The Magic of Numbers

This book is a fascinating journey into the history of science and the world of mathematics and numbers and their connection with philosophical thinking. The fundamental argument is whether the nature of existence can be explained by deductive reasoning, as Pythagoras and Plato believed, or via experimentation, and also whether mathematics is an invention or a discovery.

The review begins with Pythagoras and Plato who recognized mathematics as an expression of the divine principles of creation and order. Subsequently this view became corrupted through the dogmatization of Christianity. Then a major shift occurred through Newton’s work to understand nature via experimentation, and mathematics was relegated to backing it up. This change is seen as the cause of the industrial revolution. The next major turn about happened as a consequence of quantum physics which necessitated mathematics to dominate again not only because mathematics can explain complex issues in a comparatively simple and concise manner but also because experimental verification has become extremely difficult if not impossible. However, although mathematics has assumed the key role again, the author points out that it is now devoid of spiritual meaning.

The intriguing aspect is though that many aspects of the sub-atomic world were predicted by spiritual sources, and multidimensionality and multiple universes were in the spiritual vocabulary long before science stumbled upon their existence. Unfortunately, the author gives no credence to this. On the contrary he is often sarcastic and at best displays an amused tolerance as exemplified in his belief that ‘everything is number’ is possibly the most mischievous misreading of nature in the history of human errors. He also believes that Pythagoras’ and Plato’s ideas were directly responsible for retarding the start of modern science.

Nevertheless, the author presented a brilliant analysis of core problems of existence, and although it is one sided in some ways, we can easily fill in the gaps ourselves and allow spiritual and scientific thinking to support each other (this may horrify the author though).

After multiple cancelled and or “lost” orders, I finally got a copy of this fantastic book! An excellent walk through the history of mathematics, philosophy and religion.

E.T. Bell was on a roll when wrote his histories of mathematics. Men of Mathematics, Development of Mathematics, and Magic of Numbers all came around the same time. He must have used the same notes! Men of Mathematics and the Development of Mathematics are contrasts, but mathematicians will even say his Development of Mathematics is not technical enough. But Men of Mathematics has a little more relation to ‘Magic of Numbers.’

Both ‘Men of Mathematics’, and ‘Magic of Numbers’ relate past mathematicians and mathematics to modern ideas. ‘Men of Mathematics’ is more about as many mathematicians as E.T. Bell wished to stuff in one volume(he missed plenty; David Hilbert, Sophus Lie, Frobenius, Carmille Jordan to name a few), but he mentions who Dedekins is a modern Eudoxus, and Kronecker is a kind of Zeno(i’m thinking more like Brouner). ‘Magic of Numbers’ relates ancient philosophies of mathematics with modern, but he does more.

E.T. Bell uses Plato and Aristotle writings almost like Pauline epistles into the birth of Christianity. He’s trying to see what he can see in terms of the birth of mathematics, and the philosophy of mathematics, through the writings of Plato and Aristotle. He gives biographies of Thales, Anaxagoras, Pythagoras, and makes educated guesses on various issues with their lives. E.T. Bell gives some details on these guys you might not find elsewhere, but in some cases like Anaxagoras and Empedicles, he misses a few things; he even says he chooses to not get into some details; I think he should have. For instance, the fact that Anaxagoras had some logical reasons for thinking of evolution of life, and Empediclies discovered the idea of air. See Carl Sagan’s account in chapter/episode 7 of his Cosmos(or, you could read “Sleepwalkers” by Arthur Koestler, which is where Carl Sagan gets his ideas from).

He mentions the idea that Christianity is midrashing the old testament; this idea is considered a new exciting idea in todays New Testament comparative religion researchers – see The Jesus Puzzle by Earl Doherty for a quick introduction.

I’d like to mention that James Frazer in his “Golden Bough” finds much interesting relation between magic and religion. In it, he indirectly uncovers the idea of sungods though his gods of the seasons. He uncovers much in terms of the idea of the evolution of mankind’s idea of figuring out how the universe works. At one time, magic and religion were the scientific ideas. People have argued that this is demeaning to religions and cultures based on them. In science, disproving an idea is o.k. but we’re not allowed to do so in the field of religion. But, the religious are allowed to disprove one another and argue against science. Kind of interesting. I mention this because this book also tries to understand the evolution of mathematical thought form pre-mathematical thought, through the mathematical perspective. Basically, both mythology and mathematics are analogies; but, one is constructive, and the other is not. I find in my explorations of this relation suggested by Jacob Bronowski for instance in his “Science and Human Values”, that mathematics is a clean break despite this common trait(analogy). The Golden bough doesn’t note this connection; E.T. Bell’s “Magic of Numbers” does. They are complementary to those who want to understand rationally the evolution of mankinds explorations from ignorance to being able to figure out the universe. And, as E.T. Bell shows in his “Magic of Numbers”, the mythicists don’t believe in observation/experimental, or even logical proof confirmation of their ideas. They’re effort is to hide their ideas far away from being able to figure anything out. There’s clearly a very large social problem here.