Thursday, October 28, 2010

God Plays Bridge

 
The creationists tell us that anything in biology with a probability of 10-39 or less is impossible [see God Designed My Great-Grandparents].

That's a very tiny number. Let's see just what kind of probabilities we're dealing with.

Imagine four people sitting down to play a hand of bridge. They shuffle the deck and deal out 13 cards to each player. The probability that the particular hand would be dealt is very low because the total number of possible hands is 51!/13! = 53,644,737,765,488,792,839,237,440,000. Let's round this off to a probability of 0.2 × 10-28.

Assuming that there have been at least 100,000,000 bridge players and that they've played at least 2000 hands of bridge, that represents a total of 5 × 1010 separate hands of bridge. The probability that all of these particular hands would have been dealt in a particular time and place is 10-39. That's equivalent to the total number of bacteria and it's the kind of probability that makes creationists think of God.

I wonder if God plays bridge? If he does, I wonder if he ever loses since he can control the deal?1


1. Sounds like a good plot for a Mr. Deity video.

30 comments :

  1. I give an example like this to my statistics class and ask them where the fallacy lay.

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  2. Since there is intelligence involved in playing bridge, let's take an event from the natural world that doesn't involve human intellect. How about, for example, the conformation of the coastline of (mainland) Australia? What are the odds of a given 35877km coastline, or any part of it, having exactly that conformation? Must be utterly infinitesimal - I certainly don't see even a little bit of it repeated exactly on any other coastline on Earth. So I guess plate tectonics and the rest of geology must be due to God, eh?

    But I thought IDers propose that God's intervention was necessary only in the origin and evolution of living things. Why is that, when the rest of the natural sciences show us occurrences just as (if not more) unique and utterly improbable?

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  3. It's not that hard to construct an event with an arbitrarily low probability -- really, as low as you want to go. There are 6 billion people on this planet. Sort them by name alphabetically, then give them each a 10 sided die (with sides 0-9), ask them all to roll it, and jot down the digit next to their name. When you finish writing all the 6 billion digits down, ask yourself what is the probability of having obtained this particular 6 billion digit number out of all the other possible 6 billion digit numbers?

    Of course, the fallacy lies in ignoring the fact that the probability of occurrence of a past event that has already actually occurred is 1, but IDiots and Creationists will probably calculate something along the lines of 1/10^6billion.

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  4. You forgot to mention that the cards in the bridge hands specify what can be played, so they should count as complex specified information

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  5. Here's what I don't get: when IDers talk about some mutation or protein synthesis being absurdly improbable, it seems as though they treat it very linearly, as if only one of these processes would happen at a time. They aren't acknowledging that these kinds of reactions would be happening millions of times, all the time.

    I mean, if we talk about the improbability of RNA synthesis 4 billion years ago, you'd have to take into account that the early oceans would have been filled with the necessary chemicals, and billions upon billions of reactions would have occurred all over the world, which makes a functional byproduct of a reaction (or series of reactions) vastly less improbable – really, I would think, probable to the point of being inevitable.

    At least, that's how I understand it. Perhaps someone with a better understanding of biology can brush me up a bit.

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  6. How many cards are there in a bridge deck?

    Are bridge hands permutations or combinations of cards?

    Are bridge hands in the same game independent of one another?

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  7. Why are you wasting your time with this stuff? If you were actually using the precious remaining time in your life to play bridge, I bet you'd be alot happier.

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  8. The number is correct, but the calculation is not.
    Number of possible hands of bridge is 52!/13!^4. But, I take your point. :)

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  9. Michael M:

    52. Combinations. No.

    What's your point? Do you disagree with the calculated probability? It looks right to me, although I suppose technically, it's the probability of a given deal that consists of four hands.

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  10. Jud says,

    How about, for example, the conformation of the coastline of (mainland) Australia?

    I've always thought that Australia is highly improbable but let's not be ridiculous. Australia doesn't have a coastline. That's why the Captain von Trapp character in Sound of Music was so strange. I've been to Vienna and there's no ocean anywhere near there.

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  11. anonymous says,

    Why are you wasting your time with this stuff? If you were actually using the precious remaining time in your life to play bridge, I bet you'd be a lot happier.

    I did that in first year university with three friends. I just made it into second year with a C, 3D's, and an F. My three friends didn't make it so I had to find something else to do for fun.

    Studying did the trick, and I was a lot happier.

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  12. As a bridge player, and a decent one, I'd like to give a question inspired by Richard Pavlicek (a very good bridge player). Which hand is more probable: QJ42, A32, KT64, 75, or 13 cards of the same suit? Of course, the former is four times as likely as the latter.

