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Topic: Does anything at all exhibit specified complexity?
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Rex Kerr
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posted 05. February 2004 02:27
I should warn you that I am not a chemist. I believe my information is accurate, but you won't see any papers on total synthesis of cholesterol derivatives from me in the near future.
I'll also point out that humans don't have an exclusive license to be affected by mathematics. That is a topic for another thread, but many physical phenomena are describable in fairly simple mathematical forms, and no intelligence appears necessary to enact them. So one has to be careful about assuming too much when mathematics or physics shapes both human behavior and thought, and processes outside of human behavior and thought.
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Stephen Wright
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posted 12. February 2004 10:08
Rex, I have enjoyed reviewing your posts here for a quite while. I must admit, after a number of readings, I cannot follow your premise in this Brainstorm. The fundamental definitions for the Information Theoretic components that make up the term specified complexity are well defined and can be expressed in simple language. I may lack sophistication on some point, or many points, and you could help clarify what I’m missing, if you are so inclined.
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“In summary: I do not believe any instances of specified complexity can be found regarding human behavior”
A specification is a defined model that lists criteria that can be mapped to the measured values of an actual event, object or process. Specifications are used to declare physical or informational properties that require attention. They pattern attributes or performance standards in such a way as to achieve a goal or solve a problem. The separate criteria should, as a whole, create a reproducible pattern, that addresses context between the event, object or process and the intelligent agent that has defined not only the particulars, but the overall pattern they structure.
This holistic focus of a specification is crucial to its functional viability. Comprehensiveness and integration are highly desired. A specification requires an intelligent agent to comprehend the pattern and to choose the attributes or variables that will structure the model, hopefully not leaving out critical aspects. There is implied intent for the focus of the intelligent agent because the specification has a target or goal orientation, which creates or connects it to a contextual basis in reality.
Most often the task is to apply measured values to turn a phenomenon into a model that is describable in math or logic terms. A well-crafted specification is a model whose quantifications or descriptions can be seen to capture the assertions that will enable mapping, as an isomorphic set, to copies or equivalent versions. Successful specs are those where the particulars are supported by clear verification instructions that render the model as a definitive and discreet whole.
That humans and other living things can solve problems by through specific behaviors and leave an artifact that has the specification imbedded seems logical to me. The Preamble to the Constitution is like an abstract to a command and control plan and defines the intended results from governmental management. Whether the words are likely results from circumstances is not the issue. It is whether the specification has organized the complex pattern in such a way the behavioral prescriptions can be enforced and the results measured against a standard for performance. This takes intelligent input and we can reverse engineer much of the thought process to prove and evaluate how well the specs created a complex working system.
Specs are well understood part of process control documentation and lend themselves to measurement and statistical evaluation. There are functional and pragmatic terms existing for complexity, such as the list here in the ISCID Encyclopedia. Although, I personally would have a hard time describing what complexity is as a general idea. It’s like gravity, we all have an intuition that we know it, when we experience it, but it’s hard to plainly understand its essential nature and how it “works”.
Any actual product of an intelligent agent as an object, event or process can be seen to carry the “mark” or original conceptual model of conscious or unconscious purpose or intent, which was derived from a context of problem solving. Taken at the face value of the separate terms; specified complexity is a logical concept.
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Rex Kerr
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posted 12. February 2004 17:00
quote:
A specification requires an intelligent agent to comprehend the pattern and to choose the attributes or variables that will structure the model, hopefully not leaving out critical aspects.
Let's consider the consequences of this statement. First, we note that if an intelligent agent bungles the choice of attributes or variables that will structure the model, what they produce will no longer be specified by that specification. But if there are, say, 10^20 different choices that will all get the job done, the specification gives us no indication of which of those 10^20 will happen.
So what the statement says is that intelligent agents at a high probability can follow a specification and produce a (unspecified, possibly random, except for the part that is specified) model that matches the specification.
So if we have a specification, and we have an intelligent agent, production of such models is a high-probability event (not a low-probability one).
Therefore, I don't disagree with anything that you say. But the point is that as soon as you introduce a specification and mix with humans, you get a high-probability (and thus by definition in Dembski's nomenclature, a low-complexity) event. This is why there are no examples of human-generated specified complexity. The complexity is not specified; the specification is not complex (given human nature and history).
