Profile for Student of Trinity
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| Displayed name | Student of Trinity |
| Member number | 3431 |
| Title | Electric Sheep One |
| Postcount | 3335 |
| Homepage | |
| Registered | Thursday, September 4 2003 07:00 |
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| Regulation - Common Descent in Geneforge 4: Rebellion | |
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Electric Sheep One
Member # 3431
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written Tuesday, May 15 2007 22:31
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I'm not sure it's exactly proof that they have a common ancestor, but it would seem to be a proof, given evolution by common descent, that the modern species whose common ancestor with tyrannosaurs was most recent is the chicken. There is additional support for common descent here, although I wouldn't say it goes as far as proof. Tyrannosaur and chicken proteins are apparently more similar to each other, than chicken proteins are to the proteins of many other modern species. This is the sort of thing one would predict readily from common descent evolution, but it is otherwise a highly improbable coincidence. So, more Bayesian empirical support. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Regulation - Complexity sidebar in Geneforge 4: Rebellion | |
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Electric Sheep One
Member # 3431
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written Tuesday, May 15 2007 10:05
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That is the very question that I asked Stillness somewhere around page 2 of the first, more general incarnation of this thread. He never has answered it in any way I've been able to recognize. Since 'we have only observed X to happen this way' has no implications by itself for whether or not X has ever happened otherwise in the past, I am trying to figure out what additional premises Stillness is using to reach his conclusion. As far as I can see, he admired Behe's irreducible complexity argument, which is understandable. He wished to retreat from Behe's indefensibly extreme irreducibility premise, which was wise. So he declared a premise about a much looser kind of irreducible complexity, which was conveniently easy to defend; but it has turned out not to be strong enough to imply his desired conclusion. It seems to me that if Stillness actually had a clear argument to connect his weak premise and his objective, he would immediately have appreciated the questions we were raising, and brought his clear argument forth to answer them, with all the enthusiasm of a mousetrap inventor asked about mice. From the awkward way in which he is instead shifting to question-begging premises, excusing himself from good logic by alleging bad logic in astronomy, and demanding that we formalize our own arguments on other lines instead of looking too closely at his complexity argument, I infer that Stillness does not have as good an argument as he thought he did when he raised the complexity line, and is having trouble improvising a better argument under pressure. Maybe I'm wrong, and he has a good argument, but our language difficulties have prevented him from appreciating what we have been asking, or presenting his answers in a way we can understand. If so I invite him to try again. If I'm right, though, he should simply confess this and give up the complexity line of argument, reserving the right to raise it again in the future if he later thinks he can get it working properly. Losing a battle isn't losing a war. I know lots of true things, for which I also know some failed arguments. These arguments seem strong at first glance, but when you really dig into them, they fall apart. Nevertheless the conclusions they were trying to establish are true, and are supported well by other arguments. There are, for example, very many invalid proofs of Fermat's Last Theorem, many of which looked promising at one time. There is also one valid proof, and that is enough. Even if Stillness eventually he finds himself left with no good arguments for design against evolution, this doesn't mean he has to be come an enthusiastic neo-Darwinist. He could perfectly well say, even in that worst case, that he doesn't like NDT and feels in his heart that it must be wrong, even though at the moment he can't muster a good scientific argument against it. I have some similar attitudes to current cosmology, and I know a recent Nobel laureate in physics whose attitude to quantum mechanics is similar as well. [ Tuesday, May 15, 2007 10:15: Message edited by: Student of Trinity ] -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Regulation - Complexity sidebar in Geneforge 4: Rebellion | |
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Electric Sheep One
Member # 3431
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written Tuesday, May 15 2007 01:38
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This thread is the complexity sidebar, and the appeal to irreducible complexity is your argument, Stillness. If you want to make another thread about the logic of evolution, go ahead. But let's keep this one about your complexity argument. Not keeping focus until a conclusion is reached is what lets this discussion drag on inconclusively. What you have presented now is indeed a valid syllogism, but what it does is to establish trivial points, given a premise which is itself the entire thing that we asked you to explain logically: Why do you think that anything you class as irreducibly complex can only have resulted from purposeful agency? What we have been pressing you to do for several posts now is to break down your current 1) into a multi-step logical argument, or else admit that you are simply assuming that evolution is false. What you have been doing for several posts now looks like really blatant ducking and stalling, in the face of a very simple and basic question, several times repeated. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Regulation - Complexity sidebar in Geneforge 4: Rebellion | |
