*Catching up with Rudy Rucker's blog.
http://www.rudyrucker.com/blog/
(...)
"Over the years, I’ve noticed that certain kinds of computations are inexhaustibly greedy, and that by dialing up certain of their parameters to values that seem not all that big, you can get a computation whose demands would overwhelm the physical world.
"So what kind of computation is C. H. Hinton doing? Well, I’m going to have him computing a series of 3D fractal shapes that are based on a 27th-power polynomial equation, somewhat along the lines I described in my recent post “In Search of the Mandelbulb”
"Let’s back up a step to see how gnarly his computation needs to be. What is the computational capacity of ordinary physical space? According to quantum mechanics, the smallest meaningful length is the Planck length, which, in meters, is 1 divided by 10-to-the-35th power. And the shortest meaningful time is the Planck time, which is how long it takes a light ray to travel a distance of on Planck length. Measured in seconds, the Planck time clocks in at 1 divided by 10-to-the-43rd power.
"So if we assume that we might master a eldritch quantum computational technique that lets us carry out one computational operation per Planck length per Planck time, we’d be able to blaze along at 10-to-the-78th power operations per second per cubic meter.
"It might actually be that our physical space is in fact doing this everywhere and everywhen…effortlessly. Just keeping itself going. (((Or, it might actually not be, but you are dealing with one king-hell science fiction writer here.)))
"Planet Earth has a volume in cubic meters of about 10-to-the-21st power, so if we throw all of the planet at a problem, we can compute some 10-to-the-99th-power operations per second.
"We might just call it ten to the hundredth power, which happens to be the mathematicians’ old friend, the number googol. Googol ops per second!
"The diameter of our observable universe is currently estimated to be about 10-to-the-27th-power meters, so the whole universe has a volume on the order of 10-to-the-81st-power meters. And if you set all of that space to computing, you’ll rack up some 10-to-the-151st-power operations per second. Less than a googol squared.
"Using the whole universe as a computer doesn’t give you a very dramatic gain over just using Earth—the reason for this is that, relatively speaking, the jump from Planck length to Earth is in fact bigger than the jump from Earth to Universe. (((Yeah, that's, uh, not very dramatic. At least, not by Rudy's standards.)))
"Now let’s think of computations so greedy that they can swamp this level of computational capacity. (((Getting the popcorn.)))
"(1) Use a parallel computation which is spread out across a very large number of voxels, that is, small volume cells of idealized mathematical space. You can really increase the number of voxels by requiring that you can zoom down very deep into your views of the object.
"(2) Have the basic step of your computation per voxel be somewhat demanding. Have it use a higher-order formula, and have it require the formula to be iterated a large number of times.
"(3) Run a very large number of these computations at once because, we’ll suppose, you’re searching through a space of all possible formulae—hoping to find the best one.
"(4) And, just to keep the demand flowing, suppose that you want to update the output reasonably fast, say at a hundred times per second, so as to create a nice smooth animation.
"I’ve been thinking about three-dimensional fractals lately, so let’s suppose that’s the kind of computation we’ll use. I’ll want to look at a 3D fractal that’s twisting and changing in real time as some parameter is varied. (...)
(((Some time later:)))
"I searched for ultimate reality, and I found contentment in creativity. I tried to scale the heights of science, and I found my calling in philosophy and in science fiction. I was a loner, I found love, I became a family man. I was a rebel and I became a helpful professor. And I never stopped seeing the world in my own special way.
"It’s been a wonderful trip."
(((What a mensch this guy is. He's the guru. I don't spend every day of my life slack-jawed at the feet of Californian gurus – I recognize it as an occupational hazard, even – but when I think back, it's amazing how much solid, practical, cobweb-clearing mental benefit I got from knowing out-there California visionaries like Stewart Brand, Kevin Kelly, Tim O'Reilly and, yes, Rudy Rucker. They didn't so much break the mold as compute new ones.)))
