Sigma Algebras

Are mathematicians deliberately obscure? Or is it really so hard for them to write prose?

Check out this description of σ-algebras from Wik***dia.

In mathematics, a σ-algebra (also sigma-algebraσ-fieldsigma-field) is a technical concept for a collection of sets satisfying certain properties.[1] The main use of σ-algebras is in the definition of measures; specifically, a σ-algebra is the collection of sets over which a measure is defined.

No sh_t? It’s technical? And it satisfies properties. You don’t say.

The kernel of that paragraph is just one sentence.

In mathematics, a σ-algebra is a measurable collection of sets.

I changed the W*****dia page at 8:40pm on 3 Mar ‘11. Let’s see if I get in trouble. (I bet if I do it will be for “not being rigorous” or “original research”.)

Yes this is a specialist topic, but that doesn’t require gobbledegook. A σ-algebra is measurable like ℝ, but is not ℝ. Why can’t we just use normal words?

UPDATE: It hurts to be this right. My changes were reverted about an hour after I put them up. Am I wrong here?

I’m reminded of a story Doug Hofstadter told us about a friend of his who submitted an article in clear, everyday language to an academic journal. According to DH, the journal’s editors rejected the piece, saying it was too unprofessional. They confused jargon with sophistication, bombast with wisdom.

I don’t know the friend’s name or the journal’s name, and I half-wonder if I am just being a pr$ck about this Wikipedia article. But no, think about how people react to the word “maths”. This has got to be the reason—this and boring maths classes. Mathematicians literally refuse to write simply.

UPDATE 2: Another offender is the article on compact topological spaces. I’m actually removing some text from the garbled lede when I say:

In mathematics, specifically general topology, a compact topology is a topological space whose topology has the compactness property.

I think I’ve found a new candidate for worst sentences in the English language. Does anyone have George Orwell’s e-mail address?


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