A Statistics Question for Nick Matzke

_{Barry Arrington

December 16, 2013

Intelligent Design}

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If you came across a table on which was set 500 coins (no tossing involved) and all 500 coins displayed the “heads” side of the coin, would you reject “chance” as a hypothesis to explain this particular configuration of coins on a table?

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Chi square: null hypothesis: Coins were randomly flipped. Prediction: 50-50 split based on probabilities. Expected tail: 250. Observed: 0 Expected heads: 250. Observed: 500. (Observed-expected)^2/expected. 250 for both so 500 is value. Degrees of freedom is 1. For that degree of freedom 500 is way above the chi square value required for the null hypothesis to be accepted/not rejected. Conclusion: null hypothesis is rejected, chance is not the sole reason for the coins' position. It's simple Nick!sixthbook_{December 16, 2013
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The question was not is the design hypothesis rejected, but rather whether chance as a hypothesis is rejected:
If you came across a table on which was set 500 coins (no tossing involved) and all 500 coins displayed the “heads” side of the coin, would you reject “chance” as a hypothesis to explain this particular configuration of coins on a table?
Nick responded:
a pattern like “all heads” does not therefore reject all chance hypotheses.
Here is a paper relevant: You can load a die, but you can bias a coin They tried to do all sorts of tricks like putting putty on checkers and seeing if that would substantially bias the "coin" they invented, and it did not in any significant way. 1. a two-headed coin, if discovered for all 500 coins would immediately cause rejection of the chance hypothesis 2. a biased coin, even 60% biased towards heads would still not create a 500 heads pattern from chance, but as that paper discussed, at issue in a coin isn't its internal mechanics but the space of possible boundary conditions on that apply on the coin, which results effectively in the coin being approximately fair. And at some point, one has to start equivocating the notion of coin if one starts invoking extremely biased devices. 3. if the manufacturer or bank or whoever packed the coins packed them as all head, and then they spilled out, the pattern is still not attributable to chance, but rather the packing machine. Chance means that a random process had acted on the coins individually, and if the coins were still in some initial condition from the manufacturer, a random process has not acted on them, thus chance is ruled out. So if random process has not acted on coins individually, it's really not fair to say the coins were subject to a random process in the usually sense. 4. Only in pathological cases using loads of equivocation could one say the chance hypothesis can't be rejected. i.e. 499 coins are 2-headed, 1 is fair, thus in that case on might say "chance caused the pattern", but even then that is dubious because the 499 other coins had a deterministic outcome. And thus chance really wasn't the principal mechanism. That would also hold true for the coins slipping out of the package being heads, chance would at best play a minor role for the pattern, whereas it was the packing machine that would be the source.
a pattern like “all heads” does not therefore reject all chance hypotheses.
One can only say that if one abuses language, equivocates the notion of coins, equivocates the notion of a chance process, and accepts that deterministic processes also count as chance processes. :roll:
If you came across a table on which was set 500 coins (no tossing involved) and all 500 coins displayed the “heads” side of the coin, would you reject “chance” as a hypothesis to explain this particular configuration of coins on a table?
We have it recorded now that Nick said no, or at best refused to give a clear answer.