    Any probability calculation by a creationist is (to a first approximation) 100% false.

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  13. "Studying did the trick, and I was a lot happier.

    That's great, but what I meant by 'this stuff' is endless religion bashing. Seems to take alot of time for no benefit, other scratching an itch. Might be better not to have the itch in the first place.

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  14. > but IDiots and Creationists will probably calculate something along the lines of 1/10^6 billion.

    Well, why would you think that? This is what is called a straw man argument.

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  15. "He plays an ineffable game of His own devising, which might be compared, from the perspective of any of the other players, to being involved in an obscure and complex version of poker in a pitch-dark room, with blank cards, for infinite stakes, with a Dealer who won't tell you the rules, and who smiles all the time."
    (Sorry. Had to)

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  16. I respond to Professor Larry Moran's "God Plays Bridge" here:

    http://talkbio.blogspot.com/2010/10/giving-both-barrels-two-part-response_29.html

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  17. Now Larry, you know that Bridge is an elitist game that only the extreme left-wing fascist socialist communists play. Creationists play Texas Hold'em dontchaknow (...or Go Fish for the anti-gamblers.)

    Therefore, your example using Bridge is invalid and you are wrong... and a big poopyhead.

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  18. You should also include the odds that each individual card in each bridge hand was played in the exact order it was played.

    That way, you would not have to exaggerate the total number of bridge players in history, which, for such a silly game, can't be more than two or three dozen.

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  19. Jeebus doesn't play dice with the universe... Yhwh and Allah hate gambling - so no way. Krishna loves a good game of dice, and wins bets on horses all the time, I will ask him if he is interested in bridge. Lakshmi the devi of wealth loves gambling, and next weekend - Diwali/Dipawali - the Hindu festival of lights - we are going to be playing poker late into the night.
    Truti

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  20. My point, while fairly minor in the grand scheme of things, was that Larry's calculations were off by many orders of magnitude because:

    1) The number of hands is determined by the number of card combinations not card permutations
    2) Once a particular hand has been dealt, it is no longer available to the other players as a hand.

    The biggest error in Larry's calculations was the substitution of permutations for combinations, which inflates the number of hands by a factor of 38! (or ~5.2*10^44). The other error is that once the first card is dealt, the hands containing that card become in accessible to the other players further reducing the number of accessible hands in the game.

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  21. Here's what bugs me about these sorts of replies to those sorts of arguments (and I don't like the original arguments either, for different reasons):

    Imagine that all you have is one instance of a set of 4 bridge hands. How would you go about determining, just from the hands, if it's more likely that the cards were randomly shuffled or if the deck was stacked by the dealer? After all, the high improbability of any of those hands being dealt is the same in both cases, so what could you use to determine that you should at least consider the possibility that the dealer stacked the deck?

    The creationist/ID/TE argument is aiming at trying to figure out if the deck is stacked. It seems unlikely than the probabilistic games are going to settle it. It might refute an argument that, on its own, just says that the improbability means that it DEFINITELY was stacked, but it clearly doesn't provide any strong evidence against stacking.

    Ultimately, in my opinion, it's far more than improbability that matters in these discussions. And while I do think that a lot of atheists get that and have other arguments, and while I think Larry gets that here, what I think is sometimes missed -- on both sides -- is that improbability is just a small, introductory part of the argument. Something that is improbable is something that we do start to rationally wonder about whether it was intentional as opposed to random. It's then the other arguments that are to carry the day. On both sides.

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  22. @Livingstone Morford:

    Prof. Moran did not quote-mine you, as you allege on your blot. The statement you object to was at most a paraphrase. If you want to argue it was an inaccurate paraphrase, fair enough, but it wasn't a quote mine.

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  23. > but IDiots and Creationists will probably calculate something along the lines of 1/10^6 billion.

    Well, why would you think that? This is what is called a straw man argument.


    Nope, not a strawman. Actual Creationists make these sorts of probability calculations all the time. Here is just one of likely thousands of examples out there:

    http://www.answersingenesis.org/articles/nab2/natural-processes-origin-of-life

    Note how they state the probability of obtaining a polypeptide string of 100 left handed amino acids is the same as flipping a coin and getting 100 heads in a row. This is exactly the same faulty reasoning.

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  24. > andlp: Nope, not a strawman. Actual Creationists make these sorts of probability calculations all the time.

    But the claim was that ID people would *probably* make that mistake. That claim remains to be demonstrated.

    I call this the "Bertrand Russell strawman". He was (so the story goes) riding with a friend down the highway and remarked to his companion, "What is the probability that we would be on this highway on this day and see a car with that license plate? Therefore God must exist!"