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Electric Sheep One
Member # 3431
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written Monday, May 14 2007 22:37
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This is indeed a bit dismaying. The point is not at all that we are demanding that Stillness prove his position is true. He can state any premises he wants, so there is no reason he can't produce a valid argument from those premises to whatever conclusions he wants. That's not proof, because we will probably not all agree that those premises are true. But it will clarify greatly what Stillness is really trying to say. Normally in a discussion one does not bother with quite this level of logical pedantry, but it is very helpful in cases where the two sides are having difficulty establishing common language. Stillness's use of the term 'irreducible complexity' has puzzled and frustrated the rest of us, in that his definitions of the term do not seem to us to jibe with the conclusions he draws from it. Laying out a valid logical argument, with conclusions all following from premises, cuts through communication problems and terminological confusion. There is no need to keep wondering about what exactly a given term might mean, when we can see exactly what it has to mean for the argument in which it is used to be valid. And it's an exercise that is worth going through occasionally, for anyone. It is all too easy to lull oneself into confidence in a conclusion, with rhetoric and friendly audiences. Perhaps if popular science writers did this kind of thing more often, instead of writing so many gee-whiz texts for the choir, we would have fewer smart people wasting their talents on pseudoscience. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Regulation - Complexity sidebar in Geneforge 4: Rebellion | |
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Electric Sheep One
Member # 3431
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written Monday, May 14 2007 12:21
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Stillness, right now I am just trying to figure out what your logic acually is. As far as I can tell, you have an extra premise that gets you from 2) to 3). The closest you get to articulating this premise is to describe a principle that 'we go with what we know'. I am not at all sure what this means, though. Can you not articulate this more explicitly? Under what principle do you conclude, from the fact that the only interdependent structures whose development we have witnessed have been designed by humans, that all interdependent structures must be products of design? It would be also be nice if you stated plainly how important it is to you whether evolving interdependent structures is in principle difficult, as opposed to merely not being directly observed. At the moment you seem to be arguing only from absence of direct observations, and do not seem to be basing anything logically upon this difficulty proposition; but on the other hand you do seem to suggest that the difficulty exists, and perhaps adds weight to your argument. Since you are only defending a notion of irreducible complexity that has to do with large abrupt changes to a system, whereas evolution is about very gradual changes, I do not see how your kind of irreducible complexity poses any difficulty for evolution. So it would be nice if you either explained why you think your IC is hard to evolve, or stopped mentioning this issue of difficulty. If you read my recent posts you'll see that I have been trying to get you to clear this up for some time now. I can perhaps try to help by analyzing the example you provide, of inferring extrasolar planets from stellar wobbles. As you might imagine from remembering my numerous posts on the topic in the previous thread, Bayesian inference from accurate prediction is once again the key here. Newtonian gravity makes precise, quantitative predictions for the motion of a star perturbed by a large orbiting planet. The planet's mass and orbit parameters are used as free fitting parameters, but Keppler's Laws still provide a very enormous constraint upon a priori arbitrary motion. The orbiting planet theory of stellar wobble is inconsistent with anything but elliptical motion with a particular fixed relationship between radius and velocity. The stellar wobbles that we see obey these constraints, and this provides very strong empirical support for the orbiting planet theory. Astronomers base their inference of planets on this quantitative fulfillment of prediction, not on 'flawed logic' or any vague principle of 'going with what we know'. I don't see that your design theory can claim anything similar here, so I don't see how the astronomical reasoning can provide a parallel to yours. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Regulation - Complexity sidebar in Geneforge 4: Rebellion | |
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Electric Sheep One
Member # 3431
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written Monday, May 14 2007 07:23
