Low Probability is Only Half of Specified Complexity
| October 31, 2007 | Posted by Barry Arrington under Intelligent Design |
In a prior post the order of a deck of cards was used as an example of specified complexity. If a deck is shuffled and it results in all of the cards being ordered by rank and suit, one can infer design. One commenter objected to this reasoning on the grounds that the specified order is no more improbable than any other order of cards (about 1 in 10^68). In other words, the probably of every deck order is about 1 in 10^68, so why should we infer something special about this deck order simply because it has a low probability.
Well, last night at my friendly poker game I decided to test this theory. We were playing five card poker with no draws after the deal. On the first hand I delt myself a royal flush in spades. Eyebrows were raised, but no one objected. On the second hand I delt myself a royal flush in spades, as well as every hand all the way through the 13th.
When my friends objected I said, “Lookit, your intuition has led you astray. You are infering design — that is to say that I’m cheating — simply on the basis of the low probability of this sequence of events. But don’t you understand that the odds of me receiving 13 royal flushes in spades in a row is exactly the same as me receiving any other 13 hands. ” In a rather didactic tone of voice I continued, “Let me explain. In the game we are playing there are 2,598,960 possible hands. The odds of receiving a straight flush in spades is therefore 1 in 2,598,960. But don’t you see, the odds of receiving ANY hand are exactly the same, 1 in 2,598,960. And the odds of a series of events is simply the product of the odds of all of the events. Therefore the odds of receiving 13 royal flushes in spades in a row is about 2.74^-71. But, and here’s the clincher, the odds of receiving ANY series of 13 hands is exactly the same, 2.74^-71. So there, pay up and kwicher whinin’.”
Unfortunately for me, one of my friends actually understands the theory of specified complexity, and right about this time this buttinski speaks up and says, “Nice analysis, but you are forgetting one thing. Low probability is only half of what you need for a design inference. You have completely skipped an analysis of the other half – i.e. [don't you just hate it when people use "i.e." in spoken language] A SPECIFICATION.”
“Waddaya mean, Mr. Smarty Pants,” I replied. “My logic is unassailable. ” “Not so fast,” he said. “Let me explain. There are two types of complex patterns, those that warrant a design inference (we call this a ‘specification’ and those that do not (which we call a ‘fabrication’). The difference between a specification and a fabrication is the descriptive complexity of the underlying patterns [see Professor Sewell's paper linked to his post below for a more detailed explanation of this]. A specification has a very simple description, in our case ’13 royal flushes in spades in a row.’ A fabrication has a very complex description. For example, another 13 hand sequence could be described as ’1 pair; 3 of a kind; no pair; no pair; 2 pair; straight; no pair; full house; no pair; 2 pair; 1 pair; 1 pair; flush.’ In summary, BarryA, our fellow players’ intuition has not led them astray. Not only is the series of hands you delt yourself massively improbable, it is also clearly a specification. A design inference is not only warranted, it is compelled. I infer you are a no good, four flushin’, egg sucking mule of a cheater.” He then turned to one of the other players and said, “Get a rope.” Then I woke up.
69 Responses to Low Probability is Only Half of Specified Complexity
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Really weird error message, folks . . .
Ok kairosfocus, I’m not sure how it helps, but here you go:
“Your computer will become self-aware after Windows restarts. Please disconnect it from the network.”
If you need a weirder one, let me know.
DaveScot said:
You have no way of knowing that the first deck is randomly ordered, or that second deck isn’t, although that’s certainly the way to bet. Therefore, in order to conclude design, you must rely on facts not in evidence.
If a phenomenon is the result of random action, the fact that the odds against it are one in a gazillion doesn’t mean that it can’t happen in the first opportunity. In fact, randomness is defined by the idea that the phenomenon can occur on any opportunity, because in order for something to be random, each possible outcome must have an equal chance of occurring on each opportunity.
All of these arguments from probability seem to hinge on the mistaken idea that if the odds against something happening are a gazillion to one, we’re going to have to wait through a gazillion opportunities for it to happen.
Mickey:
You asked:
“Now a question for you: Shuffle a deck of cards throroughly, then note the order. Now keep shuffling and noting the order. How long do you believe it will be before the original order is encountered again?”
