Fibonacci Life

_{Robert Sheldon

September 20, 2010

Intelligent Design}

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galaxy 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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Comments

---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?StephenB_{September 26, 2010
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#142 As if everyone didn’t know the meaning of the law of non-contradiction and numerous other points 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.markf_{September 26, 2010
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@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.StephenB_{September 26, 2010
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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.Aleta_{September 26, 2010
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#139 If my ideal answer to a question begins "it depends what you mean by ...." should I respond "I don't know?"markf_{September 26, 2010
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---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.StephenB_{September 26, 2010
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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:
It’s just your conclusion that this points to an immaterial reality that I disagree with.
10 --> Similarly, note from EZ:
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.
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:
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.
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 TKIkairosfocus_{September 26, 2010
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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? :-)ellazimm_{September 26, 2010
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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_{September 25, 2010
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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.Aleta_{September 25, 2010
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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.kairosfocus_{September 25, 2010
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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 TKIkairosfocus_{September 25, 2010
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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_{September 25, 2010
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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.Aleta_{September 25, 2010
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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.Aleta_{September 25, 2010
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PS; This little discussion on the reality of imaginary no's on analogy to fractions [there considered as ordered pairs . . . ], is interesting.kairosfocus_{September 25, 2010
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Aleta: Pardon a very simple exercise.
1: Take out a sheet of graph paper and set up axes x and y for a convenient scale. 2: Plot the graph y = x^2, for a suitable range around x = 0, say out to +/- 5. 3: Running up from 0 to 25 on the Y axis, use a ruler to pick out the corresponding x that when squared gives y. 4: Try the same for y less than 0. Ask: Why is it that you cannot find any x values in this case? 5: Ask, again: could this be why the numbers were seen as imaginary?
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 TKIkairosfocus_{September 25, 2010
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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_{September 25, 2010
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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.Aleta_{September 25, 2010
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PS: Abstraction, courtesy Collins English Dict 2003:
abstract adj [?æbstrækt] 1. having no reference to material objects or specific examples; not concrete
Someone may well be imposing a definition, but it is not me.kairosfocus_{September 25, 2010
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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 TKIkairosfocus_{September 25, 2010
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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. Gkairosfocus_{September 25, 2010
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I agree 99.785% with what ellezim said at 114. :) kf writes,
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.
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.Aleta_{September 25, 2010
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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.ellazimm_{September 25, 2010
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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 TKIkairosfocus_{September 25, 2010
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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,,, https://uncommondescent.com/intelligent-design/fibonacci-life/#comment-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.bornagain77_{September 25, 2010
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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.Obriton_{September 25, 2010
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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.ellazimm_{September 25, 2010
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EZ:: You have put issues of truth, warrant, certainty and knowledge on the table. It would be trivial to show that something like . . .
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 . . .
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:
C1: Error exists
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. ___________
* F/N: When A AND NOT-A are affirmed or implied, we lose the ability to discern truth from false, i.e. we end in such confusion that we accept that (A AND NOT-A) is a forbidden assertion or implication. This too is a self-evident truth, aka the law of non-contradiction. We may be unsure which of A and NOT-A is so, but we can be reasonably confident that both propositions cannot be true in the same sense at the same time, despite certain claims commonly made on say Q-mech.
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.]kairosfocus_{September 25, 2010
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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.ellazimm_{September 25, 2010
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