# Mathematics and Theology

September 28, 2012 | Posted by johnnyb under Culture, Mathematics, Religion, Science |

I thought you all might be interested in an article I wrote titled Mathematics and Theology: Seeing to Infinity. The basic purpose of the article is to show how the “limit” concept from mathematics can be incorporated into theological reasoning. The larger purpose is to get theologians thinking more deeply about mathematics as a tool in theological reasoning.

One of the disheartening things about modern theology is how disconnected it is from the rest of human knowledge. It doesn’t **need** to be disconnected — it’s just that there is a habit of thought that has developed over the past two centuries that separated out theology as “other” (perhaps as a euphemism for “fictitious”) and math and science as “real”. This case was strenuously made in Stephen J. Gould’s article on non-overlapping magisteria (abbreviated as NOMA) — saying that science and theology are both good, but they should never, ever talk.

I believe in the integration of knowledge, so I tend to take the idea that they are non-overlapping as intending that one of these is false. Certainly, domains of knowledge have their boundaries, but those boundaries **do overlap**.

NOMA has been surprisingly effective. I think one of the things that makes it effective is that theologians don’t want to learn other people’s subjects. Theologians, on the whole, don’t want to really learn science and math. The want to give it lip service, but not really engage. The few who do engage, tend to only engage in one direction – have theology learn from science. What we really need is a full, two-way engagement which has been missing since Darwin.

This NOMA view has negatively affected both science and theology. It has hurt theology by removing from it concrete connections with reality. It has hurt science by making any hypothesis which can touch theology be considered out-of-bounds, thus limiting the freedom of inquiry for the scientist. My hope is that more theologians will pursue an active, two-way engagement with science and mathematics. NOMA has hurt everyone, and we need to put it to rest.

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of related note:

Leonhard Euler, the son of a Christian pastor, and a fervent Christian all his life, is simply unparalleled in mathematics:

An Evening with Leonhard Euler – video

http://www.youtube.com/watch?v=h-DV26x6n_Q

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

also of related note:

Fascinating Bible code – Pi and natural log e – video (of note: correct exponent for base of Nat Log e found in John 1:1 is 10^40, not 10^65 as stated in the video)

http://www.youtube.com/watch?v=Wg9LiiSVaes

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/

further notes:

in the equation e^pi*i + 1 = 0

,,,we find that pi is required in;

General Relativity (Einstein’s Equation)

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

,,,and we also find that the square root of negative 1 is required in;

Quantum Mechanics (Schrödinger’s Equations)

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

,,and we also find that e is required for;

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.,,, this number, e, also appears in banking, because it is the maximum limit for growth of compound interest.

Some of the various uses and equations of ‘e’ are listed at the bottom of the following page:

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

I don’t how much this will effect some peoples mathematical ‘tastes’, but Dr. William Dembski, has even related 1 and 0, which are also found in Euler’s identity, to theology here:

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

Of note: I hold ‘growing large without measure’ to be a lesser quality infinity than a fraction in which the denominator goes to zero. The reason why I hold it to be a ‘lesser quality infinity’ is stated at the 4:30 minute mark of the following video:

Can A “Beginning-less Universe” Exist? – William Lane Craig – video

http://www.youtube.com/watch?v=K8YN0fwo5J4

also of note to theology and math:

Taking God Out of the Equation – Biblical Worldview – by Ron Tagliapietra – January 1, 2012

Excerpt: Kurt Gödel (1906–1978) proved that no logical systems (if they include the counting numbers) can have all three of the following properties.

1. Validity . . . all conclusions are reached by valid reasoning.

2. Consistency . . . no conclusions contradict any other conclusions.

3. Completeness . . . all statements made in the system are either true or false.

The details filled a book, but the basic concept was simple and elegant. He summed it up this way: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove.” For this reason, his proof is also called the Incompleteness Theorem.

Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous. It was shocking, though, that logic could prove that mathematics could not be its own ultimate foundation.

