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Can the Mind Be Modeled by Mathematics? Classic ID-related Paper Now Available Online

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I don’t know how long this has been available (I have looked before, but was unable to find it), but I just noticed that Douglas Robertson’s “Algorithmic information theory, free will, and the Turing test” is available online. This paper has been highly influential in ID circles, as can be attested by its citation list.

The main thrust of the paper is that, solely on the basis of mathematics, any mathematical physical theory is incapable of producing consciousness as we know it. The reason for this is that mathematics are incapable of producing mathematical axioms. Therefore, a mathematical physical theory is incapable of producing the mathematical axioms on which it is based.

The paper is a fantastic read, and anyone who is interested in ID or in the relationship of mind to matter should give it a read. It is definitely both readable and worthwhile.

Robertson’s conclusion is this:

The existence of free will and the associated ability of mathematicians to devise new axioms strongly suggest that the ability of both physics and mathematics to model the physical universe may be more sharply limited than anyone has believed since the time of Newton.

Now, I actually disagree with this, at least in a way. I think we will continue to advance in our models of the universe, but I think we will have to rethink the *types* of models we come up with. The models we have looked at so far are deterministic, past-determines-future models. I think we will need to be looking at non-deterministic, future-influences-present models in order to accurately model the universe as we find it.

For those interested in these kinds of topics, remember that there is a conference this summer covering these things and their practical applications – The Engineering and Metaphysics 2012 Conference. I hope to see you there!

Comments
Liddle at 7.2.1.1.34
What I do recall writing, is what you quoted earlier in this thread
Liddle at 7.2.1.1.39
Quotemining is ugly
:|Upright BiPed
January 18, 2012
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And here's some from me to you: Read whole sentences. Preferably whole posts. Quotemining is ugly.Elizabeth Liddle
January 18, 2012
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Dr Liddle,
No, that is not a paraphrase, UBP. Xs have failed to… is not the same as No X is able to…
Nor is what they consider the signature the same as what he/she thinks is the signature
Your protest is noted. May I offer some advice? Try limiting the number of times you double down.Upright BiPed
January 17, 2012
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gpuccio,
So, we must start with complex language output and with dFSCI, becasue those are the marks of conscious design, and not simple passive computation.
Presumably then you can take a sample of complex language output and determine the specific amount of dFSCI that is present in that sample? Would it be possible for you to give some example texts and the associated value for dFSCI present in each? Such examples would go a long way to help me understand the basis of your claims regarding dFSCI and complex language output. I have read what I can but nowhere can I find out how to determine the specific value of dFSCI for a specific example text. It may be the case that I have totally misunderstood dFSCI and in fact specific values for it cannot be determined. If that's the case then I don't understand what "test" you can run, as you seem to be claim to be able to, to determine if a specific text has dFSCI present, never mind determining a specific value for it. It would be great if you could clarify with a couple of example calculations as I have a number of follow up questions, some of which may be rendered moot by whatever your answer is.Peter Griffin
January 17, 2012
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a) In the definition of dFSCI it is stated explicitly that the onserved result must not be explained by a known algorithm. I know, because the definition is mine :) . But in Dembski description os the explanatory filter you will find the same concept. Again, supposed or hoped possible algorithms don’t qualify as scientific arguments. They are by definition non falsifiable. Have you ever heard of Popper?
But if the definition of dFSCI includes the condition that the result must not be explained by a known algorithm, then dFSCI is useless as an explanandum. If you came across a pattern that seemed to you to have dFSCI, any claim that it really did have dFSCI would simply be an argument from ignorance. It is true that your claim would be falsifiable (by finding an algorithm that produced your pattern), but that would not make it a supported claim. The fact that a claim is falsifiable does nothing to tell you whether it is true. (And yes, I've heard of Popper. I've read Popper.)
b) New just means anything you did not know before. The result of a computation is new, because you did not know it before. “Original”, in the context of dFSCI, means “bearing a new function”, that was not available before. No algorithm can create a new function that is complex enough, and that was not implemented in some way in the algorithm.
