2015 Reading List: Love and Math

Frenkel, Edward. Love and Math: The Heart of Hidden Reality.

I discovered Numberphile back when the -1/12 video went viral. In the course of browsing their videos, I came across Love and Math, since Dr. Frenkel is one of the mathematicians consulted in the videos. The purpose of the book was billed as showing how math-haters can love math, so I thought I’d give it a shot.

I didn’t particularly care for this book. It’s half biography, half this-is-the-math-my-life’s-work-is-based-on, and my reaction to the book splits evenly down that line of demarcation. I found the biographical sections fascinating and compelling writing; I found the math sections almost impenetrably complex.

Dr. Frenkel is a native Russian, whose Jewish heritage precluded him from admission to Moscow’s highest university with the best math program. The stories of institutionalized racism and anti-Semitism are heartbreaking. The genuine affection and appreciation that Dr. Frenkel shows toward his mentors and teachers is strikingly beautiful, and many times I found myself moved by his sentiments and longing to be that kind of teacher myself.

But the math. The math that’s typically taught in US education systems is the ancient, established-for-centuries variety; Dr. Frenkel’s aim in the book is to show that there’s more to math than the quadratic equations and differential calculus that many of us suffered through in high school and college. I’m sure the modern math he describes is incredible, but I have to take his word for it. He valiantly attempts to describe and explain what’s going on in the various problems and projects he’s working on, but it’s tough sledding to read through. He even assumes in the introduction that you’ll take multiple readings, going back to dive deeper into the heavy math and footnotes on subsequent trips through the book. I’m not sure I’m up for it, honestly.

It’s highly likely that my disappointment with the book lies more in misplaced expectations than the actual content of the book itself. I wish I could combine the robust, Trinitarian orthodoxy and clarity of Vern Poythress with the compelling narrative of Edward Frenkel. That would be an amazing book on math. Alas, neither Redeeming Mathematics nor Love & Math ultimately satisfied.

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2015 Reading Log: Redeeming Mathematics

Poythress, Vern. Redeeming Mathematics: A God-Centered Approach.

Several years ago I was introduced to what is known as presuppositional apologetics. That’s a mouthful of a phrase, but the basic gist is this: the reason that anything at all exists is because of God. Or, as apologist Cornelius van Til put it, “there are no brute facts.” Probably the most famous articulation is the Great Debate between Bahnsen and Stein, in which Bahnsen danced circles around the ill-prepared Stein with the concepts of presuppositionalism.

I find this brand of apologetics compelling, because it very directly attributes maximum glory to God for all things. Further, it encompasses all the other brands of apologetics. Evidential apologetics (a la Josh McDowell) and classical apologetics (a la Sproul) are various expressions and valid tools to be used, but all based upon the truth of Scripture and its immediate application to the real world.

In that vein, Vern Poythress has written a series of books that propose to demonstrate the reality that all that we know and all that is has God as the foundation. He has written on science, sociology, chance, logic, philosophy, and this volume on mathematics. (I’ve read the first part of Redeeming Science but none of the other volumes in the series.)

I had high hopes for this book, but I was largely underwhelmed. Dr. Poythress has a long-standing and well-known friendship with Dr. John Frame, and their work overlaps often. (This is a good thing.) Poythress employs Frame’s three perspectives to explain why math necessarily comes from God alone.

The three perspectives are the normative, the situational, and the existential. The normative perspective deals with what God declares to be so (hence “norms” or “normative”). The situational perspective deals with an actual scenario to which the truth applies. The existential perspective deals with an individual’s perception of the truth. The only way mathematics can properly balance all three perspectives is if the source and foundation is the Triune God Himself.

That last paragraph pretty much sums up the last dozen or so chapters of the book. Laws and principles of math (numbers, operations, etc.) are true because they conform to the thoughts and mind of God (normative perspective); the laws and principles of math apply in actual circumstances (situational perspective); we as image-bearers of God are able to think about and reason via the mathematical laws and principles (existential perspective). Every chapter basically asserts these three sentences, just with a different topic.

This doesn’t mean in any way that I disagree with Poythress at all. I think he’s absolutely right. I just found the repetition tedious fairly quickly. I think this book would be better served as an appendix or an additional couple of chapters in Redeeming Science than as its own work.

Redeeming Mathematics is an important book as a starting point of sorts. I’d definitely use it as a springboard into more robust descriptions of presuppositional apologetics (e.g., John Frame’s Apologetics to the Glory of God is a great resource).

If you’re interested in seeing math nerds geek out about math, I’d highly recommend the Numberphile YouTube channel. I don’t always understand exactly what’s going on, but it is fun to see people who are genuinely passionate about math show how it is beautiful and amazing and strange. Whether they intend it or not, it almost always leads me to worship and wonder at the God who is the root (pun intended) of all mathematics.

