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Dave Thomas says, “Cordova’s algorithm is remarkable”

Salvador Cordova
August 17, 2006
Intelligent Design
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Dave Thomas is in a bit of a tizzy over my humble offering: Tautologies and Theatrics (part 2): Dave Thomas’ Panda Food. He responds at Pandas Thumb with: Calling ID’s Bluff, Calling ID’s Bluff. I thought I’d alert the readers at UD what horrible things I’m accused of, that I might be some sort of vile scoundrel. 🙂

[Dave writes:]

Imagine my surprise, then, when I found Salvador Cordova at Uncommon Descent spewing blatant falsehoods about this work. I was shocked – shocked, I say – to catch the UD Software Engineers in a lie. And quite a lie it is – with the help of mathematicians like Carl Gauss, I’m going to lift the veil from the obfuscations of IDers, and prove it’s a Lie, much as you would prove a mathematical theorem.
….
which the brilliant Gauss found useful

Thomas then correctly identified the formula I implemented via Genetic Algorithm:

[Dave writes:]

The Software Engineering Team of Uncommon Descent has been caught lying – Q.E.D.

Where did I ever claim there wasn’t smoke and mirrors involved in the gimmickery here? Fer cryin’ out loud, my post was talking about mathematical theatrics, and I presented that program as an example of gimmickery! I even alerted the reader with these words before presenting my program, “The following [are] computational theatrics”. Sheesh!

[Dave writes:]

As an exercise in Smoke and Mirrors, Cordova’s algorithm is remarkable

Well dog gone, he actually says something nice about my work. It’s REMARKABLE! 🙂

I fully take pride in the smoke and mirrors I used, I never pretended otherwise. In contrast, Thomas refuses to admit he’s also using smoke and mirrors in his GA. He pretends somehow his steiner-solving program should persuade us that mindless undesigned forces can hit specified targets.

Well, did he have some Chimpanzee create the fitness functions in his software for him? Without intelligent design on his part, his fitness functions will fail to guide the system to the intended target. He has thus snuck the answer his GA, much the same way I snuck the answer in my GA. At least I alert the readers of where the trickery is, but Thomas would rather have his faithful congregation at Pandas Thumb believe that mindless evolution can truly work magic.

As Haeckel said:

Evolution is henceforth the magic word by which we shall solve all the riddles that surround us.
Ernst Haeckel1

Instead of “abracadabra” the Pandas say, “evolution”. Ramen.

