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# The Fundamental Law of Intelligent Design

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After being in the ID movement for 10 years, and suffering through many debates, if someone were to ask me what is the most fundamental law upon which the ID case rests, I would have to say it is the law of large numbers (LLN). It is the law that tells us that a set of fair coins randomly shaken will converge on 50% heads and not 100% heads. It is the law that tells us systems will tend toward disorganization rather than organization. It is the law of math that makes the 2nd law of thermodynamics a law of physics. Few notions in math are accorded the status of law. We have the fundamental theorem of calculus, the fundamental theorem of algebra, and the fundamental theorem of arithmetic — but the law of large numbers is not just a theorem, it is promoted to the status of law, almost as if to emphasize its fundamental importance to reality.

To understand what the law of large numbers is, it requires understanding the notion of expected value or expectation value. Rather than giving the somewhat brutal mathematical formalism of expected value, let me give an illustration with coins. If we have large set of fair coins, there is an expectation that approximately 50% of the fair coins will be heads after a vigorous shaking or flipping of the coins (a random process). That is, the expected value for the proportion of heads is 50%.

As we examine sets of coins that are very large (say 10,000 coins), the outcome will tend to converge so close to 50% heads so frequently that we can say from a practical standpoint, the proportion will be 50% or close to 50% with every shaking of the set. If we consider each coin in the set as a “trial”, the example illustrates the law of large numbers. Formally stated the law of large numbers says:

the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.

How does this play out for ID? Before answering that question, let me classify 3 kinds of designs (or forms of organization).

A. Non-functional ordered objects (like all fair coins heads, or homochirality in biology)

B. Non-functional dis-ordered, but recognizably designed objects (like a set of numbered coins organized according to a pre-specified pattern, an binary representation of Hamlet, DNA strings that identify GMOs, etc.)

C. Functional objects (like components assembled into a functioning machine, a software bit stream, etc.)

In this essay, I’ll illustrate design using the law of large numbers with the “non-functional ordered objects”. I’ll save for later discussion the illustration of design in the more challenging cases of “non-functional dis-ordered, but recognizably designed objects” and “functional objects”.

If I had 500 fair coins in a box all heads, I would conclude the 100% proportion of heads is far away from the expected value of 50% heads, thus we have a significant violation of the law of large numbers for random processes, thus a random process is rejected as the mechanism of creating the all-heads pattern. By convention, the ID community classifies objects as designed if they do not conform to the products of law and chance. Whether they are designed in the ultimate sense is a separate question, but the practical rejection of the chance hypothesis in this case is unassailable.

A typical mistake ID proponents make is saying, “the all-heads pattern happens on average only 1 out 2^500 times, therefore the chance hypothesis is rejected”. The Darwinists will counter by saying, “that pattern is no more special than any other since every pattern happens only 1 out of 2^500 times, therefore all-coins heads is consistent with the chance hypothesis”. Last year, Darwinists at The Skeptical Zone tried to pull that same rhetorical stunt on me with these words:

if you have 500 flips of a fair coin that all come up heads, given your qualification (“fair coin”), that is outcome is perfectly consistent with fair coins,

But I came prepared to counter their maneuvers. 🙂 They obviously didn’t anticipate I’d debate them from an unorthodox angle, namely the law of large numbers and application of expected value. I pointed out based on the binomial distribution and expectation value of 50% heads, 100% heads is a violation of law of large numbers and hence a violation of the chance hypothesis from a practical standpoint. My opponents in the debate were thrown into disarray. But as always, they never admitted defeat in the exchange. They camped out at UD and would not rest until I confessed the following creed:

if you have 500 flips of a fair coin that all come up heads, given your qualification (“fair coin”), that is outcome is perfectly consistent with fair coins,

I told them, “no dice”. Or maybe I should have said, “no coins.” The Darwinists at Skeptical Zone fared so badly that even arch Darwinist Jeffrey Shallit felt it necessary to call his associates out on their folly.

