Chance, design and artificial life

In previous posts in this blog I have mentioned my experiments on artificial life: the simulation in a computer of processes similar to those that take place in living beings. Artificial life should not be confused with synthetic life: construction of artificial living beings in the laboratory.

One of the most used tools in artificial life (and in other related fields) are genetic algorithms, which simulate biological evolution within the computer, and make it act on the entities that are the subjects of the research. In these experiments, a mixture of chance and necessity (the title of Monod’s book mentioned in the previous post) is used. Chance is usually applied with a pseudo-random number generator that modifies the operation of the rest of the algorithm, which represents necessity.

Three questions without scientific answers

Although I have spoken about some of these things in other posts, I’ll put together here three questions that, for now, don’t have a scientific answer, and perhaps never will.

• Did the universe begin to exist at the Big Bang, or was there something before? This controversy is much older than many think. Three quarters of a millennium ago, Thomas Aquinas wrote this in his Summa Theologiae (Part I, Question 46):

It cannot be proven by demonstration that the world has not always existed.

In other words, according to Aquinas, the question of creatio originans (that the world had a beginning) cannot be solved by human reason. It should be noted, however, that creatio ex nihilo (the fact that the world was created) would be within the reach of reason. In other words: reason would let us reach the conclusion that the universe was created, but we cannot prove that it had a beginning.

The limits of mathematics

Kurt Gödel

In the last decades of the nineteenth century, Friedrich Ludwig Gottlob Frege, a professor in the university of Vienna, undertook an ambitious goal: formalizing the arithmetic in a set of axioms and deduction rules, in such a way that every true theorem would be deductible from the axioms by a finite number of applications of the deduction rules. The result was a monumental book, Grundgesetze der Arithmetike (1893-1903), which introduced, among other things, a basic formalization of set theory and a cumbersome notation, quickly replaced by Peano’s, which we are using now.

Unfortunately for Frege, when the second volume of his book was about to be published, he received a letter from Bertrand Russell, proving that his formulation of set theory entails an inconsistency. In Frege’s set theory, some sets are not member of themselves (as the set of all integers, which is not an integer), while other sets are members of themselves (as the set of all infinite sets, which is an infinite set). Russell then defined this set: the set of all sets that are not members of themselves. It is easy to see that this set leads to a paradox: if it is a member of itself, it cannot be a member of itself, and vice versa. Russell’s paradox wreaked havoc with Frege’s work, who had to add a hasty appendix to his book and then abandoned his research on the fundamentals of mathematics.

Chance or pseudo-chance?

Gregory Chaitin

In computer programming, certain algorithms (called pseudo-random) generate series of numbers that meet the conditions required by statistics to decide on the randomness of a sequence. These algorithms are used frequently to simulate chance.

However, these algorithms have been designed by someone (the programmer who invented them). In fact, they are not usually random, in the sense that, if they are executed several times in a row, they always give the same results.

We have a similar case with the digits of p. Ten trillion digits of p are currently known, and their number is constantly growing. So far, the digits of p have met all statistical randomization tests. However, it is evident that they cannot be truly random, that they are designed. There are simple algorithms that generate them one after another, in the correct order.

Let us go back to the mental experiment of the previous post in this blog. If intelligent beings were to emerge in an artificial life experiment,

Would these beings be able to distinguish between chance and design as the origin of their own existence?