This isn't true AFAIK. Genetic algorithms can write new algorithms - actual, functional algorithms that did not exist before the GA was run.
That’s also what I mean by “unexpected” (the information in the algorithm nust not be added information to get to that specific function, neither directly nor indirectly). This is my personal opinion, never contradicted by any example. Anyway, I am not using this point to define dFSCI, or to propose it as a marker of design. By definition, dFSCI must not be the result of a known algorithm, so there is no circularity in the definition. If the darwinian algorithm were shown to be capable to explain biological information, that would simply mean that biological information does not contain dFSCI, not that the concept of dFSCI is wrong.
Exactly. It's not your definition that is circular, and I agree that if you are not proposing it as a marker of design, then fair enough. But what use is it, then?
There is no circularity at all. I am just using the concept of kolmogorov complexity. If a result can be generated by a simpler algorithm, its Kolmogorov complexity is the complexity of that algorithm. It is not circular. I am using a very specific type of complexity for the definition of dFSCI.
OK. So your claim is that non-intelligent processes cannot produce patterns that are both functional and incompressible? So what about the output from stochastic algorithms? They would seem to me to be both. Which was exactly Darwin's insight :)Elizabeth Liddle
January 17, 2012
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I think perhaps you are going to spend the rest of your life watching yourself painted into a corner. There is only one Hamlet, and Shakespeare is a rather high bar. But algorithms can write original music that ordinary people cannot distinguish from that of famous composers. My own guess is that narrative writing is a couple decades away, maybe less. Algorithms solved the four color map problem and have defeated human chess champions. I will grant that these two involved brute force approaches, but this kind of work is in its infancy.Petrushka
January 17, 2012
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Also, I am unfamiliar with the convention that single quotation marks indicate a paraphrase. Be that as it may, your paraphrase does not convey my meaning.Elizabeth Liddle
January 17, 2012
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No, that is not a paraphrase, UBP. Xs have failed to.... is not the same as No X is able to.... Nor is what they consider the signature the same as what he/she thinks is the signature given that I said very clearly, once it become evident that it was not clear, that I had been referring to CSI. I took as my text this paper by Dembski: Specification: the pattern that signifies intelligence because I (erroneously, as it turns out) thought that this was the urtext for ID. I have fully explained this, and your continued insistence that it was somehow post hoc, and is evidence of my dishonesty, is tiresome, particularly when, having discovered the confusion, I spent time trying to find out what you considered "the signature of intentional design". I stand by my original claim, with the given caveat. I no longer think you are honest either, so we will have to agree to differ as to which of us, if either, is lacking honesty. I've been charitably assuming that the problem has been communication, and I've taken at least partial responsibility for that. I still hope that is the case. Whatever. I cannot continue to converse with someone whose response to any disagreement is to assume that the other is being dishonest. I'll respond to any post you address to me, or in which you reference me, but apart from that we'd better go our separate ways I think.Elizabeth Liddle
January 17, 2012
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Liz, The direct of yours is one I have already given in full in double quotation marks at 7.2.1.1.21: “IDists have failed to demonstrate that what they consider the signature of intentional design is not also the signature of Darwinian evolutionary processes” ...in which I paraphrased again in single quotation marks at 7.2.1.1.31: ‘no IDist is able to demonstrating what he/she thinks is the signature of design, which isn’t also the signature of Darwinian processes’ The fact that you seize upon the PROFOUND difference between those two only reaffirms my charaterization of you as dishonest.Upright BiPed
January 17, 2012
