Specification vs Likelihood revisited
Several people have been kind enough to comment on my essay on this subject on talk.reason (http://www.talkreason.org/articles/likely.cfm).
I would like to respond to two or three comments here.
1. First, a correction to simple error of fact. Thanks to Rob Igo for pointing this out. On the first page I wrote that the probability of a Royal Flush given a random deal is 1 in 2.5 million. This is the actually the probability of a Royal Flush in a given suit. The probability of a Royal Flush in any suit is four times higher – about 1 in 650,000. I have corrected the essay on talk.reason. It makes no difference to logic of the argument or the rest of the essay.
2. There have been some comments to the effect that a single Royal Flush is not a good example as the probability is not nearly low enough. When the ID community are talking about low probabilities they mean probabilities in the order of 1 in 10^100 or even lower (i.e. about 25 Royal Flushes in the same suit in a row).
I cannot see the relevance of this and can only think I was not writing clearly enough. As I say on the first page, I would dismiss the possibility that this was a random deal if it was a Royal Flush. I would be even more prepared to dismiss a random deal if it were 25 Royal Flushes in a row. The essay does not challenge this conclusion. It seeks to understand why we dismiss a random deal under these circumstances given that the observed outcome is no more improbable than any other sequence of hands. Dembski tries to account for it via specification which turns out to be quite a complicated and difficult thing to define and yet has no justification. I am pointing out that comparison of likelihoods is an established alternative with a clear justification.
Finally some comments from Salvador (I am afraid I don't know his surname):
Mark,
See my post where I state that information poor stochastic processes by definition are incompatible with highly specified events (information rich).
http://www.uncommondescent.com/index.php/archives/1285#comment-47298
I encourage you to ponder why this should be evidently true.
Salvador
Comment by scordova — July 10, 2006 @ 1:30 am
I am afraid I don’t find this evidently true and the thread that Salvador points to throws no light on this. I think it amounts to saying that stochastic processes which are not based on recognisable patterns are unlikely to produce outcomes with recognisable patterns. This may well be true but such processes are unlikely to produce any given outcome - whether the outcome corresponds to a recognisable pattern or not. This seems to be little more than a restatement of the problem the essay is trying to solve.
Salvador also wrote (starting by quoting something I wrote)
“However improbable that outcome, any other set of three or fifty hands is equally improbable”
True, but write down a specification of an exact hand. It should have the probability of a
Royal flush in spades = 1 / [ 52! / (5! (52-5)!) ]
number of bits is log2[ 52! / (5! (52-5)!) ]
Have someone completely shuffle the cards, and then deal them to you. What do you think the chances are your specification will be hit by a random shuffle?
ANY specification works as long as it is detachable and improbable.
Specification is important. How could one possibly not use specification in a copyright infringement suit (which as valid instance of the EF)?
Again I find this comment confusing. I am not denying that the chances of a Royal Flush in spades or any other given hand is very low.
He continues:
Finally, your critique obfuscated Dembski’s work rather than clarifying it. Your treatment of a no-aces hand was totally off-base.
What Dembski said:
NFL page 78:
Finally, in placing targets on a wall, it makes no sense to place targets within targets if hitting any target yields the same prize. If one target is included within another target and if all that is at issue is whether some target was hit, then all that matters is the biggest target. The small ones that sit inside bigger ones are, in that case, merely along for the ride.
For example, the spade royal flush is part of the class of royal flush. If our target of interest is any royal flush then hitting a spades royal flush is a sufficient but not necessary condition for getting a royal flush. Thus one does not have to explicitly calculate the odds of a spades royal flush, but merely the simpler class of royal flush. If a spades royal flush appears, one still has at least the surprisal value of a royal flush, and if ones detection threshhold is royal flush, then a spades royal flush(if that’s more special to you) is merely icing on the cake.
The odds of a royal flush target being hit are:
Royal flush = 4 / [ 52! / (5! (52-5)!) ]
number of bits is log2[ [ 52! / (5! (52-5)!) ] / 4 ]
When you started talking about no-ace hands, your description of Dembski’s ideas became Flawed Utterly Beyond All Recognition (FUBAR). What reason is there consider no-ace hands? The probability of that is huge compared to royal flushes. You were deliberately choosing specifications in that case which would not be very helpful in eliminating chance explanations, and thus your treatment of the matter was flawed.
Again I think I must be guilty of writing unclearly. I use the example of “hands with no aces” simply to illustrate that the definition of specification changes from page 18 to page 19 of Dembski’s paper. The definition on page 18 would include such a hand as part of the specificational resources of a Royal Flush. The definition on page 19 would not. I accept the definition on page 19 as being the one that Dembski wishes to use – so it is not an issue.
