Amazing Circumstance Of "e"

2.71828183: The number e song

Seeking surcease of sorrow at all the lies, the weary traveler turned to mathematics. Here at least was truth! But even amidst this refuge, the Non-Euclidean geometries disturbed his soul. There were problems with Euclid’s parallel lines axiom! For Ersjdamoo, it was the dark night of the soul. (Background: The Oxford Murders, Ersjdamoo’s Blog, March 22, 2015.)

I later discovered my situation was not unique. For we read in Harold E. Wolfe’s, Introduction to Non-Euclidean Geometry, how other weary travelers of yore have innocently entered the realm of the Non-Euclidean geometries “thoroughly imbued with what is almost a reverence for Euclidean Geometry.” These persons felt that in Euclidean geometry they had found a place the “one thing about which there can be no doubt or controversy.” But then, to their horror, like Cthulhu in his house at R’lyeh waiting, dreaming, the loathsome shapes of the Non-Euclidean geometries seeped down from the dark stars. Harold E. Wolfe candidly admits of these persons, “What they are told is somewhat in the nature of a shock.” [1]

It was with relief that I thereby discovered how my situation had not been unique; that others before me had been disconcerted and disabused by the Non-Euclidean geometries. Slowly I pieced together a rationalization: Euclid was still correct at the local level. But when you expanded your view to a global framework, then “spherical geometry” superseded Euclid. Further out, among the dark stars of Cthulhu, a “hyperbolic geometry” appeared to have sway.

It was while sorting out this saving rationalization for Euclid that a most uncanny presence entered from left field: something called “e”. As we journey out to infinity aboard the spaceship “n”, this “e” is the limit of (1 + 1/n)n. [2]

“e” is a constant, meaning its value is always the same. “e” is also called “Euler’s number” and is of eminent importance in mathematics, alongside 0, 1, π (Pi) and i. [2]

But what is this “i” mentioned above? It is an “imaginary number”! Sometimes the mathematicians get stumped when doing equations. When this happens, “i” works like a temporary band-aid. “Let us bring in ‘i’ for the moment,” the wizards say. They say this “i” is equal to negative one squared (i = -12). Of course you can see that “i” must be imaginary since there is no real square root for -12.

So we have the imaginary “i” and the “e”, which is connected with Leonhard Euler (1707 – 1783), a Swiss mathematician. Euler discovered the formula known as Euler’s identity:

eix = cos x + i sin x

A special case of this formula is when x = π (Pi). Plugging that in to the Euler’s identity gives us…

e = cos π + i sin π

Since cos π = -1 and sin π = 0, we have…

e = -1 + 0i, i.e., e = -1.

From there it is just a hop to the special case of Euler identity: e + 1 = 0. [3]

And this is the amazing circumstance of “e”: the Euler identity tells us that seemingly disconnected things like “i”, “e”, and trigonometry functions are in truth connected somehow beneath the surface. There must be some hidden mathematical pattern, suggests Keith Devlin about the Euler identity, in his book The Language of Mathematics. [4]

Looking for hidden patterns is what mathematics is about, says Devlin. And so too do the “conspiracy theorists” look for hidden patterns. The term “conspiracy theorist” has not been precisely defined. A paper presented at the Conspiracy Theory Conference at the University of Miami on March 13, 2015 probed “What exactly do we mean by the phrase ‘conspiracy theory’?” It turns out that, even though many people keep offering their opinions about the “conspiracy theorists”, they ipso facto do not know what they are talking about! “The problem is vexing enough in the academic literature, where scholars have made countless attempts to formulate a firm definition, none of which has managed to push its rival definitions off the stage. In everyday usage, the term is even more slippery: Its meaning constantly stretches and narrows, particularly when it is used as a pejorative.” [5]

Which brings us back to the Euler identity, where seemingly disconnected things like “i”, “e”, and trigonometry functions appear to be conspiring. Might not a definition of “conspiracy theory” be akin to Devlin’s definition of mathematics: a search for patterns? In that case, this would mean Archimedes was one of the first conspiracy theorists!

——- Sources ——-
[1] Introduction to Non-Euclidean Geometry, by Harold E. Wolfe. Mineola, NY: Dover Publications, 2012. (Originally published 1945.)
[2] “e (mathematical constant)”, Wikipedia, April 10, 2015. http://en.wikipedia.org/wiki/E_%28mathematical_constant%29
[3] “Euler’s identity”, Wikipedia, April 10, 2015. http://en.wikipedia.org/wiki/Euler%27s_identity
[4] The Language of Mathematics, by Keith Devlin. New York: Henry Holt & Co., 2000.
[5] “What We Mean When We Say ‘Conspiracy Theory'”, by Jesse Walker. Reason magazine (online), March 15, 2015. http://reason.com/archives/2015/03/15/what-we-mean-when-we-say-conspiracy-theo

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About ersjdamoo

Editor of Conspiracy Nation, later renamed Melchizedek Communique. Close associate of the late Sherman H. Skolnick. Jack of all trades, master of none. Sagittarius, with Sagittarius rising. I'm not a bum, I'm a philosopher.
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