Christians should not have been surprised. The first two conditions are true about math: it is valid and consistent. But only God fulfills the third condition. Only He is complete and therefore self-dependent (autonomous). God alone is “all in all” (1 Corinthians 15:28), “the beginning and the end” (Revelation 22:13). God is the ultimate authority (Hebrews 6:13), and in Christ are hidden all the treasures of wisdom and knowledge (Colossians 2:3).

http://www.answersingenesis.or...../equation#

The God of the Mathematicians – Goldman

Excerpt: As Gödel told Hao Wang, “Einstein’s religion [was] more abstract, like Spinoza and Indian philosophy. Spinoza’s god is less than a person; mine is more than a person; because God can play the role of a person.” – Kurt Gödel – (Gödel is considered one of the greatest logicians who ever existed)

http://www.firstthings.com/art.....ematicians

Oh yes yes yes, this is so in line with my thinking. As I was reminded recently, “university” means unity within diversity, yet theology seems to stand outside the door as a non-bearer of knowledge and irrelevant to the epistemic wellspring of our culture.

This needs to change.

It strikes me as rather ironic that many atheists see more glory in science than many Christians. This I find very intellectually disheartening, since to the atheist there is really only time and chance behind the beauty they almost worship at times.

If johnnyb is anything like me, he is seeing the hand of God in the science he is doing. And he is amazed by it. And probably be sees himself worshipping the Creator as he does his science.

PS. Thanks for the links to those papers.

I agree wholeheartedly with Johnnyb’s affirmations, and with the comments of bornagain77, and with those of Christian-apologetics.org. Recognizing the unity of truth, is a big, big deal. Without it, both sanctity and rationality are compromised.

I wonder if people could suggest like-minded IDists who are Mathematicians. Here is a starter:

Dr. David Berlinski (PhD Maths)

Dr. Marvin Bittinger (PhD Maths)

— https://twitter.com/DrBittinger

— http://www.amazon.com/The-Fait.....1933669071

— http://www.facultylinc.com/bittinger-marvin-l/

Dr. John Lennox (PhD Maths)

— http://johnlennox.org

Dr. William Dembski (PhD Maths)

Graville Sewell

excuse me,,, Granville Sewell – Mathematics Dept. University of Texas El Paso (Papers and Videos)

http://www.math.utep.edu/Faculty/sewell/

Yes, my bad, and I even have his book. And there are probably others…

a few assorted notes:

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

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

At the 4:00 minute mark of the preceding audio, Dr. Sewell comments on the ‘transcendent’ and ‘constant’ Schroedinger’s Equation;

‘In chapter 2, I talk at some length on the Schroedinger Equation which is called the fundamental equation of chemistry. It’s the equation that governs the behavior of the basic atomic particles subject to the basic forces of physics. This equation is a partial differential equation with a complex valued solution. By complex valued I don’t mean complicated, I mean involving solutions that are complex numbers, a+bi, which is extraordinary that the governing equation, basic equation, of physics, of chemistry, is a partial differential equation with complex valued solutions. There is absolutely no reason why the basic particles should obey such a equation that I can think of except that it results in elements and chemical compounds with extremely rich and useful chemical properties. In fact I don’t think anyone familiar with quantum mechanics would believe that we’re ever going to find a reason why it should obey such an equation, they just do! So we have this basic, really elegant mathematical equation, partial differential equation, which is my field of expertise, that governs the most basic particles of nature and there is absolutely no reason why, anyone knows of, why it does, it just does. British physicist Sir James Jeans said “From the intrinsic evidence of His creation, the great architect of the universe begins to appear as a pure mathematician”, so God is a mathematician to’.

i.e. the Materialist is at a complete loss to explain why this should be so, whereas the Christian Theist presupposes such ‘transcendent’ control of our temporal, material, reality,,,

John 1:1

In the beginning was the Word, and the Word was with God, and the Word was God.

