[reposted, with additions, from 22 November 2012]

**A clip: Lincoln talks about Euclid**,

from Steven Spielberg’s *Lincoln.* In the title role:Daniel Day-Lewis. Screenplay: Tony Kushner.

The film suggests that Lincoln was using mathematical concept of transitivity as a guiding principle of political consensus-building.

A more detailed discussion of political aspects can be found in Ravi Chaudhary‘s post on Huffington Post blog, and a remarkably interesting criticism (by Christopher S. Morrissey) in The Catholic World Report:

[…] screenwriter Tony Kushner portrays Lincoln’s pursuit of the Thirteenth Amendment as flowing, not from Christian charity, but from mathematical reasoning analogous to the abstractions Lincoln read about in Euclid’s *Elements*.

“Euclid’s first common notion is this,” says Lincoln in the film, “Things which are equal to the same thing are equal to each other. That’s a rule of mathematical reasoning. It’s true because it works. Has done and always will do. In his book, Euclid says this is ‘self-evident.’ You see, there it is, even in that 2,000-year-old book of mechanical law. It is a self-evident truth that things which are equal to the same thing are equal to each other.”

The scene is a fiction. The truth is more interesting. Lincoln himself actually said this: “One would start with confidence that he could convince any sane child that the simpler propositions of Euclid are true; but, nevertheless, he would fail, utterly, with one who should deny the definitions and axioms. The principles of Jefferson are the definitions and axioms of free society. And yet they are denied, and evaded, with no small show of success. One dashingly calls them ‘glittering generalities’; another bluntly calls them ‘self-evident lies’; and still others insidiously argue that they apply only ‘to superior races.’” (6)

Difficult as it is to teach someone mathematics (and to apply its self-evident truths in a process of reasoning), it is even more difficult to teach and apply the truth of the Declaration of Independence about human equality (“that all men are created equal”).

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The movie and article seem to provide at least rhetorical confirmation that we are doing right here in Istanbul in asking our students to read Euclid.

It is curious however that, while I myself spend zero time in class

talking about the Common Notions of Euclid, the students nonetheless

learn them. I mean, when they are at the board presenting

propositions, they do sometimes justify steps by (correct) reference

to one of the Common Notions, even though they may fail to recognize a

need to appeal to an earlier Proposition.

The fourth Common Notion has seemed most significant to me: “Things

that coincide with one another are equal to one another.” I think the

converse of this is taken as self-evident: if things are equal to one

another, this means they can be made to coincide. This is what

justifies Proposition 4, the “side-angle-side” property of triangle

congruence. When triangles have two sides equal to two sides

respectively, and the included angles are equal to one another, this

can only mean that the one triangle can be placed so as to coincide

with the other. So Euclid seems correct, by his own standards, to

make this proposition a proposition rather than a postulate.

Anyway, I think there is an idea that the Common Notions were not part

of Euclid’s original text. Despite the words of Spielberg’s Lincoln,

as you know, the text of Euclid that we use contains no explicit claim

that the Common Notions are self-evident.

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