Universal Probabilty Bound?

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If you ever took Dembski seriously for one second, you should read this.

scienceblogs.com/goodmath/2006/06/dishonest_dembskithe_universal_1.php

If you read it, and still take him seriously… oh well. 🤷
I see, Demski publishes his stuff with Cambridge University Press under rigorous peer review, and you present an obviously pop. level blog with an insulting title that I am supposed to take seriously? As to the more specific problems…

From the blog:
Grab two decks of distinguishable cards. Shuffle them together, and lay them out for a game of spider solitaire. What’s the probability of that particular lay of cards? 104! , or, very roughly, something larger than 1x10166. Is god personally arranging ,my cards every time I play spider?
Situation A:

You and I are playing 5 card draw. I draw the following hands:
Hand 1: 2,3,5,3,Q
Hand 2: 5,4,4,K,A
Hand 3: A,A,A,3,5
Hand 4: 6,6, Q,J, 8
Hand 5: 5,6,7,9,10
Hand 6: ,9,8,4,7,7
etc. for 12 hands.

Situation B: Same card game, I draw the following hands:

Hand 1: A,A,A,A,K
Hand 2: A,A,A,A,K
Hand 3: A,A,A,A,K
Hand 4: A,A,A,A,K
Hand 5: A,A,A,A,K
Hand 6: A,A,A,A,K
etc. for 12 hands.

I assume that we would agree that the first situation is reasonably thought to be the result of chance, right?

Now, how about the second one? If you are I were playing cards, and I drew those hands, would you shrug that off as purely the result of chance? Or would you accuse me of cheating and try to break my nose?

(P.S. if you would seriously shrug the second situation off as the result of chance, then can we get together and play cards sometime? I am a poor graduate student and could use the cash :D)
 
I see, Demski publishes his stuff with Cambridge University Press under rigorous peer review, and you present an obviously pop. level blog with an insulting title that I am supposed to take seriously? As to the more specific problems…
No mathematician would endorse that nonsense that Dembski publishes. If you have any information that such idiocy was published in a peer reviewed paper, please present the journal and the article. Your little example only shows that you did not understand the blog. You cannot argue after the deal that it was “improbable” and therefore it must have been arranged. EVERY deal is equally improbable. And yet, one of them surely will manifest itself. What is and would be extremly improbable is to PREDICT any specific outcome. But people who are ignorant of mathematics and probability theory don’t understand this.
 
I see, Demski publishes his stuff with Cambridge University Press under rigorous peer review, and you present an obviously pop. level blog with an insulting title that I am supposed to take seriously? As to the more specific problems…
No mathematician would endorse that nonsense that Dembski publishes. If you have any information that such idiocy was published in a peer reviewed paper, please present the journal and the article. Your little example only shows that you did not understand the blog. You cannot argue after the deal that it was “improbable” and therefore it must have been arranged. EVERY deal is equally improbable. And yet, one of them surely will manifest itself. What is and would be extremly improbable is to PREDICT any specific outcome. But people who are ignorant of mathematics and probability theory don’t understand this.

Look at the lottery, where you must select 5 numbers out of 90. When the numbers are drawn, you will get something like “17, 19, 23, 29, 31”. But you may also get “1, 2, 3, 4, 5”. Is the second one “surprising”, while the first one not surprising? Not at all. Both are equally non-surprising. To call the second set surprising is the so-called “odometer syndrome”. The second set “looks” ordered while the first one does not - but only to a non-mathematician. The first one happens to be consecutive prime numbers - it is just as ordered and the second one.
 
No mathematician would endorse that nonsense that Dembski publishes. If you have any information that such idiocy was published in a peer reviewed paper, please present the journal and the article. Your little example only shows that you did not understand the blog. You cannot argue after the deal that it was “improbable” and therefore it must have been arranged. EVERY deal is equally improbable. And yet, one of them surely will manifest itself. What is and would be extremly improbable is to PREDICT any specific outcome. But people who are ignorant of mathematics and probability theory don’t understand this.
Did you seriously think I was bluffing when I called Dembski a peer-reviewed publisher?

William Dembski, *The Design Inference: Eliminating Chance through Small Probabilities *(Cambridge Studies in Probability, Induction and Decision Theory), Cambridge University Press, 2006. Here.

