Cards, Probabilities and the Anthropic Principle

Pick a Card, Any Card

Let's suppose you go to visit your friend, Bobbie. As you spend a fine evening talking about old times, she pulls out a deck of cards and begins to shuffle it. You note that she is shuffling it thoroughly. She fans the cards out and asks you to pick one. You pick one at random and it turns out to be the jack of clubs. Returning the card to the deck, Bobbie thoroughly shuffles the cards several more times then fans them out and asks you to once again pick a random card. You do so only to find that you have picked ... the jack of clubs. What an interesting coincidence.

You return the card to Bobbie and she repeats the process of shuffling the cards thoroughly. Now, being the third time, you are shocked to find that you have once again picked the jack of clubs. You are probably thinking that this is getting weird. After all, picking the same card twice was pretty incredible, but three times in a row? That's pretty darned unlikely.

When she shuffles the cards annd spreads them out a fourth time, and for a fourth time you pick the jack of clubs, it will probably dawn on you that one of two things must be happening: either you are having one of the most extraordinary coincidences that have ever occurred in the picking of cards, or someone has fixed it (probably Bobbie) so that you will always pick the jack of clubs. If you repeat the process a fifth and sixth time, I would bet that you would have lost all wonder at the fact that you have picked the same jack of clubs six times in a row, and started wondering exactly how Bobbie is pulling off this trick. Is she stacking the deck? Are all of the cards in the deck the same jack of clubs? Certainly you'd believe that the odds of this happening by pure chance are way too high for this to be happening naturally. And you'd be right.

The Increasingly Long Odds

The odds of picking the same face card several times in a row is statistically very low. Starting with a standard deck of 52 cards, the odds of randomly picking any one card is 1 in 52 (or 1/52). What are the odds of picking the same card two times in a row? Using the basic probability equation of multiplying probabilities, the answer would be 1 in 2,704 (roughly .03 percent). Not unreasonable that it could happen, and so you would be justified in concluding that picking the same card twice in a row is uncommon, but not unprecedented.

But from there, it begins to become quite dicey. The odds of picking the same card three times in a row is 1 in 104,608 (which is a minuscule .0009 percent). By the fourth time the same card has been selected in a row, the probability has shrunk to only 1 in 7,311,616. The fifth time that jack of clubs appears, you are now experiencing an event that should naturally occur only 1 in 380,204,032 times. The sixth time, the probabilities have now risen to an astronomically small 1 in 19,770,609,664 which means that this should occur only .000000000055 percent of the time. Assuming you could draw six cards every minute without stopping, it would (speaking probability-wise) take roughly 37,615 years to have draw the same card six times in a row.

I don't know about you, but I would be more likely to assume that the game is fixed.

Obviously It's Natural -- You See it Happening

However, some might see the same card turn up six times in a row and comment that of course it happened naturally because obviously it happened. In other words, because I see it happening before my eyes is no reason to assume that the fix is in. After all, this one time that you pick the cards could be that 1 in 19,770,609,664th time -- after all, the one time has to happen eventually. Therefore, that person would argue, it is wrong to assume that there is some type of fix involved even in those long odds.

Yeah, it could be that you happened to have that once in 37,000 year event occur to you. But you already know that it isn't likely. Besides, is it really the case that simply because I happened to be here to see it means that it must not be fixed but must be natural? Seems like kind of unusual reasoning to me.

Yet, this is precisely the type of argument that some skeptics make when confronted with the "just right" qualities of the universe. After all, some scientists (I suspect most) would agree that the universe seems particularly fitted for human life. Consider the usually theistically unfriendly Discover Magazine in an article entitled Science's Alternative to an Intelligent Creator: the Multiverse Theory:

Physicists don’t like coincidences. They like even less the notion that life is somehow central to the universe, and yet recent discoveries are forcing them to confront that very idea. Life, it seems, is not an incidental component of the universe, burped up out of a random chemical brew on a lonely planet to endure for a few fleeting ticks of the cosmic clock. In some strange sense, it appears that we are not adapted to the universe; the universe is adapted to us.

So, how do skeptics explain this fact? For some, the answer is not to answer but simply to observe the fact as proof of the fact. They pull the old, "it's not surprising that the universe should appear finely balanced to support life because if it didn't you and I wouldn't be here to observe it." An example of this type of argument is found in the comment to a typical atheist blog entitled Saint Gasoline: The Anthropic Principle by "unbeliever" in which he says,

There’s nothing especially surprising in a flipped coin landing on “heads”, a thousand times in a row — if the only time you observe the result of a coin toss is when it lands on heads.