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Sorry to put words in your mouth, Stillness, but I'm afraid you need some help in making your own logic clear. Your point 1) is not actually used in any of the rest of your logic, so you should not list it. Your point 2) is what actually serves the logical purpose of being a premise in your argument. In your mind you may think of 1) as a reason why 2) is true, but you have never actually argued from 1) to 2). Nor do you need to; everyone will, I think, agree that 2) is empirically true. So your logic starts from 2) as its premise, which is what I said. Your point a) serves no logical purpose in your argument, either. The proposition that mutations are not observed to produce X is already implied by your 2), that only purposeful action is observed to produce X. Nothing can follow from a) that does not already follow from 2), so you should not list a). Your point 3) does not logically follow from your 2). Saying this is not a subjective judgement on my part; it is a simple fact. Consult any logician you like, and they will all agree. Creationist logicians may agree with you that 3) is true, but they will still tell you that it does not follow from 2) alone. If you do not understand this, please ask about it and I will try to explain further. If you do not simply mean to assume 3), then you must somehow show that 3) follows logically from some premise other than itself. This you have not yet done, so at present your 3) stands as a pure assumption on your part. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| GF 1 - Shaper Crypt in Geneforge Series | |
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Electric Sheep One
Member # 3431
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written Monday, May 14 2007 05:28
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I've never bothered with endurance, but just pumped Int, battle magic, and spellcraft, with some quick action to make sure I get to act first. With a strong enough offense, you don't need defense, and it's more fun to blast things than to take hits. On torment difficulty Agents aren't quite such a breeze to play as on normal, but they are still easier than the other classes. Guardians on torment are a bit tough. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Regulation - Complexity sidebar in Geneforge 4: Rebellion | |
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Electric Sheep One
Member # 3431
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written Monday, May 14 2007 05:04
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What Stillness has really said is this: 1) The particular property of his kind of irreducible complexity upon which he intends to argue further is, that it is only observed now to arise through purposeful action. 2) The conclusion he wishes to draw from this premise is that his kind of irreducible complexity can only have arisen at any time, or over any time period however long, through purposeful action. 3) Stillness has not actually said why he thinks 2) follows from 1), but he seems to be implicitly assuming that nothing can happen on very long time scales that is not observed on short time scales today. Stillness needs this assumption, because without it his 2) does not follow at all from his 1). But this assumption is, of course, tantamount to simply assuming that evolution has not occurred. So the only real role played by irreducible complexity in this argument by Stillness is to throw the spoils to design after evolution has been slain by assumption. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| To the moon in General | |
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Electric Sheep One
Member # 3431
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written Sunday, May 13 2007 23:26
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It won't be cost effective to have people living on Mars, until there are a bunch of people living on Mars. Then they will find it cost effective to survive. Eventually people will live well there, I believe. It will in some ways be radically different from the colonization of the Americas by Europeans, but in some ways similar. Until that take-off point, colonizing Mars will be a huge expense of resources for negligible material reward. It will be an enormous cultural monument, the greatest in history. But I think we'll do it, probably within a century. (Not to the level of terraforming, of course, but just maintaining a dome base or something.) We won't do it for any good reason, but just because we can. Taxpayers will vote for it, as a luxury they want to buy at an average of ten or a hundred bucks per head per year, and it will happen. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| To the moon in General | |
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Electric Sheep One
Member # 3431
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written Sunday, May 13 2007 19:23
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At the World's Fair in Hannover a few years ago, the Chinese pavilion was entirely about their upcoming moon mission. Its centerpiece was a single large room with a lunar rover in it, looking just like the old Apollo ones, except with a small PRC flag. It all gave me the feeling that they were excited about charging forward into the 1970s, and at the time all I could think was, Guys, haven't you heard? It's been done already. But they were clearly pretty keen. The fact that the Chinese pavilion looked so out of date, because everything looked just like 30 year old Apollo gear, probably just meant that they were at such an early stage they didn't really know what their stuff would look like. Or that they're seriously planning on just copying everything, I guess. Anyway, I'm sure they'll get there, at some point before too long. They do seem to want it more than the US does. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Regulation - Complexity sidebar in Geneforge 4: Rebellion | |
