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
