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?

Comments

Scordova #119: How do I figure stuff like this out? I don’t if I can, I consult literature where it was already worked out…
>> Boy or Girl paradox <<Box_{December 18, 2013
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sal
There is no mention of the ages of the children or birth order. All I did was arbitrarily call one child child1 and the other child2. I believe this to be the genesis of the error. The order is apparent when the items differ, but conflated when the same. That the known boy has either a younger or older bother, is treated as one possibility. That the known boy has either a younger or older sister, is treated as two possibilities.
c hand_{December 18, 2013
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Mr. Brown has exactly two children. At least one of them is a boy. What is the probability that the other is a girl?
There is no mention of the ages of the children or birth order. All I did was arbitrarily call one child child1 and the other child2.
I think the correct configuration is: Boy with older brother Boy with younger brother Boy with older sister Boy with younger sister the probability of the unknown sibling being a girl is 50/50.
That answers a question that different than the one being posed. The reason the question is challenging is that we usually think of the possible distribution of child1 and child2 this way: Boy-boy boy-girl girl-boy girl-girl Maybe to clarify let me use COINS instead:
Mr. Brown has exactly two coins. At least one of the coins is a heads. What is the probability that the other coin is tails?
So instead of child1 and child2, we have coin1 and coin2, and instead of boys and girls, we have heads and tails. Without any information, the distribution is: H H H T T H T T But with the information that at least one of the coins must be heads we are left with: H H H T T H The reason this is tricky is this is a problem in applying conditional probability (something I sense Mark is very very good at). By saying that at least one coin is heads, the probability distribution is changed. Statistics is not just hard because of the math, but because of the problem of conceptualizing how to apply the math. How do I figure stuff like this out? I don't if I can, I consult literature where it was already worked out...scordova_{December 18, 2013
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I'm with c hand!Box_{December 18, 2013
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you have compressed the possibilities of being either a younger or older brother into a single possibility of having a brotherc hand_{December 18, 2013
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sal Mr. Brown has exactly two children. At least one of them is a boy. What is the probability that the other is a girl? Correct answer: 2/3 Let me give it a shot. At least one boy admits the following possibilities A. Child 1: boy, Child 2: boy B. Child 1: boy, Child 2: girl C. Child 1: girl, Child 2: boy Thus 2 out of three possible scenarios involve a girl child assuming equiprobable distribution. So the probability is 2/3 as you say. I think the correct configuration is: Boy with older brother Boy with younger brother Boy with older sister Boy with younger sister the probability of the unknown sibling being a girl is 50/50.c hand_{December 18, 2013
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KF #113 sorry typo - I meant to write: So a fair die is undirected contingency while a loaded die is directed contigency? This is really confusing. After all the fair die is designed to be fair and a loaded die may well be loaded as a result of a natural mishap.Mark Frank_{December 18, 2013
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Sal
Better yet, you’re invited to help me phrase the notion of chance in a way that meets your approval given you know I’m trying to state expectation relative to an assumed distribution and a process that assumes to maximize uncertainty such as in large set of coins or a system in thermodynamic equilibrium or a communication system maximizing its channel capacity, or a bit stream with maximally compressed information, etc.
I think that is exactly what I have been doing. I have been phrasing “chance hypothesis” in this context as “each coin had an independent probability of 50% of being heads or tails” (how many times have I written this now!). I also accepted that if this is what is meant by chance hypothesis then I would reject it given 500 heads. Am I missing the point somewhere?Mark Frank_{December 18, 2013
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KF
If it is a fair ordinary six-sided die that is dropped, as I have noted for eight years, it tumbles and settles to one of six sides, due to various causes linked to the butterfly effect. As such we have the familiar flat random distribution. The fall, impact etc are deterministic but due to small uncontrolled factors and the butterfly effect, the outcome is highly contingent and accords with a statistical model. Credibly undirected contingency. With a loaded die, as I have pointed out for EIGHT years, there is a bias due to design so the distribution moves away from the fair die case. Or, an intelligent agent can simply set the die down to read as desired. Thus we see purposefully directed contingency.
So a fair die is undirected contingency while a loaded die is? This is really confusing. After all the fair die is designed to be fair and a loaded die may well be loaded as a result of a natural mishap.Mark Frank_{December 18, 2013
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KF #110,
KF #110: Have you done any information theory?
To my embarrassment I have not
The point is, if you are told, 500 coins all H, there is one possibility, this is very specific in the set of possibilities. If we are told, alternating H & T, there are two acceptable possibilities, we are less informed. If we are told 50:50 H & T, we have very little info, as there are very many possibilities.
