Is God A Mathematician?

Title: Is God A Mathematician?

Author: Mario Livio

Publisher: Simon & Schuster 2010 (First published: 2009)

ISBN: 9780743294065

Pages: 308

Science is an attempt to read God’s mind which is evident in the physical reality as the rules and principles which hold the world together. Livio’s book is an elegant attempt to tell the epic story of man’s quest to peer into nature itself and to grasp its fundamental principles with the help of his greatest intellectual tool – mathematics. Its extraordinary ability to describe the world has been a source of wonder to philosophists ever. This feat comes in two varieties. In one category named active mode, scientists deduce mathematical laws applicable to an event after carefully observing it, while in the other, passive mode, mathematical functions which were formulated long ago in totally unrelated circumstances suddenly find application to explain new discoveries in science. Judging from the closeness with which mathematical predictions approach reality, we are tempted to think that God is a mathematician. So, the answer to the rhetorical question in the title is in the affirmative and the 250-odd pages explain why it is so. It may be mentioned in passing that another book titled ‘The Loom of God’ by Clifford Pickover (reviewed earlier in this blog) also follows a similar theme. Mario Livio is a noted author who is also an astrophysicist and the head of the Office of Public Outreach at the Hubble Telescope Science Institute. This is the 314th book review in this blog and it is a happy coincidence that a book related mathematics comes out as number 314 (remember pi is approximately 3.14?).

A noteworthy feature of mathematics is its strikingly effective provenance to explain natural features and phenomena. Why should it be so? Mathematics is anyway a product of human contemplation and analysis. If this fruit of human intelligence so faithfully displays an uncanny ability to explain and predict nature, it is no wonder that a group of philosophers – a large one indeed – postulated the existence of mathematics in an idealized Platonic world, whose reflections on the physical world constituted our everyday adventures. This raises the pertinent question whether mathematics is discovered or invented. The niceties of such philosophical speculation need not detain the readers, but Livio presents a deeply speculative question in an easy to digest way. The ideas of Platonic world and discovery are compatible, in the sense that the numbers and shapes already existed in a perfect, imaginary world until man stumbled upon them in a spark of intellectual brilliance. Just like America existed before it was ‘discovered’ by Columbus, or Vikings, or even by that Turkish guy – who provided some much needed comic relief in international discourse a few months ago – mathematics existed right from the universe’s moment of being. But quite a few philosophers, and such humble beings like myself, differs from this point of view. According to this theory, mathematics is an abstract concept developed by man with the help of his extraordinary ability to detect patterns in nature. The book provides ample room for general readers to get familiar with this dichotomy that surrounds mathematics’ existence.

History of science occupies a major portion of the book, but presented in an admirable way that commands attention from readers. Freely interspersed with witty anecdotes and informative quotes from authors present and past, the text stands tall as a testimony to the immense amount of research that had gone in to the publication of it. Livio identifies Archimedes, Newton and Gauss as the three greatest mathematicians of all time, but does not restrict his pen to these three. Would any discussion on the development of science through the Renaissance era be complete without a solid reference to that mathematics professor from Padua, Italy – Galileo Galilei, no less? Galileo’s trial and the stifling overlordship of blind faith over reason is a topic you would find described umpteen number of times in any book that deals with the history of science through the turbulent 17^th century. Livio’s description would feel to be delightfully elegant to new readers. Old readers also would find the narration to be very congenial. This book extends the story to other mathematicians, including Descartes, and the Bernoullis. The sibling rivalry between Jakob and his brother Johann Bernoulli is brought to light with a quote from a letter the younger Johann wrote to his friend in which he exults at defeating his elder brother in the solution to a vexing problem. Mathematicians are also human, after all!

Even though Livio considers Gauss to be one of the three greatest ever mathematicians, nothing much is said about him apart from casual references in the context of non-Euclidean geometry. But this shortfall is more than leveled by the extensive discussion on the new developments in mathematics that took place during the last two centuries. The new sprouts are so revolutionary as to merit the epithet that man had broken free from the shackles of classical learning and began to explore nature in the light of a new creative spirit. A mind boggling array of discoveries had taken place in this period, but ordinary readers find it difficult to comprehend the practical purpose of many of them. Non-Euclidean geometry is however very helpful in estimating the shortest possible distance between any two points on a spherical surface. Aircrafts usually follow these shortest routes. But such hyperbolic geometry is extended to such extreme lengths that no apparent use is evident – yet! At around this time, logic was also linked to mathematics so as to strengthen the mutual foundations. Boolean algebra originated as the systematic representation of logic as ordinary algebra was to scientific concepts. Enhancement of geometry to many more dimensions than three enabled it to stand as the structural framework of advanced theories on the origins of the cosmos in the form of string theory, which postulates ten dimensions. This also shows the effectiveness of the discipline as a faithful representative of nature. But the long chapters on logic and discussions on its consistency are hard to enjoy for average readers.

A frequent source of controversy among mathematicians is the question whether its concepts should provide practical applications for human use. Such a notion itself is anathema to many practitioners who bask at the sheer glory of pure mathematics. Archimedes and G H Hardy were two mathematicians of this school. What would have been their impression when they saw their concepts eagerly accepted by the scholars and put to uses which provide immense value to their own societies? Archimedes is credited with the invention of a screw pump, levers of varying complexities, optical instruments and defensive apparatus, while much progress in cryptography is attributed to Hardy. There were mathematicians in the other camp as well, like Gerolamo Cardano, who wouldn’t conceptualize the definition of more dimensions than three because no practical utility was existent at that time, nor conceived to be feasible in the near future.

The book is splendidly written, having a good structure in presenting ideas. It is also graced with a good number of anecdotes, pictures and illustrations. There is an immense collection of notes mentioned in the main text and a sizable bibliography is listed. A nice and comprehensive index completes the attractive side of the book. On the negative part, about a quarter of the text starting from logic and its relations to mathematics is highly abstract, making life difficult for the readers. Fortunately, no harm is done even if you were to simply bypass those chapters and dive straight to the last one.

The book is highly recommended.

Rating: 3 Star