{"id":5042,"date":"2013-01-22T12:14:12","date_gmt":"2013-01-22T12:14:12","guid":{"rendered":"http:\/\/meeseeks:5080\/blog\/?p=5042"},"modified":"2013-01-22T12:14:12","modified_gmt":"2013-01-22T12:14:12","slug":"mathematical-thinking-and-software","status":"publish","type":"post","link":"https:\/\/vukutu.com\/blog\/2013\/01\/mathematical-thinking-and-software\/","title":{"rendered":"Mathematical thinking and software"},"content":{"rendered":"

Further to my post citing Keith Devlin <\/a>on the difficulties of doing mathematics online, I have heard from one prominent mathematician that he does all his mathematics now using LaTeX, not using paper or whiteboard, and thus\u00a0disagrees with Devlin’s\u00a0(and\u00a0my) views.\u00a0\u00a0 Thinking about why this may be, and about my\u00a0own experiences using LaTeX,\u00a0it\u00a0occurred to me that one’s experiences with thinking-support software, such as word-processing packages such as MS-WORD or\u00a0\u00a0mark-up programming languages such as LaTeX, will very much depend on the TYPE of thinking one is doing.
\nIf one is thinking with words and text, or text-like symbols such as algebra, the right-handed folk among us are likely to be using the left hemispheres of our brains.\u00a0 If one is thinking in diagrams, as in geometry or graph theory or much of engineering including computing, the right-handed among us are more likely to be using the right hemispheres of our brains.\u00a0 Yet MS-WORD and LaTeX are entirely text-based, and their\u00a0use requires the heavy involvement of our left hemispheres (for the northpaws among us).\u00a0 One doesn’t draw an arrow in LaTeX, for example, but instead types\u00a0a command such as \\rightarrow or \\uparrow.\u00a0\u00a0 If one is already using one’s left hemisphere to do the mathematical thinking, as most algebraists would be, then the cognitive load in using the software will be a lot less then if one is using one’s right hemisphere for the mathematical thinking.\u00a0 Activities which require both\u00a0hemispheres are\u00a0typically very challenging to most of us, since co-ordination between the two hemispheres adds further cognitive overhead.
\nI find LaTeX immeasurably better than any other word-processor for writing text:\u00a0 it and I work at the same speed (which is not true of MS-WORD for me, for example), and I am able to do my verbal thinking in it.\u00a0 In this case, writing is a form\u00a0of thinking<\/a>,\u00a0not merely the subsequent expression of thoughts I’ve already had. \u00a0\u00a0\u00a0 However, I cannot do my mathematical or formal thinking\u00a0in LaTeX, and the\u00a0software is at best a\u00a0tool for subsequent expression of thoughts already done elsewhere – mentally, on paper, or on a whiteboard.\u00a0\u00a0\u00a0 My formal thinking is usually about structure and relationship, and not as often algebraic symbol manipulation.
\nBill Thurston, the geometer I recently quoted<\/a>, said:<\/p>\n

I was interested in geometric areas of mathematics, where it is often pretty hard to have a document that reflects well the way people actually think.\u00a0 In more algebraic or symbolic fields, this is not necessarily so, and I have the impression that in some areas documents are much closer to carrying the life of the field.”\u00a0 [Thurston 1994, p. 169]<\/p><\/blockquote>\n

It is interesting that many non-mathematical writers also do their thinking about structure not in the document itself or as they write, but outside it and beforehand, and often using tools such as post-it notes on boards<\/a>; see the recent \u00a0article<\/a> by John McPhee in The New Yorker<\/em> for examples from his long writing life.
\nReferences:<\/em>
\nJohn McPhee [2013]: Structure:\u00a0 Beyond the picnic-table crisis<\/a>.\u00a0 The New Yorker<\/em>, 14 January 2013, pages 46-55.
\nWilliam F. Thurston [1994]:\u00a0 On proof and progress in mathematics<\/a>.\u00a0 American Mathematical Society<\/em>, 30 (2):\u00a0 161-177.<\/p>\n","protected":false},"excerpt":{"rendered":"

Further to my post citing Keith Devlin on the difficulties of doing mathematics online, I have heard from one prominent mathematician that he does all his mathematics now using LaTeX, not using paper or whiteboard, and thus\u00a0disagrees with Devlin’s\u00a0(and\u00a0my) views.\u00a0\u00a0 Thinking about why this may be, and about my\u00a0own experiences using LaTeX,\u00a0it\u00a0occurred to me that […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20,33,36,50],"tags":[],"class_list":["post-5042","post","type-post","status-publish","format-standard","hentry","category-creativity","category-hands","category-human-intelligence","category-mathematics","p1","y2013","m01","d22","h12"],"_links":{"self":[{"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/posts\/5042","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/comments?post=5042"}],"version-history":[{"count":0,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/posts\/5042\/revisions"}],"wp:attachment":[{"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/media?parent=5042"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/categories?post=5042"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/tags?post=5042"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}