From: Iain Strachan (email@example.com)
Date: Fri May 09 2003 - 14:11:08 EDT
Jim Armstrong wrote:
What I was struck by was that the complex objective was not reached until the "environment" was (apparently slightly?) enriched by the presence and interaction of other essentially similar processes. As an ensemble, they interacted constructively in sufficient measure to increase the system creativity past the tipping point, enabling the achievement of the challenging simulation objective. I was also struck by the small number and simplicity of the "rules" that governed the elements of this simulation and provided this powerful insight. However, this is consistent with the lessons of complexity and chaos.
Having worked for around 15 years in the field of numerical optimization & in providing and maintaining large scale numerical optimization solvers for engineering problems, I look at this somewhat differently.
All that is happening in the paper is that a very simple function is being optimised, with incremental values of fitness, such that a simple and smooth path exists from the start position to the final objective, like Dawkins's metaphor of "climbing mount improbable". Think of the population of a Genetic Algorithm as just a cloud of points in configuration space that wander around under mutation. Then natural selection biases the "cloud" towards the ones that happen to be better at any one point. In order for this to work, it must be possible to find an improvement with just a very few mutations at any one point. This is exactly what was the case in the paper. In fact they write:
"We also identified every mutation that fell along the line of descent in this population, and characterized the phenotypic changes associated with every step (Supplementary Information). The EQU function first appeared at step 111 (update 27,450). There were 103 single mutations, six double mutations and two triple mutations among these steps."
(They do not discuss whether the double and triple mutations were improving of the fitness; some steps produced a drop in fitness).
Now the reason why I uphold strongly to the "deck stacking" argument, and object to it being called "weak" (as you do below) is that in just about any non-trivial engineering problem that you want to solve, the above situation (where improvements can be made by one or two small localised changes) almost NEVER occurs in practice. I support optimization/Non-Linear Programming/Equation solving software that has to deal with systems of anything from a few tens to hundreds of thousands of equations. They are ALL based around computing the gradient with respect to all the variables simultaneously & update all the variables at once in each step. (This is like applying a mutation to every part of the genome). No one would seriously suggest a solver that only adjusted one or two variables at a time, leaving the rest unchanged, because they just don't work. In nearly all engineering problems of interest (certainly in numerical optimization), the variables are tightly coupled, which means that you have to make multiple coordinated changes to variables, not just one or two of them.
But if you think I'm just a crank in the minority here, let me give you an independent assessment. One of the Fortran routines in the library that we use happens to be a Genetic Algorithm. It's very well written and incorporates all the latest heuristics. One developer in my company asked about using it for a problem that they had. As it turns out, I met the person who wrote the GA routine a few days later (as he works on an adjoining site). He is a visiting Prof. at Edinburgh University, a world expert in optimization, and the author of several large scale codes. When I told him that someone was interested in his GA code he just laughed. "Good grief!! He doesn't want to use that _seriously_ ? I only wrote it for fun. Tried it on a couple of problems. It was _awful_!"
Since Nature seems to have done a pretty good job at solving difficult engineering problems, I'm therefore distinctly underwhelmed at the claim that this toy one-variable-at-a-time problem is a demonstration of the evolutionary origin of complex features.
In a way, this is not too surprising an outcome, resembling parallel processing in computer terms, as opposed to serial processing. A little bit of parallel processing can be a very powerful thing - the most powerful computers on Earth embody a great deal of parallel processing to achieve their performance!
I don't see how this resembles parallel processing, except that GA's can exploit parallel processing by having all the members of the population (the cloud of points in configuration space) evaluated on different processors. But having also worked quite a bit on parallel processing myself, the plain fact is that it can at _best_ achieve a linear speed-up in processing (linear in the number of processors), and that is only true if there is _no_ interaction between the elements running on different processors. As soon as interaction is required, then further slow-downs are incurred because of the communication overheads in sending data between different processors, and the improvement is sub-linear. If you don't get it right, the parallel processing results in a dramatic slow-down. And furthermore, with the rate at which processor speed is increasing (Moore's Law), parallelism only buys you a few years before your array will be beaten by a single processor. In the early '90's I worked on a small array of Transputers, which were the big thing in parallel processing, using a special language called Occam to incorporate parallel constructs in the programming language. But the brutal fact is that the computer I'm typing this email at, which is just a common or garden entry level domestic machine, is the equivalent of around 1000 transputers in floating point performance! (The Transputer gave around 0.7 million floating point operations per second, or FLOPS. I've tested this machine at around 700 MegaFlops. My laptop, which is about a year later vintage than this machine is twice as fast as that again).
The argument concerning the evolution of things of "irrreducible complexity" seems to embody the notion of a rather linear evolution process. But the remarkable "processors" of nature are HIGHLY parallel and, taken with the environments in which they occur, are extremely (unimaginably) rich and redundant with respect to materials, processes, and instantiations of things of a given kind and slight variations thereof (e.g., a given protein). Equally important is the fact that they are also rich with respect to the huge numbers of potential interactions among them and their products. The result is essentially EXTREME parallel processing with arguably exponential outcome possibilities.
Sorry, but I don't follow this at all. What do you mean by "linear evolution process?". Unless that's exactly what was demonstrated in the paper. Gradual increments with one change at a time. At the risk of repeating myself, the paper explicitly stated (in the Discussion) that if multiple changes were required (i.e. you didn't reward the intermediate stages), then _it did not work_. I don't agree that parallel processing has exponential outcome possibilities. This is only the case if there is interaction between the parallel elements. But the paper didn't employ any form of "crossover" (which is normally used in GA's to simulate sexual reproduction). Hence there is no interaction between the elements, except in the natural selection process. Even if there were interactions, the fact that exponential outcome possibilities are available is irrelevant. Sure, the number of _favourable_ possibilities increases exponentially, but so does the number of _unfavourable_ possibilities, at a much faster rate! (As they say in the paper, most mutations are damaging; only a very few actually improve the fitness). What this means is that the probability of finding a favourable one _decreases_ exponentially, because you are dividing an exponentially increasing number by another one that is also exponentially increasing at a faster rate; e^x / e^2x = e^(-x).
It seems to me that this result - including the evidence for different evolutionary rates - does below-the-waterline damage to some of the ID arguments. I would not be surprised to find that "stacked deck" response taken up as a rallying (but weak) riposte. But if so, it will only demonstrate that the point of this work was missed.
Actually, I think it's the critics of the "irreducible complexity" argument who are missing the point. Meanwhile, I'll carry on making money for my company by solving problems that are "irreducibly complex" every step of the way. (Irreducibly complex, in my definition, means: "requiring several coordinated changes to make any improvement").
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