In the case of the sequence of 500 coins head up, you imagine ‘a set A with 100% heads’ with one member: ‘a sequence of 500 coins head up’. Then you conclude that a sequence of 500 coins head up fully informs you about this imaginary set A – IOW the sequence of 500 coins head up is ‘highly informational’. I will not adopt this kind of reasoning, but thank you for explaining.Box_{December 18, 2013
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MF: For eight years, I have discussed the same example, and in a context that is quite familiar. A dropped heavy object near earth falls at 9.8 N/kg. That is mechanical necessity and under similar initial conditions yields similar outcomes, i.e. low contingency. If it is a fair ordinary six-sided die that is dropped, as I have noted for eight years, it tumbles and settles to one of six sides, due to various causes linked to the butterfly effect. As such we have the familiar flat random distribution. The fall, impact etc are deterministic but due to small uncontrolled factors and the butterfly effect, the outcome is highly contingent and accords with a statistical model. Credibly undirected contingency. With a loaded die, as I have pointed out for EIGHT years, there is a bias due to design so the distribution moves away from the fair die case. Or, an intelligent agent can simply set the die down to read as desired. Thus we see purposefully directed contingency. Thus, AS HAS BEEN POINTED OUT REPEATEDLY FOR EIGHT YEARS ON A VERY FAMILIAR EXAMPLE THAT ANY EDUCATED PERSON SHOULD INSTANTLY BE FAMILIAR WITH, we can see the difference between (i) mechanical necessity, (ii) chance, and (iii) design. In addition, there are -- as I have also noted again and again, cases that seem to be directly random due to quantum effects. Chance outcomes can arise because of this sort of inherent randomness -- e.g. as zener noise comes about and is used in electronic random number generators (often by feeding a special counter, to give a flat random distribution output) -- and also because of in effect accidental, uncontrolled, uncorrelated intersections of chains of events that are not random in themselves as with the die. So, chance can be seen as credibly undirected contingency of outcomes that occurs across a range of possible values. Due to various mechanisms, the die being a familiar case. In terms of mutations, when I did radiation physics, the usual idea was water molecules being git by a RA particle and splitting up then reacting with nearby cellular molecules in a way that is uncorrelated with requisites of bio- function. From this, interference with genes etc is easy to understand. And again, credibly undirected contingency that causes changes. It is not hard to see why I would look with head-shaking doubt at those who rely on such processes to rewrite genes etc to improve function so there would be elaboration through differential reproductive success leading to new body plans. Where such require 10 - 100 mn+ bits of additional info. So, chance, its capacity and limits should be plain. Finally, a word I think is needed -- after EIGHT years with the same familiar example. Frankly, at this point, you are coming across as willfully evasive and trying to scoot away behind a cloud of rhetorical ink, not as "meticulous." Please do better than this. KFkairosfocus_{December 18, 2013
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Box: Maybe here on will help? (Have you done any information theory?) The point is, if you are told, 500 coins all H, there is one possibility, this is very specific in the set of possibilities. If we are told, alternating H & T, there are two acceptable possibilities, we are less informed. If we are told 50:50 H & T, we have very little info, as there are very many possibilities. In general in an informational situation the first measure of info is a - log probability, i.e. log( 1/p). So, a very tightly defined and unlikely state has low probability of being the case before we get the message. Assuming no garbling, a message that tightly defines gives us much more info than one that is not so specific. All heads, the most info, alternating H & T less info, 50:50 H & T much, much less. Taking logs -- logarithms, Google translate gives Dutch: "logaritmen" -- allows us to add info in messages, as the linked describes. Think in terms of a source sending messages to a receiver, and the messages tell us about the source. Say, the coins are in a black box and the box transmits an accurate description as above. All H we can set up a second box to match the first. Alternating H & T and there are two possibilities from 3.27 * 10^150. 50:50 and there are ever so many possibilities. This will help us see how we are very informed in the first case, less so in the second, much less so in the third. Last, in a design context, we tend to add a wrinkle, that we measure info that is functionally specific, i.e. gibberish that does not work is not the kind of "info" we are interested in. KFkairosfocus_{December 18, 2013
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Mark wrote: For some reason no one is prepared to do this.
You actually your self somewhat clarified.
