On 5 December 1947, Kurt Gödel, the man Time magazine called the last century's greatest mathematician, had his citizenship hearing. One of Gödel's witnesses was the man the same issue of Time called the century's greatest person, Albert Einstein. The other witness was Oskar Morgenstern, co-inventor of game theory.
At the hearing, the prospective citizen has to answer a few basic questions. Not a big deal, you'd think, for the second greatest mind in the world, especially when he's got number one there to vouch for him. But Gödel, for better and for worse, was not like other people. In mathematics, Gödel could do the impossible. In the rest of life, Gödel had a way of making the easy difficult. Sixty years later, Gödel's citizenship hearing is legendary. Now, in 2008, decades after all the participants in that meeting have died, there's an important discovery about it.
Uniquely among mathematicians, Gödel was known for surprises. Most mathematicians prove things already believed to be true. Occasionally mathematicians prove things that other mathematicians weren't one hundred percent sure about. Rarely does a mathematician prove something most of the others thought must be false. And no mathematician had made a career of that kind of proof until Kurt Gödel came along.
When it came to this citizenship hearing, Einstein and Morgenstern were in no mood for surprises. So when Gödel told them he'd found a contradiction in the U.S. Constitution, one that would allow the U.S. to be turned into a dictatorship, they told him to forget it. But Gödel seemed to feel the need to share his discovery. If Gödel started expounding on defects in the U.S. Constitution to the wrong kind of judge, Einstein and Morgenstern knew there could be trouble.
In the decades since 1947, the tale of what happened at the hearing was told and retold, each time with differing incident and dialog. Certainly, there was a citizenship hearing. Probably Gödel had some kind of proof about the US constitution, one which had Morgenstern and Einstein worried. More than that I didn't think we'd ever know.
Not that there weren’t lots of stories. When I was a grad student, Gödel was still alive. In the halls and offices, I heard many a tale of Gödel's eccentric behavior. Over the years, I’ve learned that every one of those stories was unfounded and probably false.
I expected that none of the various recountings of the citizenship hearing was to be trusted. Faculty room yarnsmanship had "improved" them to the point where they were useless. I also expected that the hearsay versions omitted a lot of important details.
Now, to my surprise, we can know. I have discovered Morgenstern's original account of Gödel's citizenship hearing, lost to scholarship for decades. How I found it, I'll describe in my next post.
Sunday, November 30, 2008
Thursday, August 21, 2008
Dawkins Revisit: A Compromise between Survival and Increase?
This blog post is a long delayed reply to a question Harshad asked in a comment to "Dawkins #5: 'As Much As Possible' is Vacuous". We're talking about Richard Dawkins's theories, set out in the popular The Selfish Gene and the scholarly The Extended Phenotype. Dawkins refutes the idea that natural selection can be competition of species or even individuals. He makes the case that natural selection is driven by competition between genes. In my series of posts, I take Dawkins arguments as a starting point but find that Dawkins is ambiguous about the goal of the "selfish genes".
Specifically, most of the time Dawkins says that genes are trying to maximize their chances of "survival" (The Extended Phenotype, p. 233) but sometimes he says they are trying to increase in number (Phenotype, p. 84). When Dawkins gives examples, the genes are usually trying to increase the number of "germline" genes. (Germline genes are those actually in reproductive lineages.)
This distinction (survival vs. increase) is not a verbal quibble. The two goals produce different mathematical models and these will usually make different predictions, probably including testably different predictions. I went on to try to settle the issue of survival vs. increase, looking at the internal coherence of the two ideas, and their consistency with Dawkins methodology. Here Harshad had questions. I had decided one of the two goals was probably right, and the other wrong. Harshad wondered whether some combination of the two might be at work.
Dawkins' materialist method is the major reason for thinking survival vs. increase must be decided entirely for one goal or the other. Natural selection is driven by "selfish genes", but (from my "Dawkins #1: Are His Genes Selfish Enough?"):
The above brutally summarizes my previous Dawkins posts. I make these arguments much more carefully in them and I also examine the kind of combined goals Harshad suggests in detail.
Specifically, most of the time Dawkins says that genes are trying to maximize their chances of "survival" (The Extended Phenotype, p. 233) but sometimes he says they are trying to increase in number (Phenotype, p. 84). When Dawkins gives examples, the genes are usually trying to increase the number of "germline" genes. (Germline genes are those actually in reproductive lineages.)
This distinction (survival vs. increase) is not a verbal quibble. The two goals produce different mathematical models and these will usually make different predictions, probably including testably different predictions. I went on to try to settle the issue of survival vs. increase, looking at the internal coherence of the two ideas, and their consistency with Dawkins methodology. Here Harshad had questions. I had decided one of the two goals was probably right, and the other wrong. Harshad wondered whether some combination of the two might be at work.