Your source on the other hand is hardly an academic one, and is simply a blog, not any sort of peer-reviewed article and by no authority in probability theory.
Look at the lottery, where you must select 5 numbers out of 90. When the numbers are drawn, you will get something like “17, 19, 23, 29, 31”. But you may also get “1, 2, 3, 4, 5”. Is the second one “surprising”, while the first one not surprising? Not at all. Both are equally non-surprising. To call the second set surprising is the so-called “odometer syndrome”. The second set “looks” ordered while the first one does not - but only to a non-mathematician. The first one happens to be consecutive prime numbers - it is just as ordered and the second one.
Suppose in twelve draws in a row, I got the number, 1,2,3,4,5,6. Would you consider that the result of chance?

Actually, you mock me for not understanding the article, but your example assumes that that I understood it precisely as you do.

So for my card example, would you agree that my second example was unlikely the result of chance and would probably indicate design? Both draws are highly improbable, but in the first case, you assume chance, in the second, I have to assume (given your reticence to admit it), that you would not consider it the result of chance, but would assume that I was cheating (design).

Another situation:

Suppose I mixed a dozen black ping-pong balls into a billion billion billion white balls. I then reached in and drew twelve. I agree that for every white ball drawn, I will give you a million dollars and for every black ball drawn, you will give me a million. I reach in 12 times, and 12 times draw out a back ping pong ball. Would you think this was the result of chance, or assume I was cheating (design)?

Again:

Bob’s birthday is August 8, 1954. Suppose he get’s a car for his birthday, and the license plate reads: CDG 1263. Presumably, this would arouse no special interest.

But, suppose same situation, but he is given a car with a license plate that reads: BOB 8854.

Both license plates are equally improbable, but clearly the first could plausibly be the result of chance, yet with the second, Bob would be absurd to shrug it off saying “well, it had to be some number, and all are equally improbable…”
 
Did you seriously think I was bluffing when I called Dembski a peer-reviewed publisher?

William Dembski, *The Design Inference: Eliminating Chance through Small Probabilities *(Cambridge Studies in Probability, Induction and Decision Theory), Cambridge University Press, 2006. Here.

Your source on the other hand is hardly an academic one, and is simply a blog, not any sort of peer-reviewed article and by no authority in probability theory.
In mathematics there is no need for authorities, actually there are no authorities. I am truly surprised the Cambride Press gave its name to such a book. But editorial errors are also not unheard of.

Dembski simply says that for any event for which is the probability is less than 10[sup]-150[/sup] it is rational to assume an intelligent source and it is irrational to assume random chance. That is his “theorem”. Of course there is no proof to it, such a theory cannot be proven - but it can be disproven. But let’s apply this “theorem” to real life.

In any casino, you will see people playing blackjacks. The mechanics of the game is: “the croupier shuffles 4 decks of cards, and places them into a shoe”. In the shoe there are 208 randomly arranged cards. What is the probability of that particular card sequence? If you understand probability theory then you will know that the number is 1/(208!/(52!)[sup]4[/sup]). Now let’s approximate the number in the divisor (the formula is found here en.wikipedia.org/wiki/Stirling’s_approximation) and the value is n! ~ sqrt(2pin)*(n/e)[sup]n[/sup]. After simplifying we get:

(208/52)[sup]208][/sup] which is 4[sup]208[/sup] and that is 2[sup]416[/sup], which (since 2[sup]10[/sup] is about 10[sup]3[/sup] or 1000) finally will become 10[sup]1248[/sup]. The probability of that particular sequence is less than 10[sup]-1248[/sup], which is MUCH smaller than Dembski’s puny little 10[sup]-150[/sup].

From Dembski’s “theorem” it would follow that is reasonable to assume that the cards in the shoe were “designed”… Of course there is no card-genie in that box, there is only the croupier who did the shuffling.

Now it is not unheard of that croupiers were found cheating. But that is not the point here. Any sequence of cards in the show has an equal probability (less than 10[sup]-1248[/sup]) and according to Dembski’s bogus theorem it is rational to assume that God (or the card genie) personally arranged the cards. There is nothing else to say.
 
I see, Demski publishes his stuff with Cambridge University Press under rigorous peer review
This sounds unlikely. A couple of minutes on Google shows that Cambridge UP has only published one book by Dembski (another is part edited by him). The book, The Design Inference was published in 1998, yet the 2005 Dover trial contains the following exchange:

*Rothschild: And, in fact, there are no peer reviewed articles by anyone advocating for intelligent design supported by pertinent experiments or calculations which provide detailed rigorous accounts of how intelligent design of any biological system occurred, is that correct?

Behe: That is correct, yes.*

The decision of the court was that “After this searching and careful review of ID as espoused by its proponents, as elaborated upon in submissions to the Court, and as scrutinized over a six week trial, we find that ID is not science and cannot be adjudged a valid, accepted scientific theory as it has failed to publish in peer-reviewed journals, engage in research and testing, and gain acceptance in the scientific community.

