Saturday, October 3, 2009
Manzi on Evolution
Jim Manzi is by far my favorite writer on the nuts-and-bolts of the climate models. After reading relevant sections of the IPCC AR4, I thought I had a pretty good idea of how the simulations actually worked, but I wasn't totally confident until reading this Manzi piece.
Anyway, I recently checked out his archives at The American Scene. If you have never read Manzi, I encourage you to skim his posts and see if anything grabs you. I was very pleasantly surprised to see that he has (perhaps foolishly for his credibility in our secular age) dived into the evolution debate. In particular, I really liked his response to evolutionary biologist Jerry Coyne, who (in a book review of somebody else) had given the grandiose claims about "thank goodness Darwin set those self-important Bible-thumpers straight!"
Now note that I'm not saying Manzi is 100% in the post linked above; I think at times he overreaches. But even so, he does a great job dismantling some of the more absurdly over-the-top claims that are often put forward by evolutionary biologists in this type of debate.
I had wanted to get hip-deep into these issues, with Coyne's claims, Manzi's proferred counterexample, my commentary, etc. But I have been so busy, I know that's not going to happen anytime soon. Instead let me just give you Manzi's concluding paragraph:
UPDATE: Oh I should also mention that another flaw in Coyne's typical critique against medieval Christians, is that Coyne gets his timeline screwed up. Gene Callahan pointed out (in email) that it wasn't Galileo butKepler Copernicus [my dumb typo, not Gene's--RPM] who had "announced" that the earth wasn't the center of the universe. Furthermore, as reading Dante etc. indicates, medieval Christians didn't think it was noble to be at the center of things; that's where Hell was!! (Gene may have to clarify in the comments if I've botched his critique of Coyne.) So this standard debating ploy of "Christians can't accept Darwin because of their fragile egos" is based on bogus Church history. Yes, it's certainly true that modern Christians don't like being told, "You're not special, you serve no divine purpose, you are a statistical fluke," but the 'history' given to buttress that charge is bogus.
Anyway, I recently checked out his archives at The American Scene. If you have never read Manzi, I encourage you to skim his posts and see if anything grabs you. I was very pleasantly surprised to see that he has (perhaps foolishly for his credibility in our secular age) dived into the evolution debate. In particular, I really liked his response to evolutionary biologist Jerry Coyne, who (in a book review of somebody else) had given the grandiose claims about "thank goodness Darwin set those self-important Bible-thumpers straight!"
Now note that I'm not saying Manzi is 100% in the post linked above; I think at times he overreaches. But even so, he does a great job dismantling some of the more absurdly over-the-top claims that are often put forward by evolutionary biologists in this type of debate.
I had wanted to get hip-deep into these issues, with Coyne's claims, Manzi's proferred counterexample, my commentary, etc. But I have been so busy, I know that's not going to happen anytime soon. Instead let me just give you Manzi's concluding paragraph:
The theory of evolution, then, has not eliminated the problems of ultimate origins and ultimate purpose with respect to the development of organisms; it has ignored them. These problems are defined as non-scientific questions, not because we don’t care about the answers, but because attempting to solve them would impede practical progress. Accepting evolution, therefore, requires neither the denial of a Creator nor the loss of the idea of ultimate purpose. It resolves neither issue for us one way or the other. The field of philosophical speculation that does not contradict any valid scientific findings is much wider open to Wright [whose book was under review] than Coyne is willing to accept.Incidentally, in making his case, Manzi discusses in some detail a "genetic algorithm." I asked Silas Barta what he thought of Manzi's case, since Silas knows a lot about information theory. (See this post on Intellectual Property, and Silas' clever example, to see him deploy information theory in a different context.) Anyway, below is Silas' response to Manzi's column, and of course Silas does not necessarily agree with anything I am saying in the present post:
-I'm a bit disturbed by how Manzi didn't discuss the local optimum problem, where a genome isn't the best overall, but is better than all the other candidates and yet can't be improved without radical revision. This means that a genetic algorithm, like all general optimizers, is not guaranteed to find the global optimum on an arbitrary problem. In the example of the 100 switches, it may reach the solution slower than randomly iterating through them, which often plagues those who have high expectations of GAs. This is mentioned in the link he give[s] to Talk Origins.
