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Aurelio Smith’s Analysis of Active Information

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Recently, Aurelio Smith had a guest publication here at Uncommon Descent entitled Signal to Noise: A Critical Analysis of Active Information. Most of the post is taken up by a recounting of the history of active information. He also quotes the criticisms of Felsentein and English which have responded to at Evolution News and Views: These Critics of Intelligent Design Agree with Us More Than They Seem to Realize. Smith then does spend a few paragraphs developing his own objections to active information.

Smith argues that viewing evolution as a search is incorrect, because organisms/individuals aren’t searching, they are being acted upon by the environment:

Individual organisms or populations are not searching for optimal solutions to the task of survival. Organisms are passive in the process, merely affording themselves of the opportunity that existing and new niche environments provide. If anything is designing, it is the environment. I could suggest an anthropomorphism: the environment and its effects on the change in allele frequency are “a voice in the sky” whispering “warmer” or “colder”.

When we say search we simply mean a process that can be modeled as a probability distribution. Smith’s concern is irrelevent to that question. However, even if we are trying to model evolution as a optimization or solution-search problem Smith’s objection doesn’t make any sense. The objects of a search are always passive in the search. Objecting that the organisms aren’t searching is akin to objecting that easter eggs don’t find themselves. That’s not how any kind of search works. All search is the environment acting on the objects in the search.

Rather than demonstrating the “active information” in Dawkins’ Weasel program, which Dawkins freely confirmed is a poor model for evolution with its targeted search, would DEM like to look at Wright’s paper for a more realistic evolutionary model?

This is a rather strange comment. Smith quoted our discussion of Avida previously. But here he implies that we’ve only ever discussed Dawkin’s Weasel program. We’ve discussed Avida, Ev, Steiner Trees, and Metabiology. True, we haven’t looked at Wright’s paper, but its completely unreasonable to suggest that we’ve only discussed Dawkin’s “poor model.”

Secondly, “fitness landscape” models are not accurate representations of the chaotic, fluid, interactive nature of the real environment . The environment is a kaleidoscope of constant change. Fitness peaks can erode and erupt.

It is true that a static fitness landscape is an insufficient model for biology. That is why our work on conservation of information does not assume a static fitness landscape. Our model is deliberately general enough to handle any kind of feedback mechanism.

While I’m grateful for Smith taking the time to writeup his discussion, I find it very confused. The objections he raises don’t make any sense.

Comments
DiEb: I think, in respect of "modelling" the clip at 39 above to Bob O'H is relevant:
Let me follow up by clipping the opening words, verbatim: >> 1. The Search Matrix All but the most trivial searches are needle-in-the-haystack problems. Yet many searches successfully locate needles in haystacks. How is this possible? A success-ful search locates a target in a manageable number of steps. According to conserva-tion of information, nontrivial searches can be successful only by drawing on existing external information, outputting no more information than was inputted [1]. In previous work, we made assumptions that limited the generality of conservation of information, such as assuming that the baseline against which search perfor-mance is evaluated must be a uniform probability distribution or that any query of the search space yields full knowledge of whether the candidate queried is inside or outside the target. In this paper, we remove such constraints and show that | conservation of information holds quite generally. We continue to assume that tar-gets are fixed. Search for fuzzy and moveable targets will be the topic of future research by the Evolutionary Informatics Lab. In generalizing conservation of information, we first generalize what we mean by targeted search. The first three sections of this paper therefore develop a general approach to targeted search. The upshot of this approach is that any search may be represented as a probability distribution on the space being searched. Readers who are prepared to accept that searches may be represented in this way can skip to section 4 and regard the first three sections as stage-setting. Nonetheless, we sug-gest that readers study these first three sections, if only to appreciate the full gen-erality of the approach to search we are proposing and also to understand why attempts to circumvent conservation of information via certain types of searches fail. Indeed, as we shall see, such attempts to bypass conservation of information look to searches that fall under the general approach outlined here; moreover, conservation of information, as formalized here, applies to all these cases. >> I trust the point about reading in context is clear enough.