"It depends upon what the meaning of the word 'is' is." "I have never had sexual relations with Monica Lewinsky. I've never had an affair with her." Bill Clinton
scordova_{December 16, 2013
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Stephen, Your example is well-enough described that, sure, it is easy to reject the chance hypothesis that you specified from the data.NickMatzke_UD_{December 16, 2013
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Nck, I have been watching you with embarrassment. You have been trying desparately to evade a simple answer to a simple question. I have been embarrassed for you while you and your compadres have donned red noses, size 22 shoes and clanged cymbals between your knees. All in an effort to not concede one millimeter of ground to anyone who carries the slightest scent of ID sympathy. Let me see if I can help you out. Senario: You and I are in a room with 500 fair coins each in hand. You proceed to flip your 500 coins and arrange them in a line in the temporal order of the flips. You then leave the room while I proceed to "flip" my 500 coins. When I have completed my "flipping" I call for you to return to the room and examine the line of coins that I "flipped" Upon inspection, you note that my line of coins is in one to one correspondence identical to yours. Head for head and tail for tail. You then ask me, "Did you really arrive at your arrangement in the same way I did in your presence?" Would you be surprised if I said, "Yes!"? Would you believe me if I did say, "Yes, I flipped and arranged the flipped coins in temporal sequence just as you did your set."? There is no question that it is possible to flip the sequence that became the specification for my flips. After all, we both just saw you do it. The exact sequence is immaterial as long as it is specified. Your unspecified sequence became my specification the moment I attempted to duplicate it. It could have been all heads, or all tails, or alternating heads and tails which serve no real useful purpose. It may have been the binary representation of the ASCII code of the Gettysburg Address. It could have been a section of machine code for a CPU. The whole point of the OP is to see if you are man enough to concede that the LLN makes any specific sequence of 500 fairly flipped coins a surprising event. I suspect, if you are honest with us, that you would be surprised, if, while you watched me fairly flip my coins, I got the first ten coins to match. The LLN is that powerful. Baby steps, Nick. We'll get to multiple specifications in different contexts, their density and other aspects, later. For now, one step at a time. That's right, Nick, one foot in front of the other. Come on! You can do it! StephenSteRusJon_{December 16, 2013
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Sal, First let me state this - There is no way that all 500 coins are going to show heads up by chance alone, but you have to ask if LLN by itself can explain events? For what it's worth, here's my 2 cents: Even if the LLN is arbitrary large, what matters is the bit sequence (not taking all 500 flips as one event). For Eg THH has an odds of 7 to 1 against HHH In fact sequence odds has been worked out in Penney's Game J.A. Csirik has a formula for more than 3 bit sequence, which can be seen in the wiki reference or you could implement John Conway's algorithm to calculate odds of various sequences against each other. The point is LLN in itself is difficult to use as a guide for natural vs designed event recognition.selvaRajan_{December 16, 2013
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2-sided coins
I meant, two-headed, as I had stated previously. I was glad to hear from Gordon. It was, like all his responses, quite valuable. In most cases the distribution is not clear, but if supposing, for the case of biology we do find an easy relevant distribution for a certain question, or better yet, distributions we know are in principle are outrageously favorable to chance, then I think rejection of chance hypotheses can be made for select cases. To illustrate consider the coin pattern: H T H T ...... If we assume the law of independent trials for each coin, all possible relevant chance hypotheses can be rejected fro the pattern. Biased coins will not solve the problem because we assume the law of independent trials. Amino acids in a prebiotic soup, as far as their chirality, will obey the law of independent trials and also a simple distribution analogous to fair coins. An assumed chance hypothesis can be falsified, and thus a particular design inference can also be falsified. There is nothing wrong with that.scordova_{December 16, 2013
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Sal said: 1. two-headed coins is a rejection of the chance hypothesis
in response
Nick said: Not really.
If the pattern of 500 coins all heads on the table is due to a 2-sided coin, chance cannot be the mechanism for the pattern even in principle since there is no chance for tails. No chance, means no chance. The 2-sided coin is the mechanism for the pattern if the coins are 2-sided. But that won't stop Nick from saying, "Not really." And it won't stop him from insisting :
no, because there are many chance hypotheses, not just one,
Gee Nick, if finding 2-sided coins won't make you reject the hypothesis of chance, nothing will. :-)scordova_{December 16, 2013
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Sal, you look like you are getting mad and therefore sloppy(er) since you didn't really think this
I say yes, in principle there are patterns that will cause us to reject the chance as a hypothesis because we’ll reject irrelevant chance hypotheses
How do you know ahead of time which chance hypotheses are irrelevant? You are assuming things not stated in the original statement of the question.
