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06 February 2010

Abraham Lincoln and Euclid / Euclid teaches Lincoln to slay his political rivals / the World is Provable (with liberal doses of aspirin and hard work)

Click to enlarge, maybe.

Euclid's diagram accompanying his proof of Pythagoras' right-triangle theorem: In any right triangle, the sum of the squares of the two shorter sides equals the square of the longest side.

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Hey hey hi Mumfacolyte --

Here's the story I remember about Lincoln and Euclid, and I suspect I got it from Sandburg's bio (super-recommended),

When Lincoln first began dabbling in politics, he helped a winning candidate, and was rewarded with an Illinois state job as a surveyor -- a job for which he had no previous experience. He was given a theodolite and a crude book of instructions, and went about surveying farms and roads.

In his crude surveying primer, he kept encountering footnotes that said "qv. Euclid," was curious to know who this Euclid guy was, inquired, and was loaned a copy of The Elements. Lincoln and Euclid clicked instantly, and he dove into it like a starving man at a banquet.

Late in his life Lincoln claimed to have proven every demonstration in Euclid, and described it as the singlemost influential event of his intellectual life. As so many other geniuses before and after, he was astonished at the fundamental concept -- that things about the World could actually be PROVEN, known with absolute certainty; and that this huge volume of Proofs were interconnected, each new proof resting with perfect certainty on the proofs that had come before.

We don't normally think of Lincoln as math-minded, but in fact, if his memoir is true, he could blow just about anyone out of the water with his adoring mastery of Euclid.

The utterances from the mouths of politicians are such cotton-candy, ill-defined, evasive crap (e.g., what, exactly, do American politicians mean by "freedom" as they goose applause from unsophisticated audiences?) ... I'm convinced Euclid's demands of clear, precise definitions and ironclad logical step-by-step demonstrations evolved into the core of Lincoln's political and debating skills. More than any of his political rivals and contemporaries, he could instantly spot the flaws and lies in any political argument, and could illuminate the holes and gaffs so that audiences quickly saw which speaker was spewing fluff, and which speaker was on solid "Euclidean" ground.

The Lincoln-Douglas Debates are particularly interesting to read in detail from this perspective. Though Lincoln lost the Senate race to Douglas, the debates, widely published, launched Lincoln from backwoods obscurity to national attention. He was making sense about and illuminating very important national matters -- and Douglas, the far more florid and celebrated orator, wasn't.

I don't want to overplay the importance of Euclid to Lincoln's political success. He also had a personality that can only be described as Magic, people couldn't help but love and admire him, he was a wildly funny raconteur, and these skills made juries his adoring slaves and made Lincoln one America's most successful trial lawyers.

Two memoirs about first encountering Euclid as children (these are paraphrases from memory):

Bertrand Russell: "I never imagined anything could be so delicious."

John Stuart Mill read the first few pages of The Elements and screamed: "This is preposterous!" (That, of course, wasn't his final verdict, he kept reading every preposterous word.)

It's all aesthetics, but my absolute favorite is Euclid's proof (Book IX, Proposition 20) that there is an infinity of prime numbers; there is no greatest prime number.

And he does it all with unmarked straightedge, dividers, and line segments. (Today we'd go straight to the algebra and arithmetic of the argument.)

I think it's enough for every intelligent, civilized person just to be "touched" -- well, maybe punched and clobbered a few times -- by Euclid, to have thoroughly mastered just a half-dozen of the proofs. Mastering Euclid's proof of Pythagoras' right-triangle theorem -- that earns every woman, man and child the right to say forevermore that they truly understand the World, and how Reality is truly constructed.

Two particularly fascinating works based entirely on Euclid's example:

Spinoza's "Ethics" -- right, wrong, good, evil, in human behavior, all defined and proven precisely in the Euclid way.

Newton's "Principia" -- though he'd already invented the calculus secretly to quickly grasp the System of the World, Newton published his results entirely in the traditional Euclidean method of "The Elements," without the slightest hint that any other method could match the precision and perfection of Euclid.

My reading of the extensive Dover notes regarding the Parallel Postulate seems to make it clear that even Euclid thought there was something very fishy -- and "un-Euclidean" -- about this particular foundation of his geometry. I'm certain Euclid would have embraced the modern discoveries of non-Euclidean geometry with instant understanding and great pleasure.


Mumfacolyte said...

I never read the Sandburg, but I believe he is known to be a little fanciful or to embellish yarns that have little basis in fact -- though here I think the core of your assertion is true.

A quick Google found the following quote, purportedly from A.L. himself, all ova the web, and it is this that I recall having read, but many years ago (before I was first called an "Old Man," which didn't happen until sometime in my thirties):

"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."

At least the tone sounds like Lincoln as I remember him. Whatta concept, "demonstration," eh? I thought a cacophony of repetition was all you needed. Well, maybe today.

(I'm not familiar with Lincoln's biography to say if this jibes with fact or not -- no reason to give random snatchings from the web credence over Sandburg.)

Vleeptron Dude said...

My warm feelings towards Sandburg's biography have several sources, Absent from almost all other scholarly biographies, here Lincoln's story is voiced by a poet from Illinois, who collected Lincoln's story while Lincoln was still warm in living memory. Sandburg had heard old men mimic Lincoln's high squeaky speaking voice, and in old age Sandburg did it himself. There may be more accurate -- or more "provable" -- Lincoln biographies, but none with the intense flavor of love, place, kinship.

Somewhere in the flat, rectangular grid of central Illinois, a state highway still makes an inexplicable S curve -- a remnant of the young surveyor who came upon a widow's tiny farm and didn't have the heart to run the new state road through it, so he detoured the surveyed road around it.

Once you take the trouble to master Euclid, you can't ever lapse back to fuzzier, sloppier, less demanding standards -- not as a lawyer, not as a president and commander in chief, not as a neighbor. After Euclid, Lincoln was doomed to be nothing less than remarkable.

RheLynn said...

aha. So this is why I am drawn so deeply to my geometry books... they still haunt me daily, standing there on the shelf above the sewing machine (yes - above the SEWING MACHINE) teasing me to get back into their depths. But lately I just satisfy those urges by making dresses for the daughter... interconnecting lines and angles put together to make a 3D shape, which then in turn keeps me from having to buy another 20.00 3D shape elsewhere that someone else put together... without any such joy at all. said...

Wow, there's so much worthwhile information here!

Roberta said...

So, I do not really think this will work.