Dawkins' materialist method is the major reason for thinking survival vs. increase must be decided entirely for one goal or the other. Natural selection is driven by "selfish genes", but (from my "Dawkins #1: Are His Genes Selfish Enough?"):
Closely related to the "increase" vs. "survival" question, is the question of the exact nature of "the unit of selfishness". It's the "gene", but "the gene" can either be the collection of all genes with the same phenotype at the same place in the chromosome (which I'll call the gene-type), or one individual member of that collection (which I'll call the gene-copy). While the English language is ambiguous, Dawkins is not. His examples and his more detailed explications clearly show that he thinks the gene-type is what is "selfish", and that gene-copies subordinate their individual interests to the gene-type.If the gene-copy is the "unit of selfishness", survival is the goal. If the gene-type is the "unit of selfishness", increase is the goal. A mechanism where the two cooperate on some sort of shared goal can't be excluded, but it is hard to see how they can share responsibility in materialist terms.
The above brutally summarizes my previous Dawkins posts. I make these arguments much more carefully in them and I also examine the kind of combined goals Harshad suggests in detail.
Tuesday, February 19, 2008
Wednesday, August 1, 2007
Dawkins #6: One Goal to Rule Them All
[ This post is number 6 of a series. They will be of interest mainly to those who've read Richard Dawkins' book, The Selfish Gene. I recommend they be read in order. ]
Richard Dawkins ascribes two different goals to genes: "survival" and "increase". In previous posts, I pointed out that these produce different models, which in turn predict different results. I expanded the "goal" metaphor out into literal terms, and showed that if this "thought problem" is worked out with genes taken on a "snapshot" basis, their goal is clearly seen as survival.
In the last two posts I showed that "increase goals" will not work without a well-defined condition or "target". Pure "increase goals" had several problems, the worst of which showed up when I expanded the "goal" metaphor into literal terms. Pure increase goals require us to believe genes have an intent, not just metaphorically, but in literal fact. Unlike limited increase goals, where we can justify our statements that genes have those goals by pointing to the actual effect of the genes in the material world, pure increase goals require us to make statements about what genes "would" do if they "could". That takes us from metaphor into fantasy.
It remains to look at "increase goals" with well-defined conditions. Testable (if not necessarily realistic) examples might be "Increase the germline gene count if foraging produces more than the target level of N calories per average day, otherwise regulate the germline gene count to maintain or restore that level" or "Maintain a germline gene count which keeps the species at 9% of the epipelagic Antarctic biomass."
In one sense, these are not goals of "increase" as stated by Dawkins, but "maintenance goals". But I will give any goal based on germline gene frequency, honorary status as an "increase goal". More important than whether they track Dawkins language (Extended Phenotype, p. 84) closely is whether they make a satisfactory alternative to the survival goal. That's not a question that should be answered with a semantic quibble.
The basic problem with the limited versions of "increase goals" is best shown by their confusion in the face of outlaw genes. Assume that genes do have gene-frequency goals which, at least at points, involve maintaining a certain population level. What's to stop a new mutation that cheats? At first glance, it would seem that if the genome of a species has settled on a rule that says "stop increasing gene count at level X", any gene that ignores it will have a selection advantage over its law-abiding fellow genes.
I won't dwell on the practical side of this problem: how the law-abiding genes in a genome can "police" these outlaws. (Dawkins deals with "outlaws" in The Extended Phenotype, ch. 8.) I'm more interested in the definitional problem which the practical issues highlight.
"Population outlaws" are outlaws because they don't share the limited increase goal which is supposed to be the general goal of natural selection. But if a limited increase goal is going to be the general goal of natural selection, it needs to describe the behavior of law-abiding genes and outlaw genes alike.
The general goal of natural selection has to be a law not in the sense of the law against train robbery, but in the sense of the laws of physics. Train robbers can decide to ignore the criminal code, but they've got to shoot straight or suffer the consequences, the same as any lawman. The general goal of natural selection must impose itself on outlaw genes the way the laws of physics impose themselves on gunmen.
Ideally, in fact, the general goal of natural selection will tell us why outlaw genes do what they do. A survival goal would seem to describe "population outlaws" well: All genes try to increase their probability of survival. Population outlaws are genes that attempt to survive at the expense of the other genes in a genome by cheating on their population discipline.
The existence of "population outlaws" shows that a limited "increase goal" cannot stand in even as the law governing the genome of a single species. Limited increase goals are even worse when applied to the genes outside of a genome. Even if there were no such thing as "population outlaws", a limited increase goal would describe the behavior of, at most, a narrow range of species.