Comments
[…] Hoppe admits irreducible complexity can be evolved by random mutation and designed selection (RMDS). But this says nothing about random mutation and natural selection (RMNS). Examples of Designed Selection (DS) to achieve desired intentional goals are Dawkins Weasel, Avida, Ev, Steiner, Geometric, Digital Ears and Cordova’s remarkable evolutionary algorithm. […]Hoppe blows a gasket over Ewert’s paper, forgets to mention Avida predicts zombie apocalypse and solves OOL | Intelligent Design and Creation Science
April 15, 2014
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[…] models the Darwinian view are genetic algorithms like Avida, Tierra, Ev, Steiner, Geometric and Cordova’s remarkable algorithm. Winston Ewert discusses these […]Neutral theory and non-Darwinian evolution for newbies, Part 1 | Uncommon Descent
April 12, 2014
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[…] models the Darwinian view are genetic algorithms like Avida, Tierra, Ev, Steiner, Geometric and Cordova’s remarkable algorithm. Winston Ewert discusses these […]Neutral theory and non-Darwinian evolution for newbies, Part 1 | Intelligent Design and Creation Science
April 12, 2014
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"I think the manufacturers might be surprised by your claim to have contributed to the design." Yeah, if I accepted the disk drive as presented. But if instead the manufacturer had no clue what to do to improve the disk drive other than from my selection of random variants of it, then I think I'd have every right to claim to have designed the improvements to it. (Or the entire disk drive if this process started from scratch.) "So if selection algorithms are part of the design they have the weird propery that the design takes place after the solution has been produced." No they don't. They have the property that design takes place after slight improvement has been produced. Again and again and again. The solution is produced only after much design has occurred.j
August 26, 2006
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j You are right - I apologise. I forgot what I wrote. So I need to adjust the argument a bit. Suppose you go on to Google and you choose the fastest widget. Did you therefore contribute to the design of that widget? To make it concrete suppose you wanted an external disk drive and you selected the one with the fastest access time subject to a minimum capacity. I think the manufacturers might be surprised by your claim to have contributed to the design. You may object that the disk drives were created before the selection process. But that is exactly what happens with Dave's selection algorithm (or any selection algorithm). It selects from what already exists. It is only the repeated application of the algorithm that hides this rather obvious point. So if selection algorithms are part of the design they have the weird propery that the design takes place after the solution has been produced.Mark Frank
August 24, 2006
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[This is why I said I plan to move on.] You: "...but the organiser is doing no more than the 'facilitator' of the maths competition..." I don't agree. Because you changed the rules midstream. Back at (70) you said: "I want to find a solution to a difficult mathematical problem. So I organise a competition and offer a prize to the first person to solve it." (boldface added) That is why I said that the organizer did not design anything. The organizer did not influence the design, s/he accepted it as presented. I make myself more likely to find a [Widget To Accomplish Some Task] if I take a trip to Sears, or use Google. That doesn't mean I designed the [WTAST]. I may not know whether the [WTAST] even exists ahead of time. But if I'm willing to expend some effort, I can increase the likelihood of finding it -- I can facilitate its finding. But then at (73), you made a crucial change to the role of the organizer: "The organiser will then subject these solutions to Dave’s selection algorithm (i.e. select the ones with shortest path length) and hand them back to the children to try to find improvements..." You added his/her selectivity to the process of achieving the end product. That is why I said that the organizer is a co-designer. And I maintain that Dave Thomas can be considered the designer (not special creator) of the Steiner solutions. It is only because of the teleology that he imparted to the system that the solutions were obtained.j
August 24, 2006
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j. I am sorry you are bored with this topic. To my mind we got to an interesting point. It gives me an opportunity to have the last word - but please understand this is purely in a spirit of intellectual enquiry. In my proposed example with children you cleverly use the word "co-design" but the organiser is doing no more than the "facilitator" of the maths competition - simply selecting the best solution out of many submissions - and we earlier agreed that the facilitator was not a designer. If you accept that selecting the best of several designs is not designing the solution, then your logic seems to imply that whether the organiser designed the solution depends on what the children do and not on what the organiser does. Suppose the organiser did not know whether the proposed solutions were created through intelligence or the roll of the dice? I will keep checking for a few days in case you (or anyone else) feels moved to respond but will understand if that is the end of the discussion. Thanks for attending.Mark Frank