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Electric Sheep One
Member # 3431
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written Saturday, May 12 2007 22:20
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I'd really like to hear a serious answer to this last post by Alorael. At the moment I have the impression that Stillness is simply confused by his own term, 'irreducible complexity'. The term has a strong definition, including the impossibility of development by gradual advantageous stages. And for Stillness at least it also has a weak definition, which includes only modular interdependence of modern biological structures. The strong form of irreducible complexity has strong implications for evolution, but not even its plausibility, and far less its truth, can be demonstrated. The weak form of irreducible complexity is a banality with no implications for evolution or design, but it is undeniably true. Stillness seems to be trying to have his cake and eat it too, by claiming the consequences of strong irreducible complexity, while only offering to defend the weak version. If this is not the case, then what Stillness needs to do is state clearly and plainly: 1) exactly what properties of 'irreducible complexity' he means to draw logical conclusions from; 2) what his conclusions from those premises are; and 3) how he thinks those conclusions follow logically from his premises. It's time to cut through ambiguous terminology, and commit to a clear logical argument. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Regulation - Complexity sidebar in Geneforge 4: Rebellion | |
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Electric Sheep One
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written Saturday, May 12 2007 02:03
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Looks like we are all responding to an irreducibility argument that Stillness did not intend to make, or that he once advanced but has now withdrawn. This irreducibility argument is that certain complex structures are so complex and interdependent that they cannot possibly be altered even microscopically without total failure. I think it's too bad that this does not seem now to be Stillness's irreducibility argument, because this argument is the best one ID has. As far as I know it is the only ID argument that is valid, meaning that its conclusions really do follow from its premises. If there truly were any such structures, evolution could not explain them. But this argument is unsound, meaning that its premises are not true: in fact there do not exist any such structures. Very small and gradual alteration of even the most complicated interdependent system can easily change it, eventually dramatically, without any sudden loss of functionality. Anyway, what I now understand Stillness to be saying is that he doesn't mean this microscopic irreducibility argument, but only something much more trivial. He identifies modular interdependency, which is how he now defines irreducible complexity, as one particular property observed in modern organisms, and which has not been directly observed to develop by evolution. Of course there are zillions of other properties of which the same can be said. Having big wide ears is a property observed in modern elephants, and evolution of big wide ears has never been observed. Purely as a problem for evolution, modular interdependence is nothing special. Stillness does not seem to be claiming, now, that modular interdependence is any harder in principle to evolve than big wide ears, or long necks, or whatever. He is only claiming that, like those other properties, its evolution has not been directly observed. The reason Stillness picks on this one particular property of modular interdependence seems to be just that, unlike long necks and big wide ears, it is a property of many designed objects. So he considers this to be not just a problem for evolution, but also an argument in favor of intelligent design. Stillness, is this really what you are now trying to say when you write about irreducible complexity? -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Regulation - Complexity sidebar in Geneforge 4: Rebellion | |
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Electric Sheep One
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written Friday, May 11 2007 14:36
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quote:Okay, now we're getting a serious disconnect. This makes no sense as a response to my post, and it doesn't even make sense as a continuation of your own statements. If 'irreducible' doesn't mean 'impossible to reduce', then you've been abusing language badly. If all it means is that things break if you suddenly tear big important chunks out of them, then why on earth have you been talking so much, in this discussion of evolution and design, about such an irrelevant banality? -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Regulation - Complexity sidebar in Geneforge 4: Rebellion | |
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Electric Sheep One
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written Friday, May 11 2007 10:26
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quote:You seem to have missed the point. Yes, there are several large modules in the visual system, and abruptly removing any one of them makes it all useless. But this is absolutely not irreducibility in any sense relevant to evolution, because evolution is about changes far more gradual than anything as gross as abruptly removing an entire module. Harping on about how removing nerves or lenses or retinas makes eyes fail, and calling that irreducible complexity, is sheer dodge. It has nothing to do with the actual issue at hand. I mean, congratulations: you've proven that eyes can't evolve by having modern lenses suddenly pop into modern eyes that were only missing lenses. If you can possibly find anyone who thinks eyes could develop that way, you can really set them straight. But if you imagined that scenario had anything to do with evolution, you were really out of touch. [ Friday, May 11, 2007 10:29: Message edited by: Student of Trinity ] -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| It is done. in General | |