In addition, although Wikipedia says the Discovery Institute lists the book under “Peer-Reviewed Scientific Books”, Cambridge UP lists it under Humanities, not science, as part of a series with “a distinctly philosophical character”.
 
Anytime someone tells me that I can understand a nuanced statistical argument with elementary reasoning I know that I am dealing with someone who doesn’t understand that nuanced statistical argument.
If anyone’s interested, while googling for the previous post I found a review of Dembski’s work, it’s the first in this pdf, which explains it a bit and concludes he’s on an obscure road to nowhere.
 
This sounds unlikely. A couple of minutes on Google shows that Cambridge UP has only published one book by Dembski (another is part edited by him). The book, The Design Inference was published in 1998, yet the 2005 Dover trial contains the following exchange:

*Rothschild: And, in fact, there are no peer reviewed articles by anyone advocating for intelligent design supported by pertinent experiments or calculations which provide detailed rigorous accounts of how intelligent design of any biological system occurred, is that correct?

Behe: That is correct, yes.*

The decision of the court was that “After this searching and careful review of ID as espoused by its proponents, as elaborated upon in submissions to the Court, and as scrutinized over a six week trial, we find that ID is not science and cannot be adjudged a valid, accepted scientific theory as it has failed to publish in peer-reviewed journals, engage in research and testing, and gain acceptance in the scientific community.

In addition, although Wikipedia says the Discovery Institute lists the book under “Peer-Reviewed Scientific Books”, Cambridge UP lists it under Humanities, not science, as part of a series with “a distinctly philosophical character”.
If anyone’s interested, while googling for the previous post I found a review of Dembski’s work, it’s the first in this pdf, which explains it a bit and concludes he’s on an obscure road to nowhere.
Thanks for the research. 🙂 It is quite helpful to dismantle the myth about Dembski. I only concentrated on a simple example to show that “improbable” does no lead to “designed”.
 
This sounds unlikely. A couple of minutes on Google shows that Cambridge UP has only published one book by Dembski (another is part edited by him). The book, The Design Inference was published in 1998, yet the 2005 Dover trial contains the following exchange:

*Rothschild: And, in fact, there are no peer reviewed articles by anyone advocating for intelligent design supported by pertinent experiments or calculations which provide detailed rigorous accounts of how intelligent design of any biological system occurred, is that correct?

Behe: That is correct, yes.*

The decision of the court was that “After this searching and careful review of ID as espoused by its proponents, as elaborated upon in submissions to the Court, and as scrutinized over a six week trial, we find that ID is not science and cannot be adjudged a valid, accepted scientific theory as it has failed to publish in peer-reviewed journals, engage in research and testing, and gain acceptance in the scientific community.

In addition, although Wikipedia says the Discovery Institute lists the book under “Peer-Reviewed Scientific Books”, Cambridge UP lists it under Humanities, not science, as part of a series with “a distinctly philosophical character”.
Intelligent design is a different sort of thing from the fine-tuning argument. Dembski’s best arguments are where he applies his argument to the fine-tuning of the universe for life. I do not propose to defend the ID position here.

Serious challenged the notion that Dembski’s ideas were intellectually rigorous, so obviously I presented the most important title where he presents them, which was published with Cambridge and did indeed pass peer review. This suffices.

That Cambridge published it under humanities is not relevant or surprising, since it was published under its studies in probability series.
 
In mathematics there is no need for authorities, actually there are no authorities. I am truly surprised the Cambride Press gave its name to such a book. But editorial errors are also not unheard of.

Dembski simply says that for any event for which is the probability is less than 10[sup]-150[/sup] it is rational to assume an intelligent source and it is irrational to assume random chance. That is his “theorem”. Of course there is no proof to it, such a theory cannot be proven - but it can be disproven. But let’s apply this “theorem” to real life.

In any casino, you will see people playing blackjacks. The mechanics of the game is: “the croupier shuffles 4 decks of cards, and places them into a shoe”. In the shoe there are 208 randomly arranged cards. What is the probability of that particular card sequence? If you understand probability theory then you will know that the number is 1/(208!/(52!)[sup]4[/sup]). Now let’s approximate the number in the divisor (the formula is found here en.wikipedia.org/wiki/Stirling’s_approximation) and the value is n! ~ sqrt(2pin)*(n/e)[sup]n[/sup]. After simplifying we get:

(208/52)[sup]208][/sup] which is 4[sup]208[/sup] and that is 2[sup]416[/sup], which (since 2[sup]10[/sup] is about 10[sup]3[/sup] or 1000) finally will become 10[sup]1248[/sup]. The probability of that particular sequence is less than 10[sup]-1248[/sup], which is MUCH smaller than Dembski’s puny little 10[sup]-150[/sup].