The only way you can generate specified complexity is pretending that you don't know humans exist. But you can also generate specified complexity if you pretend that you don't know that gravity exists. (It's very improbable to have matter all clumped together in a planet, without gravity!)
So specified complexity isn't an indication of human or intelligent activity--or at least, we have no positive examples that it is. It's an indication that we have intentionally or unintentionally left a factor out of our analysis, without any indication that the factor has anything to do with intelligence.
Edited to slightly improve wording in an unclear spot.
[ 12. February 2004, 23:22: Message edited by: Rex Kerr ]
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Jules
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posted 14. February 2004 18:29
Rex: "The only way you can generate specified complexity is pretending that you don't know humans exist. But you can also generate specified complexity if you pretend that you don't know that gravity exists. (It's very improbable to have matter all clumped together in a planet, without gravity!)
So specified complexity isn't an indication of human or intelligent activity--or at least, we have no positive examples that it is. It's an indication that we have intentionally or unintentionally left a factor out of our analysis, without any indication that the factor has anything to do with intelligence."
Me: If we excavated a rocket ship from 3.5 billion year old rock (and ruled out hoaxes), wouldn't we be able to determine that it was made by some sort of Intelligence? And wouldn't we be able to make this determination because of its specified complexity?
[ 14. February 2004, 18:30: Message edited by: Jules ]
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RBH
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posted 14. February 2004 22:53
Jules wrote quote:
Me: If we excavated a rocket ship from 3.5 billion year old rock (and ruled out hoaxes), wouldn't we be able to determine that it was made by some sort of Intelligence? And wouldn't we be able to make this determination because of its specified complexity?
Depending on the kind of rocket ship it is, we may be able to infer that it's intelligently designed, but I doubt very much whether something like Dembski's "specified complexity" would play any role at all in that inference. By "depending on the kind of rocket ship" I mean that if we found the remains of an 3.5 billion year-old organic space ship, as has been suggested in some science fiction, we may well not even realize it's a space vehicle. If it were a spaceship of the general kind we're familiar with via NASA or Arthur C. Clarke, we might recognize it as an intelligently designed artifact, but that has nothing at all to do with "specified complaxity."
Look through the Design Inference Game II thread. Despite Cre8's valiant efforts, there's not one single instance of the determination of the "specified complexity" of one of the test objects/pictures used to support a "design" inference.
RBH
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Rex Kerr
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posted 15. February 2004 06:37
Jules, we would probably infer intelligence, but it would not be because of specified complexity. Rather, it would be because 3.5bn year old rocket ships are a high probability event given 3.5bn year old intelligent creatures that wanted to move around in the galaxy, and a low probability event for any other situation we can think of. This is specified simplicity (using Dembski's complexity-as-low-probability nomenclature).
If instead of a rocket ship we found an incredibly intricate yet utterly bizarre feature, we wouldn't know what to conclude, since the feature would be low-probability either with or without intelligences that we are familiar with. And anyway, without knowing what the heck we were looking at, we wouldn't be able to write any reasonable specification for it, I expect. So this would be unspecified complexity.
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Stephen Wright
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posted 15. February 2004 09:01
We are still not tracking this issue from the same perspective, although you hit on the key part of specified complexity as being a produced result.
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First, we note that if an intelligent agent bungles the choice of attributes or variables that will structure the model, what they produce will no longer be specified by that specification.
Practical applications work the other way. If the agent bungles the spec, the model will be insufficient for the task at hand and it will not produce specified complexity. The pragmatic problem-solving goal will not be fulfilled. I am assuming, and maybe incorrectly, that examples of specified complexity are functional and have adequately addressed the challenge that faced the intelligent agent. There are means to describe how well a process works in technical terms like Cp or CpK, where a value is obtained as to a level of defects allowable. No process or product is perfect, but manufacturing quality programs contain standards that define a level of performance that is acceptable or very good - such as a Six Sigma rating from a histogram recording output and defects.
W. Dembski’s argument, in my own paraphrase and limited understanding:
…we see humans solve problems by using logic and computation to organize objects, events and processes. These mental abilities are aimed at targeted results, which solve problems. We understand how humans achieve this. We see nature doing this same behavior: solving problems relative to environmental challenges. And further - nature seems to achieve levels of complexity far greater than humans can, to date. So, there must exist a source of intelligence that inputs those same skill-sets used in problem solving. He may attribute those skill-sets to a source outside of nature.