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Electric Sheep One
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written Friday, May 11 2007 08:10
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Aran is to become a 'Mathematical-Technical Assistant'. I don't really know what that qualifies him for, though. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Major problems help needed! in Geneforge 4: Rebellion | |
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Electric Sheep One
Member # 3431
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written Friday, May 11 2007 06:11
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Explore more before confronting Monarch. Search his quarters while he's still standing around to the south. If your character knows about control rods, then you may be able to find something to help. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| College, majors, etc. in General | |
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Electric Sheep One
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written Friday, May 11 2007 01:21
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I did physics, then physics, then more physics. Then, finally, some more physics. Now, I do a lot of physics. I guess it has been 13 years. Time flies when you're having fun. My undergrad program was initially going to be a double major in physics and English. Writing clever little undergraduate essays about old poems came pretty easily. I liked it, but I guess it came too easily, because it seemed as though I could handle literary criticism well enough to have fun with it, without further training; but I was never going to be able to understand modern physics at all without a lot more courses. So out of 40 one-semester-courses in my degree, in the end 32 were physics (plus a few math and chemistry). With the remaining 8 electives, I worked my way up to upper year seminars in English, by concentrating narrowly in Renaissance poetry. I suppose my main reason for spending time here is that it gives another outlet for writing little (well, tiny) essays, in between all this physics. EDIT: Woops: 23 years, not 13. Flies more than I thought. [ Friday, May 11, 2007 01:23: Message edited by: Student of Trinity ] -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Regulation - Complexity sidebar in Geneforge 4: Rebellion | |
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Electric Sheep One
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written Thursday, May 10 2007 23:41
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quote:You do not seem to be thinking through your own arguments, Stillness. Removing a retina from a human eye no doubt renders it useless. But removing a retina is a huge, abrupt change, like the ones you postulate and attribute to design. It is nothing like the tiny, gradual changes that evolution involves. So unless you can identify structures that are irreducible by tiny changes, you are not criticizing evolution: you are criticizing unintelligent design. A brief point about numbers: a fruit fly generation is some number of days, where that of a large animal is some number of years. So to see something that took a million years of historical evolution in a larger species, you would still have to run your fruit fly experiment for a millennium. And that's if you used as many flies as there were in the global population of the evolving species. [ Thursday, May 10, 2007 23:43: Message edited by: Student of Trinity ] -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Avernum 5, April Update in Avernum 4 | |
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Electric Sheep One
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written Thursday, May 10 2007 13:19
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You start as a Chitrach. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Regulation - Complexity sidebar in Geneforge 4: Rebellion | |
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Electric Sheep One
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written Thursday, May 10 2007 05:15
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Stillness, you speak as though specified complexity were obviously a meaningful concept, and so we information theory professionals ought to be able to quantify it well enough if we just tried for ourselves. But what we are telling you is that it really does not look like a meaningful concept, and so we do not know how to quantify it. The proposed quantification you cited is clearly inadequate. quote:These bacteria have somehow learned to live on artificial sugar, and you call it a loss because it is a change which 'if continued' would leave them unable to eat anything? This sure seems like taking the specified complexity theory over common sense. But then when I push the complexity picture for birds, you revert to common sense in assessing gain and loss. Doesn't this suggest that the specified complexity idea is kind of flawed? -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Regulation - Complexity sidebar in Geneforge 4: Rebellion | |
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Electric Sheep One