A pure "increase goal" is general enough to cover all life, but we were forced to rule it out because it was incoherent. We have to rule out impure, or limited increase goals precisely because they are limited and specific.
With the elimination of both limited and unlimited gene-frequency goals, my argument that survival is the general goal of natural selection is complete. "Increase" goals and gene-frequency targets are tactics employed by certain genes at certain times in the battle for survival. Gene-frequency targets themselves evolve and go extinct. The goal of survival will not go extinct before life itself does.
Richard Dawkins ascribes two different goals to genes: "survival" and "increase". In previous posts, I pointed out that these produce different models, which in turn predict different results. I expanded the "goal" metaphor out into literal terms, and showed that if this "thought problem" is worked out with genes taken on a "snapshot" basis, their goal is clearly seen as survival.
In the last two posts I showed that "increase goals" will not work without a well-defined condition or "target". Pure "increase goals" had several problems, the worst of which showed up when I expanded the "goal" metaphor into literal terms. Pure increase goals require us to believe genes have an intent, not just metaphorically, but in literal fact. Unlike limited increase goals, where we can justify our statements that genes have those goals by pointing to the actual effect of the genes in the material world, pure increase goals require us to make statements about what genes "would" do if they "could". That takes us from metaphor into fantasy.
It remains to look at "increase goals" with well-defined conditions. Testable (if not necessarily realistic) examples might be "Increase the germline gene count if foraging produces more than the target level of N calories per average day, otherwise regulate the germline gene count to maintain or restore that level" or "Maintain a germline gene count which keeps the species at 9% of the epipelagic Antarctic biomass."
In one sense, these are not goals of "increase" as stated by Dawkins, but "maintenance goals". But I will give any goal based on germline gene frequency, honorary status as an "increase goal". More important than whether they track Dawkins language (Extended Phenotype, p. 84) closely is whether they make a satisfactory alternative to the survival goal. That's not a question that should be answered with a semantic quibble.
The basic problem with the limited versions of "increase goals" is best shown by their confusion in the face of outlaw genes. Assume that genes do have gene-frequency goals which, at least at points, involve maintaining a certain population level. What's to stop a new mutation that cheats? At first glance, it would seem that if the genome of a species has settled on a rule that says "stop increasing gene count at level X", any gene that ignores it will have a selection advantage over its law-abiding fellow genes.
I won't dwell on the practical side of this problem: how the law-abiding genes in a genome can "police" these outlaws. (Dawkins deals with "outlaws" in The Extended Phenotype, ch. 8.) I'm more interested in the definitional problem which the practical issues highlight.
"Population outlaws" are outlaws because they don't share the limited increase goal which is supposed to be the general goal of natural selection. But if a limited increase goal is going to be the general goal of natural selection, it needs to describe the behavior of law-abiding genes and outlaw genes alike.
The general goal of natural selection has to be a law not in the sense of the law against train robbery, but in the sense of the laws of physics. Train robbers can decide to ignore the criminal code, but they've got to shoot straight or suffer the consequences, the same as any lawman. The general goal of natural selection must impose itself on outlaw genes the way the laws of physics impose themselves on gunmen.
Ideally, in fact, the general goal of natural selection will tell us why outlaw genes do what they do. A survival goal would seem to describe "population outlaws" well: All genes try to increase their probability of survival. Population outlaws are genes that attempt to survive at the expense of the other genes in a genome by cheating on their population discipline.
The existence of "population outlaws" shows that a limited "increase goal" cannot stand in even as the law governing the genome of a single species. Limited increase goals are even worse when applied to the genes outside of a genome. Even if there were no such thing as "population outlaws", a limited increase goal would describe the behavior of, at most, a narrow range of species.
A pure "increase goal" is general enough to cover all life, but we were forced to rule it out because it was incoherent. We have to rule out impure, or limited increase goals precisely because they are limited and specific.
With the elimination of both limited and unlimited gene-frequency goals, my argument that survival is the general goal of natural selection is complete. "Increase" goals and gene-frequency targets are tactics employed by certain genes at certain times in the battle for survival. Gene-frequency targets themselves evolve and go extinct. The goal of survival will not go extinct before life itself does.
Saturday, July 28, 2007
Dawkins #5: "As Much As Possible" is Vacuous
[ This post is number 5 of a series. They will be of interest mainly to those who've read Richard Dawkins' book, The Selfish Gene. I recommend they be read in order. ]
Richard Dawkins ascribes two different goals to genes: "survival" and "increase". In previous posts, I pointed out that these produce different models, which in turn predict different results. I expanded the "goal" metaphor out into literal terms, and showed that if this "thought problem" is worked out with genes taken on a "snapshot" basis, their goal is clearly seen as survival.