The low probability aspect only comes “into play” when the goal is to use reverse engineering to DETECT the actual implementation. The skill-set of binding ideas together into a design, which addresses an existential challenge, is assumed to leave a logical history. It is acknowledged that nature develops complexity through pathways like cellular automata. But it is the targeting toward a goal, addressed from the point of view of a living organism that separates intelligent systems from purely natural systems that can occur without guidance. Unspecified complexity needs no participation from an intelligent agent and it is the creative process of solving problems in a context of environmental urgency that does.
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The only way you can generate specified complexity is pretending that you don't know humans exist.
This is a very interesting topic, the exclusion of human intelligence as something apart from natural processes. I would stand on the side that what we do as humans is no different then natural processes, except for our ability to objectively see ourselves do it and become responsible for the ethics of our intent. Can we say that self-awareness is also “natural”? Why not?
I would assert that beaver dams, foxholes and bird nests exhibit specified complexity and are the resultant product of a specified process. Will this help us get closer if we can get the examples out of the non-human context?
P.S.: Going back over this post, I thought about the fact that many bungled specs, which failed to address one problem became a search of the design space, brilliantly discovering an answer for a difference one. But one has to recognize and correlate the other context where the spec can bring to bear a complex organization that IS functional. It is not random, but still targeted logic. This involves the creative skill-set that I am claiming is needed to cause SC.
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Rex Kerr
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posted 16. February 2004 03:03
quote:
It is the targeting toward a goal, addressed from the point of view of a living organism that separates intelligent systems from purely natural systems that can occur without guidance. Unspecified complexity needs no participation from an intelligent agent and it is the creative process of solving problems in a context of environmental urgency that does.
This experiment has been done. It is a famous, classic genetics experiment, usually called the Luria-Delbruck experiment.
You start with a single bacterium, grow it up in culture, and plate it out at low density on antibiotic-containing medium. A single mutation is enough to rescue one of the progeny bacteria, and enable it to grow into a colony. Let's say we grow up a billion bacteria and see how many colonies we get. (Typically 10-100.)
If genetic changes are a creative act, stimulated by environmental need, then we would expect each bacterium to act independently at the time when it was placed on antibiotic.
Alternatively, if genetic changes are a result of random chance, largely unaffected by environmental need, then we would expect mutations to arise spontaneously. In particular, the ancestors, growing in good conditions, are just as likely as the progeny, growing in antibiotic, to pick up a mutation.
These two cases can be distinguished. In the latter case, you'll occasionally get a great-great-great-great (etc.) ancestor who picks up the mutation. All its progeny will get the mutation, and a huge number of colonies will be found, every once in a while. In the former case, you'll never see this, since each bacterium is coping on its own.
The experiment shows a large number of surviving colonies occasionally--and the distribution of frequency vs. number surviving match the prediction for the random-chance case very precisely, and don't agree with the prediction from the creative bacteria case.
This doesn't rule out creativity in other cases, but it does indicate that creative solutions are not the norm. The norm is randomly directed mutations, followed by selection.
quote:
Humans solve problems by using logic and computation to organize objects, events and processes. These mental abilities are aimed at targeted results, which solve problems. . . The low probability aspect only comes “into play” when the goal is to use reverse engineering to DETECT the actual implementation.
But I think that you'll find that the probability is not actually low, in those cases when we can find a specification--exactly because of our knowledge of human problem solving!
Suppose we see a solution--a mousetrap, for instance--and we want to ask if it is designed. First, perhaps we come up with a candidate specification ("Automatic mouse-killing device."). Then we consider what processes could be at work...random association of wood, springs, and wire? Or perhaps humans, using their logic and computation? Mice eat humans' food, and humans are vengeful (or at least hungry) creatures, so it seems probable that the humans would try to kill the mice. Mice are vulnerable to poison, impact damage, asphyxiation, etc. etc., but with modern human engineering, impact damage is easy to generate. Therefore, given mice and humans, human capabilities lead to mousetraps as a fairly high-probability event.
There is no design inference here.
And, of course, there cannot be, because when we say "specification", we mean something that's detatchable from the event. And that means it's something that humans could have come up with--and that means that it's not a low-probability event for humans to come up with it. But if they can come up with it and have any reason to do it, then it's not low-probability that humans did it.
So the mathematics underlying Demski's method doesn't allow one to find positive examples of design. Paraphrasing is nice, but TDI is supposed to be a rigorous method (in theory), and yet we can see that positive examples of design inferences are apparently inherently impossible to get.
