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# A Statistics Question for Nick Matzke

December 16, 2013 | Posted by Barry Arrington under Intelligent Design |

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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I am no statistician, but I use this type of reasoning all the time in my job as a student affairs professional in higher education. We assign our students a user name based on the first 2 letters of their first name and their last name along with a 4 digit number that corresponds to the last four digits of their student ID. This is their log-in for email, etc. Even though we may have multiple students in our system with the name of “John Williams”, since we are a fairly large school, I can reasonably ascertain that “jowilliams2992” is going to be the John Williams that lives at 125 Strawberry Lane without having to go into further detailed searches. I am not sure if this example applies to this particular issue, but it tells me that our instinct is to use these probabilities in our daily lives to make important and reasonable decisions. The Materialist would have you believe that such instinctual logic is faulty since the likelihood of our being here is just as likely as our NOT being here.

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.

“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.

What Mark said.

Another hypothesis is that all the coins have heads on both sides.

Whats with all this threads on Matzke, you will be asking for his autograph next 😛

Which still means chance is not the mechanism of the configuration.

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.”

Or would prefer we used the phrase “stochastic process”?

A stochastic process:

And the definition of random variable:

Darwinist Derangement Syndrome. We’re into full-fledged psychosis territory now.

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.

Sal

Yes folks, here you have it:

“Chance is meaningless”,“maybe the coins have heads on both sides”and _______ <– cricketsIf you are not overwhelmed by vicarious embarrassment now, you never will.

Not really. The package could have been dumped out the other way, producing all tails. Perhaps this was a 50/50 thing.

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”.

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?

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

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. 🙂

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 😯 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.

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.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:

Instead, you essentially went into a full blown Chewbacca Defense mode.

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.

No, I was explaining how “all heads produced by coins sliding out of a package” could still be thought of as a chance explanation.

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.

Chewbacca defenses don’t make sense. Ours did. Therefore, your accusation of a Chewbacca Defense is, ironically, itself a Chewbacca Defense.

Mark & Matzke: —— <– crickets

Nick’s response:

So let’s play out the possible scenarios:

1. “You discover the coin is two-headed, do you reject the chance hypothesis?”

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?”

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?”

etc.

Here was my question:

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:

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

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:

NICK: NO!

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!

Sal, you look like you are getting mad and therefore sloppy(er) since you didn’t really think this

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.

None of the alternative chance hypotheses that we proposed involved violations of the laws of physics.

On the various quotes of:

…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.

in response

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 :

Gee Nick, if finding 2-sided coins won’t make you reject the hypothesis of chance, nothing will. 🙂

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.

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 EgTHH has an odds of 7 to 1 against HHHIn fact sequence odds has been worked out in Penney’s GameJ.A. Csirikhas a formula for more than 3 bit sequence, which can be seen in the wiki reference or you could implementJohn Conway’salgorithm 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.

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!

Stephen

Stephen,

Your example is well-enough described that, sure, it is easy to reject the chance hypothesis that you specified from the data.

The question was not is the design hypothesis rejected, but rather whether chance as a hypothesis is rejected:

Nick responded:

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.

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. 🙄

We have it recorded now that Nick said no, or at best refused to give a clear answer.

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!

SteRusJon writes

Ste, that’s why we secretly keep Nick on the payroll here at UD. One gobsmacking imbecilic blithering after another from a nationally prominent Darwinist. He’s worth his weight in gold to the ID movement, and he works for peanuts.

The “chi square” test, which sixthbook #31 aptly proposed, is technically the standard approach of statistics for problems like this. Who refutes such test is simply out of science. Not that I am surprised, because I wrote in another thread that evolutionists by denying ID, at the very end, deny the hard sciences (math/physics…), and probability/statistics belong to math.

Mr Matzke appears disingenuous. If someone bet him $1,000 that they could toss five hundred quarters in the air and they would all land on tails, (and there was no rigging or trickery involved, etc) I doubt Mr Matzke would reject the wager because he thought the odds were 50/50.

I think there is quite a lot of confusion here. I imagine I speak for Nick in what follows.

No one deny that if you walk into a room and find 500 two-sided normal looking coins on a table all heads the most plausible explanation is that someone placed them that way. People are often found in rooms and like placing things in patterns. One of the least likely explanations is that someone tossed each coin just once and they all happened to land heads. There is no need for a chi square test – it is sufficient to use the binomial distribution to calculate the probability of such an extreme result given the hypothesis.

However, the question was “would you reject chance”? and this is a vague statement that needs clarification . We were explicitly told not to assume the coins were tossed . So there is an infinite variety of hypotheses about how they ended up on the table. Almost all hypotheses involving coins, which are man-made artefacts, are going to involve intelligence at some point (even 500 coin tosses involves an element of intelligence) so just saying “chance” is meaningless. The attempt to clarify what it means resulted in a stream of abuse at Nick (I seem to be lucky on this occasion) but not much that helped clarify what was meant by “chance”. Most of the responses just emphasised how unlikely the outcome would be if the coins were tossed independently – something which no one disputes.

Mark Frank =>However, the question was “would you reject chance”? and this is a vague statement that needs clarification .

Me => What more clarification can there be? Barry Arrington clearly states the coins are set on table. I can’t think of any way chance alone can help set the coins on table in all heads up sequence.

#36 coldcoffee

Part of the problem, as I say, is that it is hard to conceive of any scenario which results in 500 coins on a table without human intervention at some stage – whether they be 500 heads or any other configuration. Even 500 coin tosses needs someone to toss them or arrange for them to be tossed by machine in a fair way. So it is hard to know what is the hypothesis Barry wishes to reject.

Assuming you allow some human intervention there are numerous ways that an element of chance might be involved. for example, they might have been delivered as 5 packets of 100 coins straight from the manufacturer where the manufacturing process would creates them all the same way up in a packet – by chance all 5 packets were heads up. There might have been far more coins, but the design of the heads side had lower friction than the tails. The table was tipped and the heads down coins slid off. etc.

Mark its right about now that you should rather put a sock in it…….

#38 Andre

I can understand that trying to explore things in a bit more detail is difficult for you – but others may be interested.

Mark,

in post #35 you suggest that the question in the OP is “would you reject chance?” – as in ‘would you exclude every involvement of chance; however small?’

That is not the question in the OP at all.

From the OP: (…) would you reject “chance” as a hypothesis to explain this particular configuration of coins on a table?

IOW: can chance alone produce this configuration?

//

This is a mistake. I should have written:

IOW: Do you believe, from a practical standpoint, that chance alone produced this configuration?

Box

‘would you exclude every involvement of chance; however small?’

That would be absurd – there is always some element of chance however much intelligence is involved.

’can chance alone produce this configuration?’