The advantage of using the law of large numbers is it brings clarity to the probability arguments. It negates the Darwinists claim that “every pattern is just as improbable as another, therefore design is nothing special”. The 500-coins heads example illustrates how to apply the law of large numbers in identifying designs for non-functional ordered objects, and thus, certain patterns are indeed special because their very nature is at variance with the chance hypothesis.

It occurred to me, since the law of large numbers was such a fruitful way to refute the materialists on the question of non-functional ordered designs, how about we use the law of large numbers when dealing with other more challenging kinds of designed objects? Those ideas, Designer willing, will be explored in subsequent discussions.

NOTES:

For some history of debates with Darwinists over the Law of Large Numbers see:

SSDD: A 22-sigma event is consistent with the physics of fair coins?

Law of Large Numbers vs. Keiths

Siding with mathgrrl on a point, alternative to CSI V2

There are so many interesting things in science to discover. It's not all evolution and Latin terminology. For example, speaking of casinos, sometimes I wonder whether plants are playing their environment as if they were pre-programmed to bet (pardon my anthropomorphisms). Most people gamble until they lose most of their cash on hand (or if they're smart, what they planned to lose). When plants collect energy, they can "skim" some of their winnings by storing energy in their starchy roots, insurance against hard times or bad luck. Or they can invest it in producing more leaves and becoming taller. Arguably, the trick for them is to remain in the game of life as long as possible. If they "choose" to invest their energy in leaves, will they purchase expensive, waxy, nasty tasting, insect-resistant leaves such as those in evergreen trees (a large bet), or cheap and yummy (to insects) throwaways as in deciduous trees? Gambling everything into leaves or height is a losing strategy. So, considering their environment, what proportions do plants maintain between roots, leaves, and height? What do seedlings do in a dark environment? Is there a mathematics or programming (with at least the appearance of intelligent design) to be discovered here? Do plants "bet" using a Fibonacci series with respect to successive growing seasons, good or poor? Would it work in a casino? ;-) -QQuerius
December 17, 2013
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Thanks for the help guys! Scordova, I am a creationist, but it's as a matter of faith, not reason. I went to school for Criminology (though I don't work in that field), and am pretty heavy into the arts side of the higher education world (History/English) - my science skills are limited to basic understanding of concepts and terms. I enjoy hearing a good debate - one where both sides make excellent points. I don't know that I am brave enough to go post on the evolutionary forums (though I enjoy reading them) - mostly because I know that I would be out of my depth there. I lack knowledge of their tenets, and the higher math, as I mentioned before, eludes me. Originally, I posted here to get a better understanding of the chance argument; and I have to say that it's been educational - the article on the universal boundary was actually very enlightening in that regard. I remember hearing a statistician (Ron Pyke) speak at my church when I was younger; his brother was the minister there. He was the first real exposure I had to a scientific view of creationism, and it's something that intrigued me since.Jbarron
December 17, 2013
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By the way, Jbarron, If you are really brave you might find some pro-evolution forum and ask them the odds of consciousness forming via evolutionary or chance processes. Ask them to give you the numbers. I posed this question here at UD: https://uncommondescent.com/mind/the-paradox-of-consciousness-challenges-for-evolutionists-and-materialists/ Ask them to provide the odds of molecules forming consciousness. When I place wagers in a casino, I always have some estimate of the odds. The only reason I place wagers with losing odds is to persuade the casino staff I'm and idiot so I don't get thrown out for being too skillful. I once sat at a blackjack table in Las Vegas and refused to place bets until I recognized via card counting the odds were in my favor. I just sat there for 15 minutes doing nothing, and when the odds were in my favor, I pushed out a modest bet and won a few hands. The casino threw me out in about 3 minutes after I won 3 hands. :-) So ask the Darwinsits what are the odds of evolving consciousness. Ask them how material things give rise to the human spirit. In my opinion, this is like asking the odds that a square circle exists in Euclidean geometry.scordova
December 17, 2013
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@JBarron
Jbarron: are you making these arguments to convince the average person, or other scientists?