In other words, if the physical constants WEREN’T just right for the development of intelligent life, we wouldn’t be here to notice it. So the fact that, when we ARE here to notice it, the constants ARE just right, isn’t really all that remarkable…

Swinburne's Card-Shuffling Thought Experiment

Well, Richard Swinburne has set up a thought experiment that responds to unbeliever's comment that features not just six identical cards being selected but ten cards being selected from shuffling machines. In The Argument From Design Swinburne posits the following:

Suppose that a madman kidnaps a victim and shuts him in a room with a card-shuffling machine. The machine shuffles ten decks of cards simultaneously and then draws a card from each deck and exhibits simultaneously the ten cards. The kidnapper tells the victim that he will shortly set the machine to work and it will exhibit its first draw, but that unless the draw consists of an ace of hearts from each deck, the machine will simultaneously set off an explosion which will kill the victim, in consequence of which he will not see which cards the machine drew. The machine is then set to work, and to the amazement and relief of the victim the machine exhibits an ace of hearts drawn from each deck. The victim thinks that this extraordinary fact needs an explanation in terms of the machine having been rigged in some way. But the kidnapper, who now reappears, casts doubt on this suggestion. 'It is hardly surprising', he says, 'that the machine draws only aces of hearts. You could not possibly see anything else. For you would not be here to see anything at all, if any other cards had been drawn.'

Keep in mind that the odds of all ten machines drawing identical cards which is approximately 1 in 145 sextillion chances. The odds are so completely and utterly impossible that the fact that it could have happened is hardly the most likely answer. It is perfectly reasonable to ask whether the results were fixed since the odds of a fix being in is much, much, much smaller than the odds of the ten card shuffling machines picking the same pre-determined ten cards naturally. Swinburne concludes his card-shuffling discussion making this same point:

The fact that this peculiar order is a necessary condition of the draw being perceived at all makes what is perceived no less extraordinary and in need of explanation. The teleologist's starting-point is not that we perceive order rather than disorder, but that order rather than disorder is there. Maybe only if order is there can we know what is there, but that makes what is there no less extraordinary and in need of explanation.

Peter Williams, in his fine, on-line critique of Richard Dawkins' arguments concerning the Anthropic Principle entitled Who's Afraid of the Big, Bad Wolf?, comments further on Swinburne's card-shuffling thought experiment:

The fact that an event is a pre-condition of its being observed does not explain the occurrence of the event, or negate the obvious fact that 'the victim is right and the kidnapper is wrong' about design being the best explanation for the event described (which Swinburne offers as being a parallel to the fine-tuning of the cosmos).

Our Finely-Tuned Planet

Exactly how close is the card-shuffling thought-experiment to the fine-tuning of the universe that scientists observe? Our friend Rich Deem at Evidence for God from Science, a scientist himself (holding a M.S. in Microbiology from CSULA) has put together a list of probabilities of seventy-five finely-tuned parameters occurring so that a particular planet could support life. The chart, entitled An Estimate of the Probability for Attaining the Necessary Parameters for Life Support, after running through the necessary parameters, concludes:

By putting together probabilities for each of these design features occurring by chance, we can calculate the probability of the existence of a planet like Earth. This probability is 1 chance in 10 [to the 99th]. Since there are estimated to be a maximum of only 10 [to the 23rd] planets in the universe (10 planets/star, see note below), by chance there shouldn't be any planets capable of supporting life in the universe. Our existence suggests divine intervention and design. The design and care with which the laws of physics, the universe, our galaxy, our solar system, and the planet Earth were crafted suggests that God is caring and loving. He put in a lot of time in the design and creation of the universe so that we would have a nice place to live for such a short period of time.

Now, this post began by noting what would be our probable reaction to having the same jack of clubs chosen out of a deck only six times in a row. While I cannot speak for everyone, I certainly would be suspicious that the deck was fixed by the time the jack of clubs was drawn a fourth time in a row. The extra two times (the fifth and sixth consecutive draws) only served to cement the suspicions that would have arisen prior to that time. But the odds in Swinburne's thought experiment are much longer than the mere six cards that I used. Swinburne's card shuffling machine would result in a probability of 1 x 10 to the 16th power (if I have done my math correctly). The convergence of the 75 factors posted on the Evidence from God chart is 1 x 10 to the 99th power. That's an additional 73 zeros at the end of the number beyond the card shuffling example.

Don't We Need To Know Who The Designer Is Before Assuming Design?

Of course, the skeptic can always point out that we know that there is someone in my example who can fix the cards (as Michael Shermer did on his debate with Greg Koukl on Hugh Hewitt earlier today). Bobbie could be dealing the cards from under the deck in my example, and someone could have monkeyed with the machines in the case of the Swinburne example. What certainty do we have that there is someone who could monkey with the universe? Without knowing for certain that such a person exists, we are left with the ideal that the convergence of the 75 factors happened naturally as the best explanation.

I think that is a decent argument. However, I think that there are two things to say in response. First, while the debate rages and not everyone accepts the fact of the existence of such a being who could set up the system to support life, a majority of people in the world do not find this a particularly difficult question. They believe that God, a god or gods exist, and that God, a god or gods would have the ability to set the parameters of creation. They believe this for many different reasons. It seems to me that the person who is going against the vast majority on this issue is the one who bears the burden of proving that God, a god or gods does/do not exist or could not, in fact, have set the parameters.