It is, perhaps, intuitive to imagine that solutions to complex problems are always found via cognitive processes, since that's how we find them. But that's the question, isn't it? And assuming the answer seems unwise given experiments (e.g. Luria-Delbruck, studies with artificial evolutionary algoritms, and so on). This is why it would be so helpful to have a rigorous method to detect intelligent design. And this is why it is important when, despite claims to the contrary, Dembski's method fails to produce any positives that can clearly be scored.
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Jules
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posted 16. February 2004 10:09
Rex: "Jules, we would probably infer intelligence, but it would not be because of specified complexity. Rather, it would be because 3.5bn year old rocket ships are a high probability event given 3.5bn year old intelligent creatures that wanted to move around in the galaxy, and a low probability event for any other situation we can think of. This is specified simplicity (using Dembski's complexity-as-low-probability nomenclature)."
Me: But if it's "a low probability event for any other situation we can think of," then aren't we using Dembski's filter to conclude that it was intelligently made? And isn't this based on the concept of specified complexity?
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Jules
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posted 16. February 2004 10:13
Rex: "If instead of a rocket ship we found an incredibly intricate yet utterly bizarre feature, we wouldn't know what to conclude, since the feature would be low-probability either with or without intelligences that we are familiar with. And anyway, without knowing what the heck we were looking at, we wouldn't be able to write any reasonable specification for it, I expect. So this would be unspecified complexity."
Me: Do you write this seriously? You mean if we found a metal device with well-fitted, intricate, moving parts, we wouldn't conclude that it was intelligently made? We would first have to know its purpose? Oh come, now.
[ 16. February 2004, 10:37: Message edited by: Jules ]
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Rex Kerr
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posted 16. February 2004 17:02
If it is not a low-probability event for a designer, then we are not using Dembski's method. Dembski's method says nothing about whether we can predict a probability of design or not: is simply asserts that if it's specified and low-probability then it must be designed, whether or not it is low probability that a designer existed who designed it. But if we know that it's not low-probability, we revert to the standard Bayesian method: pick the most probable (and stop looking when you've found something that seems probable enough).
Also, a metal device with well-fitted, intricate moving parts is not "utterly bizarre". I said nothing about purpose. We are quite familiar such things--watches and lawnmowers, for instance--and even if we don't know what a particular device does, it's still probable that such a device of unknown purpose was made by humans, since humans have a high probability of making devices like that.
If, on the other hand, we found a giant fractal lattice made entirely out of selenium with ytterbium atoms scattered throughout in a nonrandom (compressible) yet not simply regular way, I wouldn't know what to think. I wouldn't be able to write down a specification for it, though.
[ 16. February 2004, 17:04: Message edited by: Rex Kerr ]
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John Bracht
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posted 17. February 2004 01:03
Rex,
Interesting thread, but I have one problem that nobody has raised yet.
It seems obvious to me that when you say "its highly probable that humans would make" such-and-such (say the declaration of independence), you're using the concept of probability pretty oddly.
After all, what is the probability that our founding fathers chose NOT to write the declaration of independence? What if they chose to go play a game of golf instead? What if they chose to commit suicide? What if they chose to go to the local bar and drink their troubles away? What if they chose to go out with guns blazing and take out as many redcoats as possible, without bothering to write a declaration of independence first? Those seem like plausable, if not likely, alternatives. Given the fact that the document was, in fact, written, we can say it's pretty likely to have been written. But that's pretty ad-hoc (more of a fabrication than a specification). How do you realistically apply probability calculations to these scenarios?
Ok, maybe you can argue that given an abusive King in England, and the founding fathers' anger over taxation without representation etc, the probability was high for the production of the declaration of independence (or some similar document). I have problems with this, since as I mentioned before there seem any number of potential responses. So for one, you're treaing human beings as pretty highly determined. Given an abusive king in England, the founding fathers were pretty much inevitably going to write the declaration of independence. But what determined the actions of King George? Who knows, but apparently they were highly probable, whatever they were.