I suggest to you that the references to needle in haystack searches, searches and representation all directly imply a modelling approach. As, is common in many applications of mathematics to situations of interest. Wiki:
Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and then using different types of models for different aims, such as conceptual models to better understand, operational models to operationalize, mathematical models to quantify, and graphical models to visualize the subject. Modelling is an essential and inseparable part of scientific activity, and many scientific disciplines have their own ideas about specific types of modelling.[1][2] There is also an increasing attention to scientific modelling[3] in fields such as philosophy of science, systems theory, and knowledge visualization. There is growing collection of methods, techniques and meta-theory about all kinds of specialized scientific modelling.
I would suggest that Marks, Dembski, Ewert et al have been working at a mathematical modelling exercise and have been gradually making it of wider and wider applicability. They began by using flat random sampling as a reference yardstick search of a config sopace, making a reasonable case on S4S that greatly improved searches will be so case specific that a blind search of the space of possible searches when combined with the resulting search implies that the likelihood of combined success is no greater than that of a straight flat random sample in a needle in haystack context. For me, that plausibility is strengthened by reflecting on the fact that as a search is a sampled subset of a set of cardinality W, the S4S space has cardinality 2^W. That of the power set. Which becomes much harder as W ~ 10^150 - 300 at lower relevant minimum. So, I find your "fail" dismissal inappropriate, unwarranted and selectively hyperskeptical. In the 2013 paper, M, D, E explicitly set out to generalise, removing the first level search from a flat random one. This they have in fact done. They have indicated onward work that will move to shape and location shifting targets. Of course, the dominant issue is the needle in haystack challenge and linked S4S so it is reasonable that shape shifting and moving like barrier islands will not materially affect the outcome. KF PS: And oh yes, what relevant aspect of the sol system is modelled by representing planetary name length by letter counts? Is that not a blatant strawmam caricature on your part? (In context of recent activities by your side's lunatic fringe, what message does resort to such lurid caricature send to such? Especially, when it is joined to blanket dismissiveness of a serious case? Please, think again on how you are arguing, given the LF.)kairosfocus
May 2, 2015
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#73 WE
Section 5 of the paper discusses how these distributions are obtained.
I apologise. I had not properly understood this section. What would really help here would be a worked example.  However, I will try to explain my concern. I think that what you are saying amounts to: If you define a subset of all the possible probability distributions on omega (e.g. those which make the probability of finding the target > q) then this places constraints on the probability density function of the probability distributions in M(omega). To make it concrete consider the case where omega is just two items a1, a2.  There are infinitely many pdfs possible on a1 and a2 - ranging from a1 = 1 to a1 = 0.  These pdfs are the members of M(omega). At this point you have no other information about omega.  So you have no idea about the higher level pdf of the members of M(omega). It might be that only pdfs where p(a1 > 0.8) are possible. It might even be that the only possible pdf on omega is P(a1 = 1). It would depend on the process for generating pdfs. You could then define a function on all those pdfs e.g. g(pdf) = 1 if p(a1) > q, 0 if p(a1 <= q). This would enable you to conceptualise P(g(pdf)=1). But clearly you cannot deduce that probability without making some assumptions about the prior probability of the members of M(omega). And I am struggling to see where those assumptions are articulated (although I suspect you are assuming that the pdf of pdfs is uniform between 0 and 1).Mark Frank
May 2, 2015
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DiEb, Evolution doesn't predict anything.Mung
May 1, 2015
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Winston Ewert:
Saying that you don’t like or find useful the way we’ve modeled things isn’t a criticism of our work. It is pointless complaining.
Sorry, I try to make the point of my complaint more clearly: In your paper "A General Theory of Information Cost Incurred by Successful Search", you don't use the terms model or modeling, not even once. You only claim that searches can be represented as probability distributions (and I thought that even this language was a little bit strong). Now you go even further and say
When we say search we simply mean a process that can be modeled as a probability distribution.
There are countless ways to define mathematical modeling. But the unifying concept is that a model allows for (non obvious) predictions. To elaborate: 1) The simplest model in population dynamics is representing the size of the population by a real number, and to assume that the growth is proportional to time (for short amounts of time) and size. This model allows to predict the size of a given population in the future - after measuring growth rate and population size. If the predictions fails, the model will be refined - or cast away. 2) I can represent the planets of the solar system by the length of their English names, Mercury, Jupiter and Neptune by 7, Saturn and Uranus by 6, Venus and Earth by 5, and Mars by 4. The only predictions which I can draw from this model are along the way that Mars has the shortest English name. I hope we can agree that this isn't a model of the solar system. So, what predictions does your model allow for? Especially, take my example in comment above (nr. 68): what can you predict about a search which finds the target {1} with certainty - if {1} was indeed the target? I may not like your model. But what use it is even to you?DiEb
May 1, 2015
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WE:
A die can be modeled as the distribution {1/6,1/6,1/6,1/6,1/6,1/6}, but the die is not the same thing as the distribution.