    Anyway. The actual ID argument is not like that, and when people make that mistake, it doesn't somehow change the argument.

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  25. In addition to the formula error Anonymous pointed out, there's also an error in now the probabilities escalate for additional hands. Let me take a stab at re-doing the math (and, with luck, not introducing any new errors...)

    The probability of one particular bridge player being dealt 13 specific cards is 1 in 52!/(13!*39!) = 6.35e11 (i.e. 6.35 * 10^11).

    The probability of one particular deal (i.e. 4 hands) is 1 in 5.36e28. Larry's original post has this number correct, but gives the wrong formula for it. Note that this is less than the fourth power of the first probability, because the 4 hands are not independent.

    The probability of two particular deals is 1 in 2.88e57. This is the square of the single-deal probability, because (assuming perfect shuffling) the deals are independent. This is already well past the improbability threshold of 1e-39.

    If 1e8 players play 2e3 hands each (for a total of 5e10 deals), the probability of each of those hands being dealt in a particular order is 1 in 5.36e28^5e10 =roughly 1e1436458239500. That's right, that number has a 13-digit exponent.

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  26. "Anyway. The actual ID argument is not like that, and when people make that mistake, it doesn't somehow change the argument."

    Actually, Lee, yes, the ID argument is exactly like that.

    Why else would they take an extant protein/structure/system and pontificate on and on about with some contrived 'odds' about how improbably that particular extant protein/structure/system is to have come into being 'naturalistically'?

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  27. But the claim was that ID people would *probably* make that mistake. That claim remains to be demonstrated.

    The reasoning employed is EXACTLY the same. If they commit the fallacy in one context but fail to do it in the other, I'll trade the strawman for a special plead.

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  28. Actually, a much simpler example is the order of cards in a 52 card deck. Since there are 52! permutations of card order in a 52 card deck, this means that the odds against any particular order occurring after a shuffle is 1/52! or about 1 chance in 10^-68. Therefore, by the reasoning of the IDiots, every order of cards is impossible and must be the result of divine intervention.

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  29. "if it's more likely that the cards were randomly shuffled or if the deck was stacked by the dealer?"

    I think that's a really good question, probably the only interesting one in the creationist debate.

    In the case of cards - well, casinos employ methods for spotting this sort of thing. And, of course, people out to con casinos don't deal themselves four aces, or whatever, every time because that does begin to look suspicious pretty quickly.

    In the case of evolution ... God could bring all his divine powers to bear to create an illusion of what we observe: atheistic randomness. Again, though, that's basically the same argument that God buried all those dinosaur fossils six thousand years ago to test our faith.

    What would God want the universe to look like? Well, if you accept the basic premise of the question, you have to say 'this'. It ends up as a circular answer.

    And most theistic arguments now seem to be along the lines of - 'yes, but who printed those cards and laid down the rules?', rather than arguing about the hand that was dealt.

    I suppose one place to look would be the mechanism. If God's occasionally dealing from the bottom of the deck to create things like highly improbable proteins ... how is he doing that?

    The creationists always say they want to see 'evolution happening in front of their eyes'. Well, OK, right back at them: let's see the hand of God in laboratory conditions.

    We have a mechanism for evolution, we can look at DNA and say 'OK, this is how it would work', and understand all the processes involved. The only thing we can argue about is 'is that actually happening?' (spoiler: yes). What we don't observe is anything *divine* acting on anything. It's hard to imagine exactly what that would even mean - looking down a microscope and seeing tiny angels rewiring proteins? I'm not trying to be facetious, but I do find it very hard not to be. Even if we don't see God's hands, he should be leaving fingerprints.

    But I think this is a really interesting question. One of the reasons I'm an atheist is that I believe any God worth the name wouldn't be grubbing around fudging a few protein sequences in a way that looks statistically improbable.

    Someone said it elsewhere on this board recently: in the modern world, we understand more about how the world works - wouldn't miracles now be *more* impressive and inexplicable than in the Bible, not just 'one man in hospital got better after he prayed'?

    Even if this protein thing is all true - I don't think it is - it's ... well, it's a bit rubbish. Why muck about with the odds of creating a particular protein sequence when you can just magic up the finished animal?

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  30. > Actually, Lee, yes, the ID argument is exactly like that.
    >
    > Why else would they take an extant protein/structure/system and pontificate on and on about with some contrived 'odds' ...

    Only that's not the ID argument, if you want to have a good representation laid out by a respectable proponent of ID, see Behe's book The Edge of Evolution. He starts with what evolution actually did, and extrapolates from there.

    So this is not computing some contrived probability.

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