(GAs are way overrated, by the way; they don't on average do better than the other optimization methods like simulated annealing, hill-climbing, etc.)
Because you're probably wondering about it: yes, that means that evolution of earlier life by no means guaranteed humans evolving, or indeed any intelligent species capable of culture.
-Scientists do indeed claim that evolution has no long-term purpose, but...this just means that they don't believe they gain in predictive power by assuming it works toward some long-term purpose. However, they claim that evolutionary processes have the effect of attempting to maximize the fraction of the gene pool that any given gene represents. Manzi is correct to note that the constantly-shifting fitness landscape (what's optimal for animals living near wolves isn't optimal for animals living near ducks, etc.) and massive multi-directional interplay of factors make it effectively impossible to say *which* genes will increase in frequency in advance.
-As for Manzi's general theme about the purpose of the universe being outside the realm of science, I would say that under some circumstances, scientists would be able to identify a purpose, but the dynamics at play in the universe as we know it make it currently impossible for science to say one way or the other.
UPDATE: Oh I should also mention that another flaw in Coyne's typical critique against medieval Christians, is that Coyne gets his timeline screwed up. Gene Callahan pointed out (in email) that it wasn't Galileo but
Comments:
w00t! Thanks for the praise and the link. :-) But I'm still confused about what you found suspicious enough about Manzi's article to justify asking for my take. Was it his implication that, once nature starts "implementing" a genetic algorithm, it's guaranteed to find the global optimum (or intelligent beings, or humans)?
I wasn't suspicious, it was more like, "I really like this article, but I know less about genetic algorithms than I do about global climate models, so I want to get a second opinion before I add another arrow to my anti-Dawkins quiver."
Darwinian biologists are interested in EXPLANATORY power, not predictive power.
Silas is doing bad philosophy here, he's not doing science.
Silas is doing bad philosophy here, he's not doing science.
Silas says:
"the constantly-shifting fitness landscape (what's optimal for animals living near wolves isn't optimal for animals living near ducks, etc.) and massive multi-directional interplay of factors make it effectively impossible to say *which* genes will increase in frequency in advance."
Actually, the their are insuperable barriers to predictive tractability -- see my paper "Insuperable Limits to Reduction in Biology" by Greg Ransom at the Taking Hayek Seriously blog, and some papers by Alex Rosenberg, written after he'd read that paper.
"the constantly-shifting fitness landscape (what's optimal for animals living near wolves isn't optimal for animals living near ducks, etc.) and massive multi-directional interplay of factors make it effectively impossible to say *which* genes will increase in frequency in advance."
Actually, the their are insuperable barriers to predictive tractability -- see my paper "Insuperable Limits to Reduction in Biology" by Greg Ransom at the Taking Hayek Seriously blog, and some papers by Alex Rosenberg, written after he'd read that paper.
Thanks for the compliments, and the thoughtful commentary.
A few quick things on GAs:
1. Enthusiasts make all kinds of grandiose claims for what they can do, but as your correspondent correctly says, they are, like all optimization algorithms, slightly advantaged versus alternatives only for a specific problem domain.
2. I don't think the "local optimum trap" criticism is valid at the philsophical level. The purpose of mutation, and especially crossover, is to avoid (obviously imperfectly) local optimum traps. Consider that in an exterme case you could set the mutation rate to 10,000 per 10,000 genes, as opposed to the standard 1 per 10,000 genes as I had in the article, and you would just be doing random search, and therefore could never be stuck in a local optimum (and would also take a long, long time to find a good solution).