With me being somewhat in the middle, an undergrad in the field of biomedical science and aspirations of med school eventually, I can comment here. The arguments and discussions presented certainly aren't friendly to the man on the street. Most, if not all, threads will presume knowledge in logic, history, biology (and more specifically, micro/cellular biology), mathematics (my Achilles Heel) and physics, with some philosophical understanding for argument's sake. It may seem daunting at first but with some hard work, and patience, I feel it to be entirely possible for just about anyone (a priori bias notwithstanding) to grasp what is being discussed, and even participate. Ask questions. Make sure to read the links attached to posts. Search on items you may be cloudy on. Ask questions again to clarify any jargon or cloudy concepts. The only big thing that I've noticed to really draw the ire of the locals? Don't try to BS your point into validity. It isn't to say that I think you'd attempt such a thing, but it does happen. Often. It is called out and embarrassment can ensue. I hope this helps, and if I can help in any way I should be happy to do so.TSErik
December 17, 2013
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are you making these arguments to convince the average person, or other scientists?
These discussions for me are public diary of my exploration of the question of ID, and we are conversing with other individuals with pretty good math, physics, chemistry, and medical backgrounds. At least 3 UD authors are PhD physicists, 3 are PhD biologists, a few are medical doctors, and at least 2 I know of are PhD mathematicians, not to mention tons of us are engineers! If a famous evolutionary biologist like Dr. Nick Matzke won't reject chance as a mechanism for the appearance of all coins-heads, it is evident the ID side will never agree with him, nor he with us. That's fine, but we picked on him to show how determined he was to disagree with everything we say even to the point of saying things he would never say or teach his students. The reason so many of them are tossed from UD? It's simply a waste of time to engage some of the worthless arguments going around. It's better to engage cream of the crop Darwinists like Nick.scordova
December 17, 2013
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December 17, 2013
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Thanks for the math, Barry, and for that link - it was an interesting read, though I would put it as slightly higher than layperson understanding. Then again, I work in customer service, so maybe I'm biased (in the negative) towards laypersons such as myself, and our average level of understanding. I would love to see a reply on this from the other side - though I may be in the wrong place for this. From what I've read of the comment thread, most of the darwinians stay away from this thread, the replies have been - well, I don't want to say lackluster and repetitive, but perhaps it isn't too unfair to do so. This is probably a bit of confirmation bias - the thread is dominated by ID proponents, and the argument seems to go in circles - ID says "chance doesn't account for it!" while Darwinians say "Yes it does!"; so it appears that the sides have split, and there seems to be a rapidly-dwindling pool of Darwinians reading/refuting these comments. If that seems to be the case - are you making these arguments to convince the average person, or other scientists? Just calling out, if there's anyone out there on the opposite side, do you have a rebuttal in mathematical terms? Or an explanation of some glaring flaw in the argument, something that's been overlooked? Are there any die-hard darwinians/statisticians still out there, who have some numbers to refute this? I am not being sarcastic or argumentative, I'm genuinely interested in a response.Jbarron
December 17, 2013
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Scordova noted
Small correction (I think): I got C(500,250) = 500!/[(250!)(250!)] = 1.17 x 10^149
Aargh. Yes, you're right. And that's why some folks need to speculate on a multiverse of a many trillions of universes to have even a reasonable chance. And then, considering the complexity of the DNA code, and the interlocking chemical cycles with in a cell, let alone the structures in an animal or plant . . . Chance and necessity begin to look pretty feeble. -QQuerius
December 16, 2013
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Barry Arrington:
There is a name for what you are doing. It is called “chance of the gaps.”
Chance of the gaps? LOL. I like that. I guess the Darwinists deserve to get a taste of their own medicine.Mapou
December 16, 2013
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Jbarron,
“The numbers are just too big” argument doesn’t make sense – maybe because for us, all the numbers are too big.
There is a name for what you are doing. It is called “chance of the gaps.” Dembski explains the concept at a lay level here: http://www.leaderu.com/offices/dembski/docs/CHANCEGAPS.pdf Some excerpts:
