I need 556 XP to reach level 16.
The inventor of the 555 timer, Hanz Camenzind, passed away recently. Every electrical engineer knows what a 555 is. It looks like a bug with eight legs, and you can use it to create all sorts of timing circuits and oscillators, one-shots, pulse generators, modulator circuits, and so forth. I say "and so forth" not because I'm linguistically lazy, but because these little timers are so ubiquitous that when you review another engineer's designs, you think, "I would never have guessed a 555 could do that."
You set the basic period with a judicious choice of resistors and capacitors. Hmmm. Too much detail. I was going to talk about the math of this, but it would be wasted on the general readership, philistines that you are.
So anyway, that's how 556 triggered that associative path. But 555 isn't the only interesting number. The number 16 is pretty cool too.
Power of 2. In fact, doubly sweet, since it's a power of 2 to a power of 2. Two to the two to the two. So sweet!
17 is a prime. 51 is not.
A friend is turning 51 next month. She was planning a party so she told me. This burst out of my mouth, unbidden:
"Oh. 51 is a nice number. It's three times 17."
We were strolling down Market Street in Reston, and she literally stopped on the sidewalk and looked directly at me. Uh oh, I thought. Instant mistake. Exceeded my geek quotient of the day, did I?
She smiled, as she invariably does. I amuse her. It's not so much a Freudian slip as it is Euclidean.
"What a wonderful fact! I'm going to be 17 again! And this is going to be my third time!"
(It turns out, guys, that there really is a subset of women who go for math geeks. I'm fifty-seven years old and I can attest to the truth of this statement. And they're rilly rilly attractive. Do not give up hope, all who enter here.)
If you're like me, certain numbers just jump out. You can't help it: you fixate on them. I think less of 51, because it looks like it should be a prime, but it's not. It's a prime poseur! Okay, its digits do sum to a multiple of 3, which is a dead giveaway that it's not prime, but still. I'm miffed at 51 for dressing like a hipster but being so ordinary inside. On the other hand, 57 is ugly, utterly without charm. So are 58 and 59. When we hit 60, though, we re-enter the world of serene coolness. 60 is a cool number, highly composite. So that might be a good birthday.
I worry about giving myself over to the dark side of mathematics. She is a siren, and her embrace is warm like heroin. But there are times you push away from your notebook and your computer and you want to be with somebody, and suddenly no one is around, because, let's face it, most women can only take so much of your insularity.
The fact is, if I were independently wealthy, I would do what I am doing now, which is spending a considerable amount of time just doing mathematics recreationally. I am filling a notebook with geometric facts and writing a book on triangle geometry. Ha ha ha. How bizarre is that? These are naked thoughts. Some day they will come back to haunt me.
Today a fairly wealthy friend posted something on Facebook. He used to swim for UC Berkeley. His life is full of ultra-elite swimmers, the types who swim for the Olympics and then retire and model bathing suits, or do triathlons. He's an interesting guy, since he lives in the world of finance. His head of security is a babe from Finland. I wish this wasn't true, but it is. She's freaking gorgeous. And yet she talks like one of those Secret Service types. Talk about weird signals. But back to him.
He used to dabble in high tech. He was a VP for one of the space companies I used to work for. He posted something about the Mars Curiosity rover recently, probably in reaction to a few of my enthusiastic posts about the Mars project. So he posted a photoshopped pic of a pool on Mars, designed by Diane Khoury (famous, that's all you need to know) with the blue Earth rising in the evening sky, and someone jumping off a diving board and splishy splashy people in the water. Something out of southern California in the 1950s.
I react in my usual manner. I'm telling you this because you're probably wondering what is, exactly, the usually geeky response to this sort of mundane thing. And you're probably drawing a huge blank. But here's how I responded.
I got out my spiral bound physics notebook, the one with ruled pages and a translucent blue vinyl cover, and I opened it up to the pages that had all sorts of facts about the Solar System written down in neat columns, and looked up the Mars surface gravitational field strength. (Potential? whatever. Oolong, help me out here.) Well, it was not to be found. But its mass was, as well as its radius, and so I figured out the equation for computed the value of the gravitational potention at the Martian surface, small g, to be 3.6 meters per second squared. You compare this with Earth's 9.8 m/s^2 (any Big Bang Theory scientist nerd would know this) and realize that you would be feeling about 1/3 the weight you do on Earth.
I then computed the fall time of an Olympic diver jumping off a 10 meter platform. Earth: 1.4 seconds. Mars. 2.4 seconds. An extra second of hang time on Mars!
That's how the math geek rolls.
So I post something on his board, something about a diver having an extra second to do extra flips and so forth.
The thing of it is, he knows he can't build a pool on Mars. He's just throwing this shit up there because none of his fellow swimmers knows that. He's just screwing with their minds. Which makes all of this extra doubly funny.
I was sitting in a dog park the other day. Dogs were pissing, running, barking, sniffing each others' butts, and doing other loathsome activities. I was zoned out, completely. Was imagining how a Kiepert hyperbola would move, if I changed a triangle's proportions. Let's see...
You construct perpendicular bisectors on each of the three sides, then build isosceles triangles on each side so that all of them have the same base angle, then construct the lines connecting the triangle vertices to the tips of the isosceles vertices, and these three lines meet at one specific point K, so that when you move the angle of the base, all three isosceles triangles change, and then K changes location, and... wow, it sweeps out into a hyperbola! Cool!
And dogs were continuing to hump and piss and sniff butts, but I was thinking of imaginary triangles in imaginary space, and that whole grimy world of mangy mutts was so far away.
I'm thinking of building a relationship with someone. She seems pretty normal. In fact, she's one of the most normal people I've ever known. She's extraordinary, to me, precisely because she's not extraordinary.
I fade out of her life, occasionally, as I experience these more frequent mathematical reveries. She doesn't get phone calls, or text messages or emails. Hand holding is sporadic. But she doesn't seem to be bothered by it all. She takes it all in stride. I haven't gotten one of those frantic WHERE ARE YOU AND WHO ARE YOU WITH messages that are the bane of any math geek. She is good at not being bothered by my sudden disappearances.
So that's the good part, right? But what if there is a better way? Maybe it's just easier to live alone and to see her aperiodically. That way I can just have a life and have to explain it to no one.
In the meanwhile, graph theory is calling. Random graphs. The Superlarge component. The Erdós-Renyi theorem. The famous Bollabas conjecture.
And then there's my Russian friend, who tries to explain to me that the Nyquist sampling limit is an upper bound only, that you can, under certain circumstances, perfectly reconstruct a signal with sampling rates significantly lower than the Nyquist rate. I don't believe him. We're arguing. We're having a gentleman's argument over coffee at Starbuck's. He usually proves by emphatic assertion, as he is wont to do. Anyone else I would blow off. Him I have to take seriously. The man has brains. Well, fuck. Now I have to read Harry Nyquist's paper and look over the math and convince myself of my belief that this cannot be done. Or be convinced that my friend is right. Either way. Not knowing something drives me freaking insane.
For JohnnyGoodyear. Five hundred words and shitty first drafts. Damn, I miss you, brother.