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UBP: You claim that I claimed that "no IDist is able to demonstrating what he/she thinks is the signature of design, which isn’t also the signature of Darwinian processes". I do not recall claiming this, and the grammatical glitch suggests that you edited the subject of my original sentence. I may be wrong, but I'd like you to link to where I wrote that sentence, or retract the allegation that I wrote it. As you are leaving the thread, I don't expect you to do so, but I'm putting this comment here in my own defence. What I do recall writing, is what you quoted earlier in this thread: "IDists have failed to demonstrate that what they consider the signature of intentional design is not also the signature of Darwinian evolutionary processes" I was referring, as I explained, as you agree, had earlier explained, to Dembski's CSI. The other sentence does not sound like me, and if I did write it I'd like to a) see the context and b) have the opportunity to retract it if it is indeed what I wrote. I certainly do not hold the position it seems to suggest. And now, UBP, I'm going to depart from my usual habit when posting, and say that I find your last post, dishonest, self-serving, unwarranted, and obtuse. In future I will ignore your posts unless you are specifically responding to me, or referencing me.Elizabeth Liddle
January 17, 2012
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Not to belabor the point, but there are many Turing machines which do have infinite tape with infinite values preloaded. In fact, I believe that Matthew Cook's proof that Rule 110 is Turing complete he actually utilized an infinitely-many preloaded values in his cellular automaton. Nonetheless, I think in general that if you want to argue for the infiniteness of the universe, you are going to be arguing against mathematical physics, which is precisely the point that Robertson makes (not only that, but infinity itself creates a number of paradoxes). "Gödel’s theorem is not about physics." Exactly true, if by "physics" you mean the reality that we experience daily. That's actually the point of all of this. The logical structure of mathematics is not equivalent with physics. I'm not sure why you keep arguing this, because that's actually precisely the point where everyone here (you, me, and Robertson) all agree! The point - both of the paper and this post, is that Mathematical logic does not and cannot account for a lot of daily experience. Therefore, anyone who claims that mathematical physics can be entirely descriptive of reality is simply mistaken. This seems to be a point that we are agreed upon, yet you keep arguing as if you disagree.johnnyb
January 16, 2012
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"Darwinian evolution doesn’t explain how replication with heritable variation in reproductive success first came into being!" I see. So Darwinian evolution holds that it is neither sufficient nor necessary as an explanation for the very thing it attempts to explain. If this is so then Evolution must be contingent as a consequence of some other causes. And if contingent then am I to expect that I will receive the idea/knowledge of this contingent through revelation at some future date from Evolutionary Scientists? It seems we have a desperate modern need for the second-coming of Spinoza.Maus
January 16, 2012
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And once again, my apologies to GP. There is no need to sponse Dr Liddle, I am leaving the thread, and your answer is canned anyway. :/Upright BiPed
January 16, 2012
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From 7.2.1.1.29
Good
In May of last year you made the open claim that ‘no IDist is able to demonstrating what he/she thinks is the signature of design, which isn’t also the signature of Darwinian processes’. I challenged you on that remark with a singular phrase; the “rise of information”. I did not couch my challenge in the language of mathematics, or probabilities, or complexity, or CSI, or FSCI, or anything other than the “rise of information’. You took that challenge and stated that you could simulate the “rise of information” using Darwinian processes. After a couple of months of discovery, I felt that it had become perfectly clear that you would not be able to demonstrate the rise of information, and you yourself were beginning to hint at that same possible conclusion. So I went back and got your original text which had begun our exchange. I quoted you directly, and asked you to retract the comment based upon the documented facts of the conversation. Disregarding that very same documentation, you immediately refused, escaping under the childish auspices that you were “talking about Dembski”, even though a) he doesn’t appear in the quote, b) I never mentioned him in any of the discovery except to remind you that I was not talking about Dembski, or Meyers, or CSI, or any of it, and c) you did neither retract nor qualify your remark when it became clear to you that I was not talking about Dembski, or Meyers, or CSI, or any other proponent or concept . Yet to this very day you continue to equivocate and evade an ethically-fair response. And so, I asked you once again to reconsider the remark you made:
Well, I don’t know, UBP. I don’t think any IDist has demonstrated that the simplest possible Darwinian-capable self-replicator is still too complex to have arisen by chance.