August 24, 2006
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The principal characteristic of intelligent agency is choice. Even the etymology of the word intelligent makes this clear. Intelligent derives from two Latin words, the preposition inter, meaning between, and the verb lego, meaning to choose or select. Thus according to its etymology, intelligence consists in choosing between. For an intelligent agent to act is therefore to choose from a range of competing possibilities. (William A. Dembski, Intelligent Design, p. 144.)
You imply that the children use their intelligence in the generation of the proposed solutions. This being the case, then of course they are to be credited with being co-designers with whoever designed the algorithm used to choose among the proposals. However, if they had been generating their proposals by the roll of dice (for example), then they are not to be credited with having contributed to the design. They would have been slavishly implementing a mindless process. A designer is one whose choices lead to a solution. If those choices can be automated (as in Dave Thomas's program), it makes no difference. All who makes the choices (which algorithm to use, how to initialize it, what "the fittest" is defined as, possibly how to tweak the algorithm, etc.) that result in the solution, is/are the designer/s. Your evaluation of Edison agrees with this. You say that if his solution was obtained completely by chance, then he did not design it, but if he made choices that were essential to permitting the discovery to be made, then he did design it. Dave Thomas made choices that were essential to permitting the discovery of the Steiner solutions. I could easily take your hypothetical introduction of intelligent agents into the variation process as an apparent sly ploy to make it seem more reasonable that a totally blind/dumb/purposeless process has powers that it doesn't have. (Like Darwin comparing natural selection to artificial selection in the Origin of Species.) But I'll be charitable and assume this wasn't the case. [P.S. I'm getting bored with this particular topic and plan to move on.]j
August 23, 2006
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j Let's start by summarising where we agree. 1) You say "having the intention is a necessary, though not sufficient, condition for designing something". I absolutely agree. Dave had the intention to create patterns with short path lengths - but that is not sufficient to prove that he designed them. 2) In the case of the competition the organiser cannot be said to have designed the solutions (although he did design the process which lead to the solutions being designed). I believe that Dave was in the position of the organiser. He created a process where solutions emerged. I can perhaps convince you by imagining a small change to his algorithm. At the moment it creates new patterns through random mutation and crossover of "DNA". It then selects through choosing the ones with the shortest path length. It is the selection process that Salvador considers to be point where Dave adding his design. OK let's keep the selection process but change the variation process. This will mean moving the algorithm off a computer. The organiser will start by asking many small children to come up with their best solution to Dave's problem. The organiser will then subject these solutions to Dave's selection algorithm (i.e. select the ones with shortest path length) and hand them back to the children to try to find improvements (probably we mix them up so a child is not trying to improve another child's solution - not their own). The children hand in their improvements and we run them through the selection algorith and do it all again until it looks like we aren't getting anywhere (assume these are extraordinarly indefatigable children). This looks very like the competition except it has multiple rounds. I seriously doubt you that could say the organiser was designing the solutions - the children are doing that. But the element that Salvador labelled as introducing design (the selection algorithm) is identical. What has changed is the source of variation. With respect to 1 and 2. You need to be precise about what happens. If Edison simply kept putting things between two electrodes in the hope that one would one day light up - then I don't think you can say he designed that solution. He just discovered it. He also designed the process for finding a solution (trial and error). If he thought about the kind of properties that would be required for a light bulb, selected suitable elements, tried them out, and the worked out how to package them into a usable offering then he did design the solution and a bit of trial and error helped out. But Dave's algorithm is not at all like that. RgdsMark Frank
August 23, 2006
