Monday, February 14, 2011

The Law of Conservation of Mathematical Symbols

One of the frustrating things about math is that some symbols are reused again and again, as if someone was afraid of running out of symbols.

For example:

1. ' can mean a derivative of a function, or the transpose of a matrix or vector. This is confusing when a book refers to the derivative of a vector. Hmm, which is it?
2. | | can mean the absolute value of something, or the determinant of a matrix. This is confusing when transforming random variables and you need to refer to the absolute value of a Jacobian determinant.
3. ~ can mean "scales as" or "is distributed as."
4. Σ can mean the operation "sum the following" or the item "covariance matrix."

I'm reminded of Demetri Martin's line about vitamins: "When they were naming vitamins they must have thought there were going to be way more vitamins than there ended up being. OK let's name these: Vitamin A, Vitamin B...ok man slow down we've got a lot to cover here. B2, B3, B4, B5, B6, B12. Then they got to E and they were like 'We're pretty much done. We've got all those damn B's. This is embarrassing. Let's just skip to K and get the hell out of here."



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