Fractal Results

These are the results of the requests I got for Newton's fractals. Each function generates a fractal that, in principle, covers the entire plane, but I only show a small window of it. When I talk about the "range" of the fractal, I am referring to the location and dimensions of the window I chose.

Susan asked for the hyperbolic trig functions. Actually, they look more or less the same as the regular trig functions, but that's okay because the trig functions turn out well.

This is the function cosh(z) in the range -.5 to .5 on the real (horizontal) axis, and -.5 to .5 on the imaginary (vertical) axis. Note that only the first six roots get unique colors--the rest are all black.


And this is the function tanh(z) in the range -3 to 3 in the real axis and -2 to 2 in the imaginary axis.

An anonymous commenter asked for the function e^-(ixcosx)+e^(xsinx). This is a complicated one, graphed from 0 to 2 in the real and imaginary axes. I suspect those black comb-shaped things are actually artifacts of my program, but it took such a long time to generate the fractal that I wasn't going to try to figure out how to get rid of them. Besides, they look cool.

Why I'm not a humanist

There is a certain virtue in avoiding "positive" labels. On the one hand, you want to present yourself positively. On the other hand, you don’t want to present yourself as better than everyone else.

I don't consider myself to be a humanist. What exactly does that tell you about me? Does it mean that I don't view the good of humanity to be the highest good? Does it mean that I don't believe in any sort of human dignity? Does it mean that I don't value rational human inquiry? No, silly. It just means that I don't like the word "humanist". Maybe I technically qualify as a humanist, but I never call myself one.

In the atheosphere, I nearly always see the word "humanism" in only one context. Humanism is meant to be the positive counterpart to atheism. Atheism tells you what we don't believe in, and humanism tells you what we do believe in. Atheism is just one aspect of a person, while humanism is a complete philosophy. For a word that's supposed to be all-encompassing, I find it odd that I only ever see it in one place.

I just don't ever see the necessity to use the word "humanist". For one thing, no one ever asks me, "What do you believe in, if not God?" except in my dreams (dreams I attribute to my large ego). And if someone did ask, I'd probably just say, "Life? Goodness?" (I might also add "induction" on account of being a fanatical inductionist.) If I responded, "Humanism," who would know what that means? Most importantly, I don't know what it means. I only know the many things that have been told to me. My sources are a little vague about the details, but whatever humanism is, I know it's good! A bit of liberal politics here, a bit of the-good-of-the-human-race there, a dose of church-state separation, a rejection of the supernatural, along with a compatibility with religion. I figure that if it's good, it must be somewhere in the mix (and guess where that leaves the non-humanist).

I have no patience for any of that. If I wanted to say in detail what I believe in, I'll deliver it in plain words that everyone understands, not in a mystery package that not even I understand. For all those humanists out there, maybe you understand what humanism is, but does everyone else understand it the same way you do?

Of course, to be fair, I myself go with the "skeptic" label, which is also a "positive" philosophy. And though I understand what I mean by skepticism, not everyone immediately understands it the same way I do. Call me a hypocrite if you will. But I understand these things, that people can have aversions to labels even if they agree with the ideas represented by the labels. Just because a person doesn't go by a label doesn't mean they go against everything the label stands for. This applies to all labels.