Voder-Vocoder

New phone number as of now:

239-313-9375

I was reading some old notes from some math research I did in 2004. I was looking at the Soddy Equation—

(a + b + c + d)^2 = 2(a^2 + b^2 + c^2 + d^2)

—which relates the curvatures of four kissing circles (see Descartes’ theorem). Example of four kissing circles.

Given three kissing circles, one can find two possible fourth circles (it’s a quadratic, right?). This makes a cluster algebra-like thing and graphically makes a Apollonian gasket.

So far no big suprise. This has all been known since Rene Descartes.

* * *

We had an interesting idea. Draw a Apolonian Gasket. For each of the infinite number of circles in the gasket, perform a circle inversion of all the OTHER circles with respect to that circle. Then plot that out. Repeat the process on all the new circles, ad infinitum. You now have an infinite number of circles, topologically dense in R^2, with the property that no two circles intersect in anyway but tangentially.

I never came up with a decent way to program a computer to display such a set.

I called this the Dionysian Gasket.

I’ve been watching too much Home & Garden Television recently. I got sick of looking at those old bankers boxes on my shelves so I covered them in brown paper.

When we went kayaking, we took along a waterproof disposable camera. This was the first time I’ve gotten film deveoped in several years, so I din’t know what Kodak can do with digitizing these days. The Kodac Picture CD contains a bunch of extranious software, but the images themselves are 1536×1024 JPEGs (1.5 megapixels). I suppose that’s close to the limit of 35mm film.

The last time I had photos digitized by the developer was around 1999. I had Seatle Filmworks send me a floppy disc with low-quality 640×480 images in their proprietary format.

For web-purposes, I scaled them down to 900×600. Archive.

Peace River, 2006-09-10:

Estero River, 2006-09-17:

Damn you Netflix! For sending me my discs out of order!

This article tells how to burn CD using cdrecord to make it easier to run a checksum program on the burnt CD.

For future reference, here it is:

$ sudo /usr/bin/cdrecord dev=/dev/hdc -dao -v \
	driveropts=burnfree -eject ${ISOFILE}
$ sha1sum /dev/hdc

Right now I’m not buying new books because i’m in super-thrifty mode. (I did, however buy a new compass (a Brunton 26DNL) that floats for my next kayacking trip. Not that it is easy to get lost when you are on a river. You’re either going upstream or downstream. I bame the DVDs of Lost.) One book that I’m not buying due to the moratorium on new books is The Gospel of the Flying Spaghetti Monster (ISBN 0812976568).

Inside the Gospel are the The Eight “I’d Really Rather You Didn’ts”, commandments for Pastafarians. I especially like number 5:

5. I’d Really Rather You Didn’t Challenge The Bigoted, Misogynist, Hateful Ideas Of Others On An Empty Stomach. Eat, Then Go After The Bastard.

An explanation of some obscure HTML/CSS issues.

I finally got around to reading Larry Niven’s 1971 novel A World Out of Time. It has a bunch of the really classic sf elements: bussard ramships, the distant future, uploads, distopia, genetic engineering, mobile planets.

The reason I haven’t read this one before now is that it has a really ugly cover. This one really needs to be republished with a better cover.

Update 2006-09-17: Since I finished the book I’m been racking my brain trying to remember where I had read about the fusion candle. It was in a Schlock Mercenary strip from a couple of years back.

The candle is the most feasible method I’ve heard for moving planets. It involves improbable engineering, but doesn’t involve impossible physics.

from pages 200-201 of A World Out of Time:

Two tubes, concentric, each a hundred miles long; the inner tube a mile wide, with thick walls if complex construction; the outer tube thinner and twice as wide. At one end, a bell-shaped rocket nozzle. At the other […] Reworked military laser cannon, and vents, and a flared skirt, and thick stubby fins, there at the bottom end. Now temporary liquid hydrogen tanks were attached. Now the structure moved under its own power…it was a tremendous fusion motor…moving outward, circled by tiny ships…yeah.

Corbell said, “How do you move the Earth?”

“You are here to tell us that.”

“Well it’s a problem. A rocket motor won’t do the job. You need something that can pull on the entire mass of the planet, nickel-iron core and crust and oceans and air, all at once. Where do you find a force like that?”

[…] “You move something else,” Statholtz said. “The damage done by the rocket’s thrust and by mistakes you might make will not kill anyone if nobody lives on the working body. Then the working body can be moved until the world falls toward it as a rock falls to the ground. What was the working body? Ganymede?”

“Uranus. Can you stop the light show at that picture?”

The lecture froze on an “artist’s conception”: a blurred, curved arc of Uranus’s upper atmosphere. The motor looked tiny floating there. Corbell said, “You see? It’s a double-walled tube, very strong under expansion shock. It floats vertical in the upper air. Vents at the bottom let in the air, which is hydrogen and methane and ammonia, hydrogen compounds, like the air that the sun burns. You fire laser cannon up along the axis of the motor, using a color hydrogen won’t let through. You get a fusion explosion along the axis.”

