Visual Thinking in Mathematics

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1. rramadassOct 2026
   For an interesting philosophical/cognitive study see;

   Visual Thinking in Mathematics: An epistemological study by Marcus Giaquinto - https://academic.oup.com/book/11260

   From the Preface:

   This book is not a mathematical text` a la Hilbert and Cohn-Vossen, not a psychological investigation` a la Hadamard, nor a How-To manual` a la Polya. It is a work of epistemology. But unlike almost all other writing in epistemology of mathematics, it is constrained by results of research in cognitive science and mathematics education. So the book has interdisciplinary roots.

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2. WillAdamsDec 2025
   Books which I have read and would recommend include:

   - _Ashley's Book of Knots_ --- everyone should be aware of knots and now at least the basics interesting, _The Klutz Book of Knots_ was also mentioned once

   - James Clavell _Noble House_ --- part of his "Asian Saga", not sure if it has aged well --- if a person could read only one of these, I'd recommend _King Rat_, based on his experience in a Japanese prison camp in WWII.

   - Hesse _Steppenwolf_ --- that Hesse is no longer read saddens me deeply, and not just because this makes _The Glass Bead Game_ less likely --- his thoughts on the difficulties of interpersonal relationships resonate even now

   - Knuth _Literate Programming_ --- I _really_ wish this style f programming would gain traction and that there would be more instances of taking famous programs and re-writing as a Literate Program, e.g., http://literateprogramming.com/adventure.pdf

   - Knuth _Digital Typography_ (and not just because I have a reward check)

   - Knuth _Mathematical Writing_ --- if you do any work in math, you probably already have a copy --- if you don't, you probably need one

   - Dewdney _The Planiverse_ --- response to the classic _Flatland_, this has a real charm and despite the dated computer technology, has held up well

   - Walter jon Williams _Hardwired_ --- an amazing cyberpunk novel, part of which was published in _Omni_

   - Steven Brust's _Jhereg_ --- one of my favourite fantasy novels, which I've been reading since picking it up in a Waldenbooks when I was in high school, waiting for the last two books, and esp. glad of these since they made the "Paarfi Romances" exist --- anyone who enjoys Alexandre Dumas and fantasy should read _The Phoenix Guards_

   - C.J. Cherryh's _Regenesis_ --- her entire Alliance--Union series is amazing and books are so varied pretty much everyone will find something which appeals

   - Trevanian _The Eiger Sanction_ and _Shibumi_ --- not sure if this and _Shibumi_ have aged well or no, but the latter was a big part of my childhood

   - Ben Franklin's Autobiography --- read presidential biographies to my kind in chronological order as a trial and regret not continuing with the actual project: biographies of important persons in chronological order

   - Sanora Babb's _Whose Names Are Unknown_: https://www.goodreads.com/book/show/1197158.Whose_Names_Are_... (ob. discl., that was my mention)

   Other books which only I mentioned:

   - Hal Clement _Space Lash_ now available in https://www.goodreads.com/book/show/939760.Music_of_Many_Sph... --- I recommend folks read it in reverse chronological order, starting at the back, then working to the front and bailing when things get too quaint/old-school/golden-age.

   - H. Beam Piper "Omnilingual" --- this should be a part of the middle school canon, lightly updated version at: http://vrici.lojban.org/~cowan/omnilingual.html

   - _Foxfire_ --- a classic series what predated the "Maker" movement

   - Tolkien's _The Fall of Arthur_

   - Knuth _TeX: The Program_

   Books which were sufficiently striking that I have made a note of them to get to read (hopefully this will work out better than _The Black Swan_ which I found annoying)

   - _Visual Thinking in Mathematics_

   - _Hardcore VisualBASIC_ --- still a bit bummed that I managed to miss this and MacBasic....

   - _Phoebe and her Unicorn_ --- getting this for my daughter

   - _Harmony with Lego(R) Bricks_ --- book on music improvisation

   - Ornamental Origami

   Note that a number of books weren't actually mentioned, e.g., Isaac Asimov's _Book of Facts_

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3. pramodbiligiriOct 2025
   Perhaps do activities like manipulating physical objects (carpentry?, Lego, Rubiks cube), games like Tetris, or complex body movements where verbalization won't be of much use. Or standard Quantitative Reasoning problems from entrance exams. A few years back, the wordcel vs shape rotator debate/binary was being discussed online: https://roonscape.ai/p/a-song-of-shapes-and-words?r=53sw

   I'd come across this book "Visual Thinking in Mathematics" (https://www.amazon.in/Visual-Thinking-Mathematics-Marcus-Gia...) which goes into some of this.

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