Travis Garrett's Blog

(In his spirit...) The particular class of permutations of some 10,000 trillion trillion atoms - many ancient supernova ash - that conspired to form Francis Crick's brain and body have given up the ghost in our local branch of the universal wavefunction. He will not be forgotten.

The sky was beautifull today, July 30, 2004. After yesterday's dramatic storms, the sky was a deep clear blue this morning with friendly puffy white cumolous clouds that you could almost reach out and touch. Then, as dusk approached the clouds that remained were brilliant faint cirrus, and as the sun set and the tree tops were that wonderfull golden-green, the clouds glowed white, infinitely far away. And in the dark, through the tree branches, a bright white full moon rises.

The picture below is from Jared Tarbell's complexification.net, got there from a link on BoingBoing. He does lots of wonderfull, interactive computer art, and he's also featured at levitated.net. I also found this cool compilation of tall buildings from moma.

Oh, and today's fun integral is ∫ 1/(1+e*Cos(x))^2 dx, with 0 < e < 1, evaluated from 0 to 2π ...

Lots of links, part 2. First, one of the classics: Gödel's incompleteness theorem. Perhaps after going through the proof in detail I could come up with more rigorous mathematical arguments for Statistical Metaphysics, although stat meta certainly isn't any one particular formal system (which is also why Gödel-like proofs do not invalidate it - if anything they corroborate it, i.e. we will always need to add interesting new axioms...). And some more neural network webpages I found from Jenny Orr, and Ben Best. Apparently back-propogation is a big deal for training the networks, although you also don't want to overtrain them so that they can generalize better (which can be done by adding random variations). I wonder if just iterative evolutionary processes can be enough to train them - doing lots of local mutations on the connection strengths for different members of a 'species' and then selecting the best one (round-robin tournament?) and making more variations around it... And this talk of competition reminds me that I watched Lance finish off the Tour de France this morning, which was quite inspiring. And oh yeah, I met a cool new physics graduate student Michael Good last week, who is also interested in the mathematical foundations of reality. Apparently his former advisor David Finkelstein also proposes that all mathematical structures exist, which then leads to the natural statistical conclusion that we will always find more complex mathematical generalizations in physics.

More links... I found this fractal website from pages on cellular automata. It's an old-school late 90's site (with updates up through 2003), which makes me a little nostalgic - I've been online for almost 10 years now! Looking forward to the web in another 10. And this philosophy site from Stanford is (unintentionly) humorous - he goes on and on saying that it is not necessarily the case that Turing machines are capable of emulating the mind, finishing with: It is an open question whether a completed neuroscience will employ functions that are not effectively calculable. i.e. he suggests that the operation of the brain could depend on functions like the halting probability, which is absurd. The brain is a neural network working in the classical limit, and even if essential quantum effects played a role (not likely - Tegmark argues decoherence occurs at around .1 picosecond) the atoms in the brain can be simulated to arbitrary precision as programs like Gaussian make clear.

After googling for Conway yesterday, I found some cool Game of Life links: such as this quick one, and this fairly cool collection hosted at UNC's very own www.ibiblio.org: lifepatterns, which among other things has a link to Rendell's turing machine.

Awesome: hyperreal numbers and surreal numbers. I particularily like that Conway developed surreal numbers while studying the game of go.

Here's the picture I talked about in the previous entry. And what do you know, it looks like they're maybe 5 centimeters long... Also, if you look closely you can make out the tiny flashes of color on the ends of the droplets. The beach was a lot of fun. For some reason I really enjoy being out on the beach during the brightest high noon (mad dogs and Englishmen?) - and when you think about it, it is a fairly rare type of place within the galaxy... It was also really nice to relax, see the family, and work on some side projects. Started writing up some string theory in latex, and I'm thinking that doing a numerical project with membranes would be a good idea, maybe get a paper out on it before I graduate. Seeing the equations really drives home that we are composed of mathematical structures. Speaking of potentially large-dimensional matrices, I also worked on my neural-net go-playing program, which I think will have at least 7 different indices. And I'm working on a follow-up to the primordial soup story which should be awesome.

It's been a busy week, but I've got some good analytical calculations for my paper done. One amusing thing I did was go to the math/physics library to get a resource for the calculation, and seeing Newton's principia made me stand back and look at all those books and appreciate how much has been done in the last couple hundred years. I spent a good couple hours going though books with interesting titles and reading bits in them. Exponential growth... Oh, and I went out with Katie at sunset and had sushi tonight, to celebrate her getting a job, and that was a lot of fun.

Allison is coming home from Australia soon, so I thought I'd post another picture from the trip - this one's from Hong Kong. And I just got back from Hilton Head. Random impression - coming back from the beach at high noon, I'd wash off the salt water in the outdoor shower. With the sun shining down from overhead, the falling water droplets were dazzingly bright - they seemed to form centimeter-long sparks of pure light. Thinking about it now, the water droplets had fallen about a quarter of a meter, giving them a speed of v=(2*9.8*.25)^.5, about 2 meters per second. So if the eye was seeing in .1 second 'snapshots', then the streaks of light should be 20 centimeters long. Hmmm... They did flash in and out of the field of vision almost as fast as possible - say I was seeing .02 second glimmers, that would give 4 centimeter long streaks, which still seems a little long. I took a photograph of the shower in the sunlight, maybe that could help resolve the issue if the shutter speed is known. Still, the most hypnotic thing about watching it was that there were tiny refracted rainbows just barely visible at the ends of the falling water droplets - shards of red and yellow glinting at the edge of perception.