In the last post I showed that pure "increase goals" (goals of increase without condition or limit) have several serious problems. By far the worst is that when the pure "increase goal" metaphor is expanded into literal terms, it's seen to require genes to have states of mind not just metaphorically, but literally. This makes pure "increase goals" incoherent, and that's a show-stopper.
So far I have not discussed "increase goals" with some kind of condition or limit. These can be coherent, and a number of them can be seriously meaningful. At first, a goal of "increase as much as possible" may seem to be an obvious choice among them.
But "increase as much as possible" is deceptive. It probably works, but that's because it's not really an "increase goal". "Do X as much as possible" means "Do X subject to condition Y." "Increase as much as possible" means "Increase, subject to condition Y." The only other goal Dawkins mentions is survival and "as much as possible consistent with survival" is the natural reading of the meaning hidden inside "as much as possible."
If we translate this goal into terms easier to model mathematically, we get "First maximize the probability of survival, and having done that, maximize the number of germline genes." Survival is a demanding goal. Since we are talking about our goal as the candidate for the general goal of natural selection, our gene will be battling for survival against genes selected over eons for their skill at surviving, including their skill in surviving at our gene's expense whenever it's in the slightest bit useful. Unlike increase, which must happen in units at minimum one amino acid in size, survival is a probability. Arbitrarily tiny advantages built up over time can make a difference.
The issue may be clearest if we look at the goal of "first maximize survival, then decrease the count of germlines genes as much as possible". This goal is coherent, and we don't have to worry about a gene with this goal decreasing itself to extinction. The first priority for the gene's efforts is survival. No effort will be available for any second priority.
If the gene's goal is "first maximize survival and then do Z as much as possible", Z can in fact be nonsensical. For example, Z might be "attend Rolling Stones concerts" and the fact that genes don't know how to buy tickets will make no difference -- they'll never have the chance to worry about it. The "do Z as much as possible" clause is completely vacuous.
Perhaps the reader never had any taste for slippery language like "as much as possible", and has been wondering why I'm going on about it. If so, I apologize. Goals like "increase the germline gene count until you've used 9.7601% of the Antarctic biomass, then sustain that biomass level" are both coherent and substantive. Unlike the incoherent and vacuous versions of the "increase goal" that I've been discussing, which can be dismissed a priori, specific gene-frequency goals are likely to reward empirical investigation. Even so, I think they are inferior to survival as a choice for the general goal of natural selection, and in my next post, I'll show why.
Richard Dawkins ascribes two different goals to genes: "survival" and "increase". In previous posts, I pointed out that these produce different models, which in turn predict different results. I expanded the "goal" metaphor out into literal terms, and showed that if this "thought problem" is worked out with genes taken on a "snapshot" basis, their goal is clearly seen as survival.
In the last post I showed that pure "increase goals" (goals of increase without condition or limit) have several serious problems. By far the worst is that when the pure "increase goal" metaphor is expanded into literal terms, it's seen to require genes to have states of mind not just metaphorically, but literally. This makes pure "increase goals" incoherent, and that's a show-stopper.
So far I have not discussed "increase goals" with some kind of condition or limit. These can be coherent, and a number of them can be seriously meaningful. At first, a goal of "increase as much as possible" may seem to be an obvious choice among them.
But "increase as much as possible" is deceptive. It probably works, but that's because it's not really an "increase goal". "Do X as much as possible" means "Do X subject to condition Y." "Increase as much as possible" means "Increase, subject to condition Y." The only other goal Dawkins mentions is survival and "as much as possible consistent with survival" is the natural reading of the meaning hidden inside "as much as possible."
If we translate this goal into terms easier to model mathematically, we get "First maximize the probability of survival, and having done that, maximize the number of germline genes." Survival is a demanding goal. Since we are talking about our goal as the candidate for the general goal of natural selection, our gene will be battling for survival against genes selected over eons for their skill at surviving, including their skill in surviving at our gene's expense whenever it's in the slightest bit useful. Unlike increase, which must happen in units at minimum one amino acid in size, survival is a probability. Arbitrarily tiny advantages built up over time can make a difference.
The issue may be clearest if we look at the goal of "first maximize survival, then decrease the count of germlines genes as much as possible". This goal is coherent, and we don't have to worry about a gene with this goal decreasing itself to extinction. The first priority for the gene's efforts is survival. No effort will be available for any second priority.
If the gene's goal is "first maximize survival and then do Z as much as possible", Z can in fact be nonsensical. For example, Z might be "attend Rolling Stones concerts" and the fact that genes don't know how to buy tickets will make no difference -- they'll never have the chance to worry about it. The "do Z as much as possible" clause is completely vacuous.