(As an aside, I was careful to say it would "tend" toward the best possible solution. In fact, it will always get there with enough generations, though as has been correctly stated, it is theoretically possible that it would take longer than random search.)
Best,
Jim Manzi
A few quick things on GAs:
1. Enthusiasts make all kinds of grandiose claims for what they can do, but as your correspondent correctly says, they are, like all optimization algorithms, slightly advantaged versus alternatives only for a specific problem domain.
2. I don't think the "local optimum trap" criticism is valid at the philsophical level. The purpose of mutation, and especially crossover, is to avoid (obviously imperfectly) local optimum traps. Consider that in an exterme case you could set the mutation rate to 10,000 per 10,000 genes, as opposed to the standard 1 per 10,000 genes as I had in the article, and you would just be doing random search, and therefore could never be stuck in a local optimum (and would also take a long, long time to find a good solution).
(As an aside, I was careful to say it would "tend" toward the best possible solution. In fact, it will always get there with enough generations, though as has been correctly stated, it is theoretically possible that it would take longer than random search.)
Best,
Jim Manzi
# posted by 
: October 4, 2009 at 7:51 AM
: October 4, 2009 at 7:51 AM
@Jim Manzi: For low levels of mutation and crossover, it still is possible to get stuck poor local optima, because the changes don't go far enough to enter another domain of attraction. And the opposite extreme, of never preserving any continuity with previous candidates, is, as you note, indistinguishable from a random search, and therefore unrelated to the genetic algorithm nature actually uses.
And as a side note, let's not forget that it's not the *random* shifting around that gets you out of poor local optima, but the fact that the shift (in genome) is large. It's just that randomness is no worse than the alternatives when you lack enough understanding of the search space to make better guesses.
@Greg: Explanatory power is necessarily predictive. But either way, you could replace one with the other in my statement and it would still be true.
By the way, how do you determine what counts as "good philosophy" (which needs to be more than just "agreement with an elite circle of individuals") and in what respect did I not adhere to that?
And as a side note, let's not forget that it's not the *random* shifting around that gets you out of poor local optima, but the fact that the shift (in genome) is large. It's just that randomness is no worse than the alternatives when you lack enough understanding of the search space to make better guesses.
@Greg: Explanatory power is necessarily predictive. But either way, you could replace one with the other in my statement and it would still be true.
By the way, how do you determine what counts as "good philosophy" (which needs to be more than just "agreement with an elite circle of individuals") and in what respect did I not adhere to that?
@Greg: I looked over the paper you mentioned, and I think I need to clarify that I am not endorsing the standard scientific epistemology (which is in some ways too strict and in some ways not strict enough). My view is best represented by the famous Eliezer Yudkowsky essay, "A Technical Explanation of Technical Explanation".
Silas writes:
"Explanatory power is necessarily predictive. But either way, you could replace one with the other in my statement and it would still be true."
This is a false statement.
We explain things we can't predict all of the time.
"Explanatory power is necessarily predictive. But either way, you could replace one with the other in my statement and it would still be true."
This is a false statement.
We explain things we can't predict all of the time.
"Explanatory power is necessarily predictive."
I'm a philosophical moron, oh yeah!
I'm a philosophical moron, oh yeah!
# posted by : October 5, 2009 at 9:17 AM
: October 5, 2009 at 9:17 AM
Darwin did not prove anything. He suggested that species could have originated by evolution. Then he suggested what the proof of his guess might be. Scientists spent a few years trying to prove his theory, but when it became clear that most scientists didn't need any proof, they would accept the theory as fact without any proof, they quit. The evidence for Darwin's system is still seriously lacking, but few scientists care.
The really interesting question is why?
The really interesting question is why?
# posted by : October 5, 2009 at 10:04 AM
: October 5, 2009 at 10:04 AM
Silas:
I think with any non-zero mutation rate, any GA will eventually evaluate every possible genome, so while it might get "stuck" in the sense of wasting many generations climbing a spcific hill, it will eventually find the most fit genome.
