Uncommon Descent Serving The Intelligent Design Community

Mind of the Maker spotlights mathematics as evidence for design in nature


A recent book, Science and the Mind of the Maker: What the Conversation Between Faith and Science Reveals About God , by Melissa Cain Travis might be of interest. According to one of the Amazon reviews,

One of the areas in the book that is unique and very interesting is the discussion about mathematics. The author states that, “Several eminent thinkers have convincingly argued that we discover, rather than invent, the realities of mathematics.” She cites numerous references from several scientists supporting this thesis, including Max Planck, Sir Arthur Eddington, Eugene Wigner and Roger Penrose. For example, physicist Wigner (an agnostic) wrote, “The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious. There is no rational explanation for it.” Many of the scientists that recognized this mystery were agnostics or atheists. The book also asserts that, “Objective mathematical truth poses a problem for a strict materialist philosophy, which denies that there is any reality independent of matter and energy.” The problem for materialism is not just that there are mathematical truths, but also the fact that we have the capacity to understand them. The conclusion is that, “Materialism is woefully inadequate for explaining the connections that exist between mathematics, the material world, and the human mind.”

M.C. Travis 2.5
Melissa Cain Travis/Tom Liskey Photography

From her bio:

Melissa worked as a bench scientist in the fields of biotechnology and pharmaceutical research for five years after obtaining her undergraduate degree, and has spent more than a decade exploring the science, theology, and philosophy related to the origins debate.


Hat tip: Philip Cunningham

See also: Will President Dutarte have to resign? Mathematician Euler offered an equation taken as proof of God

