Having heard the clip from Spielberg’s latest film, Lincoln, where Lincoln describes Euclid’s 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’s difficult for anyone to speak about mathematics without sifting out the structure, reason and proof that characterizes mathematics, from its life-sustaining meaning. Life-giving meaning is reserved for things like poetry, music, and art. Every attempt to consider Lincoln’s fascination with Euclid falls into this trap, despite the fact that Lincoln, himself, seems to have avoided it. Euclid’s 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. 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’s presidency.

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

…it is derelict of the authors to include no consideration of how Lincoln’s 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.

Perhaps the nature of Lincoln’s own inquiry quoted on the website Math Open Reference, points to the enigmatic connection:

“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?

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.

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.”

So, what did he find out? Mathematics revealed a kind of *demonstration* 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. 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. 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. I would suggest that in order to do this, he was guided, not only by the structure of Euclid’s reasoning, but also by its content. And this is where our difficulty in understanding the development of Lincoln’s 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. 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.

Doris Kearns Goodwin, the author and historian on whose book the film Lincoln is partly based, took note of some of Lincoln’s passions in an interview with Charlie Rose. 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. I suspect that Lincoln read Euclid the way he read everything else, to see more of what could be seen. It was at once personal and a path to truth. And it is this that has been lost in our modern approach to mathematics education, understanding, and appreciation.

[…] Here’s a link to more Lincoln and Math too. […]

Correction on my earlier ‘things that are equal to the ‘same thing’

The application of Euclid first notions by Lincoln to society and the specific problems his leadership faced, and the ultimate price he paid, the legacy he left remains an inspiration to the challenges facing the world today. Life has equal worth but does our daily experience attest to this notion? the Civil Registration and Vital Statistics movement has found resonnance in Lincolns interpretation of the first notions of Euclid, that things that are equal to something are equal to each other. If life has equal worth, then life of each individual must be equal to each of the other individuals. But for such equality to be lived in practice, from cradle to grave, each of those lives must be visible, known, recorded and its traces on earth celebrated. Unfortunately, many a human life although objectively exist, remain uknown, in what is termed the scandal of invisibility. How then can that which is unknown, however, notionally equal, be in practice be equal. What Lincoln fought for, was that which was concealed be revealed and be given its rightful place. Martin Luther King did the same, so did Ghandi, Mandela and many others. Euclid first notion as interpreted by Lincoln serves the need to record and provide possibilities for material meaning to life that has to be lived to the fullest by members of society. Registration of births and deaths, life events in general provides visibility and is an inalienable right to everyone. I found Lincoln’s focused mind on this issue convincing.

First common notion. Things that are equal to the same thing are equal to each other:

If you regard man as being constituted of both body and spirit, then obviously black or white is of no importance.When it comes to spirit all men have equal access to the same thing and therefore are equal to each other. Ann Bradley

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Thanks for the link. It’s a nice site and the point they make about Lincoln is interesting. It makes sense. The Huffington Post article to which they refer is also interesting, where the methods employed by Euclid are seen as “resolving tension,” or “reasoning toward common ground.” I don’t think it’s possible to recomstruct the things that contributed to Lincoln’s fascination with Euclid, but I do find it worth thinking about.

Thanks again.

This link (http://education.lms.ac.uk/2012/12/lincoln-talks-about-euclid/) throws interesting light on Lincoln’s (as opposed to Spielberg’s) take on Euclid (if the Lincoln quote given there is authentic). Lincoln seems to be frustrated by those people who reject his arguments about a free society, not so much because they reject his logic as that they reject the premises on which his arguments are built, these being “the principles of Jefferson” which Lincoln calls “the definitions and axioms of free society”.

Lincoln seems to be making a nice point here, even though his take on the use of definitions and axioms seems narrower than the modern mathematical view, where it is not a matter of selecting premises that are ‘true’, as selecting ones that are consistent, with different sets leading to different mathematical systems.

I don’t think that anyone here is donning mathematical garb (except maybe Spielberg). The point of this blog is to challenge the popular view that mathematics is a tool with very specific value or that it is an exercise in logic devoid of content (like Spock). It seems clear to me that the body builds many things, sensory images, language, story and mathematics. Given the breadth of Lincoln’s intellectual life, I suspect he was suited to allowing the activity of mathematics to become part of how he understood many things and neither the clip nor the film actually explore this possibility.

Luke: Do you think this writer is deliberately trying to mystify us?

Jim: He seems to want to fethishise mathematics.

Luke: The situation seems quite simple.

Jim: Yes, Lincoln wants to develop arguments that are logically sound

Luke: – and he uses Euclid’s axiomatic system of proof as a model.

Jim: Although in that quote about ‘common notions’ that is doing the rounds at the moment from Spielberg’s film

Luke – Lincoln seems to have got the notion of an axiomatic system the wrong way round.

Jim: Or maybe that’s Spielberg.

Luke: Sadly, the way some people dress themselves in mathematical garb

Jim: – is not very attractive.

Joselle: Very nicely done. Surprising to connect Lincoln with Math. In my readings I have come across many different sides to Lincoln. He is remembered for being a certain person, but for many other reasons that most people would be astonished to hear about. I love that you connect Math to everything, and it always works!!!!

Best wishes and congrats on the new job, David. And it would make me very happy if you introduced my posts to some of your students.

enjoyed this one

i have just taken a job teaching again

and i’ve been given (too much) flexibility in deciding the curriculum…

i may introduce your post to some students

and i wonder what they will make of it

teenagers by the way

with english as a second language

incredibly capable

i wonder if they will make a link between what you are talking about

and what we are doing in the class?

You lived in Melbourne once?

No, I didn’t!