I think it's problematical to say that a given document is likely or unlikely, since it seems that probability doesn't really apply to the actions of intelligent agents. Sure, given the fact that I decide to do something (say write the declaration of independence), the probability is high that I will actually do so. But what is the probability that I do decide to do so? I have the ability to choose, and I feel that I am free to choose any number of possibilities without being predetermined. I often approach decisions without a clear inclination one way or another. And often the choices I'm facing are very complex, non-binary choices in which there are multiple competing scenarios I could actualize. The reasons intelligent agents do things are often clouded in mystery and not evident (just try to figure out Women! ![[Smile]](smile.gif)
I guess I'm trying to convey the fact that I don't think that probabilities apply to intelligent agents in the same way they apply to unintelligent causes. Intelligent beings act with decision and foresight, which makes all the difference. Once a goal is chosen, it is actualized with high probability (assuming it's a reasonable and achievable goal). It is the act of choosing that is non-probabilistic. It seems a category mistake to apply probabilities to the process of decision making. Perhaps for large groups of people you can do some probabilistic analysis (calculate what percentage of people vote for a given candidate etc) but for an individual person, probabilities don't really capture the way choices are made. I don't sit around saying "well, X has happened, and Y. Therefore, the probability is pretty high that I will do Z!" Rather, I think "in light of X and Y, I'll do Z" or "in order to avoid X and Y, I'll do Z". Reasons and motivation all play a role. How do you apply probabilities to reasons and motivations?
Finally, I think your analysis misses the point of Dembski's explanatory filter. I don't think it would bother him that a given event has a pretty high probability given intelligent causation. The whole point is that some events cannot happen apart from intelligent causation, and Dembski is trying to reliably sort those events from everything else. Certainly, given intelligent causation these events have a high probability of occurring--that's the ONLY way they can occur! So it's not really interesting to observe that "given intelligent causation, specified complexity is highly probable" and then conclude it's not specified complexity anymore. The reason is that specified complexity is complex in relation to unintelligent causes, ie, law and chance. It's simply trivially true that intelligently-caused events must have had intelligent causation (and hence the probability of their occurring, given intelligent causation, must be high).
In fact, if you really want to boil down your argument, it might be that "all events have causes" which is trivially true (with the exception of truly stochastic quantum events). Nobody is debating whether events have causes; rather it's a matter of sorting the intelligently caused events from all the others.
John
[ 17. February 2004, 01:07: Message edited by: John Bracht ]
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Rex Kerr
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posted 17. February 2004 03:36
John, interesting comments, although it will probably not surprise you to find that I have a different point of view.
First, note that when I say "high probability", I mean "higher than 10^-150", since that's Dembski's universal probability bound, and he uses "low probability" = "complexity" = "10^-150 > p".
Then consider what it means for something to be a specification and not a fabrication. We need to have side-knowledge that allows us to univocally (!) identify the specification. What would we use for the Declaration of Independence? Well, humans write documents, humans often make statements before doing something important as a group, etc.; stuff of that nature. But this side-knowledge is exactly what lets us predict that humans would have a "high probability" (p>10^-150) of doing such a thing. And the part of the Declaration which we could not have predicted may well be low-probability, but there would likewise be no specification for that part.
Consider the Caputo case: 41D and 1R, if I recall the numbers correctly. Our specification needn't involve Caputo's motive, but it does involve knowledge of human mathematics. Knowledge which Caputo had, and could have used to generate the pattern--and thus it wouldn't be a low-probability event for him to have generated it.
I agree that Dembski has chosen events that cannot happen apart from intelligent causation, but I don't think his method is reliable. It is not reliable because he has picked an essential feature--intelligent causation--and pretended that we don't know about it. The EF works, here, and says our causal explanation is broken.
But there is nothing about EF that is in any way specific for intelligent causation. That is simply a function of the examples Dembski felt like including. I can come up with a dozen examples that include intelligent causation as a possibility but pretend that we don't know about gravity--and the EF will return a positive for every one of them, too, since without gravity our explanations will be lousy. (And, of course, I can pick examples that show that the EF detects an evolutionary algorithm at work...the outcome of Avida, for example, would be such a case.)
Perhaps Dembski is implicitly assuming that we can (and do?) know everything about chance processes and regularities, but that intelligence is utterly inscrutable; then the flow of the EF would make sense. But this assumption is hopelessly wrong. As a scientist, I'm spending my career trying to better understand chance processes and regularities...but if I ask my students to show the fractions of alleles for F2s in a cross between dpy-20 and unc-2 mutants, there is a high probability that that's exactly what they're going to produce (and those students will get full marks). They use decision and foresight to achieve that end, but that does not in any way prevent me from characterizing the outcome, and knowing that about 60% of the class will get that answer correct on the midterm.