Aw shucks. I was wrong:
So, I’m right in reading DEM (yourself in association with Dembski and Marks) as “die” is synonymous with “search”?
Of course, unlike Aurelio, I know what I said was ludicrous. There's other ways to model a die. Say it doesn't have dots on it's six faces but colors. What prevents us from assigning a value to each color?Mung
May 1, 2015
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DiEb, Saying that you don't like or find useful the way we've modeled things isn't a criticism of our work. It is pointless complaining.Winston Ewert
May 1, 2015
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Nowhere can I find an explicit explanation of the pdf of possible searches although I think you are assuming each of those matrices which identify a search are equally probable.
Section 5 of the paper discusses how these distributions are obtained.
So, we’re right in reading DEM (yourself in association with Dembski and Marks) as “search” is synonymous with “probability distribution?
What you've said is incorrect, but what you meant is probably correct. A search is any process that can be modeled as a probability distribution. A die can be modeled as the distribution {1/6,1/6,1/6,1/6,1/6,1/6}, but the die is not the same thing as the distribution. For one, I can physically stack dice, but I can't physically stack the distributions. Similarly, a search can be modeled as a distriubtion, but they aren't the same thing.
I’m curious. What do you mean by “configuration of the universe”?
I mean the combination of the physical laws of the universe together with any initial conditions.
You’re crazy if you think anyone would waste time betting on such a stupid game.
I don't know, a lot of people play the lottery.Winston Ewert
May 1, 2015
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ok, the colored balls are either red or blue. Does that help?Mung
May 1, 2015
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Daniel King:
You’re crazy if you think anyone would waste time betting on such a stupid game.
Crazy like a fox. Looks like I caught a fish though.
Who said that there was a red ball anywhere? Who said there was a difference between the two urns?
No one. Given the amount of information, one urn is as good as the other.Mung
May 1, 2015
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A question for Aurelio (and other critics).
Hopefully, there's going to be a point to this.
There are two urns, each containing a number of colored balls. You cannot see inside the urns. You pay one dollar to play and can select one ball from either urn. If you select a red ball you win one dollar.
You're crazy if you think anyone would waste time betting on such a stupid game. Who said that there was a red ball anywhere? Who said there was a difference between the two urns? Mung is incoherent. Consistently.Daniel King
May 1, 2015
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A question for Aurelio (and other critics). There are two urns, each containing a number of colored balls. You cannot see inside the urns. You pay one dollar to play and can select one ball from either urn. If you select a red ball you win one dollar. Which urn will you choose to select from?Mung
May 1, 2015
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Dear Winston, I understand that it is necessary for the conclusions of DEM that searches can be modeled as probability distributions. The first attempt to model searches generally that way was in the paper "The Search for a Search" - and it failed. I have troubles to understand how the probability distributions introduced by the algorithm in “A General Theory of Information Cost Incurred by Successful Search” are modeling the underlying searches in any meaningful way. Take e.g., as search space the natural numbers 1..100, and as fitness function "distance to a target". Knowing this, I can construct an initiator, a terminator, an inspector, a navigator, a nominator, and a discriminator. Using those for the target {1}, I may get a probability distribution of P(S=1)=1, P(S!=1)=0 - my search will find this target every times. What conclusions can I draw from this model? Nothing meaningful - for example: what happens when the target is {2}? The probability to find this target could be 1, could be 0, could be anything in between. This "model"doesn't differ between a complete search and a search which will always return "1"... And frankly, if my target is {1} - what is the big difference between a search represented by P(S=1) = 9/10, P(S=50) = 1/10, otherwise 0 - and P(S=1) = 9/10, P(S=51) = 1/10?DiEb
May 1, 2015
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Carp, I believe God, who is omniscient and who created/creates time itself, is the Designer of the universe and of all life in it. Thus 'far off targets' in the future are child's play for Him in His infinite knowledge since even time itself belongs to Him. Moreover, I never claimed that man was omniscient in his capacity as a designer. Apparently atheists are not so humble in their assessment of their own finite abilities since they, from my repeated debates with them, obviously think they know how to design things much better than God did.
