# Is God a Mathematician?

## Mario Livio

- 320 pagine
- English
- ePUB (disponibile sull'app)
- Disponibile su iOS e Android

# Is God a Mathematician?

## Mario Livio

## Informazioni sul libro

Bestselling author and astrophysicist Mario Livio examines the lives and theories of history's greatest mathematicians to ask howâif mathematics is an abstract construction of the human mindâit can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about "the unreasonable effectiveness of mathematics" in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than thatâmathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is "a product of human thought that is independent of experience, " how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.

## Domande frequenti

## Informazioni

# CHAPTER 1 A MYSTERY

*independent of experience*[the emphasis is mine], fits so excellently the objects of physical reality?â

*Leviathan,*Hobbesâs impressive exposition of what he regarded as the foundation of society and government, he singled out geometry as the paradigm of rational argument:

Seeing then that truth consisteth in the right ordering of names in our affirmations, a man that seeketh precise truth had need to remember what every name he uses stands for, and to place it accordingly; or else he will find himself entangled in words, as a bird in lime twigs; the more he struggles, the more belimed. And therefore in geometry (which is the only science that it hath pleased God hitherto to bestow on mankind), men begin at settling the significations of their words; which settling of significations, they call definitions, and place them in the beginning of their reckoning.

*world of our conscious perceptions*, the

*physical world,*and the

*Platonic world of mathematical forms.*The first world is the home of all of our mental imagesâhow we perceive the faces of our children, how we enjoy a breathtaking sunset, or how we react to the horrifying images of war. This is also the world that contains love, jealousy, and prejudices, as well as our perception of music, of the smells of food, and of fear. The second world is the one we normally refer to as physical reality. Real flowers, aspirin tablets, white clouds, and jet airplanes reside in this world, as do galaxies, planets, atoms, baboon hearts, and human brains. The Platonic world of mathematical forms, which to Penrose has an actual reality comparable to that of the physical and the mental worlds, is the motherland of mathematics. This is where you will find the natural numbers 1, 2, 3, 4, âŚ , all the shapes and theorems of Euclidean geometry, Newtonâs laws of motion, string theory, catastrophe theory, and mathematical models of stock market behavior. And now, Penrose observes, come the three mysteries. First, the world of physical reality seems to obey laws that actually reside in the world of mathematical forms. This was the puzzle that left Einstein perplexed. Physics Nobel laureate Eugene Wigner (1902â95) was equally dumbfounded:

The miracle of the appropriateness of the language of mathematics to the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

*mind*literally born out of

*matter*? Would we ever be able to formulate a theory of the workings of consciousness that would be as coherent and as convincing as, say, our current theory of electromagnetism? Finally, the circle is mysteriously closed. Those perceiving minds were miraculously able to gain access to the mathematical world by discovering or creating and articulating a treasury of abstract mathematical forms and concepts.

*one,*the true nature of which we do not even glimpse at present.â This is a much more humble admission than the response of the schoolmaster in the play

*Forty Years On*(written by the English author Alan Bennett) to a somewhat similar question:

Foster: Iâm still a bit hazy about the Trinity, sir.Schoolmaster: Three in one, one in three, perfectly straightforward. Any doubts about that see your maths master.

*all*the electric and magnetic phenomena that were known in the 1860s, he did so by means of just four mathematical equations. Think about this for a moment. The explanation of a collection of experimental results in electromagnetism and light, which had previously taken volumes to describe, was reduced to four succinct equations. Einsteinâs general relativity is even more astoundingâit is a perfect example of an extraordinarily precise, self-consistent mathematical theory of something as fundamental as the structure of space and time.

*number theory*âthe study of the properties of the natural numbersâfound unexpected applications. In 1973, the British mathematician Clifford Cocks used the theory of numbers to create a breakthrough in cryptographyâthe development of codes. Cocksâs discovery made another statement by Hardy obsolete. In his famous book

*A Mathematicianâs Apology,*published in 1940, Hardy pronounced: âNo one has yet discovered any war-like purpose to be served by the theory of numbers.â Clearly, Hardy was yet again in error. Codes have been absolutely essential for military communications. So even Hardy, one of the most vocal critics of applied mathematics, was âdraggedâ (probably kicking and screaming, if he had been alive) into producing useful mathematical theories.

*first*, insisting that the laws of nature and indeed the basic building blocks of matter should follow certain patterns, and they deduced the general laws from these requirements. How does nature know to obey these abstract mathematical symmetries?

*knot theory*âthe mathematical study of knots. A mathematical knot resembles an ordinary knot in a string, with the stringâs ends spliced together. That is, a mathematical knot is a closed curve with no loose ends. Oddly, the main impetus for the development of mathematical knot theory came from an incorrect model for the atom that was developed in the nineteenth century. Once that model was abandonedâonly two decades after its conceptionâknot theory continued to evolve as a relatively obscure branch of pure mathematics. Amazingly, this abstract endeavor suddenly found extensive modern applications in topics ranging from the molecular structure of DNA to string theoryâthe attempt to unify the subatomic world with gravity. I shall return to this remarkable tale in chapter 8, because its circular history is perhaps the best demonstration of how branches of mathematics can emerge from attempts to explain physical reality, then how they wander into the abstract realm of mathematics, only to eventually return unexpectedly to their ancestral origins.

## Discovered or Invented?

*Alice in Wonderland,*âcuriouser and curiouserâ? After all, whatever the cosmos may be doing, business and finance are definitely worlds created by the human mind.

*traveling salesman problem*, since the 1920s. Basically, if a salesperson or a politician on the campaign trail needs to travel in the most economical way to a given number of cities, and the cost of travel between each pair of cities is known, then the traveler must somehow figure out the cheapest way of visiting all the cities and returning to his or her starting point. The traveling salesman problem was solved for 49 cities in the United States in 1954. By 2004, it was solved for 24,978 towns in Sweden. In other words, the electronics industry, companies routing trucks for parcel pickups, and even Japanese manufacturers of pinball-like pachinko machines (which have to hammer thousands of nails) have to rely on mathematics for something as simple as drilling, scheduling, or the physical design of computers.

*Journal of Mathematical Sociology*(which in 2006 was in its thirtieth volume) that is oriented toward a mathematical understanding of complex social structures, organizations, and informal groups. The journal articles address topics ranging from a mathematical model for predicting public opinion to one predicting interaction in social groups.

*discovering*mathematical verities, just as astronomers discover previously unknown galaxies? Or, is mathemat...