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?
In others words:
Would they be able to distinguish between true chance and pseudo-chance in the evolutionary processes that led to their birth?
Would they be able to figure out that what appears to be chance in their evolution is really an algorithm designed by someone?
In 1975 the mathematician Gregory Chaitin proved an incompleteness theorem in the same class as the Gödel and Turing theorems. Gödel showed that, under certain circumstances, the axiomatic systems that help us to understand the working of mathematics, if they are consistent (that is, if they do not include contradictions) must be incomplete. In short: based on those axioms, there are things that cannot be proved. On the other hand, Chaitin’s theorem says, in essence, the following:
The randomness of integers is undecidable. Although randomness can be defined accurately and can even be measured, in general it cannot be proved that a set of numbers is random. This sets a new limit to what is possible in mathematics. (Randomness and Mathematical Proof, Scientific American 232, No. 5, mayo 1975, pp. 47-52).
Chaitin’s theorem has unexpected consequences. For example, it forces us to answer in the negative to the question asked in several ways at the beginning of this post:
Our hypothetical intelligent beings would not be able to distinguish between chance and pseudo-chance (that is, design through an algorithm) in their own evolution.
In 2011, Fernando Sols pointed out that Chaitin’s theorem shows that it is also impossible to distinguish between chance and design in the evolution of life. (, Simposio Internacional Fundación Ramón Areces, noviembre 2011).
Let us go back to the three options in the previous post:
- The scientific theory of evolution, which is strongly contrasted with data from other sciences, such as embryology, comparative anatomy, paleontology, biogeography, or molecular biology (DNA analysis).
- The assertion that evolution is a consequence of pure chance. Chaitin’s theorem shows that this statement cannot be proved by means of science, so this assertion is not scientific, but philosophical, although its supporters claim –falsely– that it is scientific.
- The assertion that evolution is an example of design. Chaitin’s theorem shows that this statement cannot be proved through science, so it is not scientific, but philosophical. When the supporters of intelligent design say that it is a scientific theory, they are surely wrong.
Science cannot differentiate between chance and pseudo-chance, between chance and design. Those who affirm one thing or the other are doing philosophy, not science.
I have tried to analyze this problem elsewhere in a little more detail. I have proposed the name providential evolution for the (philosophical) theory that holds that God directs and controls the evolution of the world and of life, but the theorem of Chaitin makes it impossible to prove it scientifically. In other words, what for us is chance, may be pseudo-random for God.
Can this be proved? We have seen that it can not, in the field of science. Are there any inklings? I think artificial life experiments provide us with quite a strong one.