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Rated: 18+ · Book · Personal · #1196512
Not for the faint of art.
Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.




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May 7, 2022 at 12:21am
May 7, 2022 at 12:21am
#1032067
Thought I'd experiment with a new, occasional format today. I learn something, maybe you learn something.

On This Day
7-May-1954
End of the Battle of Dien Bien Phu  Open in new Window.


I have an appreciation for history, sure, but one aspect of it that never really grabbed my attention is detailed war chronicling. War is usually too depressing, even for me, so normally I content myself with having a vague idea of the timeline, major players, and general outcome.

And even there, some military actions are more on my radar than others. The big US conflicts, of course; the Sino-Japanese wars, the Seven Days War in the Middle East, that time the UK took back the Falklands and... ummm... well, apart from the really historical ones like the time Hannibal crossed the Alps on elephants (come on, just picture that), I'm pretty ignorant.

I was almost completely ignorant about the Battle of Dien Bien Phu.

I mean, I had a vague notion that the French got their asses handed to them in Vietnam about a decade to two before we went in and got our asses handed to us, but that's about it. I wonder if this particular battle is where they got their offensive and undeserved reputation as surrender monkeys? Look, everyone's lost a war. Including us. Several times to Canada, for fuck's sake.

I'm not going to rehash most of what's already at that link in the title, just make a few of my own observations, as is my wont:

The United States was officially not a party to the war, but it was secretly involved by providing financial and material aid to the French Union, which included CIA contracted American personnel participating in the battle.

I doubt this was the first time we were secretly egging on a war, nor was it the last. The Cold War wasn't, always.

The Peoples Republic of China and the Soviet Union similarly provided vital support to the Viet Minh, including most of their artillery and ammunition.

Yay, proxy wars!

By 1953, the First Indochina War was not going well for France.

This being Wiki and not Cracked, and having little historical perspective of the overall conflict, I'm not sure if this is comic understatement or not. I'm going with yes.

Most of the page deals with the actual weeks-long battle, and is of value, but my purpose here is to a) snark on things and b) focus on this particular day in history, the day the battle officially ended.

But the "Battle" section is interesting mostly because of the names the French gave their fortifications. French women's names. It's just so... very... French.

So, on May 7, 1954, they record this message:

The last radio transmission from the French headquarters reported that enemy troops were directly outside the headquarters bunker and that all the positions had been overrun. The radio operator in his last words stated: "The enemy has overrun us. We are blowing up everything. Vive la France!"

Bad. Ass. Even in defeat.

Afterwards:

Public opinion in France registered shock that a guerilla army had defeated a major European power.

Yeah. History doesn't repeat itself. It echoes.

One final note, from the page:

The French government in Paris then resigned, and the new Prime Minister, the left-of-centre Pierre Mendès France, supported French withdrawal from Indochina.

Pierre Mendès France. For whatever reason, I'd never heard of him. But that name. It would be like if we elected a President named Rock America. If that President was from a liberal Brazilian Jewish family.

Which, you know... we could do worse.


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