Statistical reasoning must be capable of eliminating chance when the probability of events gets too small. If not, chance can be invoked to explain anything. Scientists rightly resist invoking the supernatural in scientific explanations for fear of committing a god-of-the-gaps fallacy (the fallacy of using God as a stop-gap for ignorance). Yet without some restriction on the use of chance, scientists are in danger of committing a logically equivalent fallacy—one we may call the “chance-of-the-gaps fallacy.”
Dembski calculates the universal probability bound as follows:
In the observable universe, probabilistic resources come in very limited supplies. Within the known physical universe there are estimated around 10^80 elementary particles. Moreover, the properties of matter are such that transitions from one physical state to another cannot occur at a rate faster than 10^45 times per second. This frequency corresponds to the Planck time, which constitutes the smallest physically meaningful unit of time. Finally, the universe itself is about a billion times younger than 10^25 seconds (assuming the universe is between ten and twenty billion years old). If we now assume that any specification of an event within the known physical universe requires at least one elementary particle to specify it and cannot be generated any faster than the Planck time, then these cosmological constraints imply that the total number of specified events throughout cosmic history cannot exceed 10^80 x 10^45 x 10^25 = 10^150
Summary: Your 300 billion galaxies and 13.7 billion years still do not get you to a place where anything with a probability of less than 1 in 10^150 can happen. The 500 heads probability is less than that.Barry Arrington
December 16, 2013
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Okay - so assuming you did this once a second since the big bang, it won't happen even once. I will assume that you have the math to prove that - I'm not a statistician. But to quote Douglas Adams: "Space is big. You just won't believe how vastly, hugely, mind- bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space." So, we can't assume this is happening once a second. It's happening millions of times a second. Hubble estimated 125 billion galaxies in 1999, and they've almost doubled that since. With 300 billion stars in a galaxy. And it's not just the formation of these solar systems that count as shaking the box - it's any and all events - an asteroid strike, a supernova, maybe a white hole spits out some matter. And this is all assuming that space isn't, in fact, infinite. I do believe in Creation, mostly because the thought of random elements coming together to make life hasn't ever made any sense - We can't even do this on purpose yet, let alone prove it happened by accident. But from a layperson's perspective, the "The numbers are just too big" argument doesn't make sense - maybe because for us, all the numbers are too big.Jbarron
December 16, 2013
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For future reference for anyone possibly reading this discussion years from now, a new thread was started by Barry here: https://uncommondescent.com/intelligent-design/a-statistics-question-for-nick-matzke/ Here is my summary. The question posed was:
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 in his own words answering the more general question of rejecting 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.
Then there was discussion about the possibility of a two-head coin. If a two-headed coin was discovered as the mechanism of the 500 heads patter I said:
two-headed coins is a rejection of the chance hypothesis
to which Nick responded
Not really.
:shock: If we found the coins are 2-headed, then that is the mechanism that causes the pattern to be all heads, there is no reason whatsoever except the determination to disagree with me to say, "not really". Even in a simple hypothetical case where chance cannot even in principle be the explanation, Nick will in insist:
no, because there are many chance hypotheses
Oh well, if even a two-headed coin is the cause of a 500 coin all-heads pattern, Nick will not reject chance as a possible mechanism for the pattern. :roll: Which suggests Nick will never ever really reject chance as a hypothesis as it pertains to design. PS I would have answered by saying:
A 2-headed coin is not a chance hypotheses, so even if true, the 2-headed coin hypothesis would automatically reject the chance hypothesis. The hypothesis that coins being heads because they were already heads due to the manufacturing or packing process also automatically rejects the chance hypothesis. In addition, I reject all irrelevant chance hypotheses on principle. The one relevant chance hypothesis (subject to inspecting the coins) is the fair coin hypothesis (or even slightly biased coin hypothesis), is not consistent with expectation. Thus I reject the chance hypothesis as an explanation for the pattern since all relevant and irrelevant hypotheses are rejected.
scordova
December 16, 2013
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Jbarron,
