Thursday, October 06, 2005

Kurzweil and big numbers

I picked up Kurzweil's new book (I might review it later), The Singularity is Near. In an interesting section on the limits of computation and storage called "How Smart is a Rock", he calculates a minimum information density for a 1 kg rock to be 10^27 bits, and that it can perform at least 10^42 changes in state per second, considering EM interactions alone. This works out to roughly 10^24 bytes/cc, 10^39 cps/cc.
This seemed large until I found that 3 years ago I had "designed" a future bio-chip that was only 6 magnitudes off, and I had handicapped myself by both shielding for electron tunneling effects and only considering one mode of info storage. Eliminating both of these would put me up in that region.
Daviditron has me thinking hard about the computational power of raw nature, especially as it regards the formation of life out of non-life. Like myself, he's latched onto surface areas, although the direction he's going in seems very surreal. Not like all these large numbers seem very real either.
If we take as an approximation to 2D space a thin slice 1 micrometer thick, the info density of 1cm2 is 10^8 terabytes, executing 10^35 cps, and it's all energy-maximizing parallel processing. While this isn't human information, like sight or sound or tactile info, but rather the substrate for it, and not a human scale, it is a rough (and most likely low) approximation to Nature's evolution-wise scale.
So, for every cc of raw pre-life organic goop, we have at least 10^42 cps, operating on itself, finding ways to maximize energy use. For every cm2 of surface area on bubble membranes, on sea floor bottoms, and on crystalizing surfaces, we have 10^35 cps. For the number challenged, that calculation power is to the computer on your desk as the computer on you desk is to Paris Hilton doing long division. Roughly.

This probably doesn't help you very much, but I'm a bit closer to understanding how life could arise from non-life.

2 comments:

schmutzie said...

Yowza.

rainswept said...
This comment has been removed by the author.