[Python-Dev] [OT] Denormalized fractions [was Re: PEP 3144 review.] (original) (raw)

Steven D'Aprano steve at pearwood.info
Tue Sep 29 13:20:03 CEST 2009

On Tue, 29 Sep 2009 01🔞43 pm Guido van Rossum wrote:

I've never heard of someone who had a use case for denormalized fractions

Off-topic, but for what it's worth, I have one -- there's a mathematical operator called the mediant:

mediant(a/b, c/d) = (a+c)/(b+d)

It has a few uses, including Farey fractions. Clearly the result you get from normalized fractions will be different from denormalized (compare mediant(1/2, 3/4) with mediant(5/10, 3/4)). This leads to Simpson's Paradox, which is of importance in medical research:

http://en.wikipedia.org/wiki/Simpson's_paradox

Brief summary: consider two medical studies comparing two different treatments for an illness, treatment A and B. According to the first study, treatment A is better; according to the second study, treatment A is also better. But combining the results of the two studies into a single comparison paradoxically shows that treatment B is better!

The mediant is fascinating (to maths geeks at least) and important, and you need denormalized fractions.

-- Steven D'Aprano

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