Thursday, July 12, 2007

Writing science versus writing mathematics

Dr. Freeride at Adventures in Ethics and Science wrote a post inspired by the book A Short Guide to Writing About Science by David Porush. She quotes from that book a list of "commandments" for scientific writers. I'm going to comment on that list from the perspective of a mathematician (the only one I have!).

  • Complex sentences are more precise and intelligent than simple ones.
  • This is definitely not true. Indeed, I have had to learn to keep it simple, since mathematical english uses much simpler structures than my native language. This is a clarity requirement, particularly needed since for most of us english is not easy.

  • Passive voice is more objective than active voice because active voice involves stating the agent, who is often a human, and humans introduce subjectivity.
  • Passive voice is never used, except in extremely straightforward contexts.

  • Descriptive prose is imprecise and unscientific because descriptions rely on adjectives which are often unquantifiable.
  • You can't possibly use descriptive prose in a statement or a proof, since mathematical language is so overpicky. On the other hand, descriptive prose is welcome in introductions, and everywhere else where you are trying to give euristic comments (which should be included!).

  • Claims about scientific fact must always be cautious; thus, using very cautious language -- squirrel language -- in scientific prose is always prudent.
  • We fine tune caution when we state conjectures (we have several synonyms, referring to different degrees of confidence). But when we prove something, there's no caution: we are proud of our achievement and we're totally sure! Occasionally mistakes are found, usually before physical publication.

  • Be as wary of innovation or taking chances in language as you are in the lab.
  • We need new words all the time! We both use standard ones with new meanings (a ring, a field and a module all have a precise definition) and invent new words (my favorite is crepant, as something for which discrepancy is zero). Finding good words to describe new concepts is one of the key duties of mathematicians.

  • Revision is unnecessary because knowledge is transparent.
  • What can I say? Some of us don't revise. They are hated by the whole community. The vast majority does.

    In the comments, someone discussed whether things might have changed since Porush published the book in 1995. Maybe, but not in mathematics. We stopped writing complex sentences around roughly 1950 (reading older stuff is a pain, in any language) and the rest is even older. The only exception is the passive voice, whose perceived difficulty is in my opinion language-dependent.

    Maybe mathematicians are really different from other scientists: e.g., the difference with physics is pretty noticeable even at the stylistic level.

    6 comments:

    .mau. said...

    When I write in English, I try hard not to use passive sentences - it's hard, since in Italian they are quite common.
    But I think that the real point in the list of David Porush is something like "people should see that science is something serious!" (the same more or less happens in Italy, except that politics is involved...)
    Needless to say, maths has none of these problems :-| so we could avoid building complex sentences.

    Twice said...

    I've nominated you as a Rockin' Girl Blogger!

    MathPostdoc said...

    Was this intentionally funny?

    "Passive voice is never used..."

    Anyway, just wanted to say hi. I recently found your blog (desperately searching for a woman writing about math instead of general academia or science). Loving it so far.

    estraven said...

    No, it wasn't. When I don't write mathematics, I think in my native language, where passive voice is elegant and easy to use.
    When I write mathematics, I first write it, and then I go over it and try to simplify every sentence as much as possible. That usually gets rid of any passive voice.

    David said...

    Hi. This is David Porush. Thanks for noticing my "Commandments" in my little book about science writing. However, I think something got lost in translation. Those "Commandments" are precisely the ones the book suggests that science - and mathematics - writers AVOID and DISOBEY. I encourage authors of even the most technical material to use active voice, dynamic language, and declarative sentences.

    But thanks for the attention.

    Octavio said...

    I'am totally against irreflexive invention of words. This causes havoc when you try to translate a text. I think is wise to think in Greek or Latin before naming anything.