I suppose you can concoct some chance hypotheses totally divorced from physics, and you can thus say you don’t reject the chance hypothesis.
None of the alternative chance hypotheses that we proposed involved violations of the laws of physics. On the various quotes of:
no, because there are many chance hypotheses, not just one,
...where you added a "what if we knew X" and then ridiculed the quote. You can't add information and then criticize a statement made about the situation when we didn't have that information.NickMatzke_UD_{December 16, 2013
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Sal: The question was posed to see if you agree there are certain patterns we can use to reject chance as a mechanism.
Nick's response:
no, because there are many chance hypotheses, not just one,
So let's play out the possible scenarios: 1. "You discover the coin is two-headed, do you reject the chance hypothesis?"
no, because there are many chance hypotheses, not just one,
My response: that's stupid since there is no chance the coin can be tails. Chance hypotheses should be rejected in that case, but you won't reject it. 2. "the coin is discovered fair, do you reject the chance hypothesis?"
no, because there are many chance hypotheses, not just one,
But that's stupid too because a random process acting on a fair coin would not practically speaking create a 500 head pattern, but you won't reject the chance hypothesis in that case either. 3. "the coin is found 51% biased to tails, do you reject the chance hypothesis?"
no, because there are many chance hypotheses, not just one,
etc. Here was my question:
are certain patterns we can use to reject chance as a mechanism.
I say yes, in principle there are patterns that will cause us to reject the chance as a hypothesis because we'll reject irrelevant chance hypotheses and if the relevant chance hypotheses fail on statistical grounds, we can reject those as well. But Nick has a different view:
no, because there are many chance hypotheses, not just one,
So you feel free to always reject the chance hypothesis because you can fabricate lots irrelevant ones even if they don't conform to the physics in question. That's not very wholesome. So do you mean, Nick, in all cases you'll never find patterns to reject chance or just some cases. But for now, I'll accept your answer as meaning you'll never reject the chance hypothesis under any circumstance because
there are many chance hypotheses, not just one,
It seems you'll gladly accept irrelevant ones just so you can say "no". Fine, let the record state Nick's response to the question:
If you came across a table on which was set 500 coins (no tossing involved) and all 500 coins displayed the “heads” side of the coin, would you reject “chance” as a hypothesis to explain this particular configuration of coins on a table?
NICK: NO!
a pattern like “all heads” does not therefore reject all chance hypotheses.
I suppose you can concoct some chance hypotheses totally divorced from physics, and you can thus say you don't reject the chance hypothesis. So thanks, Nick. I'll tell everybody that if you found 500 coins all heads on a table you won't reject the chance hypothesis -- that you can imagine some set of irrelevant chance hypothesis so you'll never reject the chance hypothesis even if you're dealing with 2-headed coins!scordova_{December 16, 2013
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Mark #3: Some of these involve intelligence (someone placed them that way). Some of them do not e.g. they might have slid out of a packet of coins without a chance to turn over.

Matzke #4: What Mark said.

Groovamos #14: So the person packing them doesn’t count? A machine packing them has no intelligence in its coming into existence?
Mark & Matzke: ------ <-- cricketsBox_{December 16, 2013
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Instead, you’ll go off on any tangent that will avoid the central theme of why the question was posed in the first place. The question was posed to see if you agree there are certain patterns we can use to reject chance as a mechanism.
And our response was to say no, because there are many chance hypotheses, not just one, and a pattern like "all heads" does not therefore reject all chance hypotheses.
If I had been asked that question, I’d have said something like:
If by ‘chance’ one means random processes typically associated with fair coins, I’d have to reject the chance hypothesis
Instead, you essentially went into a full blown Chewbacca Defense mode.
Chewbacca defenses don't make sense. Ours did. Therefore, your accusation of a Chewbacca Defense is, ironically, itself a Chewbacca Defense.NickMatzke_UD_{December 16, 2013
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But the given in the question was that the coins are now in the all heads configuration, so your response of “package could have been dumped out the other way, producing all tails” doesn’t explain the all-heads configuration.