We might intutively find this to be a foolish way for a purported omnipotent being to get to a goal, but as I've argued in a related post, that same "argument from change" can be applied to any universe with any kind of change.
At a more practical level, as you know, the trade-off between greediness and comprehensiveness is the subject of extensive algortihmic research, and GAs tend to be used in situations for which strong assumptions can not be made (at least not reliably made) about the structure of the search space. So I don't think it's at all clear one way or the other whether or not a genetic evolutionary process with the kinds of crossover probabilities and mutation rates that we see in nature is an efficieint or inefficient way to search an all but infinite search space for some purported goal.
Best,
Jim Manzi
I think with any non-zero mutation rate, any GA will eventually evaluate every possible genome, so while it might get "stuck" in the sense of wasting many generations climbing a spcific hill, it will eventually find the most fit genome.
We might intutively find this to be a foolish way for a purported omnipotent being to get to a goal, but as I've argued in a related post, that same "argument from change" can be applied to any universe with any kind of change.
At a more practical level, as you know, the trade-off between greediness and comprehensiveness is the subject of extensive algortihmic research, and GAs tend to be used in situations for which strong assumptions can not be made (at least not reliably made) about the structure of the search space. So I don't think it's at all clear one way or the other whether or not a genetic evolutionary process with the kinds of crossover probabilities and mutation rates that we see in nature is an efficieint or inefficient way to search an all but infinite search space for some purported goal.
Best,
Jim Manzi
# posted by : October 5, 2009 at 10:16 AM
: October 5, 2009 at 10:16 AM
@Greg_Ransom and Anonymous: I think we're talking past each other, so let me clarify what I meant. When you come up with a valid, technical, scientific explanation for phenomenon P, you may indeed not be able to make a prediction for *that specific one-time P*. However, if your explanation is a truly technical one, you will be positing entities that are used in other contexts, making your explanation in one area coupled to the other. So your explanation does have predictive implications. Failures of the predictions you can make cut against the explanation without testable predictions.
For example, let's say that a spaceship leaves the earth at a very high speed so that it's outside our light cone and we can never get any information from it within our lifetimes.
I will posit the explanation, "The spaceship still exists, it's just that information can only be transmitted at the speed of light, which is why we can't observe it." On the face of it, that explanation makes not predictions; by stipulation, we can't go and find out if the spaceship exists. However, it is coupled to theories about light and whether objects randomly stop existing which we *can* test. My explanation therefore *is* predictive: it makes predictions that can be checked, which, together justify my inference of the spaceship still existing.
Now, there may be instances where there really is no coupled prediction to the explanation you gave: but then, in such a case I would say you didn't really explain the phenomenon either.
For example, let's say that a spaceship leaves the earth at a very high speed so that it's outside our light cone and we can never get any information from it within our lifetimes.
I will posit the explanation, "The spaceship still exists, it's just that information can only be transmitted at the speed of light, which is why we can't observe it." On the face of it, that explanation makes not predictions; by stipulation, we can't go and find out if the spaceship exists. However, it is coupled to theories about light and whether objects randomly stop existing which we *can* test. My explanation therefore *is* predictive: it makes predictions that can be checked, which, together justify my inference of the spaceship still existing.
Now, there may be instances where there really is no coupled prediction to the explanation you gave: but then, in such a case I would say you didn't really explain the phenomenon either.
@Jim Manzi:
I think with any non-zero mutation rate, any GA will eventually evaluate every possible genome, so while it might get "stuck" in the sense of wasting many generations climbing a spcific hill, it will eventually find the most fit genome.
That doesn't follow: if it just makes tiny changes to the genome, it will repeatedly discover that all of those changes just make it worse than the local optimum, and it's never able to get out, because it never finds a candidate better than the current local optimum.