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Mark Frank, As I strongly implied @65, you are using the word "design" in too strict a sense. You're using it as a synonym for "specially create." The more general definition is what ID concerns. An engineer who uses a computer program to find a solution (that correspond to a design) is considered the designer. And it's true. He had "held a particular purpose in view" and undertook "deliberate purposive planning" and "laid down means to an end in a scheme" (See my comment #46) The organizer of a design competition cannot be said to have designed anything. The proper description of their activity would be "facilitation." Yes, I did write "If it wasn’t for his intention, they wouldn’t exist." But having the intention is a necessary, though not sufficient, condition for designing something. Obviously, anyone who ever intended to design an airplane before the Wright brothers actually succeeded cannot be credited with designing an airplane. But this is what one would be led to by your interpretation of what I wrote. One has to actually come through with the goods to be considered an inventor. For example, patents aren't issued to business owners, they're issued to the employees who contributed substantively to the design. I don't quite follow what you mean regarding the Newton-Raphson method. —————————— Your (Mark Frank's) criteria @48: "(b) [to be considered a design, it must] achieve the designer’s purpose in the fashion that the designer planned." You @70: "Re #68. Neither 1 or 2 [@69] are in conflict with my conditions (a) and (b). 1 and 2 are methods for coming up with a design. This could happen through serendipity, a blinding flash of inspiration or a visit from my fairy godmother. However, once the design has been produced conditions (a) and (b) must still apply for it to be a design and not just a happy accident." This makes no sense. If the design existed before the designer even intended to design anything, or if the design is found only by a process of elimination, it cannot be in the fashion that the designer planned. M-W's dictionary:
serendipity - the faculty or phenomenon of finding valuable or agreeable things not sought for. trial and error - a finding out of the best way to reach a desired result or a correct solution by trying out one or more ways or means and noting and eliminating errors or causes of failure; also : the trying of one thing or another until something succeeds.
And my modes (3) or (4) don't meet your criteria, either.j
August 22, 2006
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Two more modes of design: 3) Subconscious daemon (initiated by previous conscious effort). Mathematician Henry Poincaré, after intensive periods of deliberate, conscious effort searching for what he called Fuchsian functions:
...I left Caen, where I was living, to go on a geologic excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.
4) Conscious inspiration. Mozart:
When I am well and in good humour, or when I am taking a drive or walking after a good meal, or in the night when I cannot sleep, thoughts crowd into my mind as easily as you could wish. Whence and how do they come? I do not know and I have nothing to do with it. Those which please me I keep in my head and hum them; at least others have told me that I do so. Once I have my theme, another melody comes, linking itself with the first one, in accordance with the needs of the composition as a whole: the counterpoint, the part of each instrument and all the melodic fragments at last produce the complete work. Then my soul is on fire with inspiration. The work grows; I keep expanding it, conceiving it more and more clearly until I have the entire composition finished in my head though it may be long. Then my mind seizes it as a glance of my eye a beautiful picture... It does not come to me successively, with various parts worked out in detail, as they will later on, but in its entirety that my imagination lets me hear it.
(Both quotes from Roger Penrose, The Emperor's New Mind)j
August 22, 2006
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Re #69. Thanks Salvador. I will restrict my involvement to your threads and see how it goes. Re #65. There is a difference between designing a method for finding a solution and designing the solution. Dave designed a method for producing patterns with short path lengths but he didn't design the patterns. Here's an analogy. I want to find a solution to a difficult mathematical problem. So I organise a competition and offer a prize to the first person to solve it. I designed the method of finding the solution (the competition) but the winner designed the solution. The winner would be justifiably pissed off if I claimed I had designed the solution because "without my intention the solution would not have existed". In the case of Newton-Raphson (and indeed Salvador's example) there is an additional complication - the solution is a single number. You can't design a number. You can come up with a design which you express as a single number - but that number must represent something more complex where the designer has to think through how the solution solves the problem. This is confusing because it means that in these examples the only occurence of design is in the method of finding the solution - not the solution itself. Re #68. Neither 1 or 2 are in conflict with my conditions (a) and (b). 1 and 2 are methods for coming up with a design. This could happen through serendipity, a blinding flash of inspiration or a visit from my fairy godmother. However, once the design has been produced conditions (a) and (b) must still apply for it to be a design and not just a happy accident. RgdsMark Frank
August 21, 2006
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Mark Frank, If it makes you feel better, my posts get held up as well. Let's be patient with the volunteer work of the moderators however. If you are on my threads, and you abide by the spirit of the forum, and I remove something of yours, it will appear on the Cutting Room Floor. Thank you by the way for visiting. Salvadorscordova
August 21, 2006
