Thursday, October 14, 2004

Missing Equations

Via Mark Liberman, I found a list of the 20 Greatest Equations. It was constructed primarily from the nominations of physicists, which probably explains why some of my favorites didn’t make the list.

I have to agree with Liberman that Bayes’ Theorem definitely deserved inclusion. Among other things, Bayes’ Theorem (a.k.a. Bayes’ Rule) explains why you shouldn’t jump out a window after testing HIV-positive, why students shouldn’t be suspended upon failing a single drug test, and why you might want to switch doors on “Let’s Make a Deal.”

I also think there should have been an equation relating to time-discounting, such as the relationship between a present value (PV) and a future value (FV):
FV = PV(1+r)^t
This equation tells you how much PV will grow into in t periods if invested at interest rate r, but you can also divide both sides by (1 + r)^t to find the value now of a claim to money to be received t years from now.

Alternatively, the list could have included the closely related formula for continuous compounding of interest:
A = Pe^(rt)
which tells you the amount A you’ll have in t years if you invest principal P at interest rate r (compounded continuously).

And, of course, I’m shocked that the list did not include the famous equations relating the actual to the apparent amount of toilet paper left on the roll.

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