# Tag: mathematics

We’ve been using our fireplace quite a bit this winter. We didn’t use it at all last winter. I like to think it has to do with the cold weather, but really, it is more about the ambiance. We have an open living room/dining room/kitchen area and the fireplace is in the living room, just beneath the TV mounted above it. Is is visible from anywhere in the living room/dining room/kitchen. In fact, it is visible from right here at my desk in the office.

There is one corner of the sofa that closer to the fireplace than others. I like to sit there and read while the fire is roaring. I can feel the warmth from the fire. The only downside is that the flames often distract me from my book. I like to watch them dance around. I enjoy watching sparks separate from the flames like miniature sky lanterns, zipping up the chimney.

The burning wood smells pleasant. The crackling of the logs and snapping of the air around the flames is calming. Perhaps why a fireplace is so enjoyable is that it engages nearly all of our senses at once. We see the flames, feel the warmth, smell the wood, and hear the snap-crack-pop of the air and logs. Lately, I’ve been keeping the fire going most of the day, allowing it to burn out at night before we head off to bed.

Sometimes, however, I am distracted. Busy with work, or stuck in meetings, the flames may die out, and when I wander from office to the living room, I’ll notice that the flames have gone out, and only smoldering embers remain. That’s my cue to get things going again.

Until this afternoon, however, I never actually witnessed the flame wink out. I was sitting on the couch, reading the essay titled, “A Mathematical Romance” in Jim Holt’s enjoyable book, When Einstein Walked With Godel. There is some tricky (for me) mathematical discussion in the book, and whenever I read tricky mathematical discussions, I have to pause and visualize each step in my head to make certain I am getting it. In this case, I looked up from the book, and stared at the fireplace. A single flame danced sluggishly about. I watched the flame flicker slowly here and there. And then, just like that, it winked out. It was just gone. All that was left was the smoldering embers of what was left of the log.

I stared at the log, all thoughts of math gone from head. I was overcome by a kind of sadness. I’d witnessed the death of a flame. I’d seen it wink out of existence. In that moment, my mind jumped billions of years into the future, to an outpost somewhere outside our solar system. I seemed to sit there, in a comfortable room, warmed from a source of heat I couldn’t quite see. I was reading a book of science essays, very much like the book I’d been reading minutes–and billions of years–ago. Before me was view of a very dim star, centered against a background of other stars.

I looked up from my book in order to visualize the math that I’d been reading about–just in time to see that dim star–our star, the sun–flicker for the last time, and then wink out completely.

Who knows if there will be anyone around in several billion years from now to watch the sun wink out the way I watched the flame in the fireplace wink out. If they happen to be our descendants, I imagine they will be unrecognizable. But, if they recognize the star that served as the life source for their ancestors, I can imagine them feeling a moment of sadness as they watch it wink out. I wondered, as I returned to the sofa, and stood to light more wood, is it better to to notice and feel that momentary sense of loss? Or is it better for flames to wink out unnoticed by others, like a dog walking into the woods to die?

One of the cool things about being a science fiction writer is the cool stuff you learn in the name of “research.” I’ve been doing a lot of reading up on black holes, in particular, “subatomic” black holes and it is a fascinating subject. Some of what I have been reading are academic papers, which can be mathematically dense at times, often going well beyond my meager abilities to differentiate and integrate, but by reading some secondary sources, I’m beginning to get the drift and some of this stuff is actually starting to make sense. What’s more, the story for which I am doing the research hinges in part on the properties of these special black holes, and some of what I learned today helps make for an interesting plot problem.

Related to this (as you will see in a moment) is that fact that one of the new features of WordPress 3.1 is that it supports LaTeX. Non-geek friends will most certainly make plenty of jokes about LaTex, but LaTex is actually a really cool markup language that evolved from TeX and allows for the rendering of arbitrarily complex mathematical formulas. Back in the day, I used to write up my calculus lecture notes in LaTex because I could render all the equations and their intermediary states. Combing this functionality with what I’ve been learning about black holes, I could tell you for instance, that for a black hole with a mass M, its effective radius, R is

$R = \frac{2GM}{c^2}$

Isn’t that just the coolest thing ever? I’m so impressed that WordPress now includes this capability. I could go on and tell you that the temperature T of a black hole with an effective radius R is

$T = \frac{hc}{4\pi kR'}$

Of course, I can render any arbitrarily complex equation with relative ease using LaTeX’s markup language directly in WordPress, but you get the point. I’ve been taking lots of notes on these black holes, incidentally, and if I can validate my understanding of these properties with some friends with backgrounds in physics, then I think I’ll have the foundation for a pretty good hard SF story. Stay tuned.

I mentioned the other day when I finished reading Death by Black Hole that I was going to read Isaac Asimov’s essay collection, The Secret of the Universe next. I have since changed my mind. This morning, I started a book that I bought back in October and have been wanting to read for some time, but just haven’t gotten around to it yet: Unknown Quantity: A Real and Imagined History of Algebra by John Derbyshire. I enjoy books on mathematical subjects and have read several. I started this one this morning on the train into work and so far, I’m not disappointed.

Incidentally, the title of this blog entry, “Nine Zulu Queens Ruled China” is a non-sense mnemonic for the nested number sets used in number theory: N represents the natural numbers, Z represents the integers, Q represents the rational numbers, R represents real numbers, and C represents complex numbers (which include imaginary numbers).