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Re #46 for an object to be designed (as opposed to appearing to be designed) it must not only satisfy the designer’s purpose but a) should be the result of some activity by the designer (a heavy shower suits my purpose for watering the garden but I didn’t design the shower) b) achieve the designer’s purpose in the fashion that the designer planned (if I lay out a hose to water the garden and the garden actually gets watered because of a leak in the hose you can’t say I designed the solution)
This is certainly a very narrow idea of design. The method of working backwards from a known goal is clearly a useful design strategy, and the inability of evolution to use this strategy is clearly the source of many of the infelicities of the design of organisms, but it is hardly the only strategy available to a designer. Two other important sources of design are: 1) Discovery/serendipity: This is arguably the most important modality of design, in which discovery of the means precedes awareness of the goal. Typically, a designer working on some other problem entirely discovers a means of achieving an end that he did not previously even conceive as a possible goal. For example, until the discovery of the laser, nobody would have imagined using optical storage for movies. Indeed, shortly after its discovery, the laser was described as "a solution in search of a problem." Truly transforming discoveries typically arise in this way. 2) Trial and error solution to a problem: Edison reportedly tried hundreds of possible filament compositions in his search for a way of making a light bulb. Historically, much pharmaceutical drug development is derived from testing a large number of chemical compounds in animal models, picking those that seem to produce useful effects, and only later figuring out how that particular compound produces those effects.trrll
August 21, 2006
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Re #65. I would like to continue this discussion but I am finding that only about 50% of my postings on UD are accepted and others are delayed by up to 24 hours (I am not aware of breaking any of the rules). This makes it almost impossible to have an intelligent debate. It also takes considerable time and effort to make a thoughtful and relevant response and it is too frustrating to do this and then find it is rejected without explanation There doesn't seem to be any logic as to why some posts are accepted and others are not. It makes me wonder if it is actually a technical or process problem rather one of censorship. Let's see if this one makes the grade :-)Mark Frank
August 20, 2006
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Tom Observed: It seems to me that the displacement theorem does not apply. The problem here is not like finding a particular amino acid sequence, as in Dembski’s “Searching Large Spaces.” That is, the problem is not to find an element of a small target, where elements outside the target are of no utility. Instead, any network that spans the fixed nodes is usable. There are a great many such networks. Some are better than others. You might argue that the set of Steiner solutions is the target, but, unlike Dembksi’s search assistant, the fitness function does not “know” which networks are Steiner solutions. There are local maxima in the fitness landscape, and the fitness function does not do anything to assist the GA in finding global maxima (Steiner solutions). This seems to me not to fit Dembski’s paradigm of assisted search.
If the Displacement Theorem does not apply then the target lacked high specificity ( high specificity means highly improbable), which means Thomas's program cannot be a counter example to CSI conservation. This would be equivalent to launching an arrow and saying where ever it landed it hit a target. But even that may be too generous if the software guarantees solutions which create connectivity (albeit of unknown length). If then we calculate the ratio of all possible connected networks versus all possible unconnected "networks", then CSI is implicated, and the displacement theorem applies. Thomas's describes his fitness function in his original essay Target? TARGET? We don’t need no stinkin’ Target!:
In this figure, the first and third “organisms” connect all the nodes, while the second has a fatal flaw: the top node is not connected to any other node. I defined the “fitness” of the organism as simply as the net length of all activated segments, or 100,000 if any fixed node is unconnected. It’s important to note that the “fitness” thus defined does not depend on the exact number of active variable nodes, or the angles between connected segments, or upon anything other than the total length of active segments. While both first and third solutions at least connect the fixed nodes, they are both far different than the proper Steiner Solution for the five-node system. The Fitness Test knows nothing of this solution, however; all it tells us is that the solution on the right is a little shorter, and therefore “fitter,” than the solution on the left. Because the middle solution misses a node, it is “unfit.”
In outher words we have 2 situations: 1. If Displacement theorem doesn't apply, then the GA cannot be used as a valid counter-example to ID claims 2. If the Displacement theorem applies, then we may be able to find how the CSI was snuck in. There is an extreme caveat here, discovering the how is a sufficient, but not necessary condition for affirming the displacement theorem. It may be the GA program is so complex, it defies analysis how the CSI was snuck in. For example, a fitness funciton may have been discovered by the designer through serendipity which he may or may not understand why it works. Meaning, random hacking of the fitness function on his part may create a local optimization, just as your paper (correct me if I'm wrong) suggested could be easy. But even such random hacking to achieve a goal is assisting the search. If the solution space is structured a certain way, then on rare occasions the quest for optimiztion may actually result in genuinely informed (learned) strategy.scordova
