On Dec 30, 2008, at 11:45 AM, Steve Richfield wrote:
Bingo! You have to "tailor" the techniques to the problem - more than just "solving the equations", but often the representation of quantities needs to be in some sort of multivalued form.
What I meant is that if the standard algebraic reduction algorithm is not possible, there are other algorithms you can use to generate a set of equations that can be solved using algebraic reduction. Humans are pretty limited in their ability to manually apply the "generate a set of equations that can be solved" algorithm(s) because there are too many dimensions, but computers have no problem. I cut my teeth working on these types of solvers (in FORTRAN, yech).
I wonder if we aren't really talking about analog computation (i.e. computing with analogues, e.g. molecules) here? Analog computers have been handily out-computing digital computers for a long time.
Since "digital" and "analog" are the same thing computationally ("digital" is a subset of "analog"), and non-digital computers have been generally superior for several decades, this is not relevant. The difference between "digital" and "analog" is the signal-to-noise ratio (SNR) that has to be maintained by the computer system. You can simulate with perfect fidelity high SNR computers on low SNR computers (like digital computers) since they are equivalent, trading SNR for frequency. If you apply the formula for converting digital bits to analog SNR (analog SNR = 1.76+6.02*bits), it becomes obvious why things like thermal noise make it impossible to directly implement e.g. a modest 32-bit digital processor as a non-digital equivalent.
When most people talk about "analog computation", they are really talking about real computers (whether they realize it or not), which are a form of hypercomputer. If it was possible to build such a computer, it would have some strange consequences for physics that are not in evidence.
Cheers, J. Andrew Rogers ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=123753653-47f84b Powered by Listbox: http://www.listbox.com