I hope this clarifies some issues.
I would like to respond to two or three comments here.
1. First, a correction to simple error of fact. Thanks to Rob Igo for pointing this out. On the first page I wrote that the probability of a Royal Flush given a random deal is 1 in 2.5 million. This is the actually the probability of a Royal Flush in a given suit. The probability of a Royal Flush in any suit is four times higher – about 1 in 650,000. I have corrected the essay on talk.reason. It makes no difference to logic of the argument or the rest of the essay.
2. There have been some comments to the effect that a single Royal Flush is not a good example as the probability is not nearly low enough. When the ID community are talking about low probabilities they mean probabilities in the order of 1 in 10^100 or even lower (i.e. about 25 Royal Flushes in the same suit in a row).
I cannot see the relevance of this and can only think I was not writing clearly enough. As I say on the first page, I would dismiss the possibility that this was a random deal if it was a Royal Flush. I would be even more prepared to dismiss a random deal if it were 25 Royal Flushes in a row. The essay does not challenge this conclusion. It seeks to understand why we dismiss a random deal under these circumstances given that the observed outcome is no more improbable than any other sequence of hands. Dembski tries to account for it via specification which turns out to be quite a complicated and difficult thing to define and yet has no justification. I am pointing out that comparison of likelihoods is an established alternative with a clear justification.
Finally some comments from Salvador (I am afraid I don't know his surname):
Mark,
See my post where I state that information poor stochastic processes by definition are incompatible with highly specified events (information rich).
http://www.uncommondescent.com/index.php/archives/1285#comment-47298
I encourage you to ponder why this should be evidently true.
Salvador
Comment by scordova — July 10, 2006 @ 1:30 am
I am afraid I don’t find this evidently true and the thread that Salvador points to throws no light on this. I think it amounts to saying that stochastic processes which are not based on recognisable patterns are unlikely to produce outcomes with recognisable patterns. This may well be true but such processes are unlikely to produce any given outcome - whether the outcome corresponds to a recognisable pattern or not. This seems to be little more than a restatement of the problem the essay is trying to solve.
Salvador also wrote (starting by quoting something I wrote)
“However improbable that outcome, any other set of three or fifty hands is equally improbable”
True, but write down a specification of an exact hand. It should have the probability of a
Royal flush in spades = 1 / [ 52! / (5! (52-5)!) ]
number of bits is log2[ 52! / (5! (52-5)!) ]
Have someone completely shuffle the cards, and then deal them to you. What do you think the chances are your specification will be hit by a random shuffle?
ANY specification works as long as it is detachable and improbable.
Specification is important. How could one possibly not use specification in a copyright infringement suit (which as valid instance of the EF)?
Again I find this comment confusing. I am not denying that the chances of a Royal Flush in spades or any other given hand is very low.
He continues:
Finally, your critique obfuscated Dembski’s work rather than clarifying it. Your treatment of a no-aces hand was totally off-base.
What Dembski said:
NFL page 78:
Finally, in placing targets on a wall, it makes no sense to place targets within targets if hitting any target yields the same prize. If one target is included within another target and if all that is at issue is whether some target was hit, then all that matters is the biggest target. The small ones that sit inside bigger ones are, in that case, merely along for the ride.
For example, the spade royal flush is part of the class of royal flush. If our target of interest is any royal flush then hitting a spades royal flush is a sufficient but not necessary condition for getting a royal flush. Thus one does not have to explicitly calculate the odds of a spades royal flush, but merely the simpler class of royal flush. If a spades royal flush appears, one still has at least the surprisal value of a royal flush, and if ones detection threshhold is royal flush, then a spades royal flush(if that’s more special to you) is merely icing on the cake.
The odds of a royal flush target being hit are:
Royal flush = 4 / [ 52! / (5! (52-5)!) ]
number of bits is log2[ [ 52! / (5! (52-5)!) ] / 4 ]
When you started talking about no-ace hands, your description of Dembski’s ideas became Flawed Utterly Beyond All Recognition (FUBAR). What reason is there consider no-ace hands? The probability of that is huge compared to royal flushes. You were deliberately choosing specifications in that case which would not be very helpful in eliminating chance explanations, and thus your treatment of the matter was flawed.
Again I think I must be guilty of writing unclearly. I use the example of “hands with no aces” simply to illustrate that the definition of specification changes from page 18 to page 19 of Dembski’s paper. The definition on page 18 would include such a hand as part of the specificational resources of a Royal Flush. The definition on page 19 would not. I accept the definition on page 19 as being the one that Dembski wishes to use – so it is not an issue.
I hope this clarifies some issues.
posted by Mark Frank at 8:32 am
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