tea.mathoverflow.net - Discussion Feed (What evidence is there that mathematical reasoning is influenced by a native language?)

Tom Boardman comments on "What evidence is there that mathematical reasoning is influenced by a native language?" (8776)

Tom Boardman — Thu, 02 Sep 2010 11:21:41 -0700

@Steve- You may be interested by the first section of this talk http://www.youtube.com/watch?v=hBpetDxIEMU by Steven Pinker, in which he seems to mention exactly what you are talking about (vis-a-vis motivation for definition of a manifold), as coming from a *universal* character of language. Worth watching, if only for the fact that his 'how we talk about space' section seems to basically be the theory of manifolds (with boundary) (which blew my mind just a tiny bit).

With regard to the question as a whole, I like it and think it's a good question, but what you are talking about is the territory of the Sapir-Whorf hypothesis (http://en.wikipedia.org/wiki/Sapir_Worf_Hypothesis), something which, at present at least, is only suspected in its weaker forms- indeed any such mathematical divergence based on language would be a *HUGE* deal in linguistics if it existed. While it is possible that such a huge deal exists unchecked, I would be skeptical that your question would give any decisive answer either way....

Qiaochu Yuan comments on "What evidence is there that mathematical reasoning is influenced by a native language?" (8725)

Qiaochu Yuan — Tue, 31 Aug 2010 09:26:27 -0700

@Gerhard, that doesn't sound like a duplicate at all. That question is about specific mathematical work done in other languages because whoever did it spoke a different language, not because of any inherent potential in that language.

Cam McLeman comments on "What evidence is there that mathematical reasoning is influenced by a native language?" (8702)

Cam McLeman — Mon, 30 Aug 2010 19:27:26 -0700

Not a comment on suitability, but Steven Pinker discusses this at length in "The Stuff of Thought," and if I remember correctly, tears it to shreds. Of course, probably not all linguists (psycholinguists? linguistic psychologists? or whatever) agree with him, but he had some pretty compelling arguments.

Kevin Lin comments on "What evidence is there that mathematical reasoning is influenced by a native language?" (8676)

Kevin Lin — Mon, 30 Aug 2010 00:43:18 -0700

Kontsevich comments on this, or on some things related to this, in his essay "Beyond Numbers" from the book "The Unravelers: Mathematical Snapshots" --- see Shizhou Zhang's answer to this question.

grp comments on "What evidence is there that mathematical reasoning is influenced by a native language?" (8673)

grp — Sun, 29 Aug 2010 21:44:04 -0700

Doing a search on "language" gives a question titled something like "What great mathematics are we missing out on because of language barriers?", which may be a near duplicate. I would scrutinize the MathOverflow database before posting the question. In particular, a better question might be to ask if people who are good at geometry in the abstract are good at directions and self-location in real life, and if there is a linguistic component attached. Or even: is there a correlation between number of languages one speaks and one's ability to do certain forms of algebra (manipulation of linguistic terms across more than one domain)? The current postulated question may be too broad.

Gerhard "Ask Me About System Design" Paseman, 2010.08.30 IST

WillieWong comments on "What evidence is there that mathematical reasoning is influenced by a native language?" (8666)

WillieWong — Sun, 29 Aug 2010 15:20:18 -0700

I feel that this is better discussed in a forum for linguists, philosophers of science, or epistemologists.

Since mathematicians tend to be experts in mathematics, and not on how their brains process mathematics, I think this question will quickly degenerate into a bunch of anecdotes and get very discussion-y. In other words, I think this belongs on a (mathematics) blog, or on a forum for different professional, and not on MO.

It would also be a perfect question for AfternoonTea, though who knows if that's going to happen or not.

Steve Huntsman comments on "What evidence is there that mathematical reasoning is influenced by a native language?" (8664)

Steve Huntsman — Sun, 29 Aug 2010 13:23:52 -0700

A recent New York Times article (http://www.nytimes.com/2010/08/29/magazine/29language-t.html?_r=2&pagewanted=1) discusses the existence of "geographical" languages, in which (to put it suggestively) local coordinates relative to one's body are foreign concepts, so that (e.g.) directions are always given as "turn west, then north" rather than "turn left, then right". The article suggests that native speakers of such languages tend to have highly acute and robust senses of direction compared to those persons with different linguistic backgrounds.

Now it seems to me that this is the sort of thing that could influence the initial formulation of an idea such as a manifold as we know it. Quite possibly there are other plausible or perhaps even demonstrable examples of this sort of thing. For instance the same article mentions a language that requires attribution of facts: it seems natural to think that this might be particularly conducive to mathematical thought. I could also imagine that (e.g.) Grothendieck's particular sense of language might have influenced his thought, rather than just the other way around. So: is there (anecdotal, concrete, or best of all scientific) evidence to support a connection between native language and aspects of mathematical reasoning?