As I am neither a mathematician nor a good card player, I have looked for the answer on the internet. I attach here a very good treament of the question, from the site of a guy whose name is matthew weathers (you can look at it directly at matthewweathers.com):
“Shuffling Cards
Every time you shuffle a deck of playing cards, it’s likely that you have come up with an ordering of cards that is unique in human history. For example, I shuffled a deck of cards this afternoon, and my friend Adam split the deck, and this is the order that the cards came out it.
How many different orders are there?
There are 52 cards in a deck of cards. Imagine an “ordering of cards” as 52 empty spots to be filled:
How many different possibilities are there for what could go in the first spot? The answer is 52 – any of the 52 cards could go there. What about the second spot? Now that you’ve already chosen a card for the first spot, there are only 51 cards left, so there are only 51 different possibilities for the second spot. And for the third spot, we only have 50 choices.
If we stop there, and just fill up the first three spots, that’s like asking how many different possibilites there are for dealing three cards in order.
How many different possible combinations are there for three cards in order? We just multiply how many possibilities there were for the first position (52) with the possibilities for the second position (51) with the possibilities for the third position (50). So there are 52 • 51 • 50 = 132600 different possibilites for three cards in order.
What about a whole deck? We just multiply the possibilities for each of the 52 positions, which is 52 • 51 • 50 • 49 • 48 • 47 • 46 • 45 • 44 • 43 • 42 • 41 • 40 • 39 • 38 • 37 • 36 • 35 • 34 • 33 • 32 • 31 • 30 • 29 • 28 • 27 • 26 • 25 • 24 • 23 • 22 • 21 • 20 • 19 • 18 • 17 • 16 • 15 • 14 • 13 • 12 • 11 • 10 • 9 • 8 • 7 • 6 • 5 • 4 • 3 • 2 • 1. A mathematical way of representing all those numbers multiplied together is called the factorial (See description on MathWorld), so we could write this as 52!, which means the same thing. When you multiply all those numbers together, you get 80658175170943878571660636856403766975289505440883277824000000000000. That number is 68 digits long. We can round off and write it like this: 8.0658X1068.
How many times have cards been shuffled in human history?
That’s an impossible number to know. So let’s overestimate. Currently, there are between 6 and 7 billion people in the world. Also, the modern deck of 52 playing cards has been around since 1300 A.D. probably. If we assume that 7 billion people have been shuffling cards once a second for the past 700 years, that will be way more than the actual number of times cards have been shuffled. 700 years is 255675 days (plus or minus a couple for leap year centuries), which is 22090320000 seconds. Now, if 7000000000 people had been shuffling cards once a second for 22090320000 seconds, they would have come up with 7000000000 • 22090320000 different combinations, or orderings of cards. When you multiply those numbers together you get 154632240000000000000, or rounding off, 1.546X1023.
So, it’s safe to say that in human history, playing cards have been shuffled in less than 1.546X1023 different orders.
Is this order unique in human history?
Probably so. When I shuffled the cards this afternoon, and came up with the order you see in the picture, that is one of 8.0658X1068 different possible orders that cards can be in. However, in the past 700 years since playing cards were invented, cards have been shuffled less than 1.546X1023 times. So the chances that one of those times they got shuffled into the same exact order you see here are less than 1 in 100000000000000000000000000000000000000000000 (1 in 1044).
At what point do you say something is impossible? If the chances are 1 in 1000? 1 in a million?1 in ten trillion?1 in 1 in 1044? In the movie Dumb and Dumber, Lloyd asks Mary what the chances are of the two of them getting together. She replies “1 in a million.” He responds, “so you’re saying there’s a chance?!”
So… if you think there’s a chance that maybe, just maybe somebody, somewhere, at some time may have shuffled a deck of cards just like this ordering you see here, then you’re like Lloyd Christmas in the movie.”
So, you see, the answer to your question: “How long do you believe it will be before the original order is encountered again?” is: practically forever, in realistic terms it will never happen.