That was not the question, Dr Liddle. Do you not have any conscience at all? Are you capable of any truly genuine sense whatsoever of right and wrong in your actions regarding this matter? I don’t see it, Dr Liddle. Where is it? Are you a scientist or not? Allow me to show you how this is done Dr Liddle: “Yes, design proponents have produced some interesting evidence with regard to the rise of recorded information transfer in biological systems. I personally remain unconvinced by that evidence, but I cannot in good conscience maintain that the evidence does not exist or that it cannot be legitimately considered as evidence of design”. Now tell me, why is such a modest yet materially-honest response so far beyond your personal and professional capabilities Dr Liddle? It sure seem like a heavy price to pay.Upright BiPed
January 16, 2012
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UB: You are always welcome! :)gpuccio
January 16, 2012
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Elizabeth: a) In the definition of dFSCI it is stated explicitly that the onserved result must not be explained by a known algorithm. I know, because the definition is mine :). But in Dembski description os the explanatory filter you will find the same concept. Again, supposed or hoped possible algorithms don't qualify as scientific arguments. They are by definition non falsifiable. Have you ever heard of Popper? b) New just means anything you did not know before. The result of a computation is new, because you did not know it before. "Original", in the context of dFSCI, means "bearing a new function", that was not available before. No algorithm can create a new function that is complex enough, and that was not implemented in some way in the algorithm. That's also what I mean by "unexpected" (the information in the algorithm nust not be added information to get to that specific function, neither directly nor indirectly). This is my personal opinion, never contradicted by any example. Anyway, I am not using this point to define dFSCI, or to propose it as a marker of design. By definition, dFSCI must not be the result of a known algorithm, so there is no circularity in the definition. If the darwinian algorithm were shown to be capable to explain biological information, that would simply mean that biological information does not contain dFSCI, not that the concept of dFSCI is wrong. c) You say: So your argument is that if something is produced by an algorithm it cannot be complex because it can be compressed to that algorithm? But that is completely circular! There is no circularity at all. I am just using the concept of kolmogorov complexity. If a result can be generated by a simpler algorithm, its Kolmogorov complexity is the complexity of that algorithm. It is not circular. I am using a very specific type of complexity for the definition of dFSCI. d) You say; But this is pure assertion! No. The meaning is: Hamlet is not compressible by any known algorithm. A new theory of reality is not compressible by any known algorithm. In the hurry, I had just forgot to defend myself in advance from your non scientific "there could always be... " arguments. I must be very careful with you :) . You say: We would normally say that Hamlet is incompressible because we have no algorithm that can produce Hamlet. That's correct. But if we saw pi to a million decimal places, it would look just as incompressible until someone showed us the algorithm. Wrong. If we saw the series of digits, withot knowing its meaning (its function), we could just think that it is a random series of digits (indeed, it has all the formal properties of a random number). Therefore, we would not see dFSCI in it, because we would see no function. It could just be a false negative (as you know, there are many). Indeed, if we can recognize the function (this is the sequence of the decimal digits of pi), then we have to ask ourselves: can that sequence be computed by an algorithm? Then its complexity is the complexity of the algorithm. We would probably correctly judge that it is dFSCI, if the algorith in itself is complex enough (and it probably is). And our judgement would be correct, because an algorithm to compute the decimal digits of pi would not arise randomly, and is certainly designed (again, I am reasoning here just to make an example, without knowing the minimal complexity in bits of such an algorithm). So, your example is not correct. If we saw Hamlet without knowing english, we could perhaps conclude that it is a random sequence of letters (false negative). But if we know english, and can read and understand its content, we would have no doubt that it cannot be generated by any known algorithm, and that it is by far too complex to be generated in a random system. So we would correctly infer design. e) You say: And if we are, in addition, allowed to specify all the input to our algorithm, when compressing the output, including every random number, every stochastic twitch, every click from the Geiger counter that we set up as additional input so that the thing was truly unpredictable, then who is to say that the output of a GA, or for that matter, the output from Shakespeare’s pen is not thus compressible? Now, this is pure assertion. Non scientific. Non falsifiable. Assuming the truth of a specific theory of consciousness that cannot be proved and has no empirical support. And anyway, as already stated, my definition of dFSCI only requires that the observe result cannot be explained by any known algorithm. And anyway the algorithm you are proposing is certainly more complex than Hamlet itself! It would not be a good form of "compression". Do you really not see the circularity here? There is no circularity. I am only assuming that you already know: 1) My definition of dFSCI 2) The empirical reasons why I consider dFSCI "a mark of conscious design". I have told you those things many times, that's why I assume you should know them.gpuccio
January 16, 2012
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No. It is not dFSCI. And it is computed by an algorithm. A new output is not necessarily original.