No, I was explaining how "all heads produced by coins sliding out of a package" could still be thought of as a chance explanation.NickMatzke_UD_{December 16, 2013
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P.s. I should note that this is one of the important things that the more recent version of Dembski's CSI (I think Sal called it version 2) gets right. In order to apply it, you must formulate a chance hypothesis and calculate the probabilities under that hypothesis. If you get s CSI value over 1 bit, you reject that specific chance hypothesis. If you want to reject chance entirely, you must test and reject each relevant chance hypothesis individually. In other words, it doesn't let you reject a chance hypothesis you haven't bothered to test. If you want your conclusions to have any validity at all, this is a good thing.Gordon Davisson_{December 16, 2013
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What you aren’t getting is that probability calculations depend on the model that you assume for the process generating the outcomes.
Wrong, Nick. I understand that. What you don't get is if you were not sure of what Barry meant you could ask for him to clarify. Or you could state the model you think his was working from. Or you could state the model you think is most appropriate (you seem to have no problem pulling models out of the air to suit your own purposes before, so why vacillate now). Instead, you'll go off on any tangent that will avoid the central theme of why the question was posed in the first place. The question was posed to see if you agree there are certain patterns we can use to reject chance as a mechanism. If I had been asked that question, I'd have said something like:
If by 'chance' one means random processes typically associated with fair coins, I'd have to reject the chance hypothesis
Instead, you essentially went into a full blown Chewbacca Defense mode.scordova_{December 16, 2013
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I would reject the hypotheses that the configuration was a result of chance under the uniform probability distribution (i.e. all coins independent, heads and tails equally likely). However, "chance" is not the same as "uniform probability", so this does not mean I would reject chance. Before you reject this as semantic quibbling, let me ask a very similar question: suppose you came across 500 atoms, each of which has two possible quantum states, but all 500 are in the same state. Would you reject “chance” as a hypothesis to explain this particular configuration of states? My answer to this would be: it depends. To see why, assume the atoms are at thermodynamic equilibrium. In this case, the atoms' states will follow the Boltzmann distribution, in which the probability of an atom being in a given state is inversely related to its energy in a way that depends on the ratio of its energy to the temperature. In other words, at low temperature, each atom has a high probability of being in the lowest-possible-energy state (the "ground state"), but at higher temperatures the probability of its being in higher-energy states increases. Call the probability that each atom is in the ground state P(T) (indicating that is depends on temperature). For T near absolute 0, P(T) will be near 1; for high T, P(T) will be close to 1/2. Now, let's look at the probability that all 500 atoms will be in the ground state: at equilibrium in the simple case I'm imagining, their states are all independent, so the probability that all 500 are in the ground state is P(T)^500. Say T is high, so P(T) ~= 1/2. Then the probability all 500 will be in the ground state is around 1e-150, which is effectively impossible. Suppose T is lower, so P(T) is only 0.9. Then the probability of all 500 being in the same state is around 1e-23, which is quite small. But while the probability of any particular group of 500 atoms being in the same state is small, a reasonable-sized object will contain a very large number of atoms. If there are more than around 5e25 (1e23*500), it's actually likely that there will be at least one group of 500 contiguous atoms in the same state. (By pure coincidence, 5e25 happens to be very close to the number of atoms in a pound of water.) Suppose T is even lower, so P(T) is 0.99. In that case, the probability of a specific groups of 500 atoms all being in the ground state is about 0.6%. That's small enough that we'd reject the null (/chance) hypothesis at a significance level of 0.01, but not nearly small enough to truly rule it out. Suppose T is lower still, so P(T) is 0.999. Now the probability of all 500 atoms being in the ground state is 61% -- it's actually more likely than not, and you can't sanely reject the chance hypothesis. Now make a more realistic supposition: the atoms aren't in equilibrium. In that case, they won't obey the Boltzmann distribution, they'll obey ... something else. And if you don't know what that something else is, you can't really make any statement at all about whether chance and explain the coincident states. In real life, uniform probability distributions are rare, and even well-behaved nonuniform distributions are the exception rather than the rule. Reality is messy, so ruling out some nice clean idealized and oversimplified hypothesis doesn't really do much in terms of telling you what'e really going on.Gordon Davisson_{December 16, 2013
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It might be informative to see why this simple is example is problematic for materialists. Are their patterns (configurations of matter) which in principle would cause us to reject chance as the mechanism for creating the configuration (assuming the configuration cannot be reduced to law)? The answer is yes, the 500 fair coins heads illustration is one such example of many. But Nick would be reluctant to admit that such patterns might even exist in principle, because that admits the possibility such patterns could exist in nature :shock: The 500 coin example proves such patterns can exists at least in principle. Whether such pattern exist in biology is another story, but Nick, like so many Darwinists will fight to defend every inch of evolutionary territory. The thought that ID proponents have a chance at identifying such patterns in nature as I have done with 500 coins, must not really sit well with them. On the other hand, Nick realizes if he disagrees with me on the details of 500 coins illustration, he'll ruin his credibility in way that is recorded on a public forum. So he's in a bad position. His only recourse is to change the subject on the simple question, trivialize the illustration, resort to a Chewbacca Defense or simply bail out of the debate -- otherwise its checkmate.scordova_{December 16, 2013
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Not really. The package could have been dumped out the other way, producing all tails. Perhaps this was a 50/50 thing.
But the given in the question was that the coins are now in the all heads configuration, so your response of "package could have been dumped out the other way, producing all tails" doesn't explain the all-heads configuration. Which is non-sensical and is in effect your version of Johnny Cochran's Chewbacca defense
PS: “Random” does not mean “flat uniform distribution with all events exhibiting complete independence”.
I never said it did. And with respect to fair coins, if you want to insist that coin orientation does not generally obey the law of independent trials, be my guest. :-)scordova_{December 16, 2013
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Mark: “Chance” is meaninglessly vague as a hypothesis as is “design”. Let's not forget the vagueness of 'random' as in 'random mutation'. You ask a Darwinist for an observed example of 'random' mutation generating morphological or functional novelty. They come back with links to paper(s) behind a firewall that documents bacteria having developed novel machinery to metabolize a nutrient. You then ask the Darwinist about the randomness of 400 or so genetic changes that express the new function. As in "where is the experimental proof of the absolute non-correlation between the so-called random events". I haven't seen such proof. I'm open to being informed. Mark: Some of them do not (involve intelligence) e.g. they might have slid out of a packet of coins without a chance to turn over. So the person packing them doesn't count? A machine packing them has no intelligence in its coming into existence?groovamos_{December 16, 2013
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scordova December 16, 2013 at 4:26 pm
they might have slid out of a packet of coins without a chance to turn over.
Which still means chance is not the mechanism of the configuration.
Not really. The package could have been dumped out the other way, producing all tails. Perhaps this was a 50/50 thing.
