[tortoise]

I can't even see this as a single instruction in interpretive language code.

Universal computers have a "finite control function", that defines the nature and granularity of manipulations of the state. Depending on the type of machine, the execution of a single "instruction" (which is an abstract rather than literal construct) can have either very simple or very complex consequences to the state. The folding of a protein is an extremely complex behavior, but it can be triggered by the execution of a single "instruction" within that computational system. 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.

One of the mental hazards of computational theory is that most people view computers as being solely like the kinds of computers we build with silicon. They way we build computers in practicing is a consequence of history and practical engineering concerns, and doesn't even scratch the surface of the entire space of things that constitute "universal computers". This is a case where limited experience leads to conceptual prejudices that aren't justified.

[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.