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written Thursday, May 10 2007 00:02
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I think I can flesh out Khoth's objection a bit. The quoted formula is part of a discussion of experiments in which bacteria evolved the ability to live on an artificial sugar. It is presented as important, that the new enzymatic activity appears not as a shifting from specificity for natural sugar to specificity for the new sugar, but as a general broadening of the range of sugars on which the enzyme acts. (Aside: This seems rather banal to me. Switching over while keeping an enzyme highly specific would be the very kind of 'magic' that evolution does not do. Broadening it, and then later narrowing it further — a loss of capability, like cave fish losing eyes — if narrowness ever became advantageous, is the obvious gradual track that could be followed.) But here is the problem I see with that analysis. It certainly seems to me that the bacteria have done something remarkable. A strain has emerged that can live exclusively on a sugar that the original population could not survive on. And the criticism mounted by the ID advocates is something like, 'This seemingly clear example of evolution does not actually break our rule about specified complexity decrease, because these new bacteria could also live on several other things as well.' But now consider: birds can fly in air. They can also fly in helium, pure carbon dioxide, neon, and many other gaseous mixtures. A land-based animal cannot fly in any of these atmospheres. Evolving the capability of flight is thus not an increase in specified complexity, but a decrease. I think maybe Thuryl made this point also, some time ago in the late lamented thread. Any change can be counted as a gain or as a loss, of something, depending on how you look at it. Losing sight is gaining specificity in adaptation to a lightless environment. In other words, it seems to me that if you look at the 'range of possibilities' in the right way, any change whatever could be presented as having decreased specified complexity. Specified complexity decrease thus does not seem itself to be adequately specified. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
| Major problems help needed! in Geneforge 4: Rebellion | |
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Electric Sheep One
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written Tuesday, May 8 2007 11:10
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Welcome to the boards! I'm not sure I can solve your problem, but here are some thoughts. Are the above ground Barrier Zone creations actually hostile to you, or are you just attacking them for fun? If you are doing the Repair Moseh mission for the Shapers, you could have gotten an amulet that makes these creations ignore you, except for the rogues that Shaftoe wants you to kill. If you do not have the amulet, then indeed it is probably hopeless to go above ground in the western Barrier Zones at your level. Have you talked with both Shaftoe and Eliza about your quest to help Moseh? They can both help you to save him, but I believe you only need one of them to help. If Shaftoe won't play along unless you go above to kill his rogues, then you will have to rely on Eliza. But since you say you have made her happy, why not try talking to Moseh again, about letting Eliza take over his creations for a while so that he can recover? This should do the trick, I think. Then maybe later you can pick up that Barrier Zone amulet, and do Shaftoe's rogue quests. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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Electric Sheep One
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written Tuesday, May 8 2007 06:51
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Quantum mechanics is also deterministic, in the sense that the quantum state evolves deterministically under the Schrödinger equation. Some element of randomness certainly seems to enter in quantum measurement, but it is pretty clear that nobody is doing any measurements on atom positions inside a steam engine, or anything like that. So the quantum version of entropy, the von Neumann entropy, is zero for any single quantum state (no matter how elaborate a superposition it may be in any particular basis). Only when one considers probability distributions over quantum states, which is by no means required by quantum mechanics per se, does one find non-zero entropy. Probability distributions over quantum states arise in the same ways I described above: we consider a historical sequence of states as a sample set, or consider the set of parts of a larger system as a sample. Quantum mechanics adds two things to the classical picture of entropy. Firstly, it means that in any finite system one has only a countable number of distinct states to consider. This means that when computing entropy we can use true probabilities, rather than probability densities. (When Boltzmann created statistical mechanics, in the late 19th century, he arbitrarily introduced finite-volume 'cells' in phase space, and considered the probability that the system should be anywhere within a given cell. In effect, quantum mechanics gives us natural phase space cells, instead of arbitrary ones.) Secondly, quantum mechanics includes the peculiar, non-classical kind of correlation known as 'entanglement'. This means that even when a large system is in a single specific quantum state, to describe any of its subsystems alone may require a probabilistic distribution (not a superposition) of states. This is a source of probability with no classical counterpart; but it has not yet to my knowledge been used to add anything to the foundations of statistical mechanics. That's one of the things I'm supposed to be doing, in fact. [ Tuesday, May 08, 2007 06:56: Message edited by: Student of Trinity ] -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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Electric Sheep One
