## Monday, May 09, 2005

### Take Care in What You Say

Here is part of a dialogue held by two people.

Person A: I don't think you'd be on her level intellectually.
Person B: Unless this person is a Nobel Prize candidate, that's pretty damn unlikely.

What is interesting here is the following question... Does B imply anything about his own level of intellect in his statement?

After taking a quick survey about this, the consensus says yes. Person B implies that his level of intellect is very likely to be a notch below that of a Nobel Prize candidate. But, some have argued that the terms in the above dialogue are subjective. This is true, so let us make things very clear by removing much of the subjectivity.

So, let's replace the phrase, "pretty damn unlikely" with "true with probability P." Let us start with an extreme case... what if P was 0.00?

Now, we have the following.

Person A: I don't think you'd be on her level intellectually.
Person B: Unless this person is a Nobel Prize candidate, that statement is true 0% of the time.

Now, with the subjectivity gone, this particular dialogue is quite clear. Person B is saying that at worst his intellect is the tiniest shade below that of a Nobel Prize candidate.

Let us move onto a more interesting case... what if P was 0.05? This value for P is a reasonable fit for the phrase, "pretty damn unlikely."

Now, let's re-examine the dialogue.

Person A: I don't think you'd be on her level intellectually.
Person B: Unless this person is a Nobel Prize candidate, that statement is true 5% of the time.

From the above dialogue, it is clear that if the person in question is not of Nobel Prize candidate intellect, then there is a 95% chance that Person B is of equal or higher intellect. So, given the above, we can conclude that there is a 95% chance that Person B is claiming his own intellect to be at worst the tiniest shade below that of a Nobel Prize candidate. Where does the remaining 5% go?

Logically, the remaining 5% must be distributed from the lowest possible level of intellect (that of a vegetable) all the way to two (tiniest) shades below the intellect of a Nobel Prize candidate. However, the distribution of the remaining 5% is unknown. It is possible that the remaining 5% is uniformly distributed, but this would certainly be quite odd given that 95% of the distribution's density is at the very high end range of intellect. Perhaps a more reasonable distribution of the remaining 5% would resemble the tailing off of a normal distribution. If this were the case, while Person B does not state outright that his intellect is a notch below that of a Nobel Prize candidate or better, he certainly implies that his level intellect is quite close. In this context, "close" is based on a rough notion of standard deviation.

You be the judge. Or maybe Person B was just being, and I quote a German colleague, "an arrogant prick."