August 20, 2006
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Mark Frank (48):
...for an object to be designed (as opposed to appearing to be designed) it must not only satisfy the designer’s purpose but...achieve the designer’s purpose in the fashion that the designer planned...
This simply isn't true. Use of various (computer-based) numerical methods to help find optimal, or at least adequate, solutions is a standard part of perhaps most engineers' educations. Necessarily, when these methods are used, the engineer doesn't know what the solution will be beforehand, but he or she must know enough to choose and set up the method in a way that it may yield a solution. I've already given an example of this in another thread: the solution of a system of nonlinear equations (that models some real-world problem) using an algorithm such as the Newton-Raphson method.
Dave Thomas had no idea how the resulting patterns were going to achieve short paths so he did not design...
He did design them. If it wasn't for his intention, they wouldn't exist. What he didn't do is specially create them. Intelligent design is not creationism. ;-)j
August 20, 2006
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Formatting error: trrll's blockquote should have ended after the first paragraph in the previous comment. Sorry. P.S. Will UD have a comment "preview" function after the coming upgrade?sophophile
August 20, 2006
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trrll wrote:
It seems clear that every existing species could in principle be generated by random chance, simply by exhaustively sampling the space of possible DNA sequences. While maximally inefficient, such an algorithm would eventually be successful. Therefore, if the design of living creatures embodies CSI, then random chance can create CSI. You're right that CSI can be produced by purely random processes, given enough time. However, my reading of Dembski is that he defines CSI with a 500-bit threshold in order to preclude such a production of CSI, except by an extreme fluke, within the projected duration of the universe. The error, of course, is in assuming that instances of CSI must come together in a single step. If the specified complexity accumulates in many smaller steps, with a non-random fitness function to select promising candidates along the way, then the odds because dramatically better for producing CSI within the time available. Given that most IDers accept natural selection on a small scale (when they aren't contradicting themselves by insisting that it is a tautology), you would think the only debate would be over whether real-life fitness functions and genomes admit of a series of steps toward structures possessing CSI, where each step is realistic given the amount of time available for it to happen. Applying this to GA's, the question is which "genomes" and fitness functions allow for achievable stepwise paths to CSI, not whether are any such genomes and fitness functions exist.
sophophile
August 20, 2006
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The question whether undesigned nature can create such genetic algorithms in real life that can originate novel CSI. The displacement theorem describes the likelihood as more remote than random chance on average.
Others have pointed out why the displacement theorem does not apply. But for the sake of argument, let's consider random chance: It seems clear that every existing species could in principle be generated by random chance, simply by exhaustively sampling the space of possible DNA sequences. While maximally inefficient, such an algorithm would eventually be successful. Therefore, if the design of living creatures embodies CSI, then random chance can create CSI. So it seems that the argument ultimately boils down to one of efficiency. Is a parallel heuristic sampling algorithm such as a genetic algorithm able to discover CSI (or whatever type of information is required to define an organism sufficiently efficiently? This is not a question that could be resolved by some sort of law of information conservation, even if such a thing could be established, because it is a kinetic question—now a question of whether it can happen, but whether it can happen fast enough to be consistent with observation.trrll
August 20, 2006
