Book report: Is God a Mathematician?, by Mario Livio
First off, this book has nothing to do with God. When scientists – and mathematicians – say “God”, they don’t mean God, they mean something like “nature” or “the universe” or “the laws of physics”. So, the title of this book actually means something like, “Why is the universe so mathematical?”
As Mario Livio points out, this question actually has to do with a couple of connected questions. You see, mathematicians split into two philosophical camps: some mathematicians believe that mathematics has a kind of independent existence of its own, and that we discover its pre-existing truths; others believe that mathematics is invented, something that we create as we go along, like the rules of a complex game. So, which is it? Is mathematics discovered or invented?
There’s a related question: why does mathematics describe the universe so well? When you took physics or chemistry classes in school, you probably had to learn a jillion formulas: namely, mathematics that describes the universe in astonishing and predictive detail. Indeed, many of the most significant advances in physics have involved corresponding advances in math: Newton’s mechanics with his invention or calculus, and Einstein’s general relativity and his use of tensors. As British physicist James Jean, said, “The universe appears to have been devised by a pure mathematician.” Einstein put it, “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” It’s certainly easy to believe that the universe is built on mathematics, and that this mathematics is out there waiting for us to discover it.
For a math geek like me, this was a fun book to read. Livio engagingly illuminates these questions by presenting the all-stars of math through the ages, including Pythagoras, Plato, Galileo, Newton, Riemann, and Godel. Along the way, he looks at topics in probability, statistics, logic, non-Euclidean geometry, and knot theory. Livio is an excellent writer. Not only is his exposition clear, but it’s also fun and appealing.
Besides the purely mathematical information, Livio also introduces several different angles on the subject. One has to do with the psychology, or neuropsychology, of mathematics. Just as it seems as if the rudiments of language are innately part of the human brain, it appears that math is built into us, too. We’re wired to do math. Admittedly, some are better at math than others, but that’s true with language also.
But why should this built-in ability be true? It makes sense if you take an evolutionary view. Math helps us to survive: how much food for how many people, how many days until harvest, how far to the water hole and how many dangerous animals on the way. This is all math, and we have evolved to think using math to figure out problems and survive. But, as a result, we tend to see the universe through math-colored glasses.
Livio, therefore, comes down on the side of the “inventeds”. We create mathematics as we need it, to help us describe, understand, and control the world. We also develop mathematics, independently of our needs, according to its internal rules and our own whimsy, something like music. The reason that math describes the universe so well, then, is precisely because math is the tool we use to describe it. Using a mathematical hammer, every problem looks like a mathematical nail.
This view matches my own experience. As much as I love mathematics, I don’t think that it describes the real world all that well. There are no real lines, planes, or circles in the real world. Sure, there are plenty of *approximate* lines, planes, and circles, but the difference between approximate and exact is, literally, infinite.
This also reminds me of a feeble physics joke (there is no other kind). An engineer, a statistician, and a physicist go to the racetrack, each with a different idea of how to pick the winning horse. The engineer intends to measure the limbs of all the horses to analyze how they’ll run. The statistician will research past performances. But the physicist sits down with a pad of paper and announces, “First, we approximate a horse by a sphere…” That’s how science uses mathematics: by simplifying the real world, and then applying math to that simplification.
What does all this mean? For one thing, perhaps it doesn’t make sense for mathematics to retain its almost transcendent status within human thought. Mathematics is not some pure, ethereal discipline: it’s a tool invented by people.
Mathematics is not necessarily universal, either. It is commonly conceived that, should we ever encounter intelligent aliens, they must inevitably understand and communicate with mathematics. This notion might well be naïve and earthropomorphic. This book offers the possibility of some ocean-based life form, with nothing to count, that might achieve intelligence without developing mathematics at all.
This doesn’t mean we scrap math, or course. Math is far too useful at giving us answers. Still, a little skepticism might be warranted. Skeptics rarely challenge the sacrosanct precincts of mathematics. But perhaps we must admit that we look at the universe through human eyes, and must inevitably see our own reflection in what we find. Regardless of whether God may be mathematical, we certainly are. But we’re so much more besides. It may well be that true comprehension of the universe involves more than just a formula or two.
