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Monday, May 31, 2010

It's the intellectual rigor, stupid!

Related Link » Wronger Than Wrong
“As evolutionary biologist Richard Dawkins observed, ‘When two opposite points of view are expressed with equal intensity, the truth does not necessarily lie exactly halfway between them. It is possible for one side to be simply wrong’.” [emphasis added]
— By Michael Shermer, November 2006 (Scientific American)
Related Link » Interpolation
“In the mathematical subfield of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.”
— From Wikipedia, the free encyclopedia
Don't let the mathematical jargon put you off. There is something simple, albeit profound, within Dawkins' observation.

Interpolation between two data points is the familiar process of finding the average of the two data values. In every-day situations we sum the two values and divide the sum by two. It's trivial. This is technically linear interpolation, which implicitly assumes that both "known" data points are of equal veracity.

For example, suppose we want to compute the average value of a $1 bill and a $5 bill. This is easy because we know that both bills are of equal veracity (or trustworthiness), hence the average value of these two bills is computed by linear interpolation (or linear averaging) as $3.

Frequently, however, we can not claim that two related data points are of equal trustworthiness. For example, suppose that one datum was provided to us by Albert Einstein; and the other by Nancy Pelosi. The former was a renowned genius; the latter is an infamous idiot. Clearly, such two data points are not of equal trustworthiness. What can we do in such a situation?

The thing to do when confronted with data of unequal veracity is to compute a weighted average. Now, here is the very important part. The weights that need to be used in such a weighted average must be based on trustworthiness, and NOT on the intensity with which the datum is held or expressed. Remember, Einstein was a soft-spoken genius; Pelosi is a shrill idiot.

Hence, for the average of the Einstein-Pelosi data, we assign a veracity-weight of nearly 1.0 to Einstein's datum, and a veracity-weight of nearly 0.0 to Pelosi's datum. Let's be generous and assign the Pelosi datum a weight of 0.001, which leaves us a weight of 0.999 for Einstein's datum. Then, the weighted average of these data becomes: (0.999)Einstein+(0.001)Pelosi. In essence, we can simply ignore Pelosi, because everyone knows she is a f*cking idiot.

Post #1,297 It's the intellectual rigor, stupid!

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