I would reject the hypothesis that someone had independently tossed each coin and each coin was fair
Now, I actually take less offense than some about your meticulousness. Whatever your reasons, my interest in engaging you is finding out how you would frame such a question given you know what I (not necessarily any other ID proponent) am trying to get at. I will grant that I can't demonstrate a designer, I can however, in some select cases argue provisionally some patterns cannot be described by chance and physical law acting on a given configuration of matter. I could be very anal and say " 'chance' means a stochastic process that maximizes the uncertainty in a system relative to the degrees of freedom permitted." Would you object if I used that as my (not yours) working definition of a chance mechanism? We know when uncertainty is maximized in certain systems, like a set of coins or systems in thermodynamic equilibrium, the system will tend to converge on expected values for certain observables: in the case of coins, its the proportion of heads, in the case of thermodynamics its the temperature. So you may object that this notion of chance wasn't used in the OP. Fine, would you object if I used such a notion in another essay? Better yet, you're invited to help me phrase the notion of chance in a way that meets your approval given you know I'm trying to state expectation relative to an assumed distribution and a process that assumes to maximize uncertainty such as in large set of coins or a system in thermodynamic equilibrium or a communication system maximizing its channel capacity, or a bit stream with maximally compressed information, etc. In my opinion, the formalism I suggested is unneeded if one wishes to grant a charitable reading of the points trying to be conveyed. But I have interest in immunizing discussions from such lengthy arguments that are far away from what ID proponents are really interested in. Talking about coin wrappers and pre-packing of coins is far away from what ID proponents are interested in. Thank you in advance. Salscordova_{December 18, 2013
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KF:
Finally, if you understand chance then why did you try to take us on a rabbit trail dance complete with the rhetorical gambit I don’t understand you.
I didn’t. I never asked what “chance” meant. I only asked what the OP meant by “chance as a hypothesis”.
What part of: 12 –> So, we come to the three distinct causal patterns: MECHANICAL NECESSITY: shown by low contingency of outcomes, e.g. F = m*a. What would happen with a stuck key on a keyboard: gggggggggggggggggg . . . CHANCE = CREDIBLY UNDIRECTED CONTINGENCY: shown by high contingency that follows the expectations of a statistical or similar distribution pattern. E.g. a dropped fair die. Also, typical random text: rfwgfvhywowadcfyweqou [--> where contingency has been stated as that under highly similar initial circumstances outcomes vary significantly with the dropping, tumbling and settling fair die as an example] DESIGN = CREDIBLY DIRECTED CONTINGENCY: often intuitively known or observed from behaviour, but detectable in many cases from its result, FSCO/I which is not credible by either chance or necessity. E.g. a loaded die, or one set to read a given value by an agent, typed coherent text with messages in English of sufficient length not to be accessible to chance under given circumstances. . . . do you find unintelligible, why?
OK: 1 what do “credibly undirected” and “credibly directed” mean? What is credible to whom? 2 the words “where contingency has been stated as that under highly similar initial circumstances outcomes vary significantly with the dropping, tumbling and settling fair die as an example” seems like a stream of words with almost no relation to each other! After several readings I think you mean something like: “by contingent I mean that under very similar initial conditions the outcome may vary significantly, for example if you throw a fair die” but why make your reader work so hard?Mark Frank_{December 18, 2013
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Mark Frank: Consciously or unconsciously, you simply refusing to see what is before you. You come into a room and on the table lie 500 coins that are all heads up, given what you know about tables, coins, and possible means by which coins might have arrived on the table, is there any remotely plausible scenario where a mechanism (that you do not see or know about) properly characterized as a "chance" means of putting the coins on the table and configuring them could account for them all being heads up? Let's look at the case of the coins all being in a sleeve heads up and being slid out onto the table; could the coins all be heads up in the sleeve by a chance process? Would whomever or whatever emptied the sleeve not have to be "careful" (or have been designed) to get the coins all out of the sleeve heads up? If the coins were tossed, wouldn't it be obvious that someone would have to toss them until he got them all heads up? If dropped from a bag or emptied from pockets, is dropping them on the table without deliberately arranging them a plausible explanation for them all being heads up? You will cling to even the absurd as long as it might just be a bare possibility to deny what is in front of you. So, you might be wrong about the coins - they may have in fact been dumped by a bag and happened to all land heads up; but the only reason that chance can possibly be your categorical "best explanation" is if you simply refuse to consider the obvious - that design was involved. Just because you have not exhausted all the possible chance mechanism scenarios doesn't mean that the current best explanation is not design. If you came upon such a table, your reaction would not be "How did this happen?"; it would be "who did this?" and perhaps "why did they do it?". "How did they do it" wouldn't even be a significant question.William J Murray_{December 18, 2013
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KF #102: The idea is that 500 coins have 3.27*10^150 possible configs, so if we see them in a very special one like 500H, that has excluded a lot, and so is highly informational.
