My question is what does distribution of canonical programs look like. Would it be anything like primes? As there should be fewer longer programs that are canonical, but still there are longer series that could be described. That got me on to thinking about the randomness of primes. How random are the digits of primes? I shall have a fiddle around and try and work out the randomness of primes vs non-primes.
This is a bit moot as working out whether a program is canonical is I believe equivalent to the halting problem.
Which brings me onto the next topic. Assuming you have a program X that is canonical that works out whether a program halts or not up to programs of the length of X.
Any program that attempts to embed X in itself would be longer than X and so not create a paradox with regards to halting.
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