Well, of course it's computed by an algorithm! Your claim was that an algorithm cannot create dFCSI! So I suggested one that could! You can't dismiss it because it's an algorithm! Am I misunderstanding you? And how are you distinguishing between "new" and "original"?
Take an algorithm which computes the diogits of pi, for example. Each new digit is new, because we had not it a moment before (unless we already knew those figures in other ways). But it is not new dFSCI.
Why not? I'm not saying it is, but why isn't it, in your view?
The function remains the same, and the new figures are computed by the same algorithm. Therefore, the output is compressible information, and therefore not complex in the Kolmogorov sense.
So your argument is that if something is produced by an algorithm it cannot be complex because it can be compressed to that algorithm? But that is completely circular!
The output of an algorithm is always compressible. The novelty in it can come from an input of outer information, but the algorithm is repetitive.
Hamlet is not compressible. A new theory of reality is not compressible. Those are cognitive creations, and require consciousness.
But this is pure assertion! We would normally say that Hamlet is incompressible because we have no algorithm that can produce Hamlet. But if we saw pi to a million decimal places, it would look just as incompressible until someone showed us the algorithm. And if we are, in addition, allowed to specify all the input to our algorithm, when compressing the output, including every random number, every stochastic twitch, every click from the Geiger counter that we set up as additional input so that the thing was truly unpredictable, then who is to say that the output of a GA, or for that matter, the output from Shakespeare's pen is not thus compressible? I mean, you can assert it, but you would be assuming your consequent. You can't argue that Hamlet doesn't possess dFCSI because it isn't produced by an algorithm plus a vast matrix of inputs, and then say, therefore it wasn't produced by an algorithm plus a vast matrix of inputs. Perhaps it was. Perhaps that's what consciousness is.
So, we must start with complex language output and with dFSCI, becasue those are the marks of conscious design, and not simple passive computation.
Do you really not see the circularity here?Elizabeth Liddle
January 16, 2012
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remember very well. I challenged you based on that particular comment.
Good.
But so then, IDist have demonstrated what they consider to be the signature of intentional design, which isn’t also the signature of Darwinian processes, but it’s just not Demski’s CSI. Is that correct?
Well, I don't know, UBP. I don't think any IDist has demosntrated that the simplest possible Darwinian-capable self-replicator is still too complex to have arisen by chance. That's what lots of people are working on. Nobody's demosntrated that it isn't, although there are promising leads, but nor has anyone demonstrated that it is (which would be harder, of course, scientific methodology being set up the way it is). But I certainly agree that Dembski's CSI is not the signature of design.Elizabeth Liddle
January 16, 2012
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I repeat that all forms of algorithmic computing are independnt from the hardware, and can be implemented on any computing machine, starting with an abacus.
That's one of those things that can be declared true by definition, but is not true in practice. the paper I linked describes the problem. Feedback driven systems cannot be modeled with precision, because the physical systems providing the feedback cannot be modeled precisely. In the case of the swarm fliers, the physical implementation of the system is not exactly equivalent to the model. The same is true of chemistry. Protein folding has not been precisely modeled, and it is not currently possible to have a predictive theory of sequence design. It may remain impossible. If you are going to posit a finite, non-theistic designer, you really need to have a theory of design.Petrushka
January 16, 2012
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sorry GP... I'll get out of the way. No need to reply Liddle.Upright BiPed
January 16, 2012
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I remember very well. I challenged you based on that particular comment. But so then, IDist have demonstrated what they consider to be the signature of intentional design, which isn't also the signature of Darwinian processes, but it's just not Demski's CSI. Is that correct?Upright BiPed
January 16, 2012
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Elizabeth: You say:
No, let’s not start with complex language output. What is wrong with my SVM output? It’s an algorithm. Its output is new (and therefore original). Its output digital. Its output is highly complex – the chances of getting that output from some comparable random data generator are tiny. Its output specified – it is one of a much smaller set of coherent sensible outputs. And its output is information. It tells me something I didn’t know before.
