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Old 5th January 2007, 12:16 PM   #42
Myriad
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The error they're making in that thread is to attempt to directly correlate the probability of an occurrence with the probability of its being a coincidence (that is, due to chance alone rather than an unknown correlation). In order to relate the probability of a specific event with its probability of being a coincidence, you must know the size of the space the distinctive event was drawn from -- that is, the number of other possible events, that did not happen, that would have appeared at least equally notable.

Perhaps the best-known example of this error is the "Bible Code" fallacy. "Bible Code" proponents point to patterns of characters in the Bible that form striking juxtapositions of words. The probability of each of the specific juxtapositions they find having occurred is astronomically small, creating an illusion that they could not be due to chance alone. But the number of possible juxtapositions that would be equally striking is astronomically large. So the "hits" found are nothing more than what chance expectation would predict, which has been confimed by using the "Bible Code" methods to find equally dramatic-looking "messages" and "prophecies" in texts of known non-divine provenance.

If we're talking about suspicious financial dealings suggesting foreknowledge of 9-11, then our event space must include all types of financial dealings that would be in that category. For instance, if unusually large amounts of gold were purchased during the first week of September 2001, then people theorizing foreknowledge would be eager to point this out (gold being generally seen as likely to rise in price during times of economic uncertainty). Ditto for unusually large purchases of oil futures betting on a price rise, the selling of shares of insurance companies, put orders or selloffs of companies with signficant operations located in the towers, purchases of shares in industries likely to benefit such as security and ground transportation, sell-offs or puts of vacation travel destination businesses, and no doubt many others. (Our possibility space of suspicious transactions must be larger still, if we hypothesize that the collapse of the towers, and not just the planned hijacking of planes, collisions, and fires, was foreknown.)

We must also define how "unusually large" an anomaly in financial dealings must be in order to qualify as suspicious. One reasonable threshold might be that either the total magnitude of transactions in the week before September 11th must be the highest for any week of the entire year preceeding September 11th, or the single day with the largest magnitude of transactions for the entire year preceeding September 11th must have occurred in the week preceeding September 11th. Note that not all of the examples pointed to in the thread necessarily meet that threshold; the various sources appear to disagree on that. (We can set lower thresholds of suspicion, but the lower we set them, the higher their probability of occurring by chance alone).

If we're fairly strict, and assume that the foreknowers apply very little imagination in predicting the likely effects of the attacks, how many possible transactions would need to be considered? Certainly puts or sell-offs of the two airlines, puts or sell-offs of any of at least half a dozen insurance companies, and puts or sell-offs of any of at least a dozen tower tenant companies should be on the list. That's forty possibilities right there. Between puts or sell-offs in other industries likely to suffer, investments in businesses likely to benefit, investments in commodities likely to rise in times of economic disruption and uncertainty, currency trades and other international transactions based on predictions of tightened borders, we could surely come up with well over another 20 possibilities, giving us a conservative total of 60.

Now, the probability of an event meeting our threshold of suspicion for any given one of these 60 types of transactions must be determined. The probability of a weekly high total occurring in any given week of the year by chance alone is 1 in 52. The probability of the highest single day occurring in any given week of the year is likewise 1 in 52. However, these two possibilities are not independent of one another, so the probability of either one happening is not simply (1 - (1 - 1/52) * (1 - 1/52)) or 1 in 26.25, but lower than that, somehwere between 1 in 26.35 and 1 in 52. I'll say 1 in 40 as a rough estimate.

So, we have sixty possible suspicious events, each with a probability of .025 (1 in 40) of happening by chance alone immediately prior to September 11 (or in any other given week). What is the probability of exactly one of them happening by chance alone? How about two, three, four, or five of them? To compute this we use the formula for a binomial distribution (see equation 2, here.

Probability of one suspicious event: .337
Probability of two suspicious events: .255
Probability of three suspicious events: .126
Probability of four suspicious events: .046
Probability of five suspicious events: .013

Oh yeah, and

Probability of no suspicious events: .219

Doesn't look like "one chance in a million" to me. It looks like the findings are well within our expectations for what we would find if we examine financial dealings prior to any event for which there was no foreknowledge.

(Permission to repost elswhere granted, if it suits anyone's needs.)

Respectfully,
Myriad
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