Do you mean by ‘highly informational’ low probability? If not, what do you mean?
KF #102: Yes that is 22 SD away from the expected, the peak. But it is also a case of a hot zone with one member from that set of possibilities. If I had said, the coins are 50:50 H and T, that would tell you much less about particular state, as IIRC there are 500!/ 250!*250! possibilities [500 things 250 each of 2 kinds, no of possible arrangements], and I am too lazy just now to drudge through Stirling’s approximation to solve that.
This I can all understand. The set '500 coins heads up' has only one member, while the set '250 coins heads up' has many members. Scordava wrote: 47.8% – 52.2% heads would cover one standard deviation or 68% of all possible outcomes, 43.4% – 56.6% would cover three standard deviations or 99.7% of the cases. Looking at distributions as sets, instead of individual sequences, is essential in order to understand why 500 coins heads up is 22 sigma from expectation.
KF #102: All H carries much more info on specific state.
Do you mean by information, that in order to define 500 coins heads up we have to be very specific? If not, what do you mean by information in this context?Box_{December 18, 2013
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MF: Finally, if you understand chance then why did you try to take us on a rabbit trail dance complete with the rhetorical gambit I don't understand you. Let me go to the chase scene. What part of:
12 –> So, we come to the three distinct causal patterns: MECHANICAL NECESSITY: shown by low contingency of outcomes, e.g. F = m*a. What would happen with a stuck key on a keyboard: gggggggggggggggggg . . . CHANCE = CREDIBLY UNDIRECTED CONTINGENCY: shown by high contingency that follows the expectations of a statistical or similar distribution pattern. E.g. a dropped fair die. Also, typical random text: rfwgfvhywowadcfyweqou [--> where contingency has been stated as that under highly similar initial circumstances outcomes vary significantly with the dropping, tumbling and settling fair die as an example] DESIGN = CREDIBLY DIRECTED CONTINGENCY: often intuitively known or observed from behaviour, but detectable in many cases from its result, FSCO/I which is not credible by either chance or necessity. E.g. a loaded die, or one set to read a given value by an agent, typed coherent text with messages in English of sufficient length not to be accessible to chance under given circumstances.
. . . do you find unintelligible, why? KFkairosfocus_{December 18, 2013
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MF: do you believe there is such a thing as a directing intelligence, a self-moved agent who can choose a particular outcome or at least input from a set of possibilities? Such as, my decision just now to reply to you and fill this combox with text more or less in English with a specific meaning and send it? Not, random typed gibberish::uhyfgifgudf, and not the equivalent of a stuck key: ppppppppppppp Or, do you believe the apparent choice of the intelligence reduces in various ways to blind chance and mechanical Necessity? If so, you don't believe in a sufficiently free mind or free will [don't even bother with the compatibilism dodge, it just pushes the absurdity back one step], and by implication undermine reason, knowledge etc ass all such requite intelligent free choice. That, I suspect is the real root problem and -- with all due respect -- it boils down to clinging to absurdity, for the reason's outlined in WJM's little gem:
If you do not [acknowledge] the law of non-contradiction, you have nothing to argue about. If you do not [admit] the principles of sound reason, you have nothing to argue with. If you do not [recognise] libertarian free will, you have no one to argue against. If you do not [accept] morality to be an objective commodity, you have no reason to argue in the first place.
KFkairosfocus_{December 18, 2013
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WJM et al To be precise (which I know is anathema to you guys) I understand what "chance" means as well as most people. So KF's 1000 words are probably wasted - but as I can't understand them it is hard to be sure. My problem is with understanding what Barry meant by "chance as a hypothesis" (There is a discussion TSZ, open to all of course, about why "chance" cannot be a hypothesis). I am not convinced anyone else here understood what Barry meant either. I repeat for the umpteenth time does it mean: “each coin had an independent probability of 50% of being heads or tails”? If the answer is "yes" then one word will suffice as an explanation. If the answer is "no" then clearly some more detail is needed. But so far no one has felt able to answer even this question which strongly suggests no one understands what the phrase meant.Mark Frank_{December 18, 2013
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Box: The idea is that 500 coins have 3.27*10^150 possible configs, so if we see them in a very special one like 500H, that has excluded a lot, and so is highly informational. Yes that is 22 SD away from the expected, the peak. But it is also a case of a hot zone with one member from that set of possibilities. If I had said, the coins are 50:50 H and T, that would tell you much less about particular state, as IIRC there are 500!/ 250!*250! possibilities [500 things 250 each of 2 kinds, no of possible arrangements], and I am too lazy just now to drudge through Stirling's approximation to solve that. All H carries much more info on specific state. BTW, if I has said 50:50, alternating H and T in a row, there would be just two possibilities, quite a collapse in no of possibilities from the 50:50. KFkairosfocus_{December 18, 2013
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As it has taken you nearly 1000 words to explain what “chance” is you can perhaps understand my request for a little more precision in the OP.