Mathematics itself exists in some type of transcendent, beyond space and time, realm which is not reducible any possible material explanation. This transcendent mathematical realm has been referred to as a Platonic mathematical world.
Platonic mathematical world – image https://image.slidesharecdn.com/quantuminformation2-120301000431-phpapp01/95/quantum-information-14-728.jpg?cb=1330561190 Naturalism and Self-Refutation – Michael Egnor – January 31, 2018 Excerpt: Mathematics is certainly something we do. Is mathematics “included in the space-time continuum [with] basic elements … described by physics”? It seems a stretch. What is the physics behind the Pythagorean theorem? After all, no actual triangle is perfect, and thus no actual triangle in nature has sides such that the Pythagorean theorem holds. There is no real triangle in which the sum of the squares of the sides exactly equals the square of the hypotenuse. That holds true for all of geometry. Geometry is about concepts, not about anything in the natural world or about anything that can be described by physics. What is the “physics” of the fact that the area of a circle is pi multiplied by the square of the radius? And of course what is natural and physical about imaginary numbers, infinite series, irrational numbers, and the mathematics of more than three spatial dimensions? Mathematics is entirely about concepts, which have no precise instantiation in nature,, https://evolutionnews.org/2018/01/naturalism-and-self-refutation/
Both Einstein and Wigner are on record as to regarding it as a miracle that we can reliably describe the universe with mathematics:
The Unreasonable Effectiveness of Mathematics in the Natural Sciences - Eugene Wigner - 1960 Excerpt: ,,certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess.,,, It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind's capacity to divine them.,,, 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/MathDrama/reading/Wigner.html On the Rational Order of the World: a Letter to Maurice Solovine - Albert Einstein - March 30, 1952 Excerpt: "You find it strange that I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way .. the kind of order created by Newton's theory of gravitation, for example, is wholly different. Even if a man proposes the axioms of the theory, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the 'miracle' which is constantly reinforced as our knowledge expands. There lies the weakness of positivists and professional atheists who are elated because they feel that they have not only successfully rid the world of gods but “bared the miracles." -Albert Einstein -
David Berlinski provocatively put the situation like this. “There is no argument against religion that is not also an argument against mathematics. Mathematicians are capable of grasping a world of objects that lies beyond space and time….” and,, "these are precisely the claims that theologians have always made as well – that human beings are capable by an exercise of their devotional abilities to come to some understanding of the deity; and the deity, although beyond space and time, is capable of interacting with material objects"
An Interview with David Berlinski – Jonathan Witt Berlinski: There is no argument against religion that is not also an argument against mathematics. Mathematicians are capable of grasping a world of objects that lies beyond space and time…. Interviewer:… Come again(?) … Berlinski: No need to come again: I got to where I was going the first time. The number four, after all, did not come into existence at a particular time, and it is not going to go out of existence at another time. It is neither here nor there. Nonetheless we are in some sense able to grasp the number by a faculty of our minds. Mathematical intuition is utterly mysterious. So for that matter is the fact that mathematical objects such as a Lie Group or a differentiable manifold have the power to interact with elementary particles or accelerating forces. But these are precisely the claims that theologians have always made as well – that human beings are capable by an exercise of their devotional abilities to come to some understanding of the deity; and the deity, although beyond space and time, is capable of interacting with material objects. http://tofspot.blogspot.com/2013/10/found-upon-web-and-reprinted-here.html
Moreover, with Gödel's incompleteness theorem, we now know that mathematics cannot play the role of God as infinite and autonomous but that mathematics is itself ultimately dependent upon God for its truthfulness.
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 (Godel) 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.org/articles/am/v7/n1/equation# A BIBLICAL VIEW OF MATHEMATICS Vern Poythress - Doctorate in theology, PhD in Mathematics (Harvard) 15. Implications of Gödel’s proof B. Metaphysical problems of anti-theistic mathematics: unity and plurality Excerpt: Because of the above difficulties, anti-theistic philosophy of mathematics is condemned to oscillate, much as we have done in our argument, between the poles of a priori knowledge and a posteriori knowledge. Why? It will not acknowledge the true God, wise Creator of both the human mind with its mathematical intuition and the external world with its mathematical properties. In sections 22-23 we shall see how the Biblical view furnishes us with a real solution to the problem of “knowing” that 2 + 2 = 4 and knowing that S is true. http://www.frame-poythress.org/a-biblical-view-of-mathematics/
As to Berlinski's claim that "Mathematicians are capable of grasping a world of objects that lies beyond space and time….”,, in regards to that claim it is interesting to note that in our best mathematical description of the universe, i.e. quantum mechanics, we find that,,, "We must explain space and time as somehow emerging from fundamentally spaceless and timeless physics."
LIVING IN A QUANTUM WORLD – Vlatko Vedral – 2011 Excerpt: Thus, the fact that quantum mechanics applies on all scales forces us to confront the theory’s deepest mysteries. We cannot simply write them off as mere details that matter only on the very smallest scales. For instance, space and time are two of the most fundamental classical concepts, but according to quantum mechanics they are secondary. The entanglements are primary. They interconnect quantum systems without reference to space and time. If there were a dividing line between the quantum and the classical worlds, we could use the space and time of the classical world to provide a framework for describing quantum processes. But without such a dividing line—and, indeed, without a truly classical world—we lose this framework. We must explain space and time (4D space-time) as somehow emerging from fundamentally spaceless and timeless physics. http://phy.ntnu.edu.tw/~chchang/Notes10b/0611038.pdf
Even more suggestive, and as would be a-priorily expected under Christian presuppositions, we find that our best mathematical descriptions of the universe are all based on 'higher dimensional' mathematics. The first part of this following video goes over that particular line of 'higher dimensional' mathematical evidence:
Quantum Mechanics, Special Relativity, General Relativity and Christianity – video https://www.youtube.com/watch?v=h4QDy1Soolo
Of supplemental note: Darwinian evolution is based on a naturalistic and/or materialistic method of science, called methodological naturalism, which holds that all possible scientific explanations for reality in general, and for biology in particular, are exhausted by purely natural and/or material explanations. Yet, completely contrary to that presupposition of Darwinian thought, and as was mentioned previously, Mathematics itself exists in a transcendent, beyond space and time, realm which is not reducible any possible material explanation. The predicament that Darwinists find themselves in in regards to denying the reality of this transcendent, immaterial, world of mathematics, and yet needing validation from this transcendent, immaterial, world of mathematics in order to be considered scientific in the first place, should be the very definition of a self-refuting worldview.
What Does It Mean to Say That Science & Religion Conflict? – M. Anthony Mills – April 16, 2018 Excerpt: In fact, more problematic for the materialist than the non-existence of persons is the existence of mathematics. Why? Although a committed materialist might be perfectly willing to accept that you do not really exist, he will have a harder time accepting that numbers do not exist. The trouble is that numbers — along with other mathematical entities such as classes, sets, and functions — are indispensable for modern science. And yet — here’s the rub — these “abstract objects” are not material. Thus, one cannot take science as the only sure guide to reality and at the same time discount disbelief in all immaterial realities. https://www.realclearreligion.org/articles/2018/04/16/what_does_it_mean_to_say_that_science_and_religion_conflict.htm
Thus in conclusion, besides Darwinian evolution already being shown to be mathematically impossible, (by Sanford, Dembski, Marks, Axe, Behe, Durston, etc.. etc..), Darwinian evolution is further falsified by mathematics as being a scientific theory since the materialistic presuppositions that undergird Darwinism thought deny the very reality of one the thing it most needs, i.e. mathematics, in order to be considered scientific in the first place.
"Nothing in evolution can account for the soul of man. The difference between man and the other animals is unbridgeable. Mathematics is alone sufficient to prove in man the possession of a faculty unexistent in other creatures. Then you have music and the artistic faculty. No, the soul was a separate creation." Alfred Russell Wallace, New Thoughts on Evolution, 1910

Leave a Reply