As I said, in the case of coins it is hard to know what this means. Intelligence involved in the manufacture and distribution of coins. Does this count? If not, where is the line drawn?

MF: “As I said, in the case of coins it is hard to know what this means.”

Typical materialist dodge. When evidence and logic fail them they can always fall back on “me no speaka zee English.”

I can’t decide if it is more sad or more pathetic.

Equal parts both.

^^^ Did Matzke just counter with “I know you are but what am I?”

#43 Barry

Barry – I made an explicit guess at what you meant:

“someone had independently tossed each coin and each coin was fair.”

If that is what you meant – fine. I think we can all safely reject that hypothesis. But I suspect you mean something else. However, you also seem very reluctant to explain what is and would prefer to fall back on personal comments. Is this what your legal training involved?

Mark,

Yet, in post #37, you are arguing for the possibility that chance may be involved in a minor way – e.g. the 5 packages scenario. From which I conclude that you interpret the question in the OP in a warped way.

Mark @ 45. By now you should know that when you say stupid things in a combox attached to one of my posts, I will point it out, often in unflattering ways. You said it is hard to know what the following phrase means: “would you reject ‘chance’ as a hypothesis to explain this particular configuration of coins on a table?”

That statement is aggressively stupid.

When you are being intentionally obtuse in order to distract and obfuscate, don’t expect to be treated gently. And yes, that is something one learns in the law.

My gruff responses to intentional obfuscation (as opposed to good faith disagreement, which I hope I treat with charity) are not gratuitous. They have a purpose, to discourage these sorts of antics. I hope you will pick up on that.

Box #46

I interpret the OP with difficulty (unless it means “someone had independently tossed each coin and each coin was fair.”)

becausechance is always involved in some way and in the case of coins human intelligence is always involved.Barry

So if it is stupid to question the meaning of:

would you reject ‘chance’ as a hypothesis to explain this particular configuration of coins on a table?

then presumably it is easy to explain what it does mean to the benighted masses who do not understand it. Would you care to do so?

More generally to all you IDists.

Many of you clearly think that asking Barry to clarify his OP is perverse stupidity and the meaning is obvious. Questions of statistics and probability are notorious for appearing to be obvious and actually being quite subtle and complex. (As it happens, the legal profession have a particularly poor reputation in this respect to the extent that they have a fallacy named after them: http://en.wikipedia.org/wiki/P.....;s_fallacy).

All I am asking for is some clarity about the hypothesis that is being rejected – to the extent that I have even suggested what that hypothesis might be. This is important because it is the same fuzzy thinking that underlies much of ID – assuming a specific probability distribution, calling it “chance” and then arguing “not chance, therefore design”.

The question is: ‘do you reject, from a practical standpoint, the possibility that chance is the

sole causefor this particular configuration of coins?’The question is

not: ‘do you rule out the possibility that chance is involved as asub-causefor this particular configuration of coins?’.BTW: I don’t think that it is correct to state, with respect to the configuration of coins – which is the subject at hand -, that chance is

always involved, as you have written. However, it doesn’t seem to make any difference for the topic at hand.MF:

I categorically reject the premise of the question. You do understand the phrase (everyone with a basic grasp of English grammar and syntax understands the phrase). But you believe it is in your interest to pretend otherwise. Not going to rise to your bait Mark.

Truth.

No, you are obfuscating and dissembling.

Mark @50, 🙂 I really can’t understand why there is hesitation in answering straight forward question of Barry.

As you know there can be no end to clarification questions -In how many rows and columns are the coins arranged? Is the arrangement of coin circular? When was the coin minted? May be it got corroded on one side so the fair coin became unfair? Was acetone applied or other cleaning chemicals applied unevenly to the coin – it could affect the weight on either side of coin, Was the wind speed varying in and around the table and so on.

I really see no reason to hesitate unless this is some kind of deliberate trap set by Barry for Nick :-), but still I can’t understand

yourhesitation.Barry,

Obfuscating and dissembling, indeed.

You have to paint these guys in so tight that they just can’t get out. If there is the slightest crack to squirm through they will try, rather than concede any point. In my opinion, an honest seeker (skeptic?) would ask for clarification if there is some ambiguity and be charitable in seeking to understand what the OP was getting at. I don’t see them doing that. Instead, they expend great effort to not deal with the issues at hand. Reminds me of someone who didn’t quite understand what was meant by “is”. Maybe they don’t really want the truth to see the light of day either.

The OP was simply stated. Of all the hypothetical scenarios of how the coins could have come to be all heads that come to my mind, a pure chance event is the lowest on my list of possibilities ranked in order of plausibility. All of the competing hypothesis rank higher. That is rejection of the pure chance hypothesis in these people’s precious scientific sense. Why they can’t just say so is beyond me. Really makes them look fanatical rather than skeptical.

Stephen

#51 Box

I am not sure that the clause “from a practical standpoint” means. However, if you literally mean “do you reject the possibility that chance is the sole cause for this particular configuration of coins?” my answer is probably yes – because I take that as equivalent to “intelligence has no role to play in the configuration” and intelligence has a role in

allconfigurations of coins so naturally it includes this configuration.Mark,

You say (post #55)

‘intelligence has a role in all configurations of coins’– and for this reason you reject the possibility that chance is the sole cause.But why should intelligence always have a role? Why can a configuration not be 100% determined by chance?

#53 and #54

selvaRajan and SteRusJon

I have several times above said that I gladly reject the hypothesis that the 500 heads is the result of tossing each coin independently. Is this not charitable in seeking to understand what the OP was getting at? If that is what you mean – then all is agreed and the discussion is over. But I think you mean something else which is why I am asking for an explanation. But you won’t even be clear whether it

issomething else, much less explain what that something else is. (SteRusJon has describes it as a “pure chance event” but this doesn’t add much!). This is why I am hesitating.#56 Box

Because they are coins. Coins are made and distributed (and tossed) by intelligent people. They never occur totally naturally.

The

configuration, is not (necessarily) caused by intelligent people. And this discussion is about the explanation of aconfiguration– not the occurrence of coins.NickMatzke_UD:

One hundred years ago, Paul Ehrenfest was analyzing Planck’s equation and the notion of the quanta proposed by Einstein. If you’ve looked at the derivation of Planck’s Equation (from which we have his ‘constant’), you’ll see that he uses Boltzman’s thermodynamic equation. Planck opposed Boltzman’s idea of the ‘statistical’ nature of thermodynamics, but he was at a complete loss. Employing Boltzman’s equation, roughly S=klogW, gave him the right answer to the UV catastrophe of ‘black-box’ radiation.