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Salvador, "The displacement theorem describes the likelihood as more remote than random chance on average." It seems to me that the displacement theorem does not apply. The problem here is not like finding a particular amino acid sequence, as in Dembski's "Searching Large Spaces." That is, the problem is not to find an element of a small target, where elements outside the target are of no utility. Instead, any network that spans the fixed nodes is usable. There are a great many such networks. Some are better than others. You might argue that the set of Steiner solutions is the target, but, unlike Dembksi's search assistant, the fitness function does not "know" which networks are Steiner solutions. There are local maxima in the fitness landscape, and the fitness function does not do anything to assist the GA in finding global maxima (Steiner solutions). This seems to me not to fit Dembski's paradigm of assisted search. "No one has yet been able to demonstrate that a GA can popup out of nowhere on its own. NO ONE!" That's in part because of the weirdness of your statement. No one claims that nature created a GA. Humans devised the GA as an abstract model of a natural process. The natural process of evolution arises by necessity when a population of self-replicators competes for resources in a bounded arena. Variation in the population arises from errors in replication necessitated by thermodynamics. The boundedness of the arena necessitates that some variants are culled from the population. Evolution is necessity operating on chance inputs. A better version of your remark: No one has yet been able to demonstrate that a self-replicator can pop up out of nowhere on its own. NO ONE! "... GA’s do not demonstrate that undesigned nature can evolve complex designs from scratch." You have a concept of undesigned nature? If I demonstrate to you that novel information in biota comes from random errors in reproduction and specificity comes from the environment (i.e., by way of selection), you'll have no choice but to tell me the environment was designed. Am I wrong?Tom English
August 19, 2006
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52. scordova: “What Thomas did not model was adding some noise into his selection routines where the less fit individual survives almost 50% of the time.” I think that this could be an interesting variation on a GA program. On the other hand, do you really want to suggest that? The reason is that by this mechanism you are permitting the possibility that mutations can accumulate without being eliminated right away by selection. So even if either of two mutations may not have a significant effect on improving fitness, the synergistic combination of the two may do just that. A few months ago, there was a big discussion about the evolution of the mineralocorticoid receptor that involved two mutations. see http://www.sciencemag.org/cgi/content/abstract/sci;312/5770/97.ofro
August 19, 2006
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You could reduce this further with a point D close to point 5. That will introduce new possibilities for tweaking B and C. I got a total length 1595.392 using D=(400,281) but then I only modified the y coord in 1 degree increments.steveh
August 19, 2006
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Here are the 4 proposed networks In Cartesian coordinates, letting Vertex 1 = be the origin, or equivalently Vertex 1 = (0,0), and Vertex 6 be at (x,y) = (800,300), I propose the following 4 solutions of equivalent length:
Solution 1: steiner points: A = (86.6025, 150) B = (313.3975, 150) C = Fermat Point joining vertex 5,6,3 = (730.42, 224.88) A connects to Vertex 1, Vertex 4, Steiner Point B B connects Steiner Point A, Vertex 5, Vertex 2 C connects to Vertex 5, Vertex 6, Vertex 3
Solution 2: steiner points: A = (86.6025, 150) B = (313.3975, 150) C = Fermat Point joining vertex 2, vertex 6, vertex 3 = (730.42, 75.13) A connects to Vertex 1, Vertex 4, Steiner Point B B connects Steiner Point A, Vertex 5, Vertex 2 C connects to Vertex 2, vertex 6, vertex 3
Solution 3: steiner points: E = Fermat Point joining vertex 1,vertex 4, vertex 5 = (69.58, 224.88) F = (486.6025, 150) G = (713.3975, 150) E connects to Vertex 1, Vertex 4, Vertex 5 F connects to Vertex 5, Vertex 2, Steiner Point G G connects Steiner Point F, Vertex 6, Vertex 3
Solution 4: steiner points: E = Fermat Point joining vertex vertex 1, vertex 4, vertex 2 = (69.58, 75.13) F = (486.6025, 150) G = (713.3975, 150) E connects to Vertex 1, Vertex 4, Vertex 2 F connects to Vertex 5, Vertex 2, Steiner Point G G connects Steiner Point F, Vertex 6, Vertex 3
Here is the sum of all the lengths where each solution has the same length, but I'll us solution one to calculate length, and then one can assume the other 3 solutions have the same length: 1 to A 173.2050808 4 to A 173.2050808 A to B 226.7949192 B to 5 173.2050808 B to 2 173.2050808 sub total left 919.6152423 5 to C 338.8521647 3 to C 235.4003099 6 to C 102.3907822 sub total right 676.6432568 total 1596.258499 Each Steiner point has degree 3 with each connected edge opening 120 degrees from the adjacent one radiating from the same steiner point. These are necessary but not yet sufficient conditions for a steiner solution. I await Dave’s correct solution, but this one I think these are at least MacGeyver's.scordova
August 19, 2006
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Here is the sum of all the lengths: 1 to A 173.2050808 4 to A 173.2050808 A to B 226.7949192 B to 5 173.2050808 B to 2 173.2050808 sub total left 919.6152423 5 to C 338.8521647 3 to C 235.4003099 6 to C 102.3907822 sub total right 676.6432568 total 1596.258499scordova
August 19, 2006
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There are 4 solutions which can be constructed via symmetry from the 1st one. I don't know if they are optimal solutions, but they'll connect the 6 verticies. Letting Vertex 1 = be the origin, and Vertex 6 be at (x,y) = (800,300) I propose the following steiner points: Here is my correction A = (86.6025, 150) B = (313.3975, 150) C = Fermat Point joining vertex 5,6,3 = (730.42, 224.88) A connects to Vertex 1, Vertex 4, Steiner Point B B connects Steiner Point A, Vertex 5, Vertex 2 C connects to Vertex 5,6,3 Each Steiner point has degree 3 with each connected edge separated by 120 degrees from the other. These are necessary but not yet sufficient conditions for a steiner solution. I await Dave's correct solution, but this one I think is adequate. The other 3 can be constructed via symmetry. Salvadorscordova