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written Tuesday, May 8 2007 01:06
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Maybe this sidebar is also a good place for my little disquisition on entropy, which is in some ways related to complexity, but not really. There are two basic definitions of entropy: thermodynamic entropy and statistical mechanical entropy. They are supposed to be the same, but as you will see this is not obvious. Thermodynamic entropy: Put some number of Joules of heat into some object, while keeping its temperature constant. The ratio of heat to absolute temperature (i.e. temperature measured in a scale where zero is absolute zero), in Joules per Kelvin, is the amount by which you have raised the object's entropy. If you can't manage to heat the object without changing its temperature (sometimes you can), just compute the entropy change for a very short time, over which the temperature changes negligibly. Then add up the entropy changes over a succession of these short stages, each with a slightly different temperature. The result is an integral of heat over temperature, and that gives the entropy change for the general case of varying temperature. Only changes in entropy are defined in this way, not absolute entropy. So we fix absolute entropy by the convention that a perfect crystal at absolute zero should have zero entropy. This is the entropy of thermodynamics. Exhaustive experience over the past two centuries has been formalized in the empirical law that it will never decrease in any closed system. It does not obviously have anything to do with complexity or disorder or anything like that. It's about heat and temperature, as empirically measurable. Statistical mechanical entropy: This is a purely theoretical concept of entropy, as a property of probability distributions. If I have N equally likely states, the entropy of this probability distribution is log(N) (the logarithm of N -- in physics, usually to base e). This can be generalized nicely to the case with arbitrary unequal probabilities, but this is not necessary for qualitative understanding. The statistical mechanical entropy is naturally a pure number; when we want to relate it to thermodynamic entropy, we multiply it by a univeral constant which has units of Joules per Kelvin (Boltzmann's constant). One might well ask, How on earth do probability distributions ever enter physics, in which everything is deterministic? Well, physics deals with large systems, for instance samples of gas containing zillions of molecules. And if even a small system is followed over a period of time, the sequence of its instantaneous states makes up a very large and possibly complicated set. Precise description of such large systems or histories would take too much work, so we use probability concepts as a way of crudely characterizing some of their large scale properties. We look at a history as a set of instantaneous states, or at the instantaneous state of a large system as the set of all the states of the parts of the large system. We then try to infer a probability distribution that might yield this set as a typical sample. We compute the entropy of this distribution, multiply by Boltzmann's constant, and hope the result matches the thermodynamic entropy of the system. In all known cases in which the statistical mechanical entropy can be unambiguously computed, it does. But as you might imagine from the above explanation, the step of inferring a distribution from a sample may be problematic; and even before this step, there is in general a lot of room for ambiguity in simply deciding how to relate histories to sets of instants, or large systems to sets of subsystems. In reality the successive instants of a history are not uncorrelated samples from a distribution, but are all determined strictly from the first instant, through the laws of physics. And the subsystems of a larger system interact with each other, so they are not independent either. Justifying the statistical approach in spite of these basic facts is a tricky business, and a subject of active (though not very productive) research. So that's the state of the science of entropy. What does it mean for applying entropy beyond physics, say in evolutionary biology? Mostly, it means that it's very hard. The Second Law really applies to thermodynamic entropy. There are no known valid proofs of it for statistical mechanical entropy. And since an encyclopedia and a book of random characters will clearly burn pretty much the same, it is hard to claim that anything like 'meaning' or 'complexity' can have any real significance for thermodynamic entropy. From the statistical mechanical point of view, both books are made of bazillions of molecules, which can be arranged in many more ways. The range of different states of printed characters, although huge, is comparatively tiny. Similar considerations will make it very difficult to draw any conclusions from entropy about biochemical evolution. [ Tuesday, May 08, 2007 01:08: Message edited by: Student of Trinity ] -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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Electric Sheep One
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written Monday, May 7 2007 02:12
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quote:Exactly. All very simple. Now, please look directly at the light. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |