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?
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?
Pseudo-random bitmap |
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. (Heisenberg, Gödel y la cuestión de la finalidad en la ciencia, Simposio Internacional Ciencia y Religión en el siglo XXI: ¿diálogo o confrontación? 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.
In conclusion:
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.
Manuel Alfonseca
No comments:
Post a Comment