The role of theology in current evolutionary reasoning - Paul A. Nelson - Biology and Philosophy, 1996, Volume 11, Number 4, Pages 493-517 Excerpt: Evolutionists have long contended that the organic world falls short of what one might expect from an omnipotent and benevolent creator. Yet many of the same scientists who argue theologically for evolution are committed to the philosophical doctrine of methodological naturalism, which maintains that theology has no place in science. Furthermore, the arguments themselves are problematical, employing concepts that cannot perform the work required of them, or resting on unsupported conjectures about suboptimality. Evolutionary theorists should reconsider both the arguments and the influence of Darwinian theological metaphysics on their understanding of evolution. http://www.springerlink.com/content/n3n5415037038134/?MUD=MP “atheists have their theology, which is basically: "God, if he existed, wouldn't do it this way (because) if I were God, I wouldn't (do it that way)." http://www.evolutionnews.org/2014/05/creationists_th085691.html On the Vastness of the Universe Excerpt: Darwin’s objection to design inferences were theological. And in addition, Darwin overlooked many theological considerations in order to focus on the one. His one consideration was his assumption about what a god would or wouldn’t do. The considerations he overlooked are too numerous to mention here, but here’s a few:,,, https://uncommondescent.com/intelligent-design/on-the-vastness-of-the-universe/comment-page-2/#comment-362918 "One of the great ironies of the atheist's mind is that no-one is more cock-sure of exactly what God is like, exactly what God would think, exactly what God would do, than the committed atheist. Of course he doesn’t believe in God, but if God did exist, he knows precisely what God would be like and how God would behave. Or so he thinks",,," Eric - UD Blogger
bornagain77
May 1, 2015
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Plurality of voices is one thing. But if our opponents want to be heard all they have to do is work on supporting unguided evolution- find a way to model it would be a great start.Joe
May 1, 2015
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Intelligent Design and evolution are NOT mutually exclusive.Joe
May 1, 2015
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How would one determine a better design for a predator in an environment that is 100 years off into the future? That is the missing information. Without an ability to foresee future environments you cannot design a solution.Carpathian
May 1, 2015
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bornagain77:
Despite all this “intelligent design,” the artificial enzymes were 10,000 to 1,000,000,000 times less efficient than their biological counterparts.
That is the problem ID has to get around. ID failed here to equal biology which is exactly my point. ID is extremely difficult in that you don't know what information you're trying to put together for a given target. Evolution may be improbable in the sense that you cannot search for a target but ID's problem is to define the required target before designing. Determining your "spec" for a design is more difficult than actual physical design.Carpathian
May 1, 2015
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Yes, Aurelio, I do bother to read the comments. That's how I came up with the Game of Life reference. You see, I thought perhaps you just didn't understand what the term synonymous means. So I performed an experiment. Here's a suggestion. If you really want your ip unblocked act less like a troll.Mung
May 1, 2015
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Winston Ewert:
When we say search we simply mean a process that can be modeled as a probability distribution.
