Quantum Conscience or Conscient Quantum?

The second hard problem of modern science is the origin of consciousness or the problem of free will. This post focuses on the relation of this problem with quantum mechanics. As an example of the difficulty of the matter, I begin by including two famous quotes from renowned scientists:

·         J. B. S. Haldane, Possible Worlds (1927): The universe [of quantum theory] is, not only queerer than we suppose, but queerer than we can suppose.

·         James Jeans, The Mysterious Universe (1930): The universe begins to look more like a great thought than a great machine.

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).

Quantum paradoxes

The Copenhagen interpretation of quantum mechanics causes paradoxes, at least apparent, when one tries to apply it to the macroscopic world. These two are the best known:

• Schrödinger’s cat paradox. A live cat, a radioactive atom, a vial filled with hydrocyanic acid, and a device that breaks the vial if the radioactive atom decays are placed in an opaque box. If the vial is broken, the cat dies. If it isn’t broken, the cat lives. While the box is closed, the Copenhagen interpretation of quantum mechanics tells us that the radioactive atom is in a superposition of states, decayed and intact, until someone checks it, at which point the superposition of states collapses into one of them. But then, while the box is closed, the cat must be in a superposition of states: alive and dead. Can a cat be alive and dead at the same time? Intuition denies it, but the Copenhagen interpretation of quantum mechanics asserts it. As its name indicates, this paradox was proposed in 1935 by Erwin Schrödinger, one of the fathers of quantum mechanics.

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.