Recommended, but only for other math geeks.
First off, this book has nothing to do with God. When scientists – and mathematicians – say “God”, they don’t mean God, they mean something like “nature” or “the universe” or “the laws of physics”. So, the title of this book actually means something like, “Why is the universe so mathematical?”
As Mario Livio points out, this question actually has to do with a couple of connected questions. You see, mathematicians split into two philosophical camps: some mathematicians believe that mathematics has a kind of independent existence of its own, and that we discover its pre-existing truths; others believe that mathematics is invented, something that we create as we go along, like the rules of a complex game. So, which is it? Is mathematics discovered or invented?
There’s a related question: why does mathematics describe the universe so well? When you took physics or chemistry classes in school, you probably had to learn a jillion formulas: namely, mathematics that describes the universe in astonishing and predictive detail. Indeed, many of the most significant advances in physics have involved corresponding advances in math: Newton’s mechanics with his invention or calculus, and Einstein’s general relativity and his use of tensors. As British physicist James Jean, said, “The universe appears to have been devised by a pure mathematician.” Einstein put it, “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” It’s certainly easy to believe that the universe is built on mathematics, and that this mathematics is out there waiting for us to discover it.
For a math geek like me, this was a fun book to read. Livio engagingly illuminates these questions by presenting the all-stars of math through the ages, including Pythagoras, Plato, Galileo, Newton, Riemann, and Godel. Along the way, he looks at topics in probability, statistics, logic, non-Euclidean geometry, and knot theory. Livio is an excellent writer. Not only is his exposition clear, but it’s also fun and appealing.
Besides the purely mathematical information, Livio also introduces several different angles on the subject. One has to do with the psychology, or neuropsychology, of mathematics. Just as it seems as if the rudiments of language are innately part of the human brain, it appears that math is built into us, too. We’re wired to do math. Admittedly, some are better at math than others, but that’s true with language also.
But why should this built-in ability be true? It makes sense if you take an evolutionary view. Math helps us to survive: how much food for how many people, how many days until harvest, how far to the water hole and how many dangerous animals on the way. This is all math, and we have evolved to think using math to figure out problems and survive. But, as a result, we tend to see the universe through math-colored glasses.
Livio, therefore, comes down on the side of the “inventeds”. We create mathematics as we need it, to help us describe, understand, and control the world. We also develop mathematics, independently of our needs, according to its internal rules and our own whimsy, something like music. The reason that math describes the universe so well, then, is precisely because math is the tool we use to describe it. Using a mathematical hammer, every problem looks like a mathematical nail.
This view matches my own experience. As much as I love mathematics, I don’t think that it describes the real world all that well. There are no real lines, planes, or circles in the real world. Sure, there are plenty of *approximate* lines, planes, and circles, but the difference between approximate and exact is, literally, infinite.
This also reminds me of a feeble physics joke (there is no other kind). An engineer, a statistician, and a physicist go to the racetrack, each with a different idea of how to pick the winning horse. The engineer intends to measure the limbs of all the horses to analyze how they’ll run. The statistician will research past performances. But the physicist sits down with a pad of paper and announces, “First, we approximate a horse by a sphere…” That’s how science uses mathematics: by simplifying the real world, and then applying math to that simplification.
What does all this mean? For one thing, perhaps it doesn’t make sense for mathematics to retain its almost transcendent status within human thought. Mathematics is not some pure, ethereal discipline: it’s a tool invented by people.
Mathematics is not necessarily universal, either. It is commonly conceived that, should we ever encounter intelligent aliens, they must inevitably understand and communicate with mathematics. This notion might well be naïve and earthropomorphic. This book offers the possibility of some ocean-based life form, with nothing to count, that might achieve intelligence without developing mathematics at all.
This doesn’t mean we scrap math, or course. Math is far too useful at giving us answers. Still, a little skepticism might be warranted. Skeptics rarely challenge the sacrosanct precincts of mathematics. But perhaps we must admit that we look at the universe through human eyes, and must inevitably see our own reflection in what we find. Regardless of whether God may be mathematical, we certainly are. But we’re so much more besides. It may well be that true comprehension of the universe involves more than just a formula or two.
Recommended, but only for other math geeks.
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