[…] “Okay. The hydrogen fusions in the middle of the motor—”

“—and the explosion goes out and up. It’s hottest along the axis, cooler when it reaches the walls of the motor. The whole mass blasts out the top, through the flared end. It has to have an exhaust velocity way higher than Uranus’s escape velocity. The motor goes smashing into deeper air. You see there’s a kind of flared skirt at the bottom. The deep air builds up there at terrific pressure, stops the tube and blasts it back up. You fire it again.”

“Elegant,” says Statholtz.

“Yeah, Nobody’s there to get killed. Control systems in orbit. The atmosphere is fuel and shock absorber both—and the planet is mostly atmosphere. Even when it’s off the motor floats high for a while, because it’s full of hot hydrogen compounds. If you let if cool off it sinks, of course, but you can bring it back up to high atmosphere by heating the tube with the laser, firing it almost to fusion.”

Let’s look at the numbers. Suppose that the acceleration is 1/1000 of a gee.

F = m a
  = (8.6832 × (10^25)kg) (0.01m/s^2)
  = 8.6832 × 10^23 Newtons

Assume the exhaust velocity averages 300,000 m/s (similar to a VASMIR)

mass flow = F / v
          = (8.6832 × 10^23 Newtons)
             /(300000 m/s)
          = 2.8944 × 10^18 kg / s

Which is insanely huge. We’d probably need a bigger exhaust velocity, but I can’t imagine it being too much bigger.

New back-of-the-envelope calculations on this subject:

Let’s say we want to calculate how much thrust you need to move Uranus to Earth’s orbit using a standard Hohmann transfer orbit. Ler’s only calculate how much thrust it would take to put Uranus into the transfer orbit, ignoring the second half of the problem—taking it out of that orbit.

radius at aphelion = ra = 2.9*(10^12) meters
radius at perhelion = rp = 1.5*(10^11) meters
gravatational constant = gc = 6.67*(10^(-11))
Mass of Sol = ms = 2.0*(10^30)
Delta-Vee at aphelion =
	sqrt(gc*ms/ra) * (1-sqrt(2*rp/(ra+rp)))

I used bc to do this calculation:

#!/usr/bin/bc -ql
ra=2.9*(10^12);
rp=1.5*(10^11);
gc=6.67*(10^(-11));
ms=2.0*(10^30);
deltavee=sqrt(gc*ms/ra)*(1-sqrt(2*rp/(ra+rp)));
print deltavee, "\n";
quit;

The answer was around 4700 m/s. Since the exaust velocity of our engine is 300,000 m/s, we need to use around 1/63rd of the total planetary mass to move it. (300000/4700 = 63).

I moved my blog over to WordPress, which I have been meaning to do for years. It’s finally come along to the point where it is fairly usable.

Update. I’ve put a lot of effort into writing a decent Wordpress theme for this site. I’m debating releasing this theme back to the community, versus keeping it all to myself.

Yesterday I worked on the comments page. The layout is somewhat reminiscent of the Livejournal comments layout. I am making use of Gravatars for user icons. So if you make a comment and want a fancy icon, be sure to use the same email as you use for your Gravatar account. For those worried about spam-bots harvesting your email from my comments page, don’t worry: the Gravatar icon encodes you email in a MD5 one-way function.

I also went through all 614 imported posts and validated the HTML and verified that the import didn’t screw up the post too much. That took a long time, but it was necessary. I think I had a lot of invalid HTML out there before the import.

I also wrote a .htaccess file to redirect every one of my old archive pages to the new archive pages. This was necessary because I intend permanent links to be permanent.

Number dead as a result of 2001 September 11 Hijackings: 2,973

Number dead as a result of Iraq War: 65,000+

Number dead as a result of Traffic Accidents in US in 2005 alone: 43,443

Update 2006-09-18: Ryan Singel says it much better here:

With that in mind, here’s a handy ranking of the various dangers confronting America, based on the number of mortalities in each category throughout the 11-year period spanning 1995 through 2005 (extrapolated from best available data).

S E V E R E
Driving off the road: 254,419
Falling: 146,542
Accidental poisoning: 140,327

H I G H
Dying from work: 59,730
Walking down the street: 52,000.
Accidentally drowning: 38,302

E L E V A T E D
Killed by the flu: 19,41
Dying from a hernia: 16,742

G U A R D E D
Accidental firing of a gun: 8,536
Electrocution: 5,171

L O W
Being shot by law enforcement: 3,949
Terrorism: 3147
Carbon monoxide in products: 1,554

Yesterday I kayacked 16 miles on the Peace River near Arcadia, FL. I saw no Aligators, but I did see llamas.