But if you took 500 quintillion boxes of 500 coins each, and shook them, aren’t the odds approaching 100% that at least one of them will end up with all heads or tails?
Actually, no. J. That is not correct. If every atom in the universe were a table and you shook out a box of 500 coins onto each of those tables once every second since the big bang, you would not expect to get that sequence through sheer random chance even once. That is why Sal choose 500. It is right at the universal probability bound. Your (wrong) intuition is also why Darwinists are able to get away with their shell game. They say, "ust put the problem in a black box labeled “deep time and chance” and poof, problem solved." Only when you actually step back and do the math do you realize that the problem is far from solved.Barry Arrington
December 16, 2013
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Okay - I'm not a scientist - nor close to one. But from a layperson's perspective, this argument seems to make sense on the surface, but fails on deeper investigation - I'll tell you why it appears that way to us: We are told that the universe is infinite. For life to evolve, you mention the 500 coins heads up. And yes, by itself, that appears to require an outside agency. But if you took 500 quintillion (or some other ridiculously large number) boxes of 500 coins each, and shook them, aren't the odds approaching 100% that at least one of them will end up with all heads or tails? Assume each star is a box of 500 coins - then no, it doesn't require an outside hand to create life, because this is only one box out of an infinite number. I haven't seen this comment pop up yet, so if there is a massive and fatal flaw in this argument, feel free to let me know - I believe I mentioned I'm no scientist (in fact, a creationist myself, but this argument for ID makes no sense to me, and never has).Jbarron
December 16, 2013
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Neil Rickart: In the case mentioned, with a sequence of 500 tosses, that full sequence is a single sampling event.
Dead ass wrong, as anyone who has studied the statistics of gambling will tell you. Each toss is independent from all previous tosses, because there is no memory in the system from one roll of the dice, or flip of the coin, to the next. Ignorant people who visit Casinos often labor under the delusion that a machine is "hot" or a craps table is "hot" because nobody has gotten a good outcome recently. But it's wrongheaded. Since there's no memory built in to the system, each play is completely independent of all previous plays. The odds do no changes from play to play. On the other hand, card games, such as Black Jack, are different. They have "memory" built into the game of a sorts because every card played rules out that same card in the deck. Card counters take advantage of this fact.CentralScrutinizer
December 16, 2013
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Graham2:
No No No No. There is nothing ‘special’ about any pattern. We attach significance to it because we like patterns, but statistically, there is nothing special about it. All sequences (patterns) are equally likely.
What utter BS. We recognize patterns precisely because they are statistically significant. This is why computer programs like speech and visual recognizers work.Mapou
December 16, 2013
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Sal, "how does evolution work?" Graham2, "it's complicated and stuff."Barry Arrington
December 16, 2013
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this fantasy of transferring results of coin tosses to complex real-world processes that are a mix of, well, everything. You cant do it. Its cartoon stuff. I cant help you.
By saying "the world is so complex we can't model it" precisely shoots your foot not mine since you can't demonstrate evolution actually accounts for those complexities, but instead promotes falsified fantasy as proven fact even without considering those complexities. So it's your foot being shot by appealing to unaccounted for complexities, not mine.scordova
December 16, 2013
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we have already said cells ... don’t emerge by chance and law alone You have just shot yourself in the foot. You then persist with this fantasy of transferring results of coin tosses to complex real-world processes that are a mix of, well, everything. You cant do it. Its cartoon stuff. I cant help you.Graham2
December 16, 2013
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They only become suspicious if we have specified them in advance.
