Tuesday, December 21, 2010

More on “Self” Organisation

I was honoured to have received a comment from Richard Johns on my blog post about his "Self Organization" paper . I have reproduced Richard’s comment and my reply below. I have also added some further remarks:

Hi Timothy,

Thanks for your detailed treatment of my paper -- actually the best I have seen.

The objection you raise is a good one, although I think it can be answered. (Jeffrey Shallit made the same point in an email to me.)

There are simple (i.e. short) algorithms that can generate irregular strings, as I define them. You mention pseudo-random sequences, and I have previously thought about the digits of Pi. Hence these things are algorithmically simple, despite their irregularity.

As I pointed out to Shallit, I claim that irregular objects are *dynamically* complex, not *algorithmically* complex. And, while it seems certain that dynamically simple objects are algorithmically simple (since dynamical systems can be emulated by computers) the converse is far less obvious. In other words, while the digits of Pi can be generated by a short program, it might not be produceable easily within a dynamical system, from a random initial state.

If a converse theorem does hold, however (i.e. algorithmically simple objects are dynamically simple) then my arguments have gone wrong somewhere. But even in that case, self-organisation theories of evolution will be in a difficult position. For they will then be committed to the claim that living organisms are algorithmically (and dynamically) simple. In other words, living organisms are like Pi, merely *appearing* to be complex, while in fact being generated by a very short program. (Vastly shorter than their genomes, for example.)

Following Richard Dawkins, who coined the term "designoid" for an apparently designed object, one might say that living organisms are "complexoid". While perhaps not obviously false, this view is likely to be very unattractive.

My reply now follows:

Thanks for the comment Richard,

I am not sure I understand what you mean by producing an object *dynamically* as opposed to *algorithmically*. In your paper you seem to be using a cellular automata model to generate your objects. No problems with that except that as far as I understand, cellular automata can be simulated algorithmically and therefore fall under the algorithmic category. Moreover, if Stephen Wolfram’s work is anything to go by (and some of my own work), cellular automata also generate complex “Pi” like patterns pretty quickly – complex in the sense you have defined in your paper; that is they show a high irregularity or “disorder” as I call it.

Now this doesn’t mean to say, of course, that life actually is the product of a clever dynamics, but given both your definition of irregularity and your use of an algorithmic cellular automata model, it seems we are back to square one – we haven’t yet succeeded in eliminating self organization from the inquiry. However, for reasons I have given in this blog entry I can see why a “soft focus” version of your limitative theorem applies. But given that the resources of an Intelligent Designer is within my particular terms of reference, then it seems not outside the bounds of possibility that should the required fruitful self organizing regime actually be a mathematically possibility, then that intelligence is capable of contriving it.

If (repeat if) this is the case then it is wrong to conclude that life must therefore be algorithmically simple for this reason: The space of all possible algorithms, though a lot smaller than the space of all possible configurations, is still a very, very large space as far as we humans are concerned. I suspect (and this is only a hunch) that not any old algorithm has the right Self Organising properties required to generate living things - in which case selecting the right algorithm is then a computationally complex task; that is, life is not algorithmically simple in absolute terms.

One more thing: Imagine that you were given the problem of Pi in reverse; that is you were given the pattern of digits and yet had no clue as to what, if any, simple algorithm generated it. The hard problem then is to guess the algorithm – generating Pi after you have found the algorithm is the easy problem. So to me life remains algorithmically complex even if it’s a product of SO.


ONE) I am still not sure just how Richard defines the word “dynamic”. The only thing I have to go on is that he drew his conclusions from a cellular automata model, which I assume is his understanding of a dynamic system (?). Wolfram’s cellular system is effectively just another model of computation and therefore I guess that it would be possible to program cellular automata to calculate Pi; such a program is likely to be “simple” in as much as it is likely to have a short length, a short execution time and start with a simple initial state. Therefore I cannot make sense of what Richard means by suggesting that Pi is likely to be dynamically complex, but algorithmically simple.

TWO) I conclude therefore, that Pi can be “easily” generated within a dynamical system. However, Richard actually says this: “In other words, while the digits of Pi can be generated by a short program, it might not be produceable easily within a dynamical system, from a random initial state.” That last phrase, “from a random initial state”, is crucial as it rescues Richard’s statement: If the algorithm is the sort where the initial state and the corresponding output have a one to one mapping then most initial conditions will not lead to Pi in a realistic time. Therefore a random initial state is very unlikely to lead to Pi being calculated in a realistic time.

THREE) As I have said above a “soft focus” version of Richard’s limitative theorem is valid: If one is selecting algorithms and initial states blindly then you are very unlikely to get the result you are looking for. In other words if you’ve got monkeys programming your cellular automata it’s going to be a “garbage in/garbage out” situation. But if the programming of a dynamical system is in the hands of an intelligent agent and you might just get what you are looking for. Richard has effectively shown that if a dynamical system is to produce a configurationally complex output of a particular kind in realistic time then the dynamical algorithm has to be carefully selected. But it is easy to misinterpret this result: It is certainly not as strong as saying there are absolutely no simple algorithms which can generate particular complex outputs in short execution times; in fact as we know simple algorithms can quickly generate complex output in the sense defined by Richard; that is in the sense of being “irregular” or “disordered”. So, basically we are left with the question I keep coming back to: Do simple “short time” dynamical algorithms exist which are fruitful in their generation of a subclass of complex forms and functions? As far as the question of evolution is concerned then, in a word, Richard’s work doesn’t eliminate Self Organization as a suspect in the inquiry. Richard is not so much wrong in his conclusions as they are easy to misinterpret. However, let me say that in my opinion the term “Self organization” is a complete misnomer: There is no “Self” about it: If evolution works it only does so because the right algorithm has been selected by some transcendent super-context; whether we believe that context to be some impersonal mindless multiverse or an all-embracing, “self explaining” intelligence. (I subscribe to the latter view)

FOUR) However, having made that last statement we have to bear in mind that in the anti-evolution community evolution and ID are likely to be portrayed as mutually excluding; that is, the anti-evolution community perceive this debate as a “evolution vs. intelligent design” dichotomy. Hence they are inclined to eliminate evolution from the enquiry by definition; that is, by defining in advance evolution to be a mindless, blind process (ironically atheists are likely to agree with this characterization of evolution!). Thus any suggestion that evolution works by way of the clever selection of a dynamical algorithm is considered an oxymoron. We can see this “definition in advance” at work in Richard’s paper: He starts by presuming that the agent selecting the program of the cellular automata to be blind and thus effectively lacking in intelligence. Not surprisingly if Richard is going to employ chimps to select his algorithm he’s going to get out bananas.
"I only employ chimps, but to get a result I need a lot of them"

FIVE) Unless one subscribes to some kind of multiverse/infinite trial system, even bog standard evolution, if it is to work, must be resourced by improbable preconditions. This improbability has the effect of triggering Demsbki’s design detection criterion and thus in the abstract evolution has the imprimatur of Intelligent Design. However, the ID community represented by Uncommon Descent are defacto anti-evolutionist and therefore they will do their damndest to try and show evolution to be a mindless process that simply doesn’t work; anyone who so much as entertains evolution as a viable “self organizing” candidate is likely to be accused of courting “naturalism” and perhaps even accused of failing a crucial faith test. The irony is that they, along with the militant atheists, seem to have subliminally bought into the deistical intuition that “well oiled” mathematical mechanisms need no divine support or perhaps not even a divine initiator. (See my blog post here)

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