I recently went to a local library seeking intellectual engagement while helping my wife and her family care for her mother. I found two recently-published books I had never heard of, but the titles and jacket blurbs sounded good so I brought them home to read and am very glad I did. The first was The Power of Mathematics by Jordan Ellenberg, a well-published professor of mathematics at the University of Wisconsin-Madison. The other book was Lost in Math by physicist research fellow at the Frankfurt Institute for Advanced Studies, Sabine Hossenfelder. Not only are both of these books fascinating, but they are also greatly relevant to Christian apologetics.
The power of Mathematical Thinking deals with applying mathematical reasoning to a wide variety of areas including the physical sciences, medicine, politics, the social sciences, the use of statistics, and even playing the lottery (Voltaire became independently wealthy by teaming with a mathematician to beat a lottery). The book greatly helps the reader to think more clearly and precisely by applying principles of mathematical analysis to everyday life and decision-making. In that way alone, the book is an excellent read for an aspiring apologist.
Lost in Math deals with the philosophy of science especially concerning the use of mathematics in theoretical physics. Sabine writes from the perspective of a theoretical physicist struggling with her own disillusionment with the way theoretical physics is conducted today. The book consists, in part, of interviews with leading physicists in particle physics, quantum mechanics, string theory, cosmology and super-symmetry among others disciplines. She carefully dissects some of the most popular theories advanced today (often portrayed as “certain knowledge” or “confirmed science” in popular science television shows) showing how shaky the theories really are.
Most interesting to me is the common ground connecting these two books. Both books point out the subjectivity found in what are usually presented as the most objective of scientific disciplines. Ellenberg wonderfully shows how mathematics can, and are, used to support all kinds of diverse and opposing views either by sloppy math, or misunderstanding of math, or even deliberate use of math to make statistically true but misleading statements. Hossenfelder, on the other hand, pokes holes in all kinds of popular theories including the multiverse, inflation, string theory, and various GUT’s and even points out some problems concerning dark matter and dark energy. In fact, she questions the very way math is used in physics (hence the title). Both authors emphasize the importance, and danger, of suppositions (more about that later).
Both authors also deal with Christian apologetics. Neither claims to be an atheist or a theist. In fact, both seem to support the NOMA concept claiming that neither mathematics or science has anything meaningful to say about the existence or non-existence of God. However, both attack some arguments based on math and/or science commonly used by Christian apologists such as Bayesian thinking and fine-tuning and Bible codes. Ellenberg even pointed out problems with Pascal’s wager. Both authors are mathematical formalists and would disdain any mathematical evidence for God’s existence. They certainly show that there are formalisms in math; but, I do not think, they show that formalisms in math show that math is all formalism or that the mathematical evidences used for the existence of God are invalid (cf. my post on mathematical evidence for God). I also think that they misunderstand the purpose and use of science and math arguments by Christian apologist. That being said, they both do show certain weaknesses that are often found in the way these arguments are used by apologists. Christian apologists would do well to understand these weaknesses to avoid them.
There are several especially significant points made by these books that I think deserve special note. First, they not only point out weaknesses in Christian apologetic arguments, but also attack those who use scientific and mathematical argument against the existence of God. In her book, Hossenfelder interviewed George Ellis, professor emeritus at the University of Capetown and a leading cosmologist, during which he attacked Stephen Hawking and Lawrence Krauss for saying that science disproves God’s existence claiming that it does no such thing and bemoaning that such statements by such scientists actually harm science (pp. 213, 214). They both also point to the importance of philosophy, again against the views held by the new atheists, to aid science and math. Both, then, also point to the limitations and subjectivity found in their respective fields in strong contrast to how popular science literature portray these fields (often in an attempt to demonstrate their superiority to philosophy and theology). However, I think the greatest implications of these books for Christian apologists have to do with the emphasis of both authors in the area of the role of presuppositions in scientific and mathematical epistemology. Both authors point out that mathematical and scientific thinking rely heavily on setting parameters, making presumptions and choosing the values of variables which then greatly affect the conclusions. In fact, Hossenfelder would say that they often drive the conclusions. She lists several logical errors commonly practiced by physicists (pp. 229-232). Her basic thesis is that the drive for “beauty,” “elegance,” and “naturalness” in the math of physics, often without any experimental support (in fact, she lists many very expensive experiments based on such ideas that have totally failed to demonstrate the predictions of the math), actually harms progress in physics. She calls for a new physics with new presumptions using a new approach to mathematics. Ellenberg demonstrates that what “works” according to the rules and procedures used often do not lead to what really is. I think that one weakness of formalism; which, however, fits well with post-modernism, is the idea that what works should be considered what is true even if we know that it often is not. It is true because our processes say it is true whether it conforms to reality or not. The two books together paint a picture of epistemology that is highly reliant on presuppositions. I have framed the concept in a different way in an earlier post pointing out that we cannot produce absolute proof of anything, not even, as these authors show, in math and science. The mathematicians and scientists have to have faith in their presuppositions. God has so designed creation that faith in something is always necessary. These books show that even such fields as mathematics and physics have, at their foundation, faith (though neither author would ever use that term).
The saddest part of these books, and especially Hossenfelder’s, is that, while calling for new thinking and new assumptions, they never consider the assumption that there is a God who created all else that exists and reveals Himself through His creation. Hossenfelder grieves over the possibility that physics has reached a kind of dead end, but would never consider that the way forward could be found in theistic assumptions.