Some non-conventional ideas about algorithmic complexity

In this paper the author presents some non-conventional thoughts on the complexity of the Universe and the algorithmic reproducibility of the human brain, essentially sparked off by the notion of algorithmic complexity. We must warn that though they evoke suggestive scenarios, they are still quite speculative. 1 Introductory remarks The algorithmic (program-size, or Kolmogorov) complexity of a binary string s is defined as the size in bits of the smallest computer program able to generate it: H(s) ≡ min U(p)=s |p| where p is a program string used by a universal computer U to produce the sequence s (Chaitin [1,2]). Let us now consider the following algorithm of size ⌊log2 N⌋+ k + 1 (see also the Appendix). It lists in order of their size all strings of length less than or equal to N bits (there are 2 − 2 of them 1 ), writing them one after the other on a computer file (or on a sheet of paper). The output should look like 0 1 00 01 10 11 000 001 010 011 100 101 110 111 ... 1 That is, we sum up the number of all possible strings of one bit (2), that of all possible strings of two bits (22), and so on up to N bits: