Empirical Computing: Unlocking Limitless Calculation Speed

[Bartholomew]

We know the basic principles behind many systems which are nevertheless too complicated to calculate accurately--turbulent flow, for example. The number of calculations required to precisely model turbulent flow is enormous, but it happens in nature and can be empirically observed. What would prevent a computer from taking physical examples of turbulent flow as ANSWERS to calculations, and finding uses for those answers in other problems? If done properly there would hardly be any upper limit on how fast calculations could be performed.

 

[Alkatran]

We know the basic principles behind many systems which are nevertheless too complicated to calculate accurately--turbulent flow, for example. The number of calculations required to precisely model turbulent flow is enormous, but it happens in nature and can be empirically observed. What would prevent a computer from taking physical examples of turbulent flow as ANSWERS to calculations, and finding uses for those answers in other problems? If done properly there would hardly be any upper limit on how fast calculations could be performed.

I don't think this would work. What would the results from problem A have to do with problem B? If the situations are similar, then the answers will be close, but doesn't that destroy the point of "accurately" calculating?

 

[HallsofIvy]

Actually, what you are describing is an "analog computer". For example, one can show that an electrical circuit, with induction coil of strength L, resitance of strength R, and capacitor of strength C connected to a voltage source V(t), gives rise to the differential equation L y"+ Ry'+ (1/C)y= V(t). One can use an electrical circuit, with variable coil, resistance, and restistance, connected to a voltage generator, to solve differential equations of the form ay"+ by'+ c= f(t).

 

[Bartholomew]

You would have to pick the system to observe and the problem to solve very cleverly, so that they are as close as possible. But since there are so many physical systems to pick from and so many ways of stating problems, this is only a practical obstacle.

Anyway, we do it already; all computing is actually "empirical computing." We choose the physical processes that go on in computer chips so that they parallel logical operators as closely as possible. When we punch in a calculation on a calculator, what we are doing is trusting that the processes inside the calculator mimic closely enough the abstract procedure of finding the answer.

The difference between that kind of empirical computing and REAL empirical computing--and it is a big one--is the trade-off between complete control of what is calculated (conventional computers) and complete speed of processing (real-world chaotic systems).

Probably it would require some new kind of AI to find the parallels. I doubt any group of humans would be smart enough unless thousands of years were devoted to the research. But... I say it's possible.