The example of the deck of cards is not perfect for DNA and protein information, but gives a good idea of the order of magnitude of the improbability. The deck of cards is a factorial problem, because once you have assigned a card, the number of the remaining possibilities is reduced by one. For proteins, each place can be occupied by any of the 20 aminoacids, with the possibility of repetition. For a 52 aminoacid protein, the combinations are 1:20^52, that is about 1:4*10^67. We are in the same order of magnitude of the deck of cards. But a 52 aminoacids protein is definitely a very small protein.
Besides, the miracle of such an improbability for proteins should have happened not once, but billions of times, each time a new protein is formed. And don’t tell me that the single steps are selected, because that’s simply impossible: each single aminoacid mutation can never bring new function and, as Behe as clearly shown, if more than 2 or 3 aminoacid mutations are necessary, that event will practically never happen.
So, I really can’t understand your last statement:
“All of these arguments from probability seem to hinge on the mistaken idea that if the odds against something happening are a gazillion to one, we’re going to have to wait through a gazillion opportunities for it to happen”
Why is the idea mistaken? If the odds are a gazillion to one, you will indeed have to wait through (approximately) a gazillion opportunities, and if I understand well the meaning of gazillion, you will have to be really patient!
And remember, that’s not happened once, it’s happened a gazillion times, for each new protein. So, you will have to wait a gazillion gazillion times. Good luck…
Did anyone bother to look at the link I posted regarding built-in instructions above with nano-particles and there thoughts how OOL possibly started like that?
I related it to the cards due to the design of suits and numbers.
But, the selection process is external for cards. Whereas the link I posted they inserted instructions into the process. Essentially, this is teleological insertions.
I believe what this shows is that DNA can no more align itself for meaningfult expression thru proteins than playing cards could by themselves. The Blueprint is both imprinted and teleological.
It takes an intelligent selection process, not a blind one prior to any bet being made on the hand.
I think they’re proving the case for ID more so in these experiments.
I thought it significant for ID.
Specification is targeted outcomes for selection processes. Nothing is random in the nano-experiments, neither is anything random in card choices. For the cards to do what Mickey “I think” would like them to do, they would in turn have to have pre-built instructions just like the nanobots to align by suit and number.
Anyone?
Mickey B:
I think you are missing the point that most of our knowledge is probabilistic to some extent or other. That is, absolute proof beyond all dispute is a mirage — even in Mathematics, post Godel.
What we deal with on scientific knowledge is revisable inference to best explanation, and the objection that something utterly improbable just may happen by accident is not the prudent way to bet in such an explanation, once it has crossed the explanatory filters two-pronged test. [The probabilities we are dealing with are comparable to or lower than those that every oxygen molecule in your room could at random rush to one end, causing you to asphyxiate; something you don't usually worry about I suspect, and BTW, on pretty much the same statistical mechanical grounds, as I discuss in the appendix A, in the always linked. In a nutshell, the statistical weight of the mixed macrostate is so much higher than that of the clumped one, that we would not expect that to happen just once at random in the history of the observed cosmos.]
Note, too, that in EVERY case where we directly observe the causal story, CSI is produced by agency.
To see what lies under it, read my always linked, Appendix A section 6.
The objections I saw in 64 above strike me as getting into the territory of selective hyperskepticism, which is self-refuting.
GEM of TKI
MickeyBitsko is no longer with us.
Hi Gpuccio — (great comments BTW)
Ok I’ll bite.
If on *exceedingly* rare occasions a random shuffling of numbers produces a long string of say, three “3333333333,” the “meaning” and “order” apparent here is just an illusion. Randomness knows no value (“3″ is a numeric value) and each “3″ is but an *independent*, fortuitous event, devoid of any connection to any other “3″ (which is yet another independent fortuitous event).
*Minds,* however perceive “whole-isticaly” (they see the whole string in the “mind’s eye”), and subsequently recognize *connections* between valued events and typically generate non-fortuitous, connected, value laden systems and sequences –”archipelagos” (thanks karios) of real order and real function in a great ocean of disorder/disfunction.
Post Mickey response:
Mickey wrote:
Design inferrence is not ciruclar like that. Even if one inferred specification, the beginning question, “How do you know it’s very complex? It’s designed.”, is false. Example: Imagine a single dot on a blank sheet of paper. This is very simple. However, it was designed as art by a person. It almost certainly would not have been ascribed to be an intelligent made design without knowledge of the intent behind it’s origin.