Perhaps the reader never had any taste for slippery language like "as much as possible", and has been wondering why I'm going on about it. If so, I apologize. Goals like "increase the germline gene count until you've used 9.7601% of the Antarctic biomass, then sustain that biomass level" are both coherent and substantive. Unlike the incoherent and vacuous versions of the "increase goal" that I've been discussing, which can be dismissed a priori, specific gene-frequency goals are likely to reward empirical investigation. Even so, I think they are inferior to survival as a choice for the general goal of natural selection, and in my next post, I'll show why.
Wednesday, July 25, 2007
Dawkins #4: Pure Increase is Incoherent
[ This post is number 4 of a series. They will be of interest mainly to those who've read Richard Dawkins' book, The Selfish Gene. I recommend they be read in order. ]
Richard Dawkins ascribes two different goals to genes: "survival" and "increase". In previous posts, I pointed out that these produce different models, which in turn predict different results. I expanded the "goal" metaphor out into literal terms, and showed that if this "thought problem" is worked out with genes taken on a "snapshot" basis, their goal is clearly seen as survival.
But I have not shown what happens if we run through the "thought problem" using methods of sampling that take into account the frequency of genes. And while I showed that "survival" works as a goal, I did not show that "increase", that is, increasing the number of germline genes, does not work even better as a goal.
If we look at multiple "snapshots" of genes from a frequency point of view, then the genes might be seen as having a goal of appearing in as many snapshots as possible. In this case we might be able to work through the "thought problem" in a way that justifies us in saying they have a goal of increasing their frequency in the sampling.
Devising an sampling method that's right for calculating gene frequency in the "thought problem" is not easy. There are genes deep in the ocean and deep inside the earth of which we know very little. And what of genes that may be traveling on meteorites, or elsewhere in the solar system? The sampling method needs to make sense as something that genes would seek to optimize. The sampling won't make sense as a "goal" for genes if it is biased in favor of genetic material that's easy for humans to find, or even in favor of genetic material humans know about.
Since we are dealing with a "thought problem", the sampling method can be one difficult or even impossible to carry out in practice, but that still leaves issues of definition. And if we can't measure what we say genes are optimizing, we can't test our assertion that they are selfish.
Picking a sampling method is not an issue for the "survival" goal. All the survival goal asserts, is that any gene having survived many generations of intense competition to end up in a snapshot can be said to have the "goal" of ending up in the snapshot. The logic of the survival goal is on a snapshot-by-snapshot, gene-by-gene basis, and sampling issues do not come up. Only if we are using frequency as determined by a sampling, which we have to if we want to define an "increase goal", does it matter whether the sampling is arbitrary, or biased.
The sampling issue may be solvable, at least in principle, so I will assume that it has been solved and move on. Increase goals have other, more serious, problems.
The pure form of the "increase goal" is incoherent. Nothing that comes in finite pieces can increase indefinitely. Every increase in the number of germline cells must be of a minimum size, certainly no smaller than the smallest possible amino acid. Long before the entire mass of the solar system is used up by germline genes in a single locus and for a single phenotype, increase must come to a halt.
At first glance, this may look like an unfair quibble. Take the statement that "Charles Ponzi's goal was to increase the amount of money in his Security Exchange Company." Ponzi's scheme itself may not have been sound or coherent, but it is certainly coherent (and probably true) to say that unlimited increase was Ponzi's goal. It is not incoherent to state that someone has an incoherent goal.
But there's a crucial difference between Charles Ponzi and a gene. A gene's goal must be coherent in terms of our "thought problem". That is, the "goal" ascribed to a gene must still make sense when the metaphor is translated into literal terms. Genes do not have minds in which to form schemes, and if translation of a goal into literal terms requires genes to have a mind of their own, then saying that genes have that goal is incoherent.
We are entitled to decide that Charles Ponzi had certain plans even if he never fully carried them out, in fact even if it would have been impossible for him to carry them out. We can do this because we believe Charles Ponzi was, in literal fact, a conscious being with a mind in which such a plan could exist. Based on Ponzi's actions and statements we can ascribe unrealized and even impossible goals to him.
We are not entitled to ascribe any "goal" to a gene if it means that we are stating that the goal was only in the gene's "mind". The gene has to actually carry out its goal, or we have no basis to say it was the gene's goal. We can't say that genes have the goal of unlimited increase, because we could never see them actually carry this goal out. Humans can be said to have impossible or unrealized goals, but genes cannot. Genes don't think and we can't go beyond metaphor and use the language of "goal" in a way that requires genes, literally and as a matter of actual fact, to have minds of their own.
I did not originally intend to use Charles Ponzi for my example. I'd wanted to use the statement "Richard Dawkins' goal is to increase the number of atheists" instead. But I couldn't, and the reason I could not is relevant. It's very difficult to come up with an example of a "pure increase goal" that doesn't involve insanity or delusion, because in the real world most such goals hit limits.