From Dembski’s “theorem” it would follow that is reasonable to assume that the cards in the shoe were “designed”… Of course there is no card-genie in that box, there is only the croupier who did the shuffling.

Now it is not unheard of that croupiers were found cheating. But that is not the point here. Any sequence of cards in the show has an equal probability (less than 10[sup]-1248[/sup]) and according to Dembski’s bogus theorem it is rational to assume that God (or the card genie) personally arranged the cards. There is nothing else to say.
Still refusing to answer any of my examples? Let me be very direct, choose to answer or ignore it at your leisure.

Suppose I played a dozen games of blackjack in a row. (we totally reshuffle the deck after each draw).

I draw blackjack 12 times in a row.

Do you shrug this off by saying that “well gee, any combination of cards is equally improbable, so I guess this isn’t the result of design (or cheating)?”
 
Still refusing to answer any of my examples? Let me be very direct, choose to answer or ignore it at your leisure.

Suppose I played a dozen games of blackjack in a row. (we totally reshuffle the deck after each draw).

I draw blackjack 12 times in a row.
That is not what Dembski’s argument is all about.
Do you shrug this off by saying that “well gee, any combination of cards is equally improbable, so I guess this isn’t the result of design (or cheating)?”
If enough people would be dealing enough hands, it would be mathematically certain that such an occurrence would happen.

In the shoe it most certainly could happen that there are 12 blackjack would be in it, somewhere. It happens quite frequently. It could even be that the frist 12 hands are blackjacks. It is exactly as probable as any other combination of cards. I bet it already did happen.

In rouletle it did happen that “red” came out 20 times in a row. No design, just random event.

What you do not understand is the difference between the a-priori and a-posteriori probability. And of course the “odometer” syndrome. If it “looks” regular, people tend to believe that it was “desinged”.
 
That is not what Dembski’s argument is all about.

.
Then you clearly never read his work, because in the book I cite above, he is explicit that it is not improbability alone that signals design, but “specified complexity.”
If enough people would be dealing enough hands, it would be mathematically certain that such an occurrence would happen.
Ah, the multiverse hypothesis. By proposing this, you seem to be admitting that the chance hypothesis actually is too weak to survive on its own. Excellent.

Of course, this assumes that the multiverse exists, which is a proposition with some absurd consequences and for which no evidence exists. And it is not even clear that a multi-verse would help solve the problem.

Btw, just for fun. Suppose, you are I were playing cards. I won 12 times in a row with blackjack.

Suppose, you actually show good sense and accuse me of cheating. Suppose then that I reply, “No! Wait Serious! I am not cheating, rather there is a multiverse where all possibilities are being actualized. Actually, in one of these, you yourself are indeed winning 12 times in a row!”

Then, to show you that there are no hard feelings, I offer you double or nothing on the next throw. You do take that bet right? 😃 (and again, if you do, can we get together for a drink and a friendly game of cards…)
 
Then you clearly never read his work, because in the book I cite above, he is explicit that it is not improbability alone that signals design, but “specified complexity.”
To use an undefined, but “good sounding” phrase will not help his case.
Ah, the multiverse hypothesis. By proposing this, you seem to be admitting that the chance hypothesis actually is too weak to survive on its own. Excellent.
No multiverse at all. I did not say and do not need that. All I am saying that if the probability phase-space is large enough, then even the most improbable events will happen.
Btw, just for fun. Suppose, you are I were playing cards. I won 12 times in a row with blackjack.

Suppose, you actually show good sense and accuse me of cheating. Suppose then that I reply, “No! Wait Serious! I am not cheating, rather there is a multiverse where all possibilities are being actualized. Actually, in one of these, you yourself are indeed winning 12 times in a row!”

Then, to show you that there are no hard feelings, I offer you double or nothing on the next throw. You do take that bet right? 😃 (and again, if you do, can we get together for a drink and a friendly game of cards…)
You are not allowed to shuffle. A simple card-shuffling device will do. And then we can play that double or nothing, Oh, yes we can. As many times as you wish, or as long as you run out of money. When can we start?
 
