Archive for July 24th, 2011
Mario Livio’s “Is God a Mathematician?” — Math as Philosophy
Posted by Barb Caffrey in Book Review on July 24, 2011
Mario Livio’s IS GOD A MATHEMATICIAN? is a book about the philosophy behind math, about great mathematicians and their discoveries, and also about the most fundamental questions mathematicians ask themselves about their discipline, to wit: was math always present in the universe, just waiting for human beings to be advanced enough to understand and “discover” it? Or is math a human invention, something that describes the universe as we see it, but isn’t so much a part of the universe as simply describing what we humans can make sense of instead? The former proposition is called the “Platonist” position because as far back as Plato this has been discussed; the newer thought of math being a human invention has been discussed openly since approximately 1880, though much more frequently since 1930.
First, Livio goes through the history of math as we know it, starting with the Greeks, diverting a bit to discuss the Chinese (who didn’t have some of the same concepts as the Greeks), then coming up to the modern day. Because the Chinese concepts were different than the Greeks, that lends support to the latter philosophical proposition that math is a human invention rather than something that was always out there to be found (a “divine language,” in short, that might lead us to God, or perhaps lead God to us). That’s because if math truly was universal in nature, why didn’t the Chinese discover the very same things as the Greeks?
As far as that goes, there is some discussion of simultaneous discoveries in IS GOD A MATHEMATICIAN?, particularly when dealing with knot theory (or the theory of knots, as to what their properties are and how they apply in various circumstances). That fact lends itself to the second philosophical argument, that of the Platonists — that mathematical concepts are universal, something anyone can understand if he or she has enough knowledge to do so — which shows in shorthand form how difficult this philosophical problem is as to whether or not math was designed by humans for humans, or designed by someone else (or something else) and is only now being discovered by humans since we now have the facility to do so.
The main point of IS GOD A MATHEMATICIAN? isn’t so much whether or not God can be deduced mathematically; in fact, Livio doesn’t try, which might be wise. It’s rather the point of whether math is a universal language/constant or not — thus, perhaps God’s own language, though this is implied rather than directly stated — and whether or not math was always there but couldn’t be described before human beings had developed the concepts, or math is a human invention, period. Livio goes through various forms of math and when they were discovered, with one of the more intriguing points being that the most abstract math, such as the theories behind knots and strings, eventually became something that applied mathematicians can use and use well. This point may be the strongest one made for the Platonist point of view, as when mathematicians started studying knots they certainly had no idea that their insights would eventually lead to real-world solutions — they studied them merely because they found knots interesting.
This partially being a history of math and mathematicians, Livio hits all the major figures in math since the dawn of recorded time. From Isaac Newton to Galileo, from Descartes to Einstein, from Boole to Goedel, they’re all here and their impact on subsequent mathematicians, engineers, etc., cannot be underestimated. Livio does a good job in making mathematicians human, such as discussing the feuds that went on within the Bernoulli family (which had no fewer than eight mathematicians in successive generations), and reminds the reader that mathematicians are no different than thee or me no matter what their skill-sets are; they get jealous, argumentative, or annoyed as easily as anyone else. Livio also makes a strong case that Isaac Newton was far from a saintly man, all of which helps humanize mathematicians and keep them from God-like status, which Livio certainly doesn’t want to imply considering his overall premise.
The way the mathematicians, physicists, etc., have built on each other’s work bit by bit is also explored in depth by Livio in a way that reminded me of Malcolm Gladwell’s assertion in OUTLIERS that no one stands alone in this world — that even geniuses need some help now and again, and wouldn’t be what they are without a whole lot of help. In this case, that “help” resides in the thousands of mathematicians who came before Isaac Newton (or Galileo Galilei) in that there’s no way, shape or form Newton could’ve done what he did without centuries of other theorists behind him. Nor was there any way Einstein could’ve come up with a theory of general relativity without all the people since Newton’s time discovering, then rejecting, other forms of math either, for that matter.
That even the greatest mathematicians make mistakes is a point Livio also makes, though not to the point of absurdity; it’s by building on those mistakes that another mathematician may find a good answer that will lead to discovery after discovery. So one man’s “mistake,” as it were, is another man’s treasure, and as such, there are perhaps no bad ideas — simply some ideas where the time for them hasn’t yet come. Mind you, this latter thought is more subtext than anything else, but it makes sense in an odd way, bolstering the idea for mathematics to be man’s way of describing the universe he sees around him.
In the end, Livio hedges his bets as to whether or not math is a human invention, or whether math truly describes the fabric of the universe in a language everyone, anywhere, of any species could understand if given enough time to do so. But by raising the questions, Livio has done a great service; he’s helped to illustrate this problem in language that’s neither too obtuse to be understood by a non-mathematician nor insufficient for a technical observer to appreciate — a neat trick indeed.
So to sum up IS GOD A MATHEMATICIAN?, we have a historical overview of math, including the problems the Catholic Church had for many, many years with Galileo’s observation that the Earth went around the sun. We have a historical overview of important mathematicians, engineers, etc., who’ve improved lives for the better by understanding how math works, then others finding ways later on to apply that esoteric knowledge for the overall betterment of mankind. And we have a profound philosophical discussion going on as to whether or not math is a human invention, designed by humans in order to describe what we observe of the universe, or whether math is instead something that was always there, just waiting for us to understand the universe well enough to describe it in a comprehensible manner.
All of this adds up to an A-plus book that should be on every writer’s desk — especially those of us in the science fiction and fantasy community — as it fully explains what’s going on with math in a way that’s engaging, interesting, sometimes humorous, and always compelling.
— reviewed by Barb
Cover image was unavailable for this review due to potential copyright concerns. Never mind.