Dawkins, once he had converted every last man, woman, and child to atheism, would stop. (At least I think he would.) I assume, for example, that he would not go on to try to create a population explosion in order to further add to the count of atheists. Ponzi was the kind of wild optimist who does not think about potential obstacles. Deluded people like Ponzi can more easily be spoken of as having pure increase goals. A real gene with anything close to a pure increase strategy, in practice, would be likely to drive itself to extinction by overexploiting the resources it needs to survive, a fate not unlike that of Ponzi's scheme.
To be coherent, an "increase goal" must be impure, that is to say, limited in some way. In the next post, I'll comment on some "increase goals" which are limited and coherent, and explain why they also don't work as alternatives to the survival goal in explaining natural selection in general.
Richard Dawkins ascribes two different goals to genes: "survival" and "increase". In previous posts, I pointed out that these produce different models, which in turn predict different results. I expanded the "goal" metaphor out into literal terms, and showed that if this "thought problem" is worked out with genes taken on a "snapshot" basis, their goal is clearly seen as survival.
But I have not shown what happens if we run through the "thought problem" using methods of sampling that take into account the frequency of genes. And while I showed that "survival" works as a goal, I did not show that "increase", that is, increasing the number of germline genes, does not work even better as a goal.
If we look at multiple "snapshots" of genes from a frequency point of view, then the genes might be seen as having a goal of appearing in as many snapshots as possible. In this case we might be able to work through the "thought problem" in a way that justifies us in saying they have a goal of increasing their frequency in the sampling.
Devising an sampling method that's right for calculating gene frequency in the "thought problem" is not easy. There are genes deep in the ocean and deep inside the earth of which we know very little. And what of genes that may be traveling on meteorites, or elsewhere in the solar system? The sampling method needs to make sense as something that genes would seek to optimize. The sampling won't make sense as a "goal" for genes if it is biased in favor of genetic material that's easy for humans to find, or even in favor of genetic material humans know about.
Since we are dealing with a "thought problem", the sampling method can be one difficult or even impossible to carry out in practice, but that still leaves issues of definition. And if we can't measure what we say genes are optimizing, we can't test our assertion that they are selfish.
Picking a sampling method is not an issue for the "survival" goal. All the survival goal asserts, is that any gene having survived many generations of intense competition to end up in a snapshot can be said to have the "goal" of ending up in the snapshot. The logic of the survival goal is on a snapshot-by-snapshot, gene-by-gene basis, and sampling issues do not come up. Only if we are using frequency as determined by a sampling, which we have to if we want to define an "increase goal", does it matter whether the sampling is arbitrary, or biased.
The sampling issue may be solvable, at least in principle, so I will assume that it has been solved and move on. Increase goals have other, more serious, problems.
The pure form of the "increase goal" is incoherent. Nothing that comes in finite pieces can increase indefinitely. Every increase in the number of germline cells must be of a minimum size, certainly no smaller than the smallest possible amino acid. Long before the entire mass of the solar system is used up by germline genes in a single locus and for a single phenotype, increase must come to a halt.
At first glance, this may look like an unfair quibble. Take the statement that "Charles Ponzi's goal was to increase the amount of money in his Security Exchange Company." Ponzi's scheme itself may not have been sound or coherent, but it is certainly coherent (and probably true) to say that unlimited increase was Ponzi's goal. It is not incoherent to state that someone has an incoherent goal.
But there's a crucial difference between Charles Ponzi and a gene. A gene's goal must be coherent in terms of our "thought problem". That is, the "goal" ascribed to a gene must still make sense when the metaphor is translated into literal terms. Genes do not have minds in which to form schemes, and if translation of a goal into literal terms requires genes to have a mind of their own, then saying that genes have that goal is incoherent.
We are entitled to decide that Charles Ponzi had certain plans even if he never fully carried them out, in fact even if it would have been impossible for him to carry them out. We can do this because we believe Charles Ponzi was, in literal fact, a conscious being with a mind in which such a plan could exist. Based on Ponzi's actions and statements we can ascribe unrealized and even impossible goals to him.
We are not entitled to ascribe any "goal" to a gene if it means that we are stating that the goal was only in the gene's "mind". The gene has to actually carry out its goal, or we have no basis to say it was the gene's goal. We can't say that genes have the goal of unlimited increase, because we could never see them actually carry this goal out. Humans can be said to have impossible or unrealized goals, but genes cannot. Genes don't think and we can't go beyond metaphor and use the language of "goal" in a way that requires genes, literally and as a matter of actual fact, to have minds of their own.