So there is much about human behavior which is quantifiable, and much about the natural world which is a mystery, and it is only by the fiat of picking one out for special treatment that the EF seems to be doing any work.
If we honestly apply all our knowledge about both the natural world and human behavior, I cannot see how we could have a positive example of the EF detecting intelligent design by humans, since if we knew enough to construct a specification, we couldn't be confident enough that humans hadn't caused the outcome.
Just to be clear, this is what the test should look like: for a specific event, caused by humans, pretend that you do not know what caused this specific event. However, one should assume general knowledge about the functioning of the natural world and of humans within that world.
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Stephen Wright
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posted 17. February 2004 11:46
Rex, I am not so sharp as to argue three points at once. Let me define these areas and maybe we can understand each other better.
a) Can humans implement systemic changes via design and organization, which create measurable changes in output efficiency? Further, can these changes be understood as a gain in complexity, due to energy expended for organizing processes? I would answer - this is well understood - and the use of specifications is an essential part. Therefore, independent of W. Dembski’s ideas about detecting it, I find specified complexity to be a logical concept and that it describes the artifacts of applied computation and logic whereby a gain in complexity is realized. I think that I can defend this, using the principles of Information Theory.
b) Can organisms other than humans implement systemic changes through design and organization, which create measurable changes in output efficiency? If given a) then this is an interesting subject to explore and although I may have opinions, there is much I could learn on the subject.
c) How well does the work of W. Dembski help detect SC in a mathematical methodology and does the Luria-Delbruck rate of mutations work contradict it? I am simply not qualified in this area. But would suggest that considered opinions from titles such as Lamarck's Signature - How Retrogenes Are Changing Darwin's Natural Selection Paradigm by Edward J. Steele, Robyn A. Lindley, Robert V. Blanden and Darwin in the Genome by Lynn Caporale may create a more complex and dynamic picture of what is going on than expressed by the linear idea of - random mutations do it all.
Are you still arguing against a)? It is the thread topic. I think where we are dislocated occurs in my assertion that SC refers to functionality. If the specification is accurate in addressing the targeted challenge that marks its purpose, it can be copied and modified to similar circumstances. The US Constitution surely fits this model. It in itself adapted SC found in prior documents and ideas as components, but when considered with the Bill of Rights it was a breakthrough in creativity. It has proved useful and effective within a range that relates to the capability measurements of any process. Not perfect - but serviceable enough to be selected naturally by others who followed and had to meet the same challenge of documenting command and control parameters for a government.
[ 17. February 2004, 11:49: Message edited by: Stephen Wright ]
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Erik
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posted 17. February 2004 14:21
Rex Kerr, I think your arguments misses the target a bit, not because the reasoning is invalid, but rather because the main point of disagreement is elsewhere. Dembski's method relies on mystifying intelligent agents to such a degree that we cannot treat a hypothesis featuring an intelligent agent as a statistical hypothesis.
John Bracht, you wrote:
quote:
John Bracht: I think it's problematical to say that a given document is likely or unlikely, since it seems that probability doesn't really apply to the actions of intelligent agents.
For the reason mentioned just a few lines above (in reply to Rex Kerr) I am not surprised that an ID advocate would find it problematical to describe actions of intelligent agents in terms of probabilities. I have never seen a justification for this, though.
First of all, what do you mean by probability? The interpretation(s) of probability values has been a hotly debated issue. (N.B. I'm not asking you to justify your preferred interpretation -- that's another debate -- just to identify it.)
Second, what is it about your interpretation of probability values that makes it more problematical to speak about the probability of an intelligent agent writing a document than the probability of a flagellum evolving? Common interpretations of probability values include: personal betting ratios in situations were we must gamble, personal subjective beliefs, the beliefs of a hypothetical and perfectly rational "inference machine", intrinsic tendencies of processes to result in certain outcomes, relative frequencies in real or imagined populations,... In none of these interpretations is it more problematical to speak of the probability of an intelligently planned action than the probability of a "natural" process resulting in a particular outcome. (Example: Marketing is an example where probabilities of intelligently planned actions are used, albeit probably informally most of the time. Paying for an ad is a good deal if it will increase the probability that people choose to buy the product enough to make the increase in expected revenue larger than the cost of the ad. Considering how common ads are I think we can conclude that companies are not entirely incompentent at making such probability estimates.)
Erik
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