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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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June 12, 2023 at 9:07am
June 12, 2023 at 9:07am
#1050969
Another one for "Journalistic Intentions"  [18+]...

Swimming


Ever wonder why you don't have fur?

Other apes are covered with their own pelts, rather than those of other animals. And yet, we humans, who manage to survive in some of the world's most extreme climate conditions, don't. Some are hairier than others, of course, and evolution played an especially big joke on men, who, with age, tend to lose the hair on our heads while gaining it in our ears and noses. (Not me, of course. But some other men.)

One hypothesis that was presented a while back is called the "aquatic ape hypothesis." Noting that most aquaphilic mammals are mostly hairless, the idea is that, at some point after diverging from our common ancestry with chimpanzees around six million years ago, some proto-humans spent a lot of time swimming.

Fur is generally not suited to swimming. Drag, I suppose. The obvious examples are whales, seals, and any number of other aquatic mammals. The same can be said for feathers; hence, penguins. And then, by this theory, we left the water and yet maintained an affinity for it, as illustrated by the popularity of swimming.

There are, of course, counterexamples, such as beavers. Maybe polar bears.

The problem with the aquatic ape hypothesis, however attractive it may be, is that it's wrong.

Well. Probably.  

Part of the problem is a misunderstanding of how evolution works. Another problem is the old chicken/egg thing: did we become (relatively) hairless because we were swimming, or did we get (relatively) good at swimming because we were hairless?

There's little doubt in my mind that lack of fur makes for better swimming (not to mention drying off after), but there are several other possible reasons for the adaptation. Including that it's not a true survival adaptation at all, but a side effect of other genetic changes, or a result of sexual selection, or some combination of factors.

What we do know is that, whatever the evolutionary reason, humans have the capacity to learn how to swim, and many do, and derive great pleasure from it, or even from watching other people swim. Not me, of course (though I did learn as a child and can at least still dog-paddle), but other people. And it can provide a survival advantage, especially when you get thrown off the boat for being too pedantic.


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