Physics, Mathematics and Mathematical Physics

Eugene Wigner

Eugene Paul Wigner was a Hungarian physicist who received the Nobel Prize in Physics in 1963 for his contribution to the theory of the atomic nucleus and elementary particles. In a famous article published in 1960, Wigner said:

It is important to point out that the mathematical formulation of the physicist's often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena. (“The unreasonable effectiveness of mathematics in the natural sciences”. Communications on Pure and Applied Mathematics 13: 1-14).

Mathematical trivia and quotes from mathematicians

I have taken the following trivia and quotes about mathematics from the book A Passion for Mathematics, by Clifford A. Pickover, which I have mentioned in another post in this blog. These are the trivia:

• Let's see four amazing properties of number 5: a) It is the hypotenuse of the smallest Pythagorean triangle. b) There are five Platonic solids. c) It is the smallest automorphic number. Automorphic numbers are those whose square ends in the number. d) It is probably the only odd untouchable number. Untouchable numbers are those that are not equal to the sum of the proper divisors of any other number.

The world of tachyons and science fiction

In previous posts in this blog I have mentioned various procedures often used by the authors of science fiction novels to make interstellar travel almost as simple and brief as today's airplane trips to different points on Earth. One of these procedures consists of disintegrating the ship and reintegrating it into the universe of tachyons: hypothetical particles, compatible with the theory of relativity, that would always travel at speeds greater than the speed of light. Thus it would be possible (in principle) to travel very fast to the point we are interested to go to, reintegrate the ship into the world of tardions (in other words, into our world), and presto! We have traveled faster than the speed of light.

In fact, the authors of these novels (of which I am one) don’t usually go into detail about what the world of tachyons would be like. We simply assume three necessary conditions for interstellar travel to be possible:

The Game of Life and the multiverse

John Horton Conway

As I said in the previous post in this blog, The Game of Life is a cellular automaton devised by John Conway. Let's see how it works, in a little more detail:

This cellular automaton acts on a potentially infinite two-dimensional space, divided into square cells. In each cell there is a simple automaton, or if you want, a program with two states that we can call alive and dead, or 1 and 0. The program in each cell takes as input its own state and the states of its eight neighbors. If it is alive (i.e. in state 1) and two or three of its neighbors are alive, in the next instant it will still be alive. If it is dead (in state 0) and exactly three of its neighbors are alive, in the next instant it will become alive. In any other case, it will become dead. Let's look at a figure to make it clearer: