Ok, I get that. Among other things it seems consistent with my thoughts above in 160: God is the ultimate cause of our free will, but once that power is ours, our decisions have no proximate cause other than our own exercise of that power – as Geisler says, “The self is the first cause of personal actions.”

But then Geisler says, “The principle of causality is not violated because every finite thing and every action has a cause.” This seems inconsistent with what came before, because he has said that our freely chosen actions are first causes, which by definition don’t have a prior cause.

It seems to me that, given the first statements, that it would be more appropriate to restate the law of causality to state that every effect is the product of a cause except for acts of free will by a human being. Otherwise human acts of free do violate the law of causality, because they are acts which have no prior cause: Geisler says, as I have suggested, that our free will acts are first causes.

gpuccio also writes: “I would say that free actions are, in a sense, uncaused causes, in the sense that they have no phenomenic cause. The proximate cause of free actions is the power of the transcendental self to choose among available options.” And since the sense we are discussing is precisely that of having no phenomic cause, I think his statement agrees with Geisler – “our free actions are … uncaused causes.”

Also, gpuccio, I did read your post at 151 with interest, and appreciate the time you put into it. I didn’t respond because I wanted to concentrate on this one philosophical point, which is now mostly cleared up to my satisfaction. The complexities of how free will interacts with the complications of all the material causal chains that impinge upon on us, including all the internal biological ones, is a fascinating topic, but I was focused on the other point.

So the picture I have is that if you conceptualize the nature world as a vast complex web of chains of cause-and-effect, stretching back to the beginning of the universe (including all the material biology which is present in our body), our free will is continually making little insertions of uncaused causes into those material chains, setting them one way or another in a different way than they would have gone if we had chosen differently: the material world is continually being perturbed, so to speak, by the uncaused causes initiated by the freely willed choices of huamn beings.

I wish I could draw a picture. Imagine a chain of events A > B > C > … in the material world, with the chain stretching backward idefinitely to the ultimate first cause, God. However, now imagine a new cause f (little f, not the big F in the chain) that represent a free will act, so that the situation looks like this: (the little dots mean nothing – there are just because I don’t think multiple spaces will parse right)

…………..f

…………..\/

A > B > C > > D > E > F > G

f has no antecedents – it’s an uncaused cause, but it enters the causal chain at C, and therefore D, E, F and G are different than they would have been if f hadn’t happened.

That’s how free will operates, if I understand this discussion correctly.

It is amazing how such a seemingly simple subject like free will, which it taken for granted by most people, can become such deep topic of conversation. I even saw a physics professor, whose name I can’t place right now, once weigh in on the topic of free will. He was talking about how quantum mechanics had completely dismantled the Newtonian notion of complete determinacy that had become prevalent in western thought. A complete determinacy that had brought many people to seriously question whether there was any free will for man whatsoever. In fact this relic is a foundational false notion that still underpins Darwinian ‘psychology’.,, the physics professor main point of his lecture, on free will and quantum mechanics, was to focus on the area of quantum wave collapse for the observer. He said something to the effect the ‘proof’ for free will comes from the indeterminacy of wave collapse.,,

Myself I struggled deeply with this ‘problem’ of free will from a slightly different perspective in my Theism, since from my perspective God knows all things that will ever happen in this universe since He is completely transcendent of time as well as being infinite in knowledge. Thus I was stuck with the nagging question of, “How can God be sovereign and yet I have free will?”,,, It was just one of those simple questions that I just could not make sense of for the longest time,,, Finally about the only way I could make peace with the seeming conflict, was to accept what one preacher had said about the topic. He said something like this,, Though God is sovereign and knows everything that will ever happen, in His sovereignty He allows us, by His ‘permissive will’, the capacity to freely choose good and evil, In His ‘permissive will’ He allows us the capacity to love Him or not.

very interesting discussion….I didn’t see anything on one very interesting number though…

One hundred thirty-seven is the value of a number called the fine-structure constant. This constant, 137, is the way physicists describe the probability that an electron will emit or absorb a photon. Because this is the basic physical mechanism of electricity and magnetism, the fine-structure constant has its own symbol, the Greek letter a, “alpha.”

