What about the fact that the best compression algorithm may be insanely expensive to run? We know the math that describes the behavior of quarks, which is to say, we can in principle generate the results of all possible experiments with quarks by solving a few equations. However doing computations with the theory is extremely expensive and it takes something like 10^15 floating point operations to compute, say, some basic properties of the proton to 1% accuracy.
Good point. My answer is: yes, we have to accept a speed/accuracy tradeoff. That doesn’t seem like such a disaster in practice.
Some people, primarily Matt Mahoney, have actually organized data compression contests similar to what I’m advocating. Mahoney’s solution is just to impose a certain time limit that is reasonable but arbitrary. In the future, researchers could develop a spectrum of theories, each of which achieves a non-dominated position on a speed/compression curve. Unless something Very Strange happened, each faster/less accurate theory would be related to its slower/more accurate cousin by a standard suite of approximations. (It would be strange—but interesting—if you could get an accurate and fast theory by doing a nonstandard approximation or introducing some kind of new concept).
What about the fact that the best compression algorithm may be insanely expensive to run? We know the math that describes the behavior of quarks, which is to say, we can in principle generate the results of all possible experiments with quarks by solving a few equations. However doing computations with the theory is extremely expensive and it takes something like 10^15 floating point operations to compute, say, some basic properties of the proton to 1% accuracy.
Good point. My answer is: yes, we have to accept a speed/accuracy tradeoff. That doesn’t seem like such a disaster in practice.
Some people, primarily Matt Mahoney, have actually organized data compression contests similar to what I’m advocating. Mahoney’s solution is just to impose a certain time limit that is reasonable but arbitrary. In the future, researchers could develop a spectrum of theories, each of which achieves a non-dominated position on a speed/compression curve. Unless something Very Strange happened, each faster/less accurate theory would be related to its slower/more accurate cousin by a standard suite of approximations. (It would be strange—but interesting—if you could get an accurate and fast theory by doing a nonstandard approximation or introducing some kind of new concept).