Now, Ehrenfest investigated this connection between ‘quanta’ (understood from Planck’s ‘constant’) and the Bohr-Sommerfeld treatment of ‘action’ used in their analysis of Bohr’s atomic theory. What Ehrenfest found was that Boltzman assumed that the phase space of molecules is completely equi-probable, i.e., a uniform distribution. He found that when he evaluated the orbital Hamiltonian of Bohr-Sommerfeld that there were regions of the phase space that had ZERO probability. This was simply imposed by the conditions of the quanta themselves (basically, atomic orbitals and spherical harmonics applied to them).

Now, this proves that Boltzman was wrong in postulating that the phase space of atoms and molecules represents a uniform distribution; and, yet, his statistical treatment of degrees of freedom still gives valid results and is still taught.

Interestingly, it is Boltzman’s equation that was utilized by Shannon in his definition of ‘information’, and then used by Dembski in defining CSI.

And the Darwinists holler and holler: “But we don’t know what the EXACT probability distribution is!!!!!!”

Boltzman was WRONG in saying the complete phase space was “uniform”–his, per your quote, “model” was wrong; however, his thermodynamics is valid.

Another post compares THH to HHH, and such. While Boltzman did not EXACTLY know the distribution he was dealing with at all times, nevertheless, he came up with the right answer.

When in doubt, assume a uniform distribution.

We know enough; and what we know tells us that “chance”, or “random”, isn’t the answer. Why spit at the truth?

#59 Box

You cannot estimate the probability of a configuration in the abstract. You have to have some hypothesis about how that configuration was produced which means having a least some idea of the physical objects which have been configured.

You may want to separate the creation and distribution of the coins from the process used to configure them but this is not a clear distinction. I believe coins are typically manufactured and distributed in packets all the same way up (if it doesn’t happen that way it certainly could). So they could easily spill out of the packet all the same way up providing the all heads configuration. This is not some fanciful option. It is quite realistic.

I have to admit, when I read the OP, I was a bit discouraged because Barry didn’t use the word “fair” to describe the coins. Why was I discouraged? Because I knew by doing so, the anti-IDists would seize on the omission. But I was willing to work with the hand dealt. Mercifully Barry didn’t ask, “was the configuration designed?”. This was a more minimal question:

Further, the question wasn’t “is chance a possible explanation” but whether “would you [Nick Matzke] reject chance”. That means, for Nick at a personal level, would he really practically speaking in his heart reject chance?

This wasn’t a philosophical question about UPB or multiverses, etc. This was a question to Nick about what he would do.

So Barry dealt the ID side a pretty good hand, and all we had to do was play the hand. But the other side simply wouldn’t fold. Darwinists never fold. Nick could have said, “If by chance you mean a stochastic process acting on the coin, I’d reject chance, but this trivial game is irrelevant to evolutionary biology, I’m done playing stupid games.” and maybe left the debate with some semblance of honor.

But instead Nick tries to argue a 2-headed coin scenario is a chance process. If the coins are 2-headed there is no chance for any other outcome, hence logically speaking, chance cannot play a role even in principle. But far be it for Nick to humble himself before a creationist and say, “actually Sal, you’re right, I made a mistake.” In stead he offers this Chewbacca Defense:

🙂

Seriously Dr. Matzke, if your students pointed out to you that 2-headed coin precludes chance as a mechanism even in principle, can you in good conscience give them this sort of Chewbacca answer?

But, nooo, if Sal points that out to you, you have to save face at all costs. It’s far beneath you to admit a mistake. You could have said something to take the edge off your error: “yes of course we’re talking the chance hypothesis, not the design hypothesis. My bad”. But no, the poster boy of the Dover trial has to appear infallible at all times, especially when sparring with a creationist.

1. If the coin was found 2-headed, you’d still reject chance

2. if the coin wasn’t 2-headed, based on the paper at Columbia University “you can load a die, but you

can’tbias a coin” you’d still reject chance. Coins, based on physics, can’t be very much biased when making randomized outcomes3. if the packing process caused the coins to be heads, that still reject the chance hypothesis

And finally, the question was entitled “A Statistics Question for Nick Matzke”. You’d think a PhD Evolutionary biologist from the Berzerkely would start thinking of textbook statistics and not Bill Clinton’s playbook of equivocations. I take that back, maybe that’s the way an evolutionary biologist is trained to think….

Thank you sixthbook for actually quoting textbook statistics!

It’s not just skepticism at this point, but defending reputations. Darwinists don’t know when to fold, if I’d face opponents like that at the poker table, I’d start playing poker.

We could milk it more by asking:

It’s no longer merely about materialist fighting ID, it’s about saving face at all costs.

I don’t think they’re “defending their reputation”; I think most of these guys think they are actually arguing in good faith. That’s why I consider a kind of psychosis. It’s more along the lines of a mental disease than it is ego.

At the end of the day, though, it really doesn’t matter if the barbarians at the gates bent on destroying society are evil or mad; they still have to be defeated and, mad or evil, reason and logic won’t get the job done.

You are safe to assume that we are talking about two-sided and fair coins.

In fact there is a clear distinction if we assume two-sided, fair and unpacked coins. In which case we can arrange a mechanism of distribution resulting in a configuration entirely caused by chance.

Contemplating this hypothetical case you rightly point out that intelligence is involved – as have others. So we are in agreement here: also in this scenario chance is ruled out as a sole cause.

Well, you see Sal, some of the coins could have adhesives on one side with a second heads printed on them and through flipping, or any activity, could cause the sticker to fall off thereby revealing a tails result and reintroducing chance!

How’d I do? Does that sound convincing enough? Am I a Darwinist now?

Mark, I can almost count on my hand the number of times I’ve ever publicly disagreed with you, but this has to be one of them.

The question posed was, whether you would reject chance as a hypothesis.

If your scenario was the case, then that means the coins didn’t really go through a stochastic process but were in the initial condition of all heads. In such case you’d still reject chance as the primary mechanism.

When we talk about chance being the mechanism, we are talking about what would be the expected outcome of a relevant chance process, and the expected outcome is 50% heads or close to it (since coins must generally be fair as elaborated in the paper I cited). If we see something 22 standard deviations from expectation, I’d reject chance as a mechanism.

The scenario you introduced is not relevant since it essentially precludes chance from acting on the coins individually. One could say, “well chance is still involved because tails could have spilled out.” In that case we could also say, chance was involved since an earthquake could have happened and prevented the coins from being on the table (even though it didn’t) and since we didn’t factor the Earthquake chance hypothesis, we haven’t rejected all chance hypotheses.

But that certainly isn’t the spirit of the question, and certainly if one has a title “A statistics question”, I’d expect an answer like the one given by sixthbook.

