[Blindmath] Math in your head

[Emanuela Ughi]

Just to add my 2 cents, as a professional (sighted) mathematician: I like
to remind this quotation

It is difficult to discover the difference entre a sleeeping mathematician
and a working one.
A. Lichnerovicz

Indeed, when I really want to concentrate on a subject (mostly if it is
difficult, or hard, or new) it is natural to me to close (and cover)  my
eyes: the world around me is confusing me, and I want to avoid it.

So I understand that mathematics can be done in someone's head. Not complex
computations, perhaps. But, to me, complex computations are not
mathematics. A true mathematician is one that understands ideas.

So, I like to add an anecdote from the “Lettre sur les aveugles” (Letter
about blind persons) by Diderot:it is about the story of Mademoiselle
Melanie de Malignancy, blind from birth, who was able to master geometric
facts; Diderot wrote: “I said one day to her: ‘Mademoiselle, figure to
yourself a cube.’ ‘I see it.’ she said ‘Imagine a point in the centre of
the cube.’ ‘It is done.’ ‘From this point draw lines directly to the
angles: you will then have divided the cube - ’ ‘Into six equal pyramids,’
she answered, ‘having every one the same faces: the base of the cube and
the half its height.’ ‘This is true; but, where do you see this?’ ‘Inside
my head, like you.’”


Emanuela


2015-12-16 3:02 GMT+01:00 Steve Jacobson via Blindmath <blindmath at nfbnet.org
>:

> John,
>
> You might find this of interest.  When we studied the revolution of a
> solid,
> a concept where a two-dimensional shape was revolved on the Y-axis, the
> instructor actually told me he thought I had an easier time with the
> concept
> because I was able to imagine it while he found most of the students tried
> to picture it as a three-dimensional drawing on a two-dimensional surface
> as
> they usually handled three dimensions.  I truly do not know if I was at an
> advantage or not, but I did seem to have an easier time with it than many
> others in the class.  I think we have to understand graphs to get a start
> at
> being able to imagine what something would look like, but where we can
> think
> beyond the paper, we'll have an advantage.  The same is true of doing math
> in our heads.  The more we're able to do, the quicker we'll be at solving
> equasions, etc.  However, I think it is a very individual thing.  I would
> venture to say that when solving complex equasions, most of us are going to
> run into that so-called brick wall and need a way to write it out
> efficiently at some point.
>
> -----Original Message-----
> From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of John G
> Heim via Blindmath
> Sent: Tuesday, December 15, 2015 8:29 AM
> To: Blind Math list for those interested in mathematics
> <blindmath at nfbnet.org>
> Cc: John G Heim <jheim at math.wisc.edu>
> Subject: Re: [Blindmath] Math in your head
>
> A faculty member here at the UW sent me this link to an article from the
> web
> site of the American Mathematical Society. It talks about blind
> mathematicians relying more on memory and something like visualization than
> typical mathematicians. IMO, relying on your memory is not a bad thing. I
> think of it as a skill blind people develop similar to listening to
> synthesized speech at a really high rate. As for visualization, when people
> ask me how I do geometry in my head, I often call it feelization. It's not
> visual. But feelization is an inadequate term because it's just made up and
> I always have to explain it. English doesn't have a word for visualizing
> something without vision. Anyway, here's that link:
>
> http://www.ams.org/journals/notices/200210/comm-morin.pdf
>
>
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-- 
Emanuela Ughi
Dipartimento di Matematica e Informatica
Via Vanvitelli 1 - 06123 Perugia
(39) 340 3341040