Now, alpha is nothing more, nothing less than the square of the charge of the electron divided by the speed of light times Planck’s constant. Thus this one little number contains in itself the guts of electromagnetism (the electron charge), relativity (the speed of light), and quantum mechanics (Planck’s constant). All in one number! Not only that, this number isn’t like the gravitational constant or the universal gas constant, full of meters and kilograms and degrees Celsius. Alpha is a pure, dimensionless number — little wonder that people have been fascinated.

http://www.137.com/137/

Aleta: I think the term first cause, or uncaused cause can be misleading in some contexts. For example, when we refer to God as the uncaused cause, or first cause, we are paying tribute to the fact that nothing at all preceded him or caused his existence. That is the way I am using the term.

There is, however, another way to use that term, that is, we can refer to “a” first cause as opposed to “the” first cause, when discussing those things that humans can do after having been given the power to be a causal agent.

When Geisler speaks of the exercise of the will as the first cause of our actions, I would argue that he is not speaking of “the” first cause but rather “a” first cause. He is saying that humans are doing something that God would not necessarily have done. I would be inclined to call it a “new” cause. As GPuccio has suggested, it makes a difference how we use those terms.

For me, the word cause simply means something or someone that brings something else about. What can we say, for example, of Adam’s first sin? Obviously, God did not bring sin into the world or, put another way, he did not bring it about. In keeping with that point, Adam brought sin into the world and was, in that sense, the first cause of sin. All the same, God is the cause of Adam’s power to exercise his will and, in that sense, Adam’s act is not a first cause.

Aleta,

You raised a good question in regard to a free will choice as a first cause. I think Stephen answered it fairly well by differentiating “the” first cause (God) with “a” first cause (human free will choices). Just one observation: God is the ultimate cause of everything. In our free will choices we often cause something entirely by our choice and not necessarily due to anything in our makeup, which compels us to a certain action. But ultimately we would not have the choice to cause anything if we were not in the first place caused by God.

Christians recognize this distinction as stemming from the sovereignty of God. God allows choice while at the same time, reserves the right to intervene when He sees fit. We may not even know that in certain instances He has intervened, and we might still believe that our current circumstance is a result of our choice. On the other hand, we may also have the view that we don’t have choices and our current circumstance is the result of someone else’s choice, such as government, a despised enemy, a devil, or even God Himself. That we are able to even think of causes other than our own seems to solidify the fact that in at least certain instances we make real choices and can cause events to happen without reference to a prior cause. Our influences in making these choices, however, I think is an entirely different matter.

Free will and destiny with regard to God’s sovereignty are tricky subjects, and are in my view somewhat paradoxical but not contradictory. It mirrors reality quite a bit.

Yes, I understand the difference between God as “the” first cause and our choices as “a” first cause – I think I referred to human choices as “little” first causes in earlier posts, and my diagram and its explanation above showed the free will choice little f intervening long after the first cause, God, had started the chain.

So I now understand clearly, I think, Stephen’s and other’s theological understanding of the relationship between God, free will, and the law of causality, as mentioned in Stephen’s list of questions way above.

Thanks to those who participated in the discussion.

OK, so our free will can act as a local first cause, and add an additional cause to the stream of natural cause-and-effects that are going on. Presumably this intervention takes place inside us – in our biology – because for an act of free will to make any difference, we must act on it.

So how does this happen? How does the immaterial will move the material world, so to speak? What is the nature of the immaterial/material interface.

Or to put it another way, if we could examine every molecule of every cell in our body, what would we see when the will acted? Would we actually see anything that was any different from, and/or was distinguishable from, what we would see when our will was not acting?

Any thoughts?

The Physics of Illusion – video (Euler’s Identity as a spiral at 23:00 minute mark)

https://www.youtube.com/watch?v=ht3sAP-GQrk