Perhaps you’re standing your ground to defend your friends, and that is an honorable thing. You raised a question that might be on the minds of some, but you seem to be stuck in thinking this was a question about ID or design, it wasn’t, it was far more minimal.

The question was asking whether you would reject chance as a hypothesis. ID and design weren’t even on the table, but Nick was unwilling to concede even one micron of ground when it was clear he made some obvious errors in basic logic and statistics.

Oh my goodness, I’m almost tempted to start a humor thread “Give Nick Matzke your best Chewbacca Defense”.

I’d say:

Give it your best guys. Johnny Cochran provided a model to defend such and indefensible case:

http://en.wikipedia.org/wiki/Chewbacca_defense

Mark,

You provided this link:

http://en.wikipedia.org/wiki/P.....;s_fallacy

That was informative. I was unaware of this data point.

Thank you.

Sal

Sal #67

Sal- the key point here is what is meant by “chance as a hypothesis”. I have said more times than I can count that if what Barry meant was:

“each coin had an independent probability of 50% of being heads or tails” (A) …. (I have labelled this hypothesis (A) because I refer to it a number of times).

then I would reject the hypothesis. I said this as my very first comment #3. All Barry had to do was say – “that’s what I meant” and the debate would have stopped there as far as I am concerned. However, no one, including yourself or Barry, has confirmed that this is what “chance hypothesis” meant. If he meant something like “some stochastic process was responsible for the configuration” then I would

notreject the hypothesis because it is easy to think of stochastic processes which are quite likely to produce 500 heads. But mainly this whole thread has been a plea for clarity which for some reason has upset a lot of people.In the light of this let me pick up some of your specific points.

A stochastic process can begin with any starting condition you care to mention including all heads. It is not the starting condition that makes it stochastic. It is stochastic if there is an element of chance (!) in the process. In my example there is – the coins could have tipped over while sliding out of their packet. I should have made that clear.

The 50% figure (and your paper) is true

if you assume (A). My whole point was to ask if that was the assumption was what was meant by “chance”.I am not sure what you mean by that. As each coin slipped out of the packet it had a chance of flipping over – albeit a very small one.

Yes – some hypotheses, like the earthquake, have very low prior probabilities and can be ignored – others have to be taken seriously. But it is really hard to assign prior probabilities without more context. Perhaps this is all happening during an earthquake!

Sixthbook’s answer assumed (A). (You should not use statistical tests unless you are clear about your assumptions – it is an elementary rule.)

I think it is a question about the meaning of the phrase “chance hypothesis” that’s all.

I won’t inspect Nick’s comments for errors but there are plenty of fundamental errors in logic and statistics on display above! Probability and statistics is a hard subject and I think I am better at it then most people.

Mark,

So predictable! Mark, this part of the discussion should be over. The question was very simple to answer. We should have long since moved on to what the implications are. It is telling that the various members of the anti-ID cohort can’t bring themselves to look for the meat and potatoes meaning of a pro-ID post and deal with it. Is it because the anti-IDist don’t like the possible implications?

But, no! Time to double down. You have to go after some more ancillary crap like “intelligence has a role in all configurations of coins.”

That is not dealing with the point of the OP. The coins are a proxy for any system of binary states and, in turn, a proxy for any and all discrete state systems (in those facets where the behavior is the same). The coin system is a simplification, an idealization, that is supposed to make the problem tractable. Instead of focusing on the pertinent aspects of the coin system, you continue to press on with irrelevancies. Anti-IDist almost invariably latch onto some imprecision (real or perceived) in a pro-ID statement to avoid dealing with the central point currently under discussion. (That is the kind of thing I was referring to when I spoke of the lack of charity.) The current thread is, as are most others here at UD, a glaring example of just that. Why do you all have such an obsessive need to muddy the waters with so much BS.

Oh, by “pure chance event” I was simply trying to get you all to focus on the crux of the issue instead of things like “humans make coins” and “humans flip coins” and “humans stack coins” therefore there is some ID in any and all events involving coins BS.

Come on guys. FOCUS!

Stephen

PS. Theoretical physics must drive some of you bananas with its idealized constructs. Spheres instead if oblate spheroids. Centers of gravity in place of distributed masses. Ideal gases, absolute vacuums and point particles.

Sal #69

I am glad you found that link interesting. Here are two more statistical paradoxes which show that the apparently obvious is not always true in probability:

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

A class of students is divided into two streams. Is it possible to raise the average intelligence of both streams without raising the average intelligence of the whole class?

Correct answer: yes

If you are interested I can explain.

My point was every chance hypothesis could be ruled out. I went through the hypothetical cases that covered all the relevant bases.

1. 2-headed coin (chance ruled out in principle)

2. biased coin (since coins can only have slight bias, chance ruled out on statistical grounds )

3. non-stochastic process like coins being packed all heads from the start (chance ruled out in principle), the only way chance is snuck in is articulating the risk the coins could have spilled out tails, but that is removing the law of independent trials on each coin, and this is an equivocation of the spirit of the discussion.

4. intelligent agencies (chance ruled out in principle)

I have suspected from the quality of your math that your PhD studies are in probability and statistics. Is that correct?

Now you may wonder why I requested Barry to post this discussion. It wasn’t so much to argue statistics, it was to illustrate Nick’s determination to disagree with everything I said, even when it was blatantly obvious I was right (like the 2-headed coin).

I respect you have some reservations about criticizing a colleague, but at some point, you should apply hold him to the same standards you are trying to hold us and say and exercise some tough love: “Nick, 2-headed coins have no chance of being tails, ever!”

When you look at the discussion in that light, you’ll see it had little to do with statistics but more about Dr. Matzke’s determination to save face even when he is wrong. That is unworthy of a scientist of his stature. It raises the question, what other ideas is he wrong about that he will defend at all costs. If he can’t even admit error on 2-headed coin, will he ever admit error on bigger questions.

You wonder why I pick on Nick and not on you. I’ve tried to be nice and civil to Nick in the past, but there was no reciprocity. I found you to always be quite civil in disagreement and I have high regard for your math. Sorry we’re on other sides of this debate.

Sal

“If Chewbacca lives on Endor, you must acquit! The defense rests.”

Anti-ID advocates are so afraid of where reasoning might lead them, they are willing to expose themselves as fools and deny the simple, the obvious, the self-evident, and the necessary.

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.

Yes, that’s why I’ve appreciated your criticisms, because you might find some error in my calculations or conception. And you’ve always been nice about pointing out my errors.