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

Alan Turing and Kurt Godel – Incompleteness Theorem and Human Intuition – video (notes in video description)

http://www.metacafe.com/watch/8516356/

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

Calvin and Hobbes – cartoon – The Mathematical Atheist

http://s3.hubimg.com/u/270622_f520.jpg

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

Why Mathematics Works, part 1 – James Nickel – video

http://www.youtube.com/watch?v=r1YssV8qi-w

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? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things?

— 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

Darwin and the Mathematicians – David Berlinski

http://www.evolutionnews.org/2.....cians.html

“Darwin’s theory is easily the dumbest idea ever taken seriously by science.”

Granville Sewell – Professor Of Mathematics – University Of Texas – El Paso

Godel and Physics – John D. Barrow

Excerpt (page 5-6): “Clearly then no scientific cosmology, which of necessity must be highly mathematical, can have its proof of consistency within itself as far as mathematics go. In absence of such consistency, all mathematical models, all theories of elementary particles, including the theory of quarks and gluons…fall inherently short of being that theory which shows in virtue of its a priori truth that the world can only be what it is and nothing else. This is true even if the theory happened to account for perfect accuracy for all phenomena of the physical world known at a particular time.”

Stanley Jaki – Cosmos and Creator – 1980, pg. 49

http://arxiv.org/pdf/physics/0612253.pdf

A Biblical View of Mathematics – Vern Poythress – doctorate in theology, PhD in Mathematics (Harvard)

Excerpt: only on a thoroughgoing Biblical basis can one genuinely understand and affirm the real agreement about mathematical truths.

http://www.theologynetwork.org.....matics.htm

Dr. David Berlinski (PhD Math)

— http://www.davidberlinski.org/books.php

Dr. Marvin Bittinger (PhD Math)

– https://twitter.com/DrBittinger

– http://amzn.to/TOK9UI (Amazon book)

– http://www.facultylinc.com/bittinger-marvin-l/

Dr. John Lennox (PhD Math)

– http://johnlennox.org

Dr. William Dembski (PhD Math)

Dr. Granville Sewell

Vern Poythress (PhD theology, PhD Math (Harvard))

Dr. David Berlinski (PhD Math)

– http://www.davidberlinski.org/books.php

Dr. Marvin Bittinger (PhD Math)

– https://twitter.com/DrBittinger

– http://amzn.to/TOK9UI (Amazon book)

– http://www.facultylinc.com/bittinger-marvin-l/

Dr. John Lennox (PhD Math)

– http://johnlennox.org

Dr. William Dembski (PhD Math)

Dr. Granville Sewell

Vern Poythress (PhD theology, PhD Math (Harvard))

Dr. Walter Bradley (PhD, Materials Science)

— http://bit.ly/UyZ6VE (CV)

I should also recommend Gregory Chaitin. He is not a Christian or an ID’er, but he knows and respects the philosophical intellectual history of mathematics. He is also not an anti-ID’er – he disagrees with ID but does so entirely on friendly terms, and uses reason and argument instead of hot air. His lectures are worth every minute of watching. Just look for his name on YouTube.

When studying as a seminarian for a brief time, I found myself putting down as my bibliography at the end of an essay, a list of books by some of the great novelists, such as Solzhenitsin, Graham Greene, J D Salinger, John Steinbeck.

I seem to have had a congenital indisposition for answering questions in the prescribed manner. It was never an asset to me in my limited tertiary studies.

The RC church has systematised theology brilliantly in the catechism, but apart from that, the formal rigidity of a system seems to me antithetical to something as ultra-personal as our Christian God and his adoptive, family relationship with us.