I did not originally intend to use Charles Ponzi for my example. I'd wanted to use the statement "Richard Dawkins' goal is to increase the number of atheists" instead. But I couldn't, and the reason I could not is relevant. It's very difficult to come up with an example of a "pure increase goal" that doesn't involve insanity or delusion, because in the real world most such goals hit limits.
Dawkins, once he had converted every last man, woman, and child to atheism, would stop. (At least I think he would.) I assume, for example, that he would not go on to try to create a population explosion in order to further add to the count of atheists. Ponzi was the kind of wild optimist who does not think about potential obstacles. Deluded people like Ponzi can more easily be spoken of as having pure increase goals. A real gene with anything close to a pure increase strategy, in practice, would be likely to drive itself to extinction by overexploiting the resources it needs to survive, a fate not unlike that of Ponzi's scheme.
To be coherent, an "increase goal" must be impure, that is to say, limited in some way. In the next post, I'll comment on some "increase goals" which are limited and coherent, and explain why they also don't work as alternatives to the survival goal in explaining natural selection in general.
Saturday, July 21, 2007
Dawkins #3: Do Genes really Care?
[ This post is number 3 of a series. They will be of interest mainly to those who've read Richard Dawkins' book, The Selfish Gene. I recommend they be read in order. ]
In previous posts I identified two distinct goals Dawkins ascribes to genes: "survival" and "increase". I pointed out that these produce different models, models that will often predict different results.
I've been speaking of genes which "strive" to achieve "goals", and which "care" about outcomes. In this I've followed Dawkins, who finds it a helpful metaphor. We're dealing with foundations, however, so we need to be careful. Neither Dawkins or I imagine that genes are really conscious, much less that they actually have goals. It's time to slow the pace and speak more literally.
Let's look at a snapshot with a single gene in it. In the rare case our snapshot is of a recent mutation, we toss it in the trash and select another. That guarantees that our gene is the result of a long process of natural selection. Our gene, typically as part of a complexly organized team of genes, has passed a long series of stringent tests.
For example, if it's a gene in a cuckoo, a bird that lays its eggs in the nests of other birds and whose nestlings must trick the other birds into rearing them, it "is descended from a long line of ancestral cuckoo nestlings, every single one of who must have succeeded in manipulating its foster-parent. Any cuckoo nestling that lost its hold, even momentarily, over its host would have died as a result." (Dawkins, The Selfish Gene, 30th Anniversary Edition, 2006, p. 250). None of the genes in those nestlings who failed momentarily and died would, of course, have survived to be in our snapshot.
The gene's success is not because it, or anything or anyone else, planned for it. All the gene did was produce the amino acids which its chemistry forced it to produce. Fortunately for the gene, these were animo acids which helped produce successful cuckoos, generation after generation.
The gene in our snapshot originated long ago in a mutation, a random, purposeless accident. There were many other mutations, random like the one which created our gene, and almost all of them were disastrous. Those other mutated genes usually killed any cuckoo unlucky enough to inherit them, and disappeared along with the birds they killed. Because it is in our snapshot, our gene was one of the very rare ones which did not result in failure. It somehow survived alongside other, already successful germlines. Our gene may have added useful variation to the genes already in the cuckoo gene pool and found a comfortable niche among them. It may have survived by pushing other genes to extinction. Because it is in our snapshot, we know that whatever it took to survive, our gene did it.
At no point did our gene, the cuckoo, any other gene or anything or anybody else think this out, form any plans or set any goals. The gene in our snapshot was the result of a long series of accidents, each one by itself completely without purpose or meaning.
But over the millenia, this random series of separately meaningless events became something our brains see as having a purpose. This cuckoo gene produced amino acids which resulted in an intricate mix of behaviors and traits which resulted in the gene being in our snapshot. As for any of its comrade-genes that during that long period produced even slightly less successful amino acids, they are nowhere to be seen.
So it feels natural to us to speak of the gene as having undertaken the project of surviving so that it could appear in our snapshot. The length of the process which brought it into our snapshot makes it natural for us to speak of the gene "striving", of it "caring" about whether it wound up in our snapshot or not, and of it having "survival" as its "goal". The complexity of that process makes it natural for us to speak of the gene "planning" that success. The idea of genes which "care", and are "selfish" or "altruistic" comes naturally to our minds and lets the non-linear parts of our brain assist in putting together a picture of natural selection. But we need to remember this anthropomorphic language is a metaphor, and we must always be prepared to translate the metaphor into the unconscious, random processes which are the actuality of natural selection.
The reader who's been following me carefully will have noticed that "snapshot" was a crucial choice of words in the above. If we think of our selection of a gene for our thought problem as a "snapshot", the "goal" that falls out of following Dawkins logic through the "thought problem" is "survival", instead of an increase of the number of germ-line cells.
