Path: utzoo!news-server.csri.toronto.edu!cs.utexas.edu!swrinde!mips!dimacs.rutgers.edu!aramis.rutgers.edu!athos.rutgers.edu!nanotech From: toms@fcs260c2.ncifcrf.gov (Tom Schneider) Newsgroups: sci.nanotech Subject: Re: Is this stuff for real? Keywords: reality nanotech questions Message-ID: Date: 16 Mar 91 03:33:22 GMT Sender: nanotech@athos.rutgers.edu Organization: NCI Supercomputer Facility, Frederick, MD Lines: 48 Approved: nanotech@aramis.rutgers.edu In article cphoenix@csli.stanford.edu (Chris Phoenix) writes: >Picture the following nanomachine, designed to prevent mutation: >*everything* will be under the control of one or more computers. ... What you are constructing is a way to make error correcting codes. Shannon showed many years ago that it is possible to construct codes that reduce the error rate to as low as you may desire. This stunning result is still not well appreciated by communications engineers. (I have a recent book in which it is incorrectly stated.) Basically it goes like this. If you want a communications line which runs at (say) 10^6 bits per second with one error in 10^5, it can be built. If instead you insist on 1 in 10^10 with the same data rate, sure that can be built. Well! You need 1 in 10^20? sure! And so on! HOWEVER the price you must pay is that you must encode the signal before transmission and decode it afterward. There will be delays in these operations. Actually, you can do this only so long as the data rate is below a certain level called the channel capacity which depends on the power absorbed by the receiver, the thermal noise and the bandwidth. If you go above the channel capacity, you'll get lots of errors that force you back (at least) to the channel capacity. How does this apply to nanotech? What we need to do is make a correlation between the little molecular machines and Shannon's mathematics. I did that in the papers I mentioned previously (JTB 148:83-123,125-137,1991). The translation is a bit bizarre from a biologists viewpoint: so long as the machine capacity is not exceeded, the error rate may be as low as is necessary for survival of the organism the machine is part of. ("desire" has no meaning in evolutionary biology.) Shannon's theorem shows that you can get the mutation rate as low as you might want, but you can't make it zero. (This is based on the assumption that there is white gaussian noise affecting the machine, so if you can get around that, you could beat the capacity.) So what it will come down to in the end is we will have to decide how likely we want errors to be, and then pay the design and material costs to get there. Encoders and decoders are not free. Tom Schneider National Cancer Institute Laboratory of Mathematical Biology Frederick, Maryland 21702-1201 toms@ncifcrf.gov