Logarithmically Right
Friday, July 23rd, 2010In Kathryn Schulz’s new book about being wrong (Being Wrong), she makes an interesting mistake:
In the instant of uttering ["I told you so"], I become right squared, maybe even right factorial, logarithmically right — at any rate, really, extremely right.
Schulz doesn’t know that the logarithm of a number 1 or more is much less than the number itself. For example, log 100 = 4.6.
What’s interesting is that logarithmically right is a good way of describing how one’s beliefs should be transformed to be a fair approximation of the truth. When you think you are right, you probably are — but logarithmically. Much less than you think.
When faced with a scientific paper — the sort that press releases are written about, for example — the naive reader takes it at face value. The little-knowledge-is-a-dangerous-thing reader finds many shortcomings and dismisses it (“how did this get through peer review?”). The more likely interpretation, in my experience, is that the paper, in spite of its imperfection, moves us a little bit forward. Much less than appearances, but more than zero.