At a more practical level, as you know, the trade-off between greediness and comprehensiveness is the subject of extensive algortihmic research
No, I didn't know this, and now that I do know I can safely say that it's a waste of time. If you don't know enough about the search space to use a better method than randomness to find new genomes, then neither do you know enough to say how much greediness is optimal. Randomness is only used at all in any general optimization algorithms as a stand-in for our ignorance: it does no better or worse than any other (e.g. deterministic) method for finding new genomes when you don't know enough about the search space's structure to do something non-random, so you might as well just use something that's not computationally expensive.
I know I won't get this insight published in any journal, but that's more of an issue of lacking the street cred for whatever journals are talking about this. I will note, however, that a cottage industry has sprung up in de-randomizing algorithms.
I think with any non-zero mutation rate, any GA will eventually evaluate every possible genome, so while it might get "stuck" in the sense of wasting many generations climbing a spcific hill, it will eventually find the most fit genome.
That doesn't follow: if it just makes tiny changes to the genome, it will repeatedly discover that all of those changes just make it worse than the local optimum, and it's never able to get out, because it never finds a candidate better than the current local optimum.
At a more practical level, as you know, the trade-off between greediness and comprehensiveness is the subject of extensive algortihmic research
No, I didn't know this, and now that I do know I can safely say that it's a waste of time. If you don't know enough about the search space to use a better method than randomness to find new genomes, then neither do you know enough to say how much greediness is optimal. Randomness is only used at all in any general optimization algorithms as a stand-in for our ignorance: it does no better or worse than any other (e.g. deterministic) method for finding new genomes when you don't know enough about the search space's structure to do something non-random, so you might as well just use something that's not computationally expensive.
I know I won't get this insight published in any journal, but that's more of an issue of lacking the street cred for whatever journals are talking about this. I will note, however, that a cottage industry has sprung up in de-randomizing algorithms.
We can explain earthquakes but we cant' predict them.
We can explain speciation, but we can't predict it.
We can explain the 3 body problem, but we can't predict the full future historical course of the path of of these interactions.
See the work of Mark Stone on the difference between explanation and the myth of Laplacian prediction / explanation, especially in the context of non-linear dynamic phenomena and the problem of the specification of initial conditions, etc.
Gleick's boom _Chaos_ presents a popular version of some of the issue involved.
Are we talking past each other? -- then make yourself clear.
We can explain speciation, but we can't predict it.
We can explain the 3 body problem, but we can't predict the full future historical course of the path of of these interactions.
See the work of Mark Stone on the difference between explanation and the myth of Laplacian prediction / explanation, especially in the context of non-linear dynamic phenomena and the problem of the specification of initial conditions, etc.
Gleick's boom _Chaos_ presents a popular version of some of the issue involved.
Are we talking past each other? -- then make yourself clear.
@Greg, we are indeed talking past each other, but *I* have clearly explained the terms I am using and their implications, so it should be obvious to you what my response is to your examples. It's now *your* turn to make an effort to make yourself clear instead of listing of simplistic arguments that reveal not having read what I posted.
Let's look at what you're (incorrectly) claiming is relevant to my position and disconfirmatory of it:
We can explain earthquakes but we cant' predict them.
Predicting the arrival time of a specific earthquake is one kind of prediction that could come out of a well-developed theory of earthquakes. But it is not necessary to make that specific kind of prediction in order to have a scientific explanation of earthquakes.
What you seem to be doing is taking an arbitrary kind of prediction and equating failure to make that prediction with the claim that that scientific field's explanations "don't make predictions". This is incorrect. As I stated clearly in my above post, and am repeating for a second time, all that's necessary for an explanation to be predictive is that it make claims logically coupled to predictions we *can* make -- see the example about explaining why we can't see the spaceship but it still exists.
Our (scientific!) explanation of earthquakes is intimately bound up with the general theory of plate techtonics (and, to the extent possible, trimmed of unnecessary or arbitrary suppositions), which posits various (discovered) fault lines, plate locations, situation of continents, etc.