1. two-headed coins is a rejection of the chance hypothesis
Not really. Under this hypothesis, the arrangement and sides of the coins are all random. It's just the thing we are scoring, heads, happens to be found on both sides of the coins. You seem frustrated by our responses. What you aren't getting is that probability calculations depend on the model that you assume for the process generating the outcomes. You have been implicitly assuming things like: - the coins have two different sides - the coins are fair (i.e. the probability of heads or tails is a discrete uniform distribution) - the independence of the process for each coin Sure, in many real-life situations in current human societies, these are all reasonable assumptions about coins. But they don't HAVE to be true. Any serious investigator would want to check the plausibility of the assumptions before reaching a conclusion based on a probability calculation. Of course, when we get to creationist probability calculations about DNA/protein sequences etc., we often get them making the same sorts of assumptions as you made with the coins. The assumptions are reasonable (though not obligatory) for coins, but they are ludicrous for describing the origin of DNA/protein sequences, and thus calculations based on such assumptions are worthless. PS: "Random" does not mean "flat uniform distribution with all events exhibiting complete independence".NickMatzke_UD_{December 16, 2013
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Yes folks, here you have it: "Chance is meaningless", "maybe the coins have heads on both sides" and _______ <-- crickets If you are not overwhelmed by vicarious embarrassment now, you never will.Box_{December 16, 2013
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Barry, Thank you for granting my request to start this discussion. Nick responded pretty much as I would expect. Nick and Mark, Thank you for responding. It's obvious we'll never agree even on the simplest of things that are marginally relevant to the topics at hand. Thank you anyway for taking the time. Salscordova_{December 16, 2013
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Darwinist Derangement Syndrome. We're into full-fledged psychosis territory now.William J Murray_{December 16, 2013
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“Chance” is meaninglessly vague as a hypothesis
Or would prefer we used the phrase "stochastic process"? A stochastic process:
In probability theory, a stochastic process /sto??kæst?k/, or sometimes random process (widely used) is a collection of random variables; this is often used to represent the evolution of some random value, or system, over time. This is the probabilistic counterpart to a deterministic process (or deterministic system). Instead of describing a process which can only evolve in one way (as in the case, for example, of solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy: even if the initial condition (or starting point) is known, there are several (often infinitely many) directions in which the process may evolve.
And the definition of random variable:
In probability and statistics, a random variable or stochastic variable is a variable whose value is subject to variations due to chance (i.e. randomness, in a mathematical sense).[1]:391 As opposed to other mathematical variables, a random variable conceptually does not have a single, fixed value (even if unknown); rather, it can take on a set of possible different values, each with an associated probability.
scordova_{December 16, 2013
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What Mark said.
Mark didn't answer with a simple yes or no. Is this the sort of answer you'd give your students if they posed the question to you? The question was would you reject chance as the hypothesis for explaining the configuration. 1. two-headed coins is a rejection of the chance hypothesis 2. sliding out of a coin wrapper in the original configuration is a rejection of the chance hypothesis 3. having a robot mechanically order them is a rejection of the chance hypothesis 4. having some space intelligent space alien configure them is a rejection of the chance hypothesis You'd almost never hear such silly evasions in the discussion of simple statistics. You can't find it in yourself Dr. Matzke to say, "Yes, I would reject chance (as in some sort of random process) as an explanation". You'll stress irrelevancies, start talking about anything rather than say, "Yes."scordova_{December 16, 2013
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they might have slid out of a packet of coins without a chance to turn over.
Which still means chance is not the mechanism of the configuration.scordova_{December 16, 2013
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Whats with all this threads on Matzke, you will be asking for his autograph next :PTheisticEvolutionist_{December 16, 2013
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Another hypothesis is that all the coins have heads on both sides.NickMatzke_UD_{December 16, 2013
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What Mark said.NickMatzke_UD_{December 16, 2013
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"Chance" is meaninglessly vague as a hypothesis as is "design". I would reject the hypothesis that someone had independently tossed each coin and each coin was fair. There are many other plausible mechanisms which are far more likely to produce that configuration. Some of these involve intelligence (someone placed them that way). Some of them do not e.g. they might have slid out of a packet of coins without a chance to turn over.Mark Frank_{December 16, 2013
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In my experience watching this debate, the materialist response to this general area of ID (CSI = ID) is one of the following: 1.) no response 2.) science has already proven this to be false (no relevant reference given) 3.) appeal to deep time and stochastic resources (no attempt to prove that it's enough to overcome CSI) 4 ) ad hominem Oh, and the heavily loaded term "creationists" is used throughout to pacify any passerby materialists that the conversation is under control.uoflcard_{December 16, 2013
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