Sal

Sal

The trouble is these

don’tcover all the relevant bases. Look again at 2. Coins can only have a slight biasif they are tossed.You are making the same assumption about how the coins got there. It is an easy one to make because that is traditionally how we think of coins in a probability context. It is such a traditional assumption I asked if that was what was meant. To date no one has confirmed this. If you remove that assumption then the probability of a coin being a head on that table is totally dependent on the mechanism used to get it there. This is highly relevant to ID because it frequently uses the assumption that the probability of a string of DNA or protein meeting some specification is the result of the equivalent of a coin toss without taking account of the process for evolving the DNA.Thanks for asking about my My PhD. It is in open data and democracy. I have a diploma in statistics but more background than that qualification suggests.

This is harder. Feel free to elaborate. Thanks in advance.

Sal

Sal #76

Correct – can you solve the other one?

Sal – sorry I didn’t see you #78 when I posted #79.

The answer is to move the lowest performing students in the top stream into the bottom stream (think about it).

This is known as the Will Rogers paradox.

One can argue that not tossing the coins (like say spinning them) will cause a severe bias in something like the putty-plus checkers coin. But at that point one is equivocating the notion of coin.

I respect you raising the question. That’s why in future iterations in regards to statistics, I will frame the questions hopefully in ways you will find rigorous.

Though some take offense at some of your meticulousness, I don’t, I’d rather say, “Mark, what is the way I can frame the discussion so there is less ambiguity.”

As far as ID invoking probability arguments based on assumed distribution functions which can be falsified by future discoveries, I see no problem with that. Science is about putting out falsifiable hypotheses. The Genetic Entropy hypothesis, the non-evolvability of polyconstrained DNA are falsifiable hypotheses based on assumed distributions.

From a philosophical standpoint and logic, no one can assert they have the correct distribution, but it’s perfectly fine to assert them for scientific inquiry and for practical matters.

Sal

Sal -sliding the coins out of the packet will cause a severe bias even for standard coins.

I think I see it. I was trying to keep the streams with the same number of members, but if I relax that constraint I can do the following :

Stream 1: average IQ 135 (ha!), the dunce in this stream has IQ of 100

Stream 2: average IQ 80 (ouch), the smartest one in this stream has IQ 85

I move the dunce out of Stream 1 to join stream 2.

I could not solve the problem earlier because I assumed you wanted both streams to maintain the same number of members.

Am I conceptualizing this correctly? Thanks in advance.

Sal #83 – that’s it.

WJM at #75,

Where do you think this line of reasoning takes anti-ID advocates?

WOW! This thread is awesome.

Another likely evolutionist explanation is that there is glue on the tails side of each coin such that once it lands tails, it’s stuck there permanently. Inevitably, after enough “random” trials are done, all the coins eventually end up heads. This is basically equivalent to Dawkins’s silly computer program.

The problem is that just pushes the design up a level, where you have to assume that an intelligent agent chose to place glue on all the tails side of the coins, as opposed to on a random side of the coins. The evolutionist would then argue that glue only sticks to the tail side of the coins, because the head side of the coin is coated with Teflon. Or that a meteorite contained the coins all facing heads up, and so when it landed they were already just like that. The evolutionist makes up another explanation, ad nauseum, with each explanation being more unlikely than the last.

It’s hard to win an argument when the other side can introduce new unsupported premises as fact at any time.

“Ideological contamination” as well as “situational blindness” can easily lead anyone astray. For the sake of scientific progress, it’s better to follow the data, which can take some interesting and surprising turns, hold on to theories loosely, expecting discordant data to upset things once in a while, and always maintain a sense of curiosity and wonder.

This is true regardless of your beliefs, ID or Darwinist.

Unfortunately, I so far haven’t been able to persuade professor Matzke to join us in a voyage to explore a small, blue, hypothetical planet nearly identical to Earth, but on which all life was ***seeded*** by scientists, researchers, and their students. The research and class projects resulted in a vast spectrum of life there.

Now, first thousands and later perhaps millions of years later, we will analyze the results, applying Dr. Matzke’s knowledge to determine exactly what we will expect to find.

We can travel there instantaneously, and all travel expenses are covered.

Professor Matzke, we’re knocking on your door. We know you’re in there. Please answer. Don’t be a grouch. We’ll all probably learn things, and it will be fun! 🙂

-Q

Henry Crun:

Anti-ID advocates don’t have a “line of reasoning”. They have a line of denial that serves their emotional commitments.

SteRusJon #71

Stephen

It would be over in no time if someone would confirm that by “chance hypothesis” the OP means “each coin had an independent probability of 50% of being heads or tails”. For some reason no one is prepared to do this.

The use of coins and the implication they have been tossed drags in a whole load of assumptions that are not true in general of binary states. I am simply trying to isolate those assumptions.

MF:

Pardon me but coins are a classic binary system, in effect two-sided dice. And, as can be easily confirmed, the 50:50 H:T expectation on tossing or otherwise stirring them is reasonable.

If any reasonable person came across a tray of 500 coins, all H or all T or alternating H and T, s/he would very reasonably conclude the best explanation is that that was by design not random tossing.

In short, the normal expectation on tossing 500 coins is a near 50:50 ratio, in no particular order.

If the coins were in a near 50:50 ratio but turned out to hold the ascii code for the first 72 or so characters of this post, that too would strongly support the inference that this is by design.

Shifting to D/RNA, it is a f-state discrete state system, G/C/A/T or U. In living systems, we see not 500 bits worth of code, but more like 500 k bits up to gigabits. Code seen to function in the synthesis of proteins and in the regulation of that. Where a cluster of molecular nanomachines are involved in the processing system.

That alone is more than sufficient to conclude that the best explanation for such a system is design.

First, 500 – 1,000 bits of FSCO/I is beyond the plausible blind search capacity of the solar system and at the upper end, the observed cosmos. For needle in haystack reasons repeatedly explained. A search involving he atomic resources of the solar system for its plausible lifespan at the fastest chem rxn rates being able to sample the config space of 500 bits as one straw to a cubical haystack 1,000 light years across (as thick as our galaxy’s central bulge) boils down to a supertask not expected to come up with anything but the bulk of the distribution, coins or whatever in no particular order.

Mechanical necessity does not create high contingency information systems, period. Chance based on a search that is facing a supertask joined to necessity and trial and error will predictably fail.

The only reasonable, empirically grounded explanation of what we see is design.

The problem is, this cuts across a dominant ideology that is now on notice once the cellular info systems were elucidated.

Playing with definition games and the like, as I am seeing just confirms that you have no sound answer tot he heart of the matter.

And BTW, a simple case like coin tosses with 50:50 H:T is a good test of reasonableness in addressing the matter.

Yes we can go on to more complex cases [and note that the injection of constraints that bias coins will reduce effective info carrying capacity, but so long as reasonable contingency remains, the point on a tray of all H’s etc remains], but if one shows himself unwilling at this level, there is no hope at the more advanced levels.

I think you need to pause, take a look back and see whether you are being reasonable.