"Snapshotting" is the simplest way to picture sampling genes for our thought problems, and the above description shows it's a natural way of looking at the problem. But while simplicity and naturalness can and should give the feeling that we are on the right track, they are not proofs. Might not other ways of sampling genes for our thought problem result in the "goal" appearing to be an increase in the germ-line population?
If we view our sampling not as a "snapshot", but as some kind of "random sample", concepts of gene frequency enter into the picture. As natural and simple as the snapshot/survival viewpoint is, might not the viewpoint based on "random samples" be more revealing? And if so, wouldn't that support seeing the gene's goal as "increase"? In my next post, I'll examine that issue.
In previous posts I identified two distinct goals Dawkins ascribes to genes: "survival" and "increase". I pointed out that these produce different models, models that will often predict different results.
I've been speaking of genes which "strive" to achieve "goals", and which "care" about outcomes. In this I've followed Dawkins, who finds it a helpful metaphor. We're dealing with foundations, however, so we need to be careful. Neither Dawkins or I imagine that genes are really conscious, much less that they actually have goals. It's time to slow the pace and speak more literally.
Let's look at a snapshot with a single gene in it. In the rare case our snapshot is of a recent mutation, we toss it in the trash and select another. That guarantees that our gene is the result of a long process of natural selection. Our gene, typically as part of a complexly organized team of genes, has passed a long series of stringent tests.
For example, if it's a gene in a cuckoo, a bird that lays its eggs in the nests of other birds and whose nestlings must trick the other birds into rearing them, it "is descended from a long line of ancestral cuckoo nestlings, every single one of who must have succeeded in manipulating its foster-parent. Any cuckoo nestling that lost its hold, even momentarily, over its host would have died as a result." (Dawkins, The Selfish Gene, 30th Anniversary Edition, 2006, p. 250). None of the genes in those nestlings who failed momentarily and died would, of course, have survived to be in our snapshot.
The gene's success is not because it, or anything or anyone else, planned for it. All the gene did was produce the amino acids which its chemistry forced it to produce. Fortunately for the gene, these were animo acids which helped produce successful cuckoos, generation after generation.
The gene in our snapshot originated long ago in a mutation, a random, purposeless accident. There were many other mutations, random like the one which created our gene, and almost all of them were disastrous. Those other mutated genes usually killed any cuckoo unlucky enough to inherit them, and disappeared along with the birds they killed. Because it is in our snapshot, our gene was one of the very rare ones which did not result in failure. It somehow survived alongside other, already successful germlines. Our gene may have added useful variation to the genes already in the cuckoo gene pool and found a comfortable niche among them. It may have survived by pushing other genes to extinction. Because it is in our snapshot, we know that whatever it took to survive, our gene did it.
At no point did our gene, the cuckoo, any other gene or anything or anybody else think this out, form any plans or set any goals. The gene in our snapshot was the result of a long series of accidents, each one by itself completely without purpose or meaning.
But over the millenia, this random series of separately meaningless events became something our brains see as having a purpose. This cuckoo gene produced amino acids which resulted in an intricate mix of behaviors and traits which resulted in the gene being in our snapshot. As for any of its comrade-genes that during that long period produced even slightly less successful amino acids, they are nowhere to be seen.
So it feels natural to us to speak of the gene as having undertaken the project of surviving so that it could appear in our snapshot. The length of the process which brought it into our snapshot makes it natural for us to speak of the gene "striving", of it "caring" about whether it wound up in our snapshot or not, and of it having "survival" as its "goal". The complexity of that process makes it natural for us to speak of the gene "planning" that success. The idea of genes which "care", and are "selfish" or "altruistic" comes naturally to our minds and lets the non-linear parts of our brain assist in putting together a picture of natural selection. But we need to remember this anthropomorphic language is a metaphor, and we must always be prepared to translate the metaphor into the unconscious, random processes which are the actuality of natural selection.
The reader who's been following me carefully will have noticed that "snapshot" was a crucial choice of words in the above. If we think of our selection of a gene for our thought problem as a "snapshot", the "goal" that falls out of following Dawkins logic through the "thought problem" is "survival", instead of an increase of the number of germ-line cells.
"Snapshotting" is the simplest way to picture sampling genes for our thought problems, and the above description shows it's a natural way of looking at the problem. But while simplicity and naturalness can and should give the feeling that we are on the right track, they are not proofs. Might not other ways of sampling genes for our thought problem result in the "goal" appearing to be an increase in the germ-line population?
If we view our sampling not as a "snapshot", but as some kind of "random sample", concepts of gene frequency enter into the picture. As natural and simple as the snapshot/survival viewpoint is, might not the viewpoint based on "random samples" be more revealing? And if so, wouldn't that support seeing the gene's goal as "increase"? In my next post, I'll examine that issue.
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