Mathematics

Lots of science today (meteorology, cosmology) is based on computer simulation or modeling for those phenomena that are difficult to observe directly. If a computer simulation gives me a result consistent with what we can see (star distribution for two galaxies that collide) can we infer that the underlying process is the same in the simulation and in physical world? The simulation is just numbers (or symbols) input as data about the system(s) modeled. Are numbers the underlying "stuff" of objects, too, rather than atomic particles, etc.?

Comments

Suppose that instead of a

Suppose that instead of a computer producing a simulation, we have an army of thousands of worker-bee science grad students performing and assembling vast numbers of calculations matching all the steps that a computer simulation would call for. Suppose the results are consistent with observation. We wouldn't ask whether what's being simulated is really nothing but desperate grad students chained to desks doing tedious math.

Computer simulations are ways of finding out what our equations and assumptions entail. In an example where it would be feasible to calculate the behavior of the model by hand, we wouldn't doubt that the real target of the exercise is external-world stuff—particles or economic agents or pathogens or whatever. That doesn't change if we move to cases where there's no serious possibility of doing the calculations by hand. The computer simulation doesn't represent itself. It represents what it simulates. If we've done things right, the representation will be more or less accurate. But how we represent doesn't determine what's represented.

Read another response by Allen Stairs

Read another response about Mathematics