No volume or quality of words can successfully explain a thing to a person ideologically committed to not understanding that thing.William J Murray_{December 18, 2013
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#98 Box
Unfortunately I still don’t understand what you mean.
You are not alone!Mark Frank_{December 18, 2013
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That's a happy typo . . . leaded should be loaded . . .kairosfocus_{December 18, 2013
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Kairosfocus #95,
KF #92: 4 –> It is complex and if the coins are as normal, informational, so the design inference would be design.

Box #95: Can you rephrase or elaborate on your point 4? Are you saying that all 500 coins heads up is ‘complex and informational’? If so, what do mean exactly?

KF #95: For normal coins read standard, fair H & T coins that tend to give about 50:50 H/T patterns on tossing. Such coins have the highest possible info bearing potential. And if we see 500 such all H, a reasonable person will immediately infer design, directed contingency. KF
The way I understand it is that a reasonable person would infer design, because 500 coins heads up is 22 sigma from expectation - IOW this event has an extremely low probability. Maybe you try to include other arguments for inferring design? One has to do with ‘information bearing potential’ and yet another has to do with complexity (post #95). Unfortunately I still don’t understand what you mean.Box_{December 18, 2013
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MF: With all due respect, the only reason I needed to take that much is that there has been ever so much of obfuscation of something that is quite familiar from coins, dice and cards, which we all played with as children. And BTW, thanks to an unfortunate toss of the dice, you just landed on Park Avenue leaded up with hotels: RENT!!!!!KFkairosfocus_{December 18, 2013
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KF #94 As it has taken you nearly 1000 words to explain what "chance" is you can perhaps understand my request for a little more precision in the OP.Mark Frank_{December 18, 2013
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Box: For normal coins read standard, fair H & T coins that tend to give about 50:50 H/T patterns on tossing. Such coins have the highest possible info bearing potential. And if we see 500 such all H, a reasonable person will immediately infer design, directed contingency. KFkairosfocus_{December 18, 2013
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MF: I see where in was it 49, you challenged design thinkers to define chance, asserting that the definitions we use are "fuzzy." (Given what we just saw, I translate: can be wiggled out of.) Let's start with the AmHD . . . and I have a distinct feeling we have been here before and can predict the likely outcome on your side. But at this stage I am going to appeal to the presumed reasonable onlooker:
chance (chns) n. 1. a. The unknown and unpredictable element in happenings that seems to have no assignable cause. b. A force assumed to cause events that cannot be foreseen or controlled; luck: Chance will determine the outcome. 2. The likelihood of something happening; possibility or probability. Often used in the plural: Chances are good that you will win. Is there any chance of rain? 3. An accidental or unpredictable event . . .