2015 Reading Log – The Science of Interstellar

Thorne, Kip. The Science of Interstellar. Amazon

In December 2014, Christopher Nolan’s Interstellar was released. As a nerd in general and a space nerd in particular (I grew up on Star Trek: The Next Generation and still appreciate the campy wonderfulness of the original Star Trek series), I knew I had to see it. Sure enough, the movie did not disappoint.

I read a lot about the movie prior to actually seeing it, and one detail that really intrigued me was Nolan’s extensive use of actual astrophysicist Kip Thorne as a consultant. The visualization of the black hole Gargantua is the most scientifically supported and accurate one in any film. At this point, my nerd-o-meter was red-lining, and the desire to see the film only deepened.

I also learned that Thorne had written a book, The Science of Interstellar, in which he attempted to explain the scientific underpinnings of the movie. The book assumes that you’ve seen the movie first, and the cover even has a helpful spoiler alert to that effect.

I took physics and astronomy in college because lab sciences were required for my major, and I did well in the classes. I was interested in the subject matter and had very good professors (Drs. Lionel Crews and Cahit Erkal). All that to say, I’m not an astrophysicist or the son of an astrophysicist.

Nonetheless, I found Thorne’s writing generally accessible. I don’t pretend to understand all of what he wrote, but much of it was understandable. The chapters include many diagrams and illustrations, without which most of the text would be unintelligible. Thorne certainly has the spirit of a teacher, and it comes through in his writing.

The book generally walks through the flow of the movie, stopping to note background history and science as appropriate. The chapters and even subsections within chapters are also marked based on the scientific confidence upon which Thorne stands with respect to them: T for Truth, EG for Educated Guess, and S for Speculation. That which is mathematically and/or physically certain is marked T, that which is largely supported but not yet provable is marked EG, and that which is assumed for the sake of the story based on what is known presently is marked S. I found this simple scheme remarkably helpful in delineating where creativity and empiricism intersected. I also found it refreshingly humble.

Some (perhaps many) Christians might be fearful of or put off by Dr. Thorne’s rabid empiricism, or even more simply by his unabashed acceptance of the Big Bang theory, evolution, and billions-of-years age of the universe. I didn’t find anything in the book that was untoward or offensive; Dr. Thorne simply stated his foundations and presuppositions and showed his work from there.

While I personally do not believe in evolution or a billions-year-old universe, I was still moved to wonder by both the film and the book. (I could’ve watched 45 minutes alone of the Saturn approach and orbit, then the other 1.5 hours of Gargantua. But, as I’ve already said, I’m a general nerd and a space nerd, so…) The God who created the heavens and the earth is the God whose mind is the basis for all logic, mathematics, physics, and every bit of knowledge in the universe. The complex mathematics of Einstein’s relativity and everything known and unknown about the universe is upheld and maintained every moment by the word of Jesus’ power (Hebrews 1:3).

This book is not for the faint of heart, but certainly for those who enjoy science, physics, space, and other matters of nerdiness. It’s a helpful guide to seeing the mind-boggling bigness of the God who made all things, and an indirect reminder that He who made all things loves and cares for me.

2015 Reading Log – The Signal and the Noise

The Signal and the Noise: Why So Many Predictions Fail–But Some Don’t. Nate Silver. Amazon

Silver’s fame as a statistical analyst and election prognosticator at FiveThirtyEight have thrust him into the limelight (to the applause of us kindred nerds). This book is an explanation of the philosophy behind his analysis and predictions.

This was a fascinating book to me–the subjects discussed range from weather forecasting (which has remarkably improved in the last 20 years or so) to Garry Kasparov vs. Deep Blue to stock markets to foreign policy, and more.

Bayes’ theory, which Silver uses and advocates in the book, emphasizes probability or “percent chances” of predictions, as opposed to making absolute declarations. The theory has as its foundation the principle of humility (whether or not it’s explicitly stated as such); make predictions, learn from what actually happens, and refine your models accordingly.

Admit what you don’t know. Learn. Don’t disregard data or results you don’t like. It’s actually refreshing (as well as interesting).

You don’t have to be a nerd to appreciate or enjoy the book (although it helps). Silver is actually a funny and insightful writer, and he casually throws in pop culture and obscure references to serious discussions. I certainly appreciate his sense of humor.

Probably the best summary of the book I can give (without giving away the book in a sense) is his discussion of Phil Tetlock’s distinction between hedgehogs and foxes. These are two kinds of thinkers: hedgehogs (popular TV pundits, columnists, bloggers, etc.) are specialists who have dug their heels in on their position; they insist that the world operates as they articulate and stubbornly refuse to hedge or alter predictions in the face of new data. Foxes, on the other hand, tend to be multidisciplinarians who adapt their predictions and approaches based on new data or additional expertise. Foxes are extremely cautious about their predictions, rarely if ever speaking in absolute terms.

The Signal and the Noise is a book that defends a foxy approach to analysis and prediction as opposed to a hedgehog-y approach. (It’s really more intriguing than it sounds.)

Kindle rating: 4/5 stars