Re: Another tedious hypothetical
rmiller wrote:
>
>At 05:22 PM 6/8/2005, Jesse Mazer wrote:
>>rmiller wrote:
>>
>>>
>>>At 02:45 PM 6/7/2005, Jesse Mazer wrote:
>>>(snip)
>>>
>>>
>>>>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.
>>>>
>>>>RM wrote:
>>>In two words: Conclusions first.
>>>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. . ."
>>>
>>>You're shaking your head. This, I assume is already a done deal, for
>>>you.
>>>
>>>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.
>>
>>
>>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).
>
>Good starting premise. But words have meaning, and while "the sun also
>rises" may be interpreted to presage the bomb, it in fact is about
>bullfighting. No nukes there.
My example had nothing to do with nukes, it was just about the fact that
Hemingway's book title "anticipated" three of the words on my random list of
100 words.
>Heinlein's story is clearly about energy being derived from uranium--*and*
>has the name "Silard." These can not be compared with random number
>associations, simply because these words involve more information. To use
>a crude example, in the science community the name "Szilard" conjures up
>one prime association.
This is a complete non sequitur--the fact that the words have meaning has
nothing to do with calculating the probability that someone like Heinlein
would guess them by chance (similarly, in my example it wouldn't really make
a difference if the 100 words were part of a meaningful poem rather than
being selected at random). The point of the analogy is just that there are
lots of other words associated with the Manhattan Project ('Oppenheimer',
'mushroom', 'fat man', etc.), words which of course all have meaning too,
and that calculating the probability of the *particular* words
"Szilard/lens/uranium/etc." appearing in a story is not legitimate because
that choice of target is completely based on your hindsight knowledge of
Heinlein's story. You should instead calculate the probability that a story
would contain *any* combination of meaningful words associated with the
Manhattan project. This is exactly analogous to the fact that in my example,
you should have been calculating the probability that *any* combination of
words from the list of 100 would appear in a book title, not the probability
that the particular word combination "sun", "also", and "rises" would
appear.
>
>
>>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".
>
>To repeat, Heinlein's story is about uranium energy, the possibility of the
>factory blowing up, etc. The context is fairly clear. Hemingway's story
>is about Spain, bullfighting and affairs of the heart. No nukes there.
I thought it was pretty clear that my analogy was about general issues
relating to calculations of probabilities, it wasn't meant to have anything
to do with nukes specifically.
>
>
>>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.
>>
>>Sorry. In the raw sense, numbers merely represent values---unless you want
>>to get into that weird set of coincidences about 1/139--i.e. Enrico
>>Fermi's hospital room, etc. (And I sincerely hope you *don't*.)
Another non-sequitur. When you talk about the probability of someone
guessing something in advance by pure luck (ie under the null hypothesis of
no ESP), it doesn't make a difference whether the thing he is supposed to be
guessing is meaningful words, meaningless words, numbers, playing cards,
Presidents, etc. (unless the nature of the thing is such that even without
ESP, he can narrow down the options somehow by using information available
to him--but there was no information available to Heinlein at the time that
would allow him to reasonably anticipate that a name like "Szilard" was any
more likely to be associated with a nuclear bomb than any other name).
>>
>>Again, my concern is that scientists are too willing to prejudge something
>>before diving into it.
OK, but this is a tangent that has nothing to do with the issue I raised in
my posts about the wrongness of selecting the target (whose probability of
guessing you want to calculate) using hindsight knowledge of what was
actually guessed. If you don't want to discuss this specific issue then say
so--I am not really interested in discussing the larger issue of what the
"correct" way to calculate the probability of the Heinlein coincidences
would be, I only wanted to talk about this specific way in which *your*
method is obviously wrong. Like I said before, any method that could be
invented by someone who didn't know in advance about Heinlein's story would
avoid this particular mistake, although it might suffer from other flaws.
Jesse
Received on Thu Jun 09 2005 - 00:23:08 PDT
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