From *that* theory, the very same one explaining earthquakes, one can make predictions: what will happen at specific fault lines, where earthquakes are more likely than others (hey, that kinda *is* a prediction!), how to find the origin of an earthquake (which itself has testable implications), where volcanos are likely to form, which direction continents will drift, etc.
You seem to be falling to the trap of believing that if you haven't gained a full understanding of something, you haven't gained any knowledge at all. But when you go from e.g. 60% accuracy in guessing, to 70%, you have gained knowledge, even though you're not at 100%. Likewise, when you go from "ignorance about where earthquakes will hit" to "a probability distribution over earthquake locations closer to the true one that arises in the future", you have gained scientific knowledge, and indeed, predictive power.
Now, cross-apply that analysis to all of the other examples you gave. And please read this comment in its entirety before responding.
Let's look at what you're (incorrectly) claiming is relevant to my position and disconfirmatory of it:
We can explain earthquakes but we cant' predict them.
Predicting the arrival time of a specific earthquake is one kind of prediction that could come out of a well-developed theory of earthquakes. But it is not necessary to make that specific kind of prediction in order to have a scientific explanation of earthquakes.
What you seem to be doing is taking an arbitrary kind of prediction and equating failure to make that prediction with the claim that that scientific field's explanations "don't make predictions". This is incorrect. As I stated clearly in my above post, and am repeating for a second time, all that's necessary for an explanation to be predictive is that it make claims logically coupled to predictions we *can* make -- see the example about explaining why we can't see the spaceship but it still exists.
Our (scientific!) explanation of earthquakes is intimately bound up with the general theory of plate techtonics (and, to the extent possible, trimmed of unnecessary or arbitrary suppositions), which posits various (discovered) fault lines, plate locations, situation of continents, etc.
From *that* theory, the very same one explaining earthquakes, one can make predictions: what will happen at specific fault lines, where earthquakes are more likely than others (hey, that kinda *is* a prediction!), how to find the origin of an earthquake (which itself has testable implications), where volcanos are likely to form, which direction continents will drift, etc.
You seem to be falling to the trap of believing that if you haven't gained a full understanding of something, you haven't gained any knowledge at all. But when you go from e.g. 60% accuracy in guessing, to 70%, you have gained knowledge, even though you're not at 100%. Likewise, when you go from "ignorance about where earthquakes will hit" to "a probability distribution over earthquake locations closer to the true one that arises in the future", you have gained scientific knowledge, and indeed, predictive power.
Now, cross-apply that analysis to all of the other examples you gave. And please read this comment in its entirety before responding.
Silas says:
"You seem to be falling to the trap of believing that if you haven't gained a full understanding of something, you haven't gained any knowledge at all."
No, I'm rejecting a false picture of knowledge tied to a false picture of science (e.g. something like the Carnap/Popper/Nagel tradition, or the older Laplacean tradition, etc.)
"You seem to be falling to the trap of believing that if you haven't gained a full understanding of something, you haven't gained any knowledge at all."
No, I'm rejecting a false picture of knowledge tied to a false picture of science (e.g. something like the Carnap/Popper/Nagel tradition, or the older Laplacean tradition, etc.)
@Greg: Ah, so you were making improper inferences about my epistemology based on only having been exposed to similar-sounding philosophers, even after I clearly explained what my epistemology *is* and linked you to an author's exposition of it.
Now, what do you think about my actual views on the relationship between explanation and prediction, as applied to your attempted examples of their difference?
Now, what do you think about my actual views on the relationship between explanation and prediction, as applied to your attempted examples of their difference?
Also, Greg, when you equate "not being able to predict earthquakes" with "having no predictive power in your explanation of earthquakes", you most certainly *are* making the error of equating partial understanding with zero understanding, no matter what your rejection of past scientific paradigms might be.
Silas,
well, I'd say you are "stretching" the standard meaning of _prediction_, and YES this is done exactly the way you do it in the literature I'm talking about.