No. It is not dFSCI. And it is computed by an algorithm. A new output is not necessarily original. Take an algorithm which computes the diogits of pi, for example. Each new digit is new, because we had not it a moment before (unless we already knew those figures in other ways). But it is not new dFSCI. The function remains the same, and the new figures are computed by the same algorithm. Therefore, the output is compressible information, and therefore not complex in the Kolmogorov sense. The output of an algorithm is always compressible. The novelty in it can come from an input of outer information, but the algorithm is repetitive. Hamlet is not compressible. A new theory of reality is not compressible. Those are cognitive creations, and require consciousness. So, we must start with complex language output and with dFSCI, becasue those are the marks of conscious design, and not simple passive computation.gpuccio
January 16, 2012
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What I will say, though (as I've said before): if the ID argument was that the simplest possible Darwinian-capable self-replicator is still too complicated to have arisen by chance, you'd have a point (and sometimes I see that argument made). However, that wouldn't be an argument against Darwin's theory, or Darwinian evolution, or Darwinism at all. It would be an inference of design from the unlikelihood of abiogenesis. And the counter argument is, simply: you cannot infer that because we do not know how simple the simplest Darwinian-capable self-replicator is that it is necessarily too complex to have arisen by chance. Therefore we cannot infer "design". We can only conclude that we do not yet know the answer.Elizabeth Liddle
January 16, 2012
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until the rise of symbollic representations and transfer protocols has been shown to have an unguided origin
It's been rather rare in the history of science to find processes that have unequivocally been guided by unseen intelligences. Off the top of my head I can't think of a single physical physical event studied by science that has been explained by non-material or non-human intelligent guidance. To unguided will remain the default hypothesis for people who are actually interested in the origin of life. Certainly the search continually yields new chemistry.Petrushka
January 16, 2012
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Then this statement: “IDists have failed to demonstrate that what they consider the signature of intentional design is not also the signature of Darwinian evolutionary processes” is false by your own observations, and should be retracted until the rise of symbollic representations and transfer protocols has been shown to have an unguided origin (iow, in favor of the evidence as it actually is). Correct? No. What I meant by "the signature of intentional design" was CSI. I should have been specific then, but I later clarified it. I had assumed we were talking about Dembski's position. As you will remember.Elizabeth Liddle
January 16, 2012
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BIPED: Now you’ll need a source of symbollic representations and transfer protocols operating in a coordinated system. LIDDLE: You know, Upright BiPed, you are absolutely right! BIPED: Then it doesn’t explain the rise of the very thing that organizes inanimate matter into functioning organic systems, does it? LIDDLE: No, it doesn’t!
Then this statement: "IDists have failed to demonstrate that what they consider the signature of intentional design is not also the signature of Darwinian evolutionary processes" is false by your own observations, and should be retracted until the rise of symbollic representations and transfer protocols has been shown to have an unguided origin (iow, in favor of the evidence as it actually is). Correct?Upright BiPed
January 16, 2012
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Heh. Yeah, damn varifocals. Still, it made for an interesting variant :) But yeah, Darwinian evolution can't get going without the minimal information transfer system required for self-replication with variance that results in differential reproductive success. Once you've got that, you've got the ability to bootstrap in lots more information (which I thought you might mean by "Darwinian" information).Elizabeth Liddle
January 16, 2012
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Well, the interesting thing about Szostak's work, is that he's pushing back the boundaries for the simplest self-replicator capable of Darwinian evolution. If he can get it simple enough, then the chances of spontaneous formation go up, and then it's Darwinian evolution all the way from there.Elizabeth Liddle
January 16, 2012
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"Darwinian Information"? That was an equivocation taken directly in the face of contrary evidence.Upright BiPed
January 16, 2012
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Without equivocation, that's the problem being studied by Szostak and others. It's not like the problem has been hidden away.Petrushka
January 16, 2012
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