Second, as the Discovery article makes clear the universe seems designed for us. And it certainly isn't wrong to conclude that design exists based upon the evidence. If we weren't able to look at something and see that it is designed there would be no science of anthropology. For that matter, efforts to break what sounds to be random code (both in war and in connection with the SETI project) would be considered wastes of time. Moreover, we don't have to identify the designer to recognize design. An anthropologist does not have to know prior to determining that a chipped bit of rock that looks like an arrowhead is a created object exactly who the creator might be. That can be determined later. Science is satisfied when the anthropologist looks at the arrowhead and sees evidence that the rock was intentionally shaped to have a purpose, i.e., to act as an arrow. Likewise, a person breaking a coded Morse code message does not have to know who sent the message (and may not even know at the time that she starts to evaluate the various beeps that it really was a message rather than just background noise) to recognize that there is a designed pattern in the noise. Exactly who sent the message can be determined later. The same obviously holds for the SETI alien signal hunters who not only don't know who would send a message, but don't know for certain that a sender is even out there. To give a slight variation to what Greg Koukl said in the debate, one does not need to know that a shoe has been made with a particular tread to recognize that a footprint in the sand is the result of a shoe landing on the sand with a particular tread. Exactly who (or what) stepped on the sand can be determined later.


In sum, if you find it difficult to believe that someone can draw six cards in a row without a fix being in, then you understand the problems presented for skeptics from the Anthropic Principle. The fact that the universe appears designed (or delicately balanced) to support life is a reality that is not removed by noting that it has to be that way or we wouldn't be here to notice. Finally, there is no reason that we have to identify the designer behind the design before recognizing the design.


David said…
Loftus: I responded to this. See what you think.

I think that once again you have missed the point. Your response is not an unexpected reaction to the original argument, that is, the claim that the universe is apparently rigged; Swinburne's kidnapping example is an answer to that objection, but you simply repeat what was an objection to the original claim, thus indicating you simply did not understand the example at all. The point is that there needs to be some explanation for why the universe is the way it is, even if we weren't here to observe it. Your reply that "it's just statistics" seems to be admitting that on the atheistic view, there is no reason, stuff "just is" — in other words, it's an anti-intellectual view that denies logical explanation. If you're trying to tell me that atheism is illogical, then OK, you've convinced me!

What you haven't done is explain the universe even in a way comparable to random card deals. We know how and why cards can show up a certain way; it's simple physics, and thus there is an excellent explanation for why any hand of cards came out a certain way. (We usually don't have enough details to calculate the outcome of a deal in advance, but there's nothing magical going on, and the basic physics behind picking up a card and moving it are well understood.) You have not provided the slightest evidence for how to "calculate" the universe's being the way it is, nor even presented a hypothetical theory as to why its nature should be thus statistically-driven. So trying to say that it's no different from picking ten cards is baseless equivocation.

If you really think it doesn't matter and any statistically-likely outcome is as good as any other, why don't you put your money where your mouth is? I'll shuffle a deck of ordinary cards and deal off the top four cards, ten times in a row. If each time, the cards come up four aces, hearts/diamonds/clubs/spades, in that exact order, then you will pay me your house or your income for the next 10 years. If not, I'll pay you $10,000 cash. The odds are far, far better in your favour than Swinburne's example, so if you really believed what you're saying about the odds, you'd be foolish not to accept my terms. Do we have a deal? I'll start shuffling now, and as soon as you accept, I'll post what the results were.
John W. Loftus said…
David, the odds that I posted exactly what I said here at the time I did and you responded using the exact words you did at the time you did are staggering from the perspective of 500 years ago, and thus quite literally impossible from an earlier perspective. But it happened. This is what these types of arguments fail to understand. The odds for anything happening are quite literally impossible and yet events happen all of the time. One cannot punt to God as an explanation for why something rather than something else happens given these facts.

This discussion is endless though, and I'm involved with too many of them to respond further at this time.

David said…
Loftus: The odds for anything happening are quite literally impossible and yet events happen all of the time.

What?? If something was impossible then it WOULDN'T happen. That's what "impossible" means. Either you don't know that(!) or you don't know what "literally" means. Or maybe you just don't understand "odds".

One cannot punt to God as an explanation for why something rather than something else happens given these facts.

You haven't given any facts. (And obviously one can appeal to God as an explanation — there's your problem with "impossibility" again!) You haven't even given any reason why one shouldn't appeal to God. Suppose some act of God actually is the true explanation for some event. Surely in that case, we ought to explain it accordingly. You have not come up with any logical contradiction in the hypothesis that God created the universe to be this way, nor have you come up with an alternative.

This discussion is endless though, and I'm involved with too many of them to respond further at this time.

Uh-huh. I notice you didn't even take me up on my bet. Since according to what you just said it would be "literally impossible" for you to lose, then either you don't like having money [you can send me yours even without the bet!], or else you recognize that your objection holds no water.

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