[Alamo-Girl]

Thank you for your post!

You are having problems with this because you are thinking of things like machine code, which is a very narrow instance of all possible control functions.

Not so fast! My protest was against such a hard-wired macro emulating a Universal Turing Machine and thus effecting Kolmogorov Complexity of the result!

In a sense, you have addressed my complaint with the discussion of infinite v finite in the above post. Nevertheless, I still have an issue - based on your post to gore3000 at 506:

In the url you provided, the Iota language which reduces to two instructions is expressed by this statement in R5RS Scheme:

(let iota ()
(if (eq? #\* (read-char)) ((iota)(iota))
(lambda (c) ((c (lambda (x) (lambda (y) (lambda (z) ((x z)(y z))))))
(lambda (x) (lambda (y) x))))))

Scheme is interpretive like Algol or Lisp. To me that indicates if Iota is actualized, it is hard-wired to perform a macro of even greater order than this, much like the example Doctor Stochastic gave.

This is obviously relevant to information theory, but looking at biological autonomous self-organizing complexity - the instruction set for determining Kolmogorov complexity in abiogenesis surely isn't at a macro or super-macro level.

IOW, for Rocha’s abiogenesis theory to work, RNA must toggle between states of autonomy for editing and not for gathering, much like a computer. At each autonomous toggle-step, the opportunity rises to increase or decrease complexity. Presumably where complexity increases, including syntax, conditionals, memory and recursives - entropy increases as well – or stays the same - but never decreases.

It seems to me that entropy, and not Kolmogorov Complexity, is the best tool to evaluate what might have happened in abiogenesis theory.

[gore3000]

This is obviously relevant to information theory, but looking at biological autonomous self-organizing complexity - the instruction set for determining Kolmogorov complexity in abiogenesis surely isn't at a macro or super-macro level.

Yes, it seems that the discussion is running in circles due to terms being used way too loosely. The simplest instruction in a computer whether the smallest or the most advanced is yes/no or rather 0/1. That is all that present computers understand. The 'instruction sets' of advanced computers are just a hardware implementation of what was previously in software. Nowadays the difficult math of multiplication and division and even higher math is often put on a chip (in fact some computers used to have entire programming languages on a chip).

However, that does not mean that it does not take a vast amount of instructions - the 0/1 kind to accomplish it a simple division. It is just that it is not as visible as it used to be. In biological systems, instead of base 2 (binary) we see the simplest instructions are in base 4 (a bit pair of DNA has 4 possible values). To implement rules in such a system one will need a lot of instructions in order to accomplish anything, certainly much more than the 5-6 rules which Wolfram speaks of.