Even your scenario of coins packed all H up spilling out and ending up all H (have you seen how easy it is for coins to flip or roll and bounce? . . . ) is not reasonable and implies design that set the coins to that state to begin with.

My take away is that the strained nature of objections being made inadvertently shows the strength of the design inference on this simple case.

KF

F/N Let us refocus the OP:

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.

KF

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?

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:

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:

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.

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. KF

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.

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!!!!!KF

Kairosfocus #95,

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.

That’s a happy typo . . . leaded should be loaded . . .

#98 Box

You are not alone!

No volume or quality of words can successfully explain a thing to a person ideologically committed to not understanding that thing.

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. KF

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.

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:

KF

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:

. . . do you find unintelligible, why?

KF

Do you mean by ‘highly informational’ low probability? If not, what do you mean?

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.

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?

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.

KF:

I didn’t. I never asked what “chance” meant. I only asked what the OP meant by “chance as a hypothesis”.

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

contingentI 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?You actually your self somewhat clarified.

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.

Sal

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.

KF

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.

KF

KF #110,

To my embarrassment I have not

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.

KF

So a fair die is undirected contingency while a loaded die is? This is

reallyconfusing. 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.Sal

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?

KF #113 sorry typo – I meant to write:

So a fair die is undirected contingency while a loaded die is directed contigency? This is

reallyconfusing. 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.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.

you have compressed the possibilities of being either a younger or older brother into a single possibility of having a brother

I’m with c hand!

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.

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:

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…

sal

>> Boy or Girl paradox <<

Box,

Yes indeed. I actually remembered something like Mark’s question from statistics class a long time ago, but it was phrased in terms of coins. The class text pointed out even this simple example would frequently trip up the best students.

So I didn’t have to consult the net on that question because I had been already taught it but using coins instead. Looking back, I don’t think I would have solved it without some serious pondering. Simple problems aren’t always so simple are they? 🙂

Sal

How about this; no arithmetic involved:

There is obviously no relation between the fact coin A is heads and the state of coin B. The knowledge that coin A is heads is therefore irrelevant. So the probability that the other coin is tails is 50%

sal,

the two coins are not and can not be interchangeable. If you label one a dime the other a quarter you get:

dH qH

dH qT

dT qH

The first coin(which you see is heads) must either be the dime or the quarter, and you know that you are looking at 50/50 odds

C hand,

I can appreciate that you are convinced the odds are 50/50 that the other coin is tails. That would have been true in the absence of other information such as “at least one coin is heads.” But now we have more information and we must revise our odds accordingly in light of the information in order to make an accurate estimate of the probability of certain outcomes.

There are 3 possible outcomes:

Two of the outcomes have tails (the bolded ones). Thus two out of the 3 possible outcomes have tails thus the odds are two out of three or 2/3 of the time the other coin is tails.

The problem is the English language and our intuition about the problem will distort our perception. The challenge isn’t learning the problem, it’s un-learning how we usually conceive of the problem.

What I’ve provided are the odds as calculated in basic statistics and discrete math books. If you are sure I’m wrong, you can cross check the link Box provided (it appears Box may have changed his mind).

The reason this example is emphasized in textbook math is students have great difficulty unlearning the way they think about such problems. Student instinctively think 50/50 odds as you have. The odds here are 2/3, just as Mark has said.

Sal

the illusion is created by treating the boys or the head side of coin as interchangeable entities , while the girls or the tails side of the coin remain discrete.

You don’t need to stipulate the birth order of the boy, he is either the older or the younger, but he can’t be both.

you have been placing boy-girl combinations in a birth order and counting each, but you have allowed for only one boy-boy birth order

Box:

Have you looked at the summary presentation on information theory which I linked? (This is a good slice of the basis for the modern information age that we are in, e.g. it is the root of the term, “bit.”)

Also, I did not speak of how we have

exhaustiveinformation on the coins, obviously we do not, we don’t even know the denomination, or the dates or the metals etc. What I spoke to is how, on knowing that one has 500 coins in a row — all H, one has sufficient information to know the relevant state in the context of H/T as defining state.Knowing that coins are alternating H and T gives less info, and knowing only that coins are 50:50 H and T gives even less.

In the context of having a vocabulary or alphabet of possible signal states [H/T is an example, so is T/F, 1/), or A/B/C . . . or A/G/C/T or U . . . . ], it is possible to construct a metric of information carrying capacity, commonly called Shannon information. Where the Shannon info of symbols from such an alphabet, is the avg info per symbol based on a weighted average of info carried per symbol. Info being developed as a log of reciprocal probability metric: Is = – log ps, for various reasons. As was outlined here.

KF

PS: I note that design thought moves beyond the concept of Shannon info carrying capacity of symbols, to metrics developed in various ways that are tied to function based on specific configurations. For instance, consider a case of 500 coins spelling out in ASCII code, the first 72 or so characters of this message.

MF:

Pardon, but with all due respect, the last comment at 115 is utterly revealing of rhetorical squid ink evasive gamesmanship:

FYI, if a die is defective it is

defective, not LOADED.A LOADED die is one that has been manufactured or altered to be biased for a purpose. A fair die has been manufactured successfully to be fair, i.e. give a near flat distribution. And that a die is always a manufactured entity is irrelevant to the issues on the table.Here is Wiki, FYI — or rather for the onlooker who actually evidently wants to deal seriously with the matter at stake instead of running away behind a cloud of rhetorical squid-ink:

Your attempt to artfully manufacture an error on my part by way of an evasive, context-switching red herring side track word game both fails the basic English test, and is a sign of willful manipulation.

A fair die is indeed manufactured to be fair, that was never at stake, dice are artifacts.

The EIGHT YEARS LONG context — which you artfully tried to switch — is that, first, a dropped heavy object falls reliably showing mechanical necessity. Then, if it is a die . . . notice no discussion of manufacture that is irrelevant at this point . . . it will tumble and settle to a reading that is a manifestation of high contingency.

An extremely familiar example.

One on the table for EIGHT years.

Then, in that context we can introduce a distinction: that some dice are fair, and tumble in ways driven by the butterfly effect (aided by twelve edges and eight corners) that leads to an outcome that is unpredictable in the specific case, and in effect will take a flat random distribution value on the range 1 to 6. Which last implies that we are discussing common dice.

Where also the butterfly effect is a popular way of saying what more specifically is sensitive dependence on initial and/or intervening conditions, which will magnify small initial or intervening variations to yield drastically dissimilar outcomes. The chaos phenomenon in short.

Then in that context we consider another known source of high contingency, design. This can be by loading the die or by simply setting a die to read a given value.

The squid ink cloud, rhetorical game now becomes utterly apparent:

Games over.