You're views have a history and they don't come out of thin air - and they also have a motivation coming from this history ...
Trust me on this.
well, I'd say you are "stretching" the standard meaning of _prediction_, and YES this is done exactly the way you do it in the literature I'm talking about.
You're views have a history and they don't come out of thin air - and they also have a motivation coming from this history ...
Trust me on this.
Um, no Greg. I'm not stretching anything. I said that explanatory power is predictive power. That means any genuine, fully-specified explanation will make predictions.
You took that to mean "any arbitrary prediction you can think of", which would make them no longer equivalent, but would also be a non-standard usage on *your* part.
And based on the exchange, I'm not inclined to look anything up on your say-so. You come off as woefully-misinformed, unable to even summarize your own views on the topic. If you represent "real, professional" philosophy, well, you're exhibit QZ in why I don't expect mainstream philosophy to produce any practical results in the near future.
You took that to mean "any arbitrary prediction you can think of", which would make them no longer equivalent, but would also be a non-standard usage on *your* part.
And based on the exchange, I'm not inclined to look anything up on your say-so. You come off as woefully-misinformed, unable to even summarize your own views on the topic. If you represent "real, professional" philosophy, well, you're exhibit QZ in why I don't expect mainstream philosophy to produce any practical results in the near future.
Silas:
I said:
"I think with any non-zero mutation rate, any GA will eventually evaluate every possible genome, so while it might get "stuck" in the sense of wasting many generations climbing a spcific hill, it will eventually find the most fit genome."
You responded by saying to me:
"That doesn't follow: if it just makes tiny changes to the genome, it will repeatedly discover that all of those changes just make it worse than the local optimum, and it's never able to get out, because it never finds a candidate better than the current local optimum."
But that's obviously not true. To see why not, take the numbers from my post, and assume a genome length of 100 genes and a mutation rate of 1 per 10,000 genes. In the extreme, assume what you have posited has occured absolutely and every genome in the population has an identical, sub-optimal, list of genes. Because of mutation, every 10,000 ^ 100th generations, you will flip every gene on one organism's genome to the opposite value, and therefore create an organism with a genome through that is the exact opposite of one that was very close to this suboptimal one. With enough of these events occuring every 10,000 ^ 100th geberations, you will eventually explore the entire space (VERY slowly).
Obviously, less severe mutation and random crossover point selection, will in fact, create more frequent, though less radical jumps. This is what prevents absolute convergence on a sub-optimum.
Best,
Jim Manzi
Post a Comment
I said:
"I think with any non-zero mutation rate, any GA will eventually evaluate every possible genome, so while it might get "stuck" in the sense of wasting many generations climbing a spcific hill, it will eventually find the most fit genome."
You responded by saying to me:
"That doesn't follow: if it just makes tiny changes to the genome, it will repeatedly discover that all of those changes just make it worse than the local optimum, and it's never able to get out, because it never finds a candidate better than the current local optimum."
But that's obviously not true. To see why not, take the numbers from my post, and assume a genome length of 100 genes and a mutation rate of 1 per 10,000 genes. In the extreme, assume what you have posited has occured absolutely and every genome in the population has an identical, sub-optimal, list of genes. Because of mutation, every 10,000 ^ 100th generations, you will flip every gene on one organism's genome to the opposite value, and therefore create an organism with a genome through that is the exact opposite of one that was very close to this suboptimal one. With enough of these events occuring every 10,000 ^ 100th geberations, you will eventually explore the entire space (VERY slowly).
Obviously, less severe mutation and random crossover point selection, will in fact, create more frequent, though less radical jumps. This is what prevents absolute convergence on a sub-optimum.
Best,
Jim Manzi
# posted by : October 7, 2009 at 7:27 PM
: October 7, 2009 at 7:27 PM Subscribe to Post Comments [Atom]
<< Home
Subscribe to Posts [Atom]