What you are probably asking is “can you predict something without simulating it faithfully?” The answer is yes and no and worse than no.
A generic sequence of symbols is not losslessly compressible. Lossy compression is relative to the set of salient features one wants to predict. For example, white noise is unpredictable if you want every point, but very predictable if you want its spectrum to a reasonable accuracy. There are special sequences masquerading as generic, such as pseudorandom number generators, which can be losslessly “predicted.” Whether it counts as a “simulation” depends on the definition, I guess. There are also sequences whose end state can be predicted without having to calculate every intermediate state. This probably unambiguously counts as “predicting without simulating”.
Again, most finite sequences (i.e. numbers) are not like that. They cannot be predicted or even simulated without knowing the whole sequence first. That’s the “worse than no” part.
There are also sequences whose end state can be predicted without having to calculate every intermediate state. This probably unambiguously counts as “predicting without simulating”.
What you are probably asking is “can you predict something without simulating it faithfully?” The answer is yes and no and worse than no.
A generic sequence of symbols is not losslessly compressible. Lossy compression is relative to the set of salient features one wants to predict. For example, white noise is unpredictable if you want every point, but very predictable if you want its spectrum to a reasonable accuracy. There are special sequences masquerading as generic, such as pseudorandom number generators, which can be losslessly “predicted.” Whether it counts as a “simulation” depends on the definition, I guess. There are also sequences whose end state can be predicted without having to calculate every intermediate state. This probably unambiguously counts as “predicting without simulating”.
Again, most finite sequences (i.e. numbers) are not like that. They cannot be predicted or even simulated without knowing the whole sequence first. That’s the “worse than no” part.
Could give an example of this?
say, f(n) = exp(-n)
Thanks!
The Bailey-Borwein-Plouffe formula is a nice one.