In steps of thought: 1 --> That's a good layperson level first thought, namely that we are looking at something like a tossed fair die or coin that can go one way or another under similar enough initial conditions . . . it is highly contingent . . . so that the exact outcome is unpredictable beyond some distribution or range of possibilities similar to tossing a fair coin or fair dice. (notice the use of examples.) 2 --> That is, if something is Highly Contingent, not credibly directed, with outcomes that fit some distribution of possibilities, chance is the presumed best candidate. 3 --> So, already, we are at the key point made in the design inference filter process -- which contrary to your bare dismissive assertion DOES entail a definition of chance that is sufficiently clear for use. 4 --> Namely, the key first issue is to mark mechanical necessity apart from high contingency outcomes. If under similar initial conditions the outcome is more or less determined, we are dealing with necessity, not chance or design. Drop a heavy object near earth's surface, it reliably falls under 9.8 N/kg acceleration. (This is the example I have used for about 8 years in my always linked note.) 5 --> Now, let that object be a common six sided die, a fair one not a loaded one. And we know how to make fair dice -- ask the houses in Vegas -- so that rabbit trail is locked off. Predictably, having fallen it will roll and tumble coming to rest with a face uppermost reading from 1 to 6, in a nearly flat distribution. 6 --> This is a paradigm example of chance: under similar initial conditions, there is an unpredictable, uncontrolled distribution of possible outcomes, subject to some probability or possibility distribution that in some cases can be identified a priori and can often be observed after the fact. 7 --> This can be by taking advantage of clashing mechanically determined trends that collide in ways that lead to unpredictability due to chaos. With the die we have twelve edges and eight corners, leading to highly unpredictable sensitive dependence on initial conditions so that tiny irregularities that are not controlled guarantee the distributed outcome on multiple tries. (This too I have explained any number of times. Likewise the box of marbles example here shows how this gives rise to a Maxwell-Boltzmann distribution relevant to the ideal gas model.) 8 --> In other cases, there is an apparent in-built randomness, e.g. with quantum processes. But chance is not simply equal to randomness, as the case of the die shows: deterministic dynamics acting through chaos and the irregularities at work give rise to distributions that are effectively flat random in outcome. 9 --> In both these cases we have credibly undirected contingency across a range of possible outcomes that in at least some cases we may see following a distribution. Which can of course include something like a loaded die or the sort of summation that gives a sharply peaked binomial result for 500 fair coins. For that matter the Maxwell Boltzmann distribution is peaked. 10 --> By contrast in certain cases, we have a decision that shifts the outcome in a controlled fashion towards a goal of some sort, i.e. design. 11 --> That design can then interact with the state of nature to have a distribution on outcomes [my usual example is playing a game with nature where the state of nature is effectively the product of a chance process], but there is evident choice as we experience it in the inputs to the situation. (This is often detected from its characteristic outcome, functionally specific complex organisation and/or associated information as in the message of this post which is utterly different from and implausibly improbable on a chance based random typing exercise.) 12 --> So, we come to the three distinct causal patterns:
MECHANICAL NECESSITY: shown by low contingency of outcomes, e.g. F = m*a. What would happen with a stuck key on a keyboard: gggggggggggggggggg . . . CHANCE = CREDIBLY UNDIRECTED CONTINGENCY: shown by high contingency that follows the expectations of a statistical or similar distribution pattern. E.g. a dropped fair die. Also, typical random text: rfwgfvhywowadcfyweqou DESIGN = CREDIBLY DIRECTED CONTINGENCY: often intuitively known or observed from behaviour, but detectable in many cases from its result, FSCO/I which is not credible by either chance or necessity. E.g. a loaded die, or one set to read a given value by an agent, typed coherent text with messages in English of sufficient length not to be accessible to chance under given circumstances.
Where of course we notice three interacting concepts, with markers of distinctness. But we may safely predict that there will be attempts to wiggle out. KF PS: And yes, a designer may mimic chance or necessity, and a chance outcome can in principle come to resemble either of the other two. But that is not the way to bet if you have something significant on the line -- not if cheating can give an advantage! And, if you see a Jumbo jet you do not normally infer to a tornado in a junkyard, or even if you see a watch in a field or a panel instrument from the jumbo. Where also, Paley in Ch 2 of his Nat Theol, 1804 or so, pointed out that if you see a watch that tells the time and replicates itself that is a STRONGER index of design.kairosfocus_{December 18, 2013
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Kairosfocus #92, Can you rephrase or elaborate on your point 4? Are you saying that all 500 coins heads up is ‘complex and informational’? If so, what do mean exactly?
4 –> It is complex and if the coins are as normal, informational, so the design inference would be design.
Box_{December 18, 2013
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F/N Let us refocus the OP:
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?
1 --> 500 coins, where coins normally are H & T. 2 --> Set, i.e. sitting on the table. 3 --> All coins H up, a case that is 1 in 3.27*10^150 possible configs if coins are H & T, and this is a single case specification. (Blind search capacity of the solar system, implicit in coins, is such that such a config by chance is on these odds with the usual fair coins 50:50 possibilities.) 4 --> It is complex and if the coins are as normal, informational, so the design inference would be design. 5 --> What of H:H coins? Immediate: design, just one level up. 6 --> Coins made with magnets so they will form the polarisation seen? Design again. 7 --> One side glued? Design again. 8 --> Etc etc? Predictably the design will be moved up one or a few steps, but design will be implicated. _______________ Conclusion: It is very hard to escape the conclusion that this is a case of CSI implicating design, save by very strained and convoluted processes, which will strongly tend to imply design at some state in the process. KFkairosfocus_{December 18, 2013
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