Back to the basic point, the first key concern in a causal process is high vs low contingency. Low contingency situations will reliably have essentially the same effect on similar initial circumstances and are characterised by mechanical necessity manifest in law-like regularities, e.g. classically F = m*a and deterministic dynamics expressed in more complex differential or difference equations. A dropped heavy object near earth’s surface falling at 9.8 N/kg is a classic, highly familiar illustration.

But there are situations that are highly contingent, where under similar initial circumstances, highly diverse outcomes are possible or observed. The tumbling of a dropped die and its settling to different readings is a familiar example, indeed a paradigm. (NB: This also takes in coins, the coin being a two-sided die.)

That high contingency has two commonly known explanations: (i) undirected and (ii) directed contingency.

The former is a more sophisticated description of what we call chance and is in the design inference filter the default explanation for high contingency. (There is a deliberate choice to err on the side of chance, in order to be conservative in e4stimateing that something is caused by design.)

Directed contingency is also familiar, with a loaded die or a die simply set to a reading as simple and familiar illustrations.

So, chance is sufficiently characterised for those who are serious as credibly undirected contingency as a causal factor or influence. By contrast, design is directed contingency, and mechanical necessity denotes low contingency, reliable patterns that are generally driven by law-like forces similar to falling under gravitational attraction.

Yes, there can be elaborations and complexities, so that the design filter is applied on a per aspect basis, an aspect being a view of part of an overall situation isolated for analytical purposes.

For classic instance if one does a pendulum exercise, one will see that there are patterns that fit in with law-like regularities, but also scatter around the trend line then at a certain point — about 6 degrees of amplitude — where the accuracy of the simple law usually given falls off, showing a built in bias of design. In this case, the simple pendulum law is limited to small amplitude swings.

the scatter about the trend line is usually held to be a matter of chance factors disturbing the situation and its measurement, and often show a Gaussian curve. That is, a summation of many small positive or negative factors clustering around a mean in a familiar bell-pattern.

We could elaborate this into a discussion on errors of observation, sources of scatter, personal equations and the like but that would be pointless. MF needs to understand that the analysis of causal factors seen above is based on well known physical phenomena and cases, some of them actually famous or historically important, e.g. systematic errors due to wear were important in the characterisation of the metre based on a major survey.

KF

=> Mark Frank,

If you take a fair die as a Discrete uniform distribution, various probabilities can be computed for fair value.

For Eg the probability of getting a total greater than or equal to 10 in two dice roll is 0.167, the probabilty of getting greater than or equal to 10 in 3 dice roll is 5/8=0.625.

So if there is deviation from the probability, we can say the dice is either defective or loaded. The loaded die will have a greater frequency of a PARTICULAR dice value than a merely defective die.

Coldcoffee

The key difference between a loaded die and a defective die is that the loaded die has been made to give non-uniform probability distribution

intentionallywhile in the case of a defective die this has happenedaccidentally. For example, a dice might have an off-square face or an uneven weight distribution by accident or on purpose. However, it would be impossible to tell the difference by looking at a series of throws. It would be necessary to know something about the process of making the die.What I found confusing about KF’s example was that he offered a fair die as an example of non-directed contingency and a loaded die as an example of directed contingency (I took took “loaded” to mean “biased” – but I happy to be corrected and accept that “loaded” means intentionally biased). My impression was that KF was proposing:

a) non-directed contingency corresponds to “chance” and directed contingency corresponds to “design”.

b) it is possible to tell whether a series of throws is directed or non-directed by looking at the throws and without understanding the process by which the die was made.

(However, I have the greatest difficulty understanding KF’s writing – so I may be wrong)

However, a fair die is almost always intentionally designed and while a loaded die may, by definition, be designed a biased die resulting in the same series of throws may well be accidentally biased.

MF:

With all due respect I must say:

there you go again.You have an extremely familiar situation — dropping a die that comes to rest with a side uppermost. Something that I don’t doubt that if you really wanted to you could scrounge around in your home and set up as an experimental exercise. However, I doubt that you need to do so as the matter is abundantly familiar to one and all from board games.

Aspects of the situation — dropping a die that falls, tumbles and rolls then settles to a reading — have been brought out that distinguish the causal factors:

1 –> mechanical necessity, manifest in the falling

2 –> chance, manifest through the tumbling and settling (with an injection of the butterfly effect)

3 –> design, as would happen with a loaded die or by simply reaching over and setting the die to a required value.

From these cases, we can identify to short definitions; and yet, you are off playing context-switching word games and tangent games again.

I repeat, for record, that:

a: mechanical necessity leads to reliable regularities of low contingency,

b: chance denotes credibly undirected contingency, and

c: design, denotes directed contingency.

If you still don’t understand the difference between b and c, think about driving a car down a country lane with an unpaved rugged surface. Intelligent steering is obviously different from keeping the hands off the wheel and letting the car bounce from one rut to the next. And the results will be quite different, too.

At this point, what chance is and what design is, and what m4echanical necessity is, have been adequately explained for a reasonable person.

I strongly suspect that at root, you don’t believe that there is real free intent and decision making leading to design, as if you run true to the form of your announced worldview — evolutionary materialism, you don’t believe in a self-moved actuating cause that can freely make decisions and act on them. That is, you want in the end to implicitly reduce design to other factors.

The problem with that being, once you write off freedom to choose and act, you write off freedom to reason, which undermines the whole project of intelligent thought and discussion.

That is, reduction to absurdity.

KF

KF – I think it is best for both of us if I stop trying to understand and respond to your comments. It would only lead to tears.

Of course, I would never go there. You are stating the obvious.

You are talking about a scenario in which we are

toldthat there are 500 coins on the table and that they are all heads up. In this scenario we aretoldabout the coins but we cannotseefor ourselves. Now you say: we have enoughto know the exact sequence.informationOk, clear, obvious, I understand what you are saying.

But, why did you change Barry’s scenario into your own?

In Barry’s scenario we are not

told“500 coins all heads”, instead weseethe coins and their configuration directly ourselves.And if we are not told about the coins on the table there is no sentence “500 coins all H” which contains

informationabout the configuration of the coins.Changing scenarios, without telling, causes a lot of confusion.

Box,

I think you may be wading in too deep with the see vs told. Recognize that “seeing” and “having being told” simply mean “knowing”. In other words, “having information.”

If I were to ask you the state of coin 47 in a set of 500 coins, (you know to be) all heads, you already have all the information you need to answer. If I were to ask for the state of coin 47 in a set of coins, (you know to be) alternating heads and tails, you could not tell me until you examined at least one, any one, of the coins. If I asked for the state of coin 47 in a completely unspecified (unknown states) set of 500 coins you would have to locate coin 47 and examine it to give me the correct answer since learning the state of any, or even all, of the other coins is of no help.