Again I appreciate your participation because it raises issues I'm sure are in the minds of some. Consider the following illustration. To help understand the illustration, I use the following convention 1-H means coin #1 is heads, 252-T means coin number 252 is tails 1-H 2-T 3-H 4-H 5-H 6-T 7-H 8-T 9-T .... 251-H 252-T 253-H 254-H 255-H 256-T 257-H 258-T 259-T .... I basically repeat the pattern in the first 250 coins in the remaining 250 coins. If I presented this set of coins to you and if I worked hard at making it not be anything you've seen before, the pattern would not be technically specified in advance. Even though you have never seen it before, would that raise your suspicion that the total 500 coin configuration was not the pure product of chance and law? This obviously is relevant to cells of the same species because we have identical patterns in separate objects (each cell is an approximate copy of the other), much like they all came from an intelligently designed factory. Cells are not the product of chance and law alone but the product of other cells. But that raises the question, if cells today are not the product of chance and law, could chance and law make the first ancestral cell? So clearly, in biology we can identify patterns that can't be explained in terms of chance and law alone. We would attribute the patterns to be the result of the factory-like machinery in parent cells -- but this only defers the question of where the first cell came from, since we have already said cells in the current day don't emerge by chance and law alone.scordova
December 16, 2013
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Sal, Unlikely patterns (eg: life) are only problematic if you reject variation+selection.
I do, but more importantly so does nature. I commend your valor in engaging me in this debate, which is more than I can say for Dr. Matzke who is usually so eager to steal the microphone to try to put me down.scordova
December 16, 2013
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No No No No. There is nothing 'special' about any pattern. We attach significance to it because we like patterns, but statistically, there is nothing special about it. All sequences (patterns) are equally likely. They only become suspicious if we have specified them in advance.Graham2
December 16, 2013
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Sal, Unlikely patterns (eg: life) are only problematic if you reject variation+selection. Its called 'straw man'. All this guff about coins is irrelevant.Graham2
December 16, 2013
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Graham2, If I saw 500 heads, I would suspect interference by some external agency.
Thank you for your courageous response. But what is it about that particular pattern versus any other. Is it because the pattern in not consistent with the expectation of a random pattern? If so, then the pattern is special by its very nature. Thanks again for responding.scordova
December 16, 2013
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It might be informative to see why this simple is example is problematic for materialists. Are there 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, or simply bail out of the debate -- otherwise its checkmate.scordova
December 16, 2013
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If I saw 500 heads, I would suspect interference by some external agency.Graham2
December 16, 2013
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Graham2, Thank you for your response, but I was hoping you tell the readers if my procedure for rejecting chance as a mechanism of all fair coins heads was correct. I mean, I know Darwinists don't like to ever be seen publicly agreeing with a creationist, but think about all those prospective science students out there wanting to learn basic statistical notions. So for the sake of science, will you tell them specifically what you agree or disagree about in my analysis of 500 fair coins heads. Is if fair to say you would reject chance as the mechanism because all coins heads is far away from expectation? Salscordova
December 16, 2013
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If you invent a cartoon to replace evolution, then all you have left is design, so good luck.Graham2
December 16, 2013
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Graham2, By selection do you mean real natural selection or DFFM. You obviously are thinking evolution proceeds by DFFM (Darwin's Falsified Fantasy Mechanism), it doesn't. But thank you for you comment any way. Now, since it seems Nick is so reluctant to answer a simple question, and you're one of the few Darwinists remaining at UD, perhaps you tell the readers what you think: 1. for 500 fair coins found on a table, would you reject chance as an explanation for the configuration? 2. for 500 fair coins, is the all-heads pattern particularly special for inclining you to reject chance as the mechanism that created the configuration? 3. does this illustration indeed show there are some patterns that, if found in a particular system, would incline you to reject the chance hypothesis? 4. for pre-biotic soups, where like coins the amino acids and DNAs would be heterochiral and not homochiral, would you reject chance as a mechanism for homochirality?scordova
December 16, 2013
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Sal, If evolution was entirely due to chance variation, you would have a point, but it isnt (and you dont). Evolution is variation + selection. The LLN is irrelevant because it isnt a 'fair' coin. Selection makes sure of that.Graham2
December 16, 2013
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