To use an undefined, but “good sounding” phrase will not help his case.
That you don’t understand it is beside the point.
No multiverse at all. I did not say and do not need that. All I am saying that if the probability phase-space is large enough, then even the most improbable events will happen.
You said if there are enough draws, then it is not surprising if any combination comes up. This is the multiverse hypothesis.
Originally Posted by danserr View Post
Btw, just for fun. Suppose, you are I were playing cards. I won 12 times in a row with blackjack.
Suppose, you actually show good sense and accuse me of cheating. Suppose then that I reply, “No! Wait Serious! I am not cheating, rather there is a multiverse where all possibilities are being actualized. Actually, in one of these, you yourself are indeed winning 12 times in a row!”
Then, to show you that there are no hard feelings, I offer you double or nothing on the next throw. You do take that bet right? (and again, if you do, can we get together for a drink and a friendly game of cards…)
You are not allowed to shuffle. A simple card-shuffling device will do. And then we can play that double or nothing, Oh, yes we can. As many times as you wish, or as long as you run out of money. When can we start?

Why Serious, I am hurt. It is almost like you don’t trust me. Like, you think the previous 12 hands were not the result of chance after all. Like they may have been the result of, dare I say it… Design!

I wonder why you would think that though, I mean, since any hand is equally improbable, why should me drawing blackjack 12 times in a row make you suspicious?
 
That is not what Dembski’s argument is all about.

If enough people would be dealing enough hands, it would be mathematically certain that such an occurrence would happen.
Is he arguing on the basis of multiple trials? Or is asking about the occurrence of a given outcome given a single trial? (And, in the course of that argument, demonstrating that even if there were a multiplicity of trials, there would still be an insufficient number of them to demonstrate a greater-than-negligible chance of the outcome occurring?)
I bet it already did happen.
Hmm… that’s quite the assumption, don’t you think?
In rouletle it did happen that “red” came out 20 times in a row. No design, just random event.
Again, we’re talking multiple trials. In any case, 20 reds is only slightly less than 2^20, which is 10^6. That’s orders of magnitude smaller than numbers we’re talking about here! To get to an equivalent number to our blackjack example, we’d be talking about something like 1130 reds coming up. I think, at that point, someone would have started asking “is there something about this table that explains things better than ‘well, it could happen, mathematically speaking!’…?”

On the other hand, make your roulette wheel have 10^340 slots, identify one as “win” and the others as “lose”, and we can start talking. (My back-of-an-envelope calcs, if I did them right, put 1-in-10^340 as the odds of the first 16 hands coming up blackjack in a four-deck shoe.)
What you do not understand is the difference between the a-priori and a-posteriori probability.
Right – it seems that the difference here is that the trial has already occurred; we are, in fact, here. Now we calculate the odds of the outcome occurring. The odds are so mind-bogglingly against, that it’s not unreasonable to ask whether there’s something else in the mix. Must there be something else in the mix? Not necessarily. Is the probabilistic argument the most reasonable argument available? That’s precisely what’s in play.

After all, the odds of a “red” coming up in roulette are about 1/2, but the odds of “red” coming up, given that it’s come up 1129 times in a row? Still possible, yet negligibly so.
And of course the “odometer” syndrome. If it “looks” regular, people tend to believe that it was “desinged”.
Hmm… I haven’t heard of this one before…
 
Oh… BTW – just to keep being a math geek…

Dembski proposes 10e-150 as the threshold for crossing from probabilistic analysis to looking for some other reason. In the example of the roulette table, then, that means that, the first 498 times it comes up “red” in a row, you think “it could happen this way…” but with that 499th time comes around, and it’s red again, you start thinking “maybe there’s a better explanation…”!
 
You said if there are enough draws, then it is not surprising if any combination comes up. This is the multiverse hypothesis.
No, it is a Kolmogorov space. Simple mathematics, has nothing to do with the physical universe. Have you studied probability theory?
Why Serious, I am hurt. It is almost like you don’t trust me. Like, you think the previous 12 hands were not the result of chance after all. Like they may have been the result of, dare I say it… Design!

I wonder why you would think that though, I mean, since any hand is equally improbable, why should me drawing blackjack 12 times in a row make you suspicious?
It is not suspicion. There is nothing to be suspicious about - since nothing suspicious has happened. First show me those 12 blackjacks in a row using a card shuffling machine - then and only then we can speak. The universe is not a “conscious” opponent. The proper experiment must emulate reality, and there is no “shuffler” out there. That is what you attempt to show, but you are not allowed to use “dirty pool”.

There is an old saying: the roulette ball has no memory. If it happens that the ball stops on red 20 times in a row, then the probability of then red is still the same. It does not change because of the previous rolls.
 
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