That Christianity has been marginalised by science, instead of its theology’s being acccepted as the Queen of the Sciences, is grotesque beyond belief, and would be hilarious had its effect not been so crippling on science; a point often reiterated in more general, but no less pointed, terms, here, at UD, as we all know.

as to George Chaitin, here is what Gregory Chaitin, a world-famous mathematician and computer scientist, said about the limits of the computer program he was trying to develop to prove evolution was mathematically feasible:

Here is the video where, at the 30:00 minute mark, you can hear the preceding quote from Chaitin’s own mouth in full context:

Moreover, at the 40:00 minute mark of the video Chaitin readily admits that Intelligent Design is the best possible way to get evolution to take place, and at the 43:30 minute mark Chaitin even tells of a friend pointing out that the idea Evolutionary computer model that Chaitin has devised does not have enough time to work. And Chaitin even agreed that his friend had a point, although Chaitin still ends up just ‘wanting’, and not ever proving, his idea Darwinian mathematical model to be true!

Chaitin figures prominently in these following videos about Godel’s incompleteness theorem:

As to why Chaitin would be trying to develop a mathematical model/computer simulation, to prove evolution was even feasible in the first place, well contrary to popular belief, it turns out that Darwinism doesn’t really even have a basic mathematical equation by which it can be analyzed (although I have heard Darwinists insist time and again that Darwinism does have a rigid mathematical foundation within science):

a few more notes of interest:

Infinity is pseudoscientific, self-contradicting nonsense. It should be in neither science not theology.

Bruce Gordon – Associate Professor of Science and Mathematics – The King’s College

B.S. Applied Mathematics – University of Calgary

M.A. Philosophy – University of Calgary

M.A.R. Apologetics/Systematic Theology – Westminster Theological Seminary

Ph.D. History and Philosophy of Science (Physics)- Northwestern University

http://www.tkc.edu/academics/f......asp?id=82

A few notes on seeing ‘infinity':

Also of related interest to this ‘Zero/Infinity conflict of reconciliation’, between General Relativity and Quantum Mechanics, is that a ‘uncollapsed’ photon, in its quantum wave state, is mathematically defined as ‘infinite’ information:

Thus every time we see (observe) a single photon of ‘material’ reality we are actually seeing just a single bit of information that was originally created from a very specific set of infinite information that was known by the consciousness that preceded material reality. i.e. information known only by the infinite Mind of omniscient God!

It is important to note that the following experiment actually encoded information into a photon while it was in its infinite dimensional quantum wave state, thus destroying the notion, held by many, that the wave function was not ‘physically real’ but was merely ‘abstract’. i.e. How can information possibly be encoded into something that is not physically real but merely abstract?

What would it take to impress a infinite amount of information onto the infinite dimensional quantum wave state?

As to empirical proof,,, Kevin Moran, a scientist working on the mysterious ‘3D’ nature of the Shroud image, states the ‘supernatural’ explanation of how the Shroud formed this way:

Verses and music:

Further notes:

Thus every time we see (observe) a single photon of ‘material’ reality we are actually seeing just a single bit of information that was originally created from a very specific set of infinite information that was known by the consciousness that preceded material reality. i.e. information known only by the infinite Mind of omniscient God!

It is important to note that the following experiment actually encoded information into a photon while it was in its infinite dimensional quantum wave state, thus destroying the notion, held by many, that the wave function was not ‘physically real’ but was merely ‘abstract’. i.e. How can information possibly be encoded into something that is not physically real but merely abstract?

What would it take to impress a infinite amount of information onto the infinite dimensional quantum wave state?

As to empirical proof,,, Kevin Moran, a scientist working on the mysterious ‘3D’ nature of the Shroud image, states the ‘supernatural’ explanation of how the Shroud formed this way:

Verses and music:

Further notes:

Chaitin’s ‘wanting’ and Richie’s ‘hoping’, sounds like a pop-song of the sixties, Bornagain?

I’ve just googled it. A song of Dusty Springfield, called, Wishing and Hoping’.

‘Wishing and hoping and

…. (don’t laugh)…

thinking and praying’!!!

Either one would be more than acceptable in this particular parish, wouldn’t it. At least as a start.

OT: Just ran across N.T. Wright today, and thought I’d post a link in case interested folks here might want to take a look. His arguments for the historicity of the resurrection are the best I’ve seen (video at link).

N.T. Wright is among my favorite authors. Good stuff.