By the way, the specification need not be as simple as “all heads” to “know” the state of coin 47 without examination. The specification could be “the ASCII representation of the first 72 characters of this text” (which may have a nearly 50/50 blend of apparently random bits) and you would “know” the state of coin 47 with out examination of any of the coins.

Does that help?

Stephen

Sal MF,

There are two variables to apply to Mr. Browns children, known-unknown, and boy-girl. Since the known child is a boy we get possibilities of:

known BOY – unknown Boy

unknown Boy – known BOY

known BOY – unknown GIRL

unknown GIRL – known BOY

It is obvious that the birth pattern can alternate with girl-boy, less obvious with boy – boy

When Mr. Brown introduces you to his son, you know that the missing sibling could be either a girl or a boy with 50/50 probabilities.

I agree with everything you have said, providing that there is a (tossing) sequence involved. Talking about

“alternating heads and tails”, like you do, only makes sense in the context of a tossing sequence. However, by assuming such a tossing sequence (or any sequence) are you not changing Barry’s scenario – just like KF did?A sequence does not follow from the OP. From the OP we just know that there are 500 coins on the table and they all display the “heads” side of the coin. We do not know if they are lined up in a row or in which sequence the configuration appeared – if any.

It doesn’t make sense to say you have

informationabout a sequence which may not be there.Box,

I understand your point about the need for a sequence, temporal or spacial, in order for alternating or ASCII text specification to make any sense. All heads and nearly 50/50 states can be detected irrespective of any arrangement. The original OP used all heads as an uncontroversial (Yeah, right!) way of highlighting a state that should have been readily dismissed as due to chance alone. In that case the “order” of the coins was irrelevant.

However, what is the purpose of discussing the heads/tails states 500 coins (as proxy for more interesting systems) if their only relationship is that they are in the same room? The more interesting systems typified by the 500 coins do have temporal or spacial relationships among their elements. Is it not those systems we are seeking to better understand? So, I think it is appropriate to examine the question with order of some sort within the coin set. If you disagree, so be it, but there is little to be learned in that case.

Stephen

You are assuming that the way that you got the information about one child being a boy was by you meeting the boy yourself. That is not what is stated in the original problem.

The original question:

Answer: 2/3

Your scenario is different, and I’ll word it this way to hopefully get the point across:

Answer : 1/2 (or using your term “50/50” )

In fact an even more minimal version:

Answer : 1/2

c hand,

A more clear way of stating the original problem

There are only 3 ways the above statement can be true:

A. Child 1 is a boy, Child 2 is a boy

B. Child 1 is a boy, Child 2 is a girl

C. Child 1 is a girl, Child 2 is a boy

Talking about the children’s ages and you meeting them is creating a different question than the one posed.

The designation of Child1 has nothing to do with age, it’s just something to distinguish him/her form child2.

MF: At this point, I seriously doubt that your problem is lack of clarity. KF

Box: First, 500 coins on a table could be scattered every which way, so I shifted to in a row. Next, being “told” [presumably accurately] that we have all H, alternating H & T etc is a way of saying we are informed by a message. What I am trying to do is help you see why information is measured the way it is. KF

PS: BTW, in the original post, explicitly tossing is ruled out.

sal,

There are only 4 ways the above statement can be true:

A. Child 1 is a boy, Child 2 is a DIFFERENT boy

B. Child 1 is a boy, Child 2 is a girl

C. Child 1 is a girl, Child 2 is a boy

D. Child 1 is a DIFFERENT boy, Child 2 is a boy

Child one and child two CANNOT be the same boy

c hand,

I think I finally get this. You are doubling the probability of boy/boy. With first sentence, “Mr. Brown has exactly 2 children”, there are 4 equal possibilities – bb,bg,gb,gg, and 3 out of the 4 have a girl. With new information that “at least one is a boy”, you eliminate gg. That leaves the other 3 possibilities, which are still equal, 2 of which have a girl. So the probability of having at least one girl dropped from 3/4 to 2/3 (and the probability of having a boy rose from 3/4 to 3/3).

If you identify a particular child as a boy (or a girl), it’s a different scenario. In that case, you are left with 2 equal possibilities for the unknown child – either boy or girl, so the chance the unknown child is a girl is 1/2.

You say that ‘the designation of Child1 has nothing to do with age’. What then is the difference between B and C? If we discard age how does B and C constitute a different outcome?

When we discard age why isn’t accurate to say:

“Mr. Brown has exactly 2 children”, there are 3 equal sets:

A: (a set of) 2 boys

B: (a set of) 2 girls

C: (a set of) 1 girl & 1 boy

Do we need a sequential (?) distinction between the two children? Why not instead think of them as mathematical sets? A set of 100% boys, a set of 100% girls and a set of 50% boy & 50% girl.

No. That’s why it’s better to talk coins even quarters and dimes. Now there is a subtlety, if I say at least one coin is heads, you don’t know if I’m talking about the quarter, the dime, or both.

That’s why this problem is difficult. The problem used phrases we are not familiar with. I would never tell you in the course of normal conversation:

chances of the other child being a girl is 2/3

I’d say something like this

Chance the other kid is a girl is 1/2. Why? Because in the course of normal conversation, Mr. Brown is making it clear which child he is talking about (i.e. Child1). It would be like Mr. Brown saying “the quarter is heads”.

The reason the original word problem is difficult to understand is that it is state din a very vague and confusing manner.

That was the point of the exercise to see if one can actually sort out the truth from confusion. You almost never hear things stated in that way.

Usually you’ll here, “Mr. Brown has two kids, one kid in college, a boy, I don’t know about the other.” In that case the probability of the other child being a girl is 1/2 because now we have identified which child (the one in college) is definitely a boy.

In the case of the original problem Mark posed, the is severe ambiguity as to which child is a boy. It could be child1, child2, or both.

The problem is difficult because it is far removed from ordinary experience and ordinary language.

It is ambiguous as to which child is a boy. It could be child1, child2 but not both at the same time and in the same sense.

In this case there are only two possible outcomes.

1. college-child is a boy, non-college child is a boy

2. college-child is a boy, non-college child is a girl

probability of the other child being a girl is 1/2 since one of the two possible outcomes involves the other child being a girl.

That would be true if ONLY one child were a boy, if at least one child is a boy, then both children can be boys.

#148 I think is the right answer

I like #148 too, but it’s not the original problem.

from #145:

You can use 3 sets but they won’t be equal. The mixed pair will happen twice as often as either 2 boys or 2 girls. The coin toss example is more intuitive for this – flip a coin twice and probabilities are:

25% both heads

25% both tails

50% combination of heads and tails.