[Alamo-Girl]

Thank you so much for the post and for all the information and leads!

Since my hypothesis is algorithm at inception is proof of intelligent design - I’m very much interested in self-organizing complexity. In that regard, Rocha’s work is especially engaging because he suggests how self organizing systems might evolve the symbols necessary for syntactic autonomy!

I've been off researching since reading your post, trying to figure this out myself - but it appears I will need your help:

Random objects may be highly structured, in fact more so than non-random ones. There's no contradiction between Chaitin and Wolfram here.

Mathematically speaking, “structure” doesn’t comport with what I understand to be the definition of algorithmic randomness Randomness and Complexity in Pure Mathematics – Chaitin - i.e. algorithmically irreducible information.

I also was under the impression that the consequence of initial random states was still at issue with Cellular Automata. Perhaps I misread. Twenty Problems in the Theory of Cellular Automata - i.e. problem 10, What is the correspondence between cellular automata and stochastic systems?

Cellular automata satisfy deterministic rules. But their initial states can have a random form. And the patterns they generate can have many of the properties of statistical randomness. As a consequence, the behaviour of cellular automata may have a close correspondence with the behaviour of systems usually described by basic rules that involve noise or probabilities. So for example domain walls in cellular automata execute essentially random walks, even though the evolution of the cellular automaton as a whole is entirely deterministic. Similarly, one can construct a cellular automaton that mimics say an Ising spin system with a fixed total energy (microcanonical ensemble) [32]. Apparently random behaviour occurs as a consequence of randomly-chosen initial conditions, just as in many systems governed by the deterministic laws of classical physics.

I would appreciate any help you can give me in understanding this.

For lurkers following our discussion: Toward A Mathematical Definition Of "Life" - Chaitin (ResearchIndex)

[Alamo-Girl]

It was mighty late when I posted last night and it didn't occur to me that, for the lurkers following this discussion, I was doing a terrible job of communicating - that I ought to explain the terminology and relate it to the examples that you used. Sorry about that! In my layspeak, for lurkers following the discussion:

When Chaitin speaks of randomness he is saying that the string of numbers we are looking at cannot be created by a set of instructions (algorithm) smaller than the numbers themselves. If the string of numbers can arise from an algorithm, it would be algorithmically reducible information.

For instance, if you see a string of 300 numbers that look like "12312312312313123123123123..." you would say that is algorithmically reducible because it can be created in three steps:

For N=1 to 100
X$=X$+"123"
Next N

Various researchers believe the genetic code, which looks something like a string of a limited number of characters, can also be reduced in this fashion.

In the "airplane parts laying around v. assembled aircraft" illustration, the assembly manual is like an algorithm for building the aircraft.

Although I don't wish to venture whether the aircraft is algorithmically reducible under Chaitin, if we were talking about genetics instead of airplanes, that assembly manual would roughly parallel the subject of evolutionary computing. That is a very interesting subject to me, but not the one that has caused my ears to perk.

If the airplane came alive - was self-organizing and reproducing itself with ever increasing diversity and sometimes, complexity - we would be looking for the algorithm whereby it accomplishes it. That's the part that interests me, because (thanks to Nebullis) I now know that the genetics involved have the characteristics of information theory.

That is to say, it works like a software program, remembering the past (database), being able to decide friend or foe (conditionals/symbols) as well as actually doing the deed (process.) In other words, it can be reduced to algorithm.

Wolfram has shown that complex, seemingly random, structures can arise from very simple algorithms. We are trying to sort out the distinction between complex, random, and structure (and perhaps more before we are done.)