Aurelio probably thinks evolution is synonymous with Conway's Game of Life.Mung
May 1, 2015
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Aurelio, that you would think that DEM mean "search" to be synonymous with "probability distribution" says all about you that Winston needs to know. And from your own mouth.Mung
May 1, 2015
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Carp, so you want to jump directly from just trying to get a firm handle on studying, and understanding, the unfathomed complexity being found in biology to creating the unfathomed complexity of biology? Good luck with all that:
Francis Collins on Making Life Excerpt: 'We are so woefully ignorant about how biology really works. We still don't understand how a particular DNA sequence—when we just stare at it—codes for a protein that has a particular function. We can't even figure out how that protein would fold—into what kind of three-dimensional shape. And I would defy anybody who is going to tell me that they could, from first principles, predict not only the shape of the protein but also what it does.' – Francis Collins - Former Director of the Human Genome Project http://www.pbs.org/wgbh/nova/tech/collins-genome.html The Challenge to Darwinism from a Single Remarkably Complex Enzyme - Ann Gauger - May 1, 2012 Excerpt: How does a neo-Darwinian process evolve an enzyme like this? Even if enzymes that carried out the various partial reactions could have evolved separately, the coordination and combining of those domains into one huge enzyme is a feat of engineering beyond anything we can do. http://www.evolutionnews.org/2012/05/the_challenge_t059191.html Creating Life in the Lab: How New Discoveries in Synthetic Biology Make a Case for the Creator - Fazale Rana Excerpt of Review: ‘Another interesting section of Creating Life in the Lab is one on artificial enzymes. Biological enzymes catalyze chemical reactions, often increasing the spontaneous reaction rate by a billion times or more. Scientists have set out to produce artificial enzymes that catalyze chemical reactions not used in biological organisms. Comparing the structure of biological enzymes, scientists used super-computers to calculate the sequences of amino acids in their enzymes that might catalyze the reaction they were interested in. After testing dozens of candidates,, the best ones were chosen and subjected to “in vitro evolution,” which increased the reaction rate up to 200-fold. Despite all this “intelligent design,” the artificial enzymes were 10,000 to 1,000,000,000 times less efficient than their biological counterparts. Dr. Rana asks the question, “is it reasonable to think that undirected evolutionary processes routinely accomplished this task?” http://www.amazon.com/gp/product/0801072093
Dr. Fuz Rana, at the 41:30 minute mark of the following video, speaks on the tremendous effort that went into building the preceding protein:
Science - Fuz Rana - Unbelievable? Conference 2013 - video http://www.youtube.com/watch?v=-u34VJ8J5_c&list=PLS5E_VeVNzAstcmbIlygiEFir3tQtlWxx&index=8 Computer-designed proteins programmed to disarm variety of flu viruses - June 1, 2012 Excerpt: The research efforts, akin to docking a space station but on a molecular level, are made possible by computers that can describe the landscapes of forces involved on the submicroscopic scale.,, These maps were used to reprogram the design to achieve a more precise interaction between the inhibitor protein and the virus molecule. It also enabled the scientists, they said, "to leapfrog over bottlenecks" to improve the activity of the binder. http://phys.org/news/2012-06-computer-designed-proteins-variety-flu-viruses.html
Engineering principles, not Darwinian principles, lead to breakthroughs in designing new, relatively simple, proteins!:
Computer-designed proteins recognize and bind small molecules - September 5, 2013 Excerpt: In conducting the study, the researchers learned general principles for engineering small molecule-binding proteins with strong attraction energies. Their findings open up the possibility that binding proteins could be created for many medical, industrial and environmental uses.,,, The researchers adapted a computational tool called Rosetta developed in the Baker lab to craft new proteins that would bind the steroid digoxigenin, which is related to the heart-disease medication digoxin.,,, After generating many designs for digoxigenin-binders on a computer, the researchers chose 17 to synthesize in a lab. Experimental tests led the researchers to hone in on the protein they called DIG10. Further observations revealed that the binding activities of this protein were indeed mediated by its computer-designed interface, just as the researchers had intended. To upgrade their overall design methods, the researchers then used next-generation deep gene sequencing to probe the effect of each amino acid molecular building block on binding fitness. Using this method, they were able to discover how various engineered genetic variations affect the designed protein's binding capabilities. The binding fitness map gave the researchers ideas for enhancing the binding affinity of the designed protein to the picomolar level, tighter than the nano-level.,,, http://phys.org/news/2013-09-computer-designed-proteins-small-molecules.html
bornagain77
May 1, 2015
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Aurelio:
Evolution explains the how, not the why.
Except that evolution has yet to explain the how. The only thing so far is we are told to be comforted by the fact that evolution did happen.Joe
May 1, 2015
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Carpathian:
There is nothing to indicate that more sophisticated methods of biological reproduction did not arise through evolutionary pressure applied on simpler methods of reproduction used in the past.
Just the evidence: The cell divsion processes required for bacterial life
On the other hand, I have yet to see anyone write something describing how Intelligent Design methods could be applied to biology.
