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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May 14, 2022 at 12:01am

#1032374

Any Storm in a Port

And now for another fragment of history...

On This Day
14-May-1915
May 14 Revolt

As with most of my oeuvre, I select these things semi-randomly, and in this case, I find myself way out of my comfort zone. That's okay. That's one reason I'm doing this.

Portugal is not a country I think about often. I mean, sure, I have a vague desire to visit there, but I have a vague desire to visit lots of places. I'm aware that it was once a major naval power -- for one thing, they achieved what Columbus failed to do, find a sea route to Asia -- and that it once controlled Brazil. Other than that, the true importance of Portugal to me has always been the existence of port wine, which is delicious and can get really expensive.

So, apparently, Portugal was a monarchy up until 1910, at which point the peasants revolted. This was, of course, long after France, a few years before Russia, and don't ask me about Spain because that history is a real mess.

This Wiki page is particularly questionable, and when that happens I usually look at their listed sources for clarification. But in this case, all the sources are books that I can't be arsed to buy, and web pages that are in -- believe it or not -- Portuguese. Half of them are 404 anyway.

But of course that's not stopping me from riffing on it.

Anyway, from what I can gather, the May 14 Revolt was a revolt of the revolt. That is, the supposedly representational government that got installed after the 1910 overthrow of the monarchy. According to this Wiki page

, "The Republican Party presented itself as the only one that had a programme that was capable of returning to the country its lost status and place Portugal on the way of progress."

Wow, history really does echo, doesn't it?

Point is, as is often the case in these situations, the government they replaced the government with was dysfunctional, so another revolt was called for in order to restore the values that the first revolt was supposed to have installed but didn't. At least that's my take on it; like I said, there's not a lot of detail on that page.

The insurrection was, from what I can gather, swift, bloody, and successful.

At least, at first. A few years later, there would be yet another bloody revolution, this one getting the country back to a dictatorship. It wouldn't be until 1975 that the country returned to some semblance of democracy.

From this, I have learned several things, including but not limited to:

Sometimes, revolution is necessary and ultimately beneficial, if bloody

I would not have wanted to live in Portugal before 1975

I'd venture to guess that most people don't know this bit of history, from which it follows that they are doomed to repeat it.

Democracy is fragile

Those bullets are meant to be bottles of port. Preferably 40 year vintage port, which at this point could have been produced after Portugal achieved a semi-stable democracy. Port gets its name from the city of Porto, where, historically, the wine was shipped out to the great benefit of other countries (and the financial benefit of the vineyards and Portugal).

Oh, and one other interesting bit. The name "Portugal" is of somewhat disputed origin, but is most recently derived from the Roman name for it, Portus Cale. You can guess what Portus means. Cale is the disputed part

. It might have been a Celtic word for "port," which would make the name of the country translate to "Port port."

I like that.

As a final disclaimer, I might have gotten some of this shit wrong; like I said, it's not something I've looked into before. Don't take my words (or Wikipedia's) as the gospel truth. Just consider this another port in the storm.

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