[BlindMath] Question about the visualization of mathematical Concepts

[prayner at unimelb.edu.au]

I'll second the comments on the advantages of being blind for this
kind of task. I particularly enjoyed topics like real analysis and
metric spaces where many problems could be visualised with hard or
fuzzy balls for example. for the original question, my tactile analogy
for a continuous function is a smooth piece of wire. discontinuous
functions are left as an exercise for the reader :-)
I remember reading somewhere that the great contemporary mathematician
Terry Tao will occasionally try to literally embody geometric
analogies with his own body. I don't think a blind mathematician would
need to do this; at least I wouldn't. Unfortunately this doesn't make
me as good at Maths as Tao :-)
Really interesting topic.
Peter
Niels Luithardt via BlindMath writes:
>Hello John,
>
>that's a good point you raise. Sighted people visualize things by
>drawing things on paper. We as blind people can of course try to
>simulate this approach of the sighted world with technical aids as
>Louis described. But is that the way we should go as blind people?
>Mathematics takes place in the head.
>
>The question that concerns me is how the conceptualization takes place
>in the blind, how the anchoring takes place. Isn't it better to learn
>in pictures than to dully memorize complicated quantifier chains?
>Without having a picture of what all the quantifiers want to tell me?
>
>
>Kind Regards
>
>
>
>Am Mo., 29. Nov. 2021 um 19:29 Uhr schrieb John G. Heim via BlindMath
><blindmath at nfbnet.org>:
>>
>> IMO, the main problem with getting a sense for mathematical concepts if
>> you are blind is that sighted people insist that you show them what you
>> are thinking by drawing it on a piece of paper. To get a sense of what I
>> mean, challenge a sighted person to a game of tic tack toe of the mind.
>> Each player just says where they want their X or O to go. You might need
>> a third  person to write it down for you because your opponent probably
>> won't be able to picture the game in his/her mind. Maybe I'm not a
>> typical blind person but I have no problem just picturing something as
>> simple as a tick tack toe game in my head. But sighted people, if they
>> can't draw it, they are in trouble.
>>
>> I really think being blind is a huge advantage when picturing 3
>> dimensional spaces. Sighted people are struggling to draw it on paper
>> whereas a blind person can just "see" it in their head.
>>
>> On 11/28/21 1:15 AM, Niels Luithardt via BlindMath wrote:
>> > Hello,
>> >
>> > I have a question. What techniques do you use to visualize
>> > mathematical relationships?
>> >
>> > Mathematics is more than calculating with letters. How do you create
>> > pictures in your head and what kind of techniques do you use to
>> > sharpen the view, the pictures?
>> >
>> > Maybe a conceptual example would help:
>> >
>> > What kind of picture do you have in your mind when you think of a
>> > continuous function?
>> >
>> > I would be very happy about your answers!
>> >
>> > kind Regards
>> >
>> > Niels
>> >
>> > Translated with www.DeepL.com/Translator (free version)
>> >
>> > _______________________________________________
>> > BlindMath mailing list
>> > BlindMath at nfbnet.org
>> > http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>> > To unsubscribe, change your list options or get your account info for BlindMath:
>> > http://nfbnet.org/mailman/options/blindmath_nfbnet.org/jheim%40math.wisc.edu
>> > BlindMath Gems can be found at <http://www.blindscience.org/blindmath-gems-home>
>> >
>>
>> --
>> ###
>> John G. Heim, 608-263-4189, jheim at math.wisc.edu
>>
>> _______________________________________________
>> BlindMath mailing list
>> BlindMath at nfbnet.org
>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>> To unsubscribe, change your list options or get your account info for BlindMath:
>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/niels.luithardt%40googlemail.com
>> BlindMath Gems can be found at <http://www.blindscience.org/blindmath-gems-home>
>
>_______________________________________________
>BlindMath mailing list
>BlindMath at nfbnet.org
>http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>To unsubscribe, change your list options or get your account info for BlindMath:
>http://nfbnet.org/mailman/options/blindmath_nfbnet.org/prayner%40unimelb.edu.au
>BlindMath Gems can be found at <http://www.blindscience.org/blindmath-gems-home>
>

-- 
Peter Rayner (he/him), Level 1, 187 Grattan St.
Academic Lead - Climate & Energy College <https://www.climatecollege.unimelb.edu.au>
mobile +61 402 752 379, skype: petermorag 
zoom id 4431343191, join at  <https://unimelb.zoom.us/j/4431343191?pwd=a1E5Z3JEOTRVQUJsaVdRbVUvR1QyZz09>
mail-to: prayner at unimelb.edu.au TWITTER: @raynerstrings
I acknowledge the Traditional Custodians of the land on which I work, the Wurundjeri people of the Kulin nation, and pay my respect to their Elders, past and present