{"id":911,"date":"2012-11-26T12:38:01","date_gmt":"2012-11-26T19:38:01","guid":{"rendered":"https:\/\/mathrising.com\/?p=911"},"modified":"2012-11-26T12:44:12","modified_gmt":"2012-11-26T19:44:12","slug":"lincoln-euclid-and-vision","status":"publish","type":"post","link":"https:\/\/mathrising.com\/?p=911","title":{"rendered":"Lincoln, Euclid and vision"},"content":{"rendered":"

Having heard the clip from Spielberg\u2019s latest film<\/a>, Lincoln, where Lincoln describes Euclid\u2019s first common notion, I tried to investigate the extent to which the connection between Lincoln and mathematics has been pursued, and I was disappointed.\u00a0\u00a0 It\u2019s difficult for anyone to speak about mathematics without sifting out the structure, reason and proof that characterizes mathematics, from its life-sustaining meaning.\u00a0 Life-giving meaning is reserved for things like poetry, music, and art.\u00a0 Every attempt to consider Lincoln\u2019s fascination with Euclid falls into this trap, despite the fact that Lincoln, himself, seems to have avoided it.\u00a0 Euclid\u2019s first common notion, as described by Lincoln in the film, says that things that are equal to the same thing are equal to each other.\u00a0 The purpose of the reference must be to get us to wonder about how this rational statement about equality would be relevant to the slavery issue that defined the crisis of Lincoln\u2019s presidency.<\/p>\n

Lincoln\u2019s preoccupation with Euclid inspired the book Abraham Lincoln and the Structure of Reason<\/span> by David Hirsch and Dan Van Haften.\u00a0 The authors describe how their work took shape in an interview on the book\u2019s website<\/a>, where the authors claim to have cracked the code of Lincoln\u2019s speeches, identifying the underlying structure that made them beautiful and effective.\u00a0 But a review of the book<\/a>, by author and historian Jason Emerson, points to the weakness of a purely analytic approach to how mathematics influenced Lincoln.<\/p>\n

\u2026it is derelict of the authors to include no consideration of how Lincoln\u2019s logical and mathematical mind could have impacted his presidency, such as how the logic in his speeches allowed him to convince the public of the correctness of his policies and to therefore lead them in the direction he wanted them to go; his rationalizations for legal issues such as suspension of habeas corpus or the issuance of the Emancipation Proclamation; his decisions on military tactics and planning; his penchant for technology and innovation in weapons, medicine, transportation, and communication, which is all a direct corollary to his logical and technically-inclined intellect.<\/p><\/blockquote>\n

Perhaps the nature of Lincoln\u2019s own inquiry quoted on the website Math Open Reference<\/a>, points to the enigmatic connection:<\/p>\n

“In the course of my law reading I constantly came upon the word “demonstrate”. I thought at first that I understood its meaning, but soon became satisfied that I did not. I said to myself, What do I do when I demonstrate more than when I reason or prove? How does demonstration differ from any other proof?<\/p>\n

I consulted Webster’s Dictionary. They told of ‘certain proof,’ ‘proof beyond the possibility of doubt’; but I could form no idea of what sort of proof that was. I thought a great many things were proved beyond the possibility of doubt, without recourse to any such extraordinary process of reasoning as I understood demonstration to be. I consulted all the dictionaries and books of reference I could find, but with no better results. You might as well have defined blue to a blind man.<\/p>\n

At last I said,- Lincoln, you never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my father’s house, and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out what demonstrate means, and went back to my law studies.”<\/p><\/blockquote>\n

So, what did he find out?\u00a0 Mathematics revealed a kind of demonstration<\/em> the meaning of which was not fully captured by all the dictionaries and books of reference Lincoln consulted. It seems clear that Lincoln was not interested in making an analogy between mathematical truth and living truth.\u00a0 He followed a path carved out by mathematics to clarify his own vision, and then he communicated what he saw using some of the same structure in the speeches he gave.\u00a0 He chose an arrangement of words, words that were tied to the experience and hopes of the people around him, and moved many of them to see what he saw.\u00a0 I would suggest that in order to do this, he was guided, not only by the structure of Euclid\u2019s reasoning, but also by its content.\u00a0 And this is where our difficulty in understanding the development of Lincoln\u2019s thoughts begins. The difficulty we have in fully understanding the impact of Euclid on Lincoln highlights the difficulty we have understanding the nature and power of the insight mathematics can provide. Mathematics, as most people see it, looks like structure more than content.\u00a0 But I consistently argue that mathematics produces insight because of the way it is tied to the cognitive processes that, from the bottom up, build our lives.<\/p>\n

Doris Kearns Goodwin, the author and historian on whose book the film Lincoln is partly based, took note of some of Lincoln\u2019s passions in an interview with Charlie Rose<\/a>.\u00a0 She tells us that Lincoln, a mostly self-taught man, was excited to the point of not sleeping, to read Shakespeare and the King James Bible.\u00a0 I suspect that Lincoln read Euclid the way he read everything else, to see more of what could be seen.\u00a0 It was at once personal and a path to truth.\u00a0 And it is this that has been lost in our modern approach to mathematics education, understanding, and appreciation.<\/p>\n","protected":false},"excerpt":{"rendered":"

Having heard the clip from Spielberg\u2019s latest film, Lincoln, where Lincoln describes Euclid\u2019s first common notion, I tried to investigate the extent to which the connection between Lincoln and mathematics has been pursued, and I was disappointed. It\u2019s difficult for anyone to speak about mathematics without sifting out the structure, reason and proof that characterizes […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[54,5],"tags":[55,70],"class_list":["post-911","post","type-post","status-publish","format-standard","hentry","category-history","category-mathematics","tag-lincoln","tag-mathematics","odd"],"_links":{"self":[{"href":"https:\/\/mathrising.com\/index.php?rest_route=\/wp\/v2\/posts\/911","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathrising.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathrising.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathrising.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathrising.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=911"}],"version-history":[{"count":3,"href":"https:\/\/mathrising.com\/index.php?rest_route=\/wp\/v2\/posts\/911\/revisions"}],"predecessor-version":[{"id":913,"href":"https:\/\/mathrising.com\/index.php?rest_route=\/wp\/v2\/posts\/911\/revisions\/913"}],"wp:attachment":[{"href":"https:\/\/mathrising.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=911"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathrising.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=911"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathrising.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=911"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}