# Re: Another tedious hypothetical

```rmiller wrote:

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At 02:45 PM 6/7/2005, Jesse Mazer wrote:
(snip)

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Of course in this example Feynman did not anticipate in advance what licence plate he'd see, but the kind of "hindsight bias" you are engaging in can be shown with another example. Suppose you pick 100 random words out of a dictionary, and then notice that the list contains the words "sun", "also", and "rises"...as it so happens, that particular 3-word "gestalt" is also part of the title of a famous book, "the sun also rises" by Hemingway. Is this evidence that Hemingway was able to anticipate the results of your word-selection through ESP? Would it be fair to test for ESP by calculating the probability that someone would title a book with the exact 3-word gestalt "sun, also, rises"? No, because this would be tailoring the choice of gestalt to Hemingway's book in order to make it seem more unlikely, in fact there are 970,200 possible 3-word gestalts you could pick out of a list of 100 possible words, so the probability that a book published earlier would contain *any* of these gestalts is a lot higher than the probability it would contain the precise gestalt "sun, also, rises". Selecting a precise target gestalt on the basis of the fact that you already know there's a book/story containing that gestalt is an example of hindsight bias--in the Heinlein example, you wouldn't have chosen the precise gestalt of Szilard/lens/beryllium/uranium/bomb from a long list of words associated with the Manhattan Project if you didn't already know about Heinlein's story.
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RM wrote:
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```In two words: Conclusions first.
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Can you really offer no scientific procedure to evaluate Heinlein's story? At the cookie jar level, can you at least grudgingly admit that the word "Szilard" sure looks like "Silard"? Sounds like it too. Or is that a coincidence as well? What are the odds. Should be calculable--how many stories written in 1939 include the names of Los Alamos scientists in conjunction with the words "bomb" , "uranium. . ."
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And that, in my view, is the heart of the problem. Rather than swallow hard and look at this in a non-biased fashion, you seem to be glued to the proposition that (1) it's intractable or (2) it's not worth analyzing because the answer is obvious.
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I think you misunderstood what I was arguing in my previous posts. If you look them over again, you'll see that I wasn't making a broad statement about the impossibility of estimating the probability that this event would have happened by chance, I was making a specific criticism of *your* method of doing so, where you estimate the probability of the particular "gestalt" of Szilard/lens/beryllium/uranium/bomb, rather than trying to estimate the probability that a story would anticipate *any* possible gestalt associated with the Manhattan Project. By doing this, you are incorporating hindsight knowledge of Heinlein's story into your choice of the "target" whose probability you want to estimate, and in general this will always lead to estimates of the significance of a "hit" which are much too high. If you instead asked someone with no knowledge of of Heinlein's story to come up with a list of as many possible words associated with the Manhattan Project that he could think of, then estimated the probability that a story would anticipate *any* combination of words on the list, then your method would not be vulnerable to this criticism (it might be flawed for other reasons, but I didn't address any of these other reasons in my previous posts).
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Look over the analogy I made in my last post again:

Suppose you pick 100 random words out of a
dictionary, and then notice that the list contains the words "sun", "also",
and "rises"...as it so happens, that particular 3-word "gestalt" is also
part of the title of a famous book, "the sun also rises" by Hemingway. Is
this evidence that Hemingway was able to anticipate the results of your
word-selection through ESP? Would it be fair to test for ESP by calculating
the probability that someone would title a book with the exact 3-word
gestalt "sun, also, rises"? No, because this would be tailoring the choice
of gestalt to Hemingway's book in order to make it seem more unlikely, in
fact there are 970,200 possible 3-word gestalts you could pick out of a list
of 100 possible words, so the probability that a book published earlier
would contain *any* of these gestalts is a lot higher than the probability
it would contain the precise gestalt "sun, also, rises".

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To simplify things even further, let's say you simply make a list of ten random numbers from 1 to 100, and before you make the list I make the prediction "the list will contain the numbers 23 and 89". If it turns out that those two numbers are indeed on your list, what is the significance of this result as evidence for precognition on my part? Your method would be like ignoring the other 8 numbers on the list and just finding the probability that I would hit the precise target of "23, 89" by chance, which (assuming order doesn't matter) would be only about a 1 in 5025 shot, if my math is right. But the probability that both the numbers I guess will be *somewhere* on the list of ten is significantly higher--I get that the probability of this would be about 1 in 121. So if this experiment is done in many alternate universes, then if in fact I have no precognitive abilities, in about 1 in 121 universes, both numbers I guess will happen to be on your list by luck. But then if you used the method of tailoring the choice of target to my guess, in each such universe you will conclude that I only had a 1 in 5025 chance of making that guess by chance. Clearly, then, you get bad conclusions if you use hindsight knowledge to tailor the choice of target to what you know was actually guessed in this way. But it's also clear that this example is sufficiently well-defined that I would have no general objection to estimating the probability that my "hit" could have occurred by chance, it's just that the correct answer is 1 in 121, not 1 in 5025.
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Jesse

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