Complex Numbers (Book)

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Complex Numbers

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.

http://www.ddewey.net/mandelbrot/

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June 10, 2022 at 12:03am

#1033671

Drink of the Gods

We have another Cracked link today, and it's about beer. Of course I had to share it. It is, however, from way, way back in March.

Egyptians Got Drunk To Celebrate Beer Defeating The Gods

Many cultures have their own drunken festivals. Just last week, for example, we celebrated St. Patrick's Day.

I told you it was from March.

Other alcohol festivals include Marathon Monday, Mardi Gras, New Year's Eve, and of course payday.

And Cinco de Mayo. For some reason we imported most of our drunken festivals here in the US - SPD from Ireland, Mardi Gras from France, and that one from Mexico. It's not actually Mexican Independence Day, if you didn't know; it's way more complicated than that, but that's a story for another time. "For some reason" means "because this country is infested with prohibitionists and Puritans."

You know what else usually happens in March (besides the equinox)? Purim. Purim is a Jewish festival based on the Book of Esther from the OT. When I was a kid, a rabbi told us that while kids celebrate Purim with noisemakers, adults are supposed to get so drunk that they can't tell the good guys from the bad guys.

As Purim is based on the Hebrew lunar calendar, it moves around year to year like Hanukkah. This year it was, coincidentally, on St. Patrick's Day. This is probably why you almost never hear about Irish Jews.

I mention the bit about Purim mostly because... well, I'll get to it later.

[Egyptians'] annual Festival of Drunkenness, less commonly known as the Tekh Festival, was devoted to the "lady of drunkenness," the goddess Hathor. Everyone got very drunk, collapsed in a stupor, then awoke to drums (the drummers didn't pass out, as drummers all have a high tolerance for alcohol).

Vouch.

They celebrated alcohol for all the expected reasons (alcohol means joy and life and wealth), but also because in their mythology, beer had once saved them all.

Beer. Is there anything it can't do?

The article goes on to describe exactly how, according to the Egyptians, beer saved everyone. It's short, so I won't quote more from it here. You can go read it if you're interested. Instead, I'm going to go back to Esther. In a kind of roundabout way. Bear with me here.

One of the earliest surviving odes to the wonder beverage is the story of the goddess Inanna and the god Enki. As it's translated from ancient Sumerian tablets, you might find different translations. Here are two of them:

This one

appears to be the most literal.

And this one

probably has more accessible language, but leaves out the most prurient parts.

I first saw it in a different form, but I think the gist of it stays the same in all translations: Inanna and Enki get into a drinking contest; Inanna wins, and she steals all the keys to civilization from a passed-out Enki.

Supposedly it's a myth used to explain why the seat of power in Sumeria changed from Enki's city of Eridu to Inanna's city of Uruk. Both of those cities are now dust, but beer remains (albeit in a more modern formulation), and we're still using it for drinking contests. Some things are literally as old as civilization; I have, in fact, heard compelling arguments that it was beer that caused the beginnings of civilization, because of the logistics involved in growing the grain and making the stuff.

In Babylonia, Sumeria's effective successor civilization, Inanna became Ishtar. Later offshoots of Babylonia included the writers of the Old Testament; stories from Babylon (including the bit about the flood) were pretty obviously copied there. The Semitic goddess cognate with Inanna and Ishtar was Astarte or Astaroth, an obvious linguistic link.

It was only later in life that I realized that Esther is another linguistic mutation of Ishtar. Further, the "good guy" in the Book of Esther is Mordecai, and the Babylonians had a god named Marduk. (Admittedly, I never found a link with the "bad guy," Haman, and the story itself takes place in Persia, which was further east and a different civilization entirely. Sumeria and Babylonia were, as we all know, roughly where modern Iraq is, while Persia was located approximately in what would become Iran.)

I do not believe for one second that this naming thing is in any way a coincidence: Esther can be traced back to Inanna, the winner of the Drinking Contest of the Gods in ancient Sumeria.

Is that why we get drunk on Purim? I don't know. But until I hear a compelling argument against it, that's my working theory

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