There has been plenty written about it.Joe
May 1, 2015
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bornagain77: Your quotes support that biology has analogies in human design but you have not shown a design methodology. The first question to ask if I'm going to design a biological species is, "What is the future going to look like?" If I don't know the environment, what is my specific goal? Secondly, how many initial copies will I make? It has to be more than two and maybe less than a million, but how do I know that?Carpathian
May 1, 2015
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Carpathian claims "There is nothing to indicate that more sophisticated methods of biological reproduction did not arise through evolutionary pressure applied on simpler methods of reproduction used in the past." and yet the facts say something very different: https://uncommondescent.com/darwinism/300-mya-vampire-squid-has-quite-different-reproduction-from-other-squid/#comment-561891 Carp goes on to state: "On the other hand, I have yet to see anyone write something describing how Intelligent Design methods could be applied to biology." Here you go:
"It has become clear in the past ten years that the concept of design is not merely an add-on meta-description of biological systems, of no scientific consequence, but is in fact a driver of science. A whole cohort of young scientists is being trained to “think like engineers” when looking at biological systems, using terms explicitly related to engineering design concepts: design, purpose, optimal tradeoffs for multiple goals, information, control, decision making, etc. This approach is widely seen as a successful, predictive, quantitative theory of biology." David Snoke*, Systems Biology as a Research Program for Intelligent Design podcast: "David Snoke: Systems Biology and Intelligent Design, pt. 1" http://intelligentdesign.podomatic.com/entry/2014-08-11T17_19_09-07_00 podcast: David Snoke: Systems Biology and Intelligent Design, pt. 2 http://intelligentdesign.podomatic.com/entry/2014-08-13T16_30_01-07_00 How the Burgeoning Field of Systems Biology Supports Intelligent Design - July 2014 Excerpt: Snoke lists various features in biology that have been found to function like goal-directed, top-down engineered systems: *"Negative feedback for stable operation." *"Frequency filtering" for extracting a signal from a noisy system. *Control and signaling to induce a response. *"Information storage" where information is stored for later use. In fact, Snoke observes: "This paradigm [of systems biology] is advancing the view that biology is essentially an information science with information operating on multiple hierarchical levels and in complex networks [13]. " *"Timing and synchronization," where organisms maintain clocks to ensure that different processes and events happen in the right order. *"Addressing," where signaling molecules are tagged with an address to help them arrive at their intended target. *"Hierarchies of function," where organisms maintain clocks to ensure that cellular processes and events happen at the right times and in the right order. *"Redundancy," as organisms contain backup systems or "fail-safes" if primary essential systems fail. *"Adaptation," where organisms are pre-engineered to be able to undergo small-scale adaptations to their environments. As Snoke explains, "These systems use randomization controlled by supersystems, just as the immune system uses randomization in a very controlled way," and "Only part of the system is allowed to vary randomly, while the rest is highly conserved.",,, Snoke observes that systems biology assumes that biological features are optimized, meaning, in part, that "just about everything in the cell does indeed have a role, i.e., that there is very little 'junk.'" He explains, "Some systems biologists go further than just assuming that every little thing has a purpose. Some argue that each item is fulfilling its purpose as well as is physically possible," and quotes additional authorities who assume that biological systems are optimized.,,, http://www.evolutionnews.org/2014/07/when_biologists087871.html Systems Biology as a Research Program for Intelligent Design - David Snoke - 2014 http://bio-complexity.org/ojs/index.php/main/article/viewArticle/BIO-C.2014.3
On the other hand, presupposing everything is just a cobbled together series of accidents, as Darwinism does, has hindered research into biology with, (dogmatically held), erroneous concepts such as vestigial organs and junk DNAbornagain77
May 1, 2015
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Joe:
Why can’t evolution occur in a static environment? Is Aurelio really suggesting that mutations will not occur in a static environment? Isn’t Lenski’s experiment a static environment?
I think Joe right. I don't see what would stop a better configuration than a current one developing in any given environment even if that environment is static.Carpathian
May 1, 2015
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So, I’m right in reading DEM (yourself in association with Dembski and Marks) as "die" is synonymous with “search"?Mung
May 1, 2015
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Joe:
Basic biological reproduction is irreducibly complex and as such requires an Intelligent Designer.
There is nothing to indicate that more sophisticated methods of biological reproduction did not arise through evolutionary pressure applied on simpler methods of reproduction used in the past. On the other hand, I have yet to see anyone write something describing how Intelligent Design methods could be applied to biology.Carpathian
May 1, 2015
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Aurelio Smith:
So, we’re right in reading DEM (yourself in association with Dembski and Marks) as “search” is synonymous with “probability distribution?
Could you be any more dense?Mung
May 1, 2015
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Bob O'H. There's no problem with the rolling of a die as a search. When you roll a die it's an experiment.Mung
May 1, 2015
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