August 19, 2006
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trrll commented: Re #50. While I understand that this is a moderated forum, and you are entitled to censor whatever you choose for whatever reasons that you choose, it hardly seems fair to choose not to post a response yet still write a rebuttal to a selected snippet from that response
trrll, Apparently while I was moving your earlier comment, Michaels was still typing a response to it. However, feel free to continue participating, I do appreciate your participation. Salvadorscordova
August 19, 2006
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Otherwise, life can pop up anywhere, in any form, any planet.
We don't exactly know that it can't. Whether the origin of life is a low probability or a high probability event is unclear. It seems to have happened pretty quickly here on earth once the crust stabilized, which suggests that it is a high probability event under primordial earth conditions, but how common those conditions are in the universe is unclear.
The fact is you’re defining living contraints of the program, thermo being just one of the external considerations in your example. Your cost/efficiency ratios are but one of many conditions that must be optimized, not including interactions, immune systems, repair systems, catalyst(enzymes). But cost/efficient ratios can be overcome by larger energy input/output.
Yes, organisms are more complicated than this simple system, and there are certainly more complicated forms of artificial life evolving in computer simulations. But other concerns, such as overall energy input/output do not obviate the importance of efficient design of biological networks. It is certainly true that a mutation that increases overall energy input would be strongly selected for. But once that mutation has gone to fixation, the individuals with more efficient networks will once again have a selective advantage.
I’d appreciate any links which may dispute the articles findings at Biocompare posted in 2003 on a study by Dr. Richard Wolfenden who claims it to be an enigma as to enzymes arising within the currently accepted universal timeline.
What is the relevance to evolution of a reaction whose uncatalyzed rate is negligible? Do you imagine that enzymes are the only catalysts in nature? All sorts of things have been observed to catalyze chemical reactions, including inorganic clays, minerals, and ions. Moreover, studies of the evolution of novel enzymatic activities by mutation/selectioin in vitro have shown that catalytic activity, with rates less than an enzyme, but much greater than the uncatalyzed rate, can readily be found in mixtures of random peptides or nucleic acids.trrll
August 19, 2006
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Re #50. While I understand that this is a moderated forum, and you are entitled to censor whatever you choose for whatever reasons that you choose, it hardly seems fair to choose not to post a response yet still write a rebuttal to a selected snippet from that response.trrll
August 19, 2006
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trrll wrote: For example, the Steiner network problem models a biological problem that organisms must solve, the problem of “designing efficient networks. Networks are used heavily in biology neural networks, vascular networks. They need to connect crucial targets within the body, but thermodynamics imposes an energetic cost per unit length. An organism that grows excessively long vascular and neural pathways will be at a disadvantage compared to an otherwise identical organism that grows its pathways more efficiently, because it will require more nutrition and be at greater risk when food is scarce.
But that presumes the existence of a functional network in the first place, and that the signal-to-noise ratios are adequate enough to make small differences in network topology sufficiently visible to seleciton forces. If this is not the case, the appropriate model for the fitness might as well be a random number generator with a teeny tiny slight bias toward a goal. What Thomas did not model was adding some noise into his selection routines where the less fit individual survives almost 50% of the time. What Thomas used was truncation selection, and as John Sanford noted in Genetic Entropy that is a highly inappropriate model of selection in the wild. And then there is yet one other nasty issue, what chooses the number of network points in the first place? A very good example of this problem is the excessive overkill in terms of brain cells in the human mind. It is widely acknowledged that the human brain seems far beyond what natural selection requires. Why then add all these network points, if energy is the selection criteria? The human brain consumes 20% of energetic resources. From an energetic standpoint, this seems a bit excessive, don't you think? I hate to say this, but if average intelligence is declining per generation, this would not bode well for Darwinian evolution as the designer of the human mind. Some impetus greater than thermodynamic efficiency was at work in creating such a thermodynamically expensive apparatus as the human mind.scordova
August 19, 2006
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