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.

Is homo economicus rational?

Nicolás Bernoulli

In 1713, Nicolás Bernoulli formulated the St. Petersburg paradox, which can be summarized as follows:

Let us consider the following game: a coin is tossed. If it comes up heads, you receive $2. If it comes up tails, it is tossed again. If it comes up heads, you receive $4. If it comes up tails, it is tossed again. And so on. With each toss, the prize is multiplied by 2. How much would you be willing to pay to participate in the game?

The probability of winning $2 is 0.5; the probability of winning $4 is 0.25; the probability of winning $2^k is 2^-k. The expected value is obtained by multiplying each value by its probability and adding them all together. So the expected value of the profit that could be obtained by playing that game is:

Information and intelligence

Von Neumann’s architecture, which applies to almost every computer ever built during the history of computing, builds computers from two clearly separate parts: the processing unit, where instructions are executed, and the memory, where data is stored. Consequently, almost all the programs we run on our computers are divided into two different sections: the algorithm (the executable instructions) and the data that provides the information needed by the algorithm (its input).

Such a clear separation reminds the difference between the two concepts in the title of this post:

Cellular automata and the game of life

John Horton Conway

On April 11, the mathematician John Horton Conway, age 82, died of the coronavirus disease (COVID-19). Conway became famous during the 1970s for inventing a very special cellular automaton, the Game of Life, which turned out to possess peculiar properties.

Contrary to what is done with most scientific discoveries, Conway did not publish his invention of the Game of Life in a typical scientific journal. It was first published in the Mathematical Games section of the Scientific American magazine, written by Martin Gardner. The article, titled The Fantastic Combinations of John Conway's New Solitaire Game 'Life', appeared in the October 1970 issue.