If simulations are programs, don’t they just tell us what we program it to?
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As others mentioned, simulations involve coming up with “rules” that describe how a “system” or “model” behaves. An example of what these “rules” can be are the laws of physics, and an example of a “system” could be our solar system.
A cool example imo is the Three-Body Problem, which asks: if you have three massive objects in space, each of which is pulling on one another via gravity, how will they “evolve” over “time” given their “initial conditions” (positions and velocities)?
For two bodies, like the earth and the moon, this is hardly a problem at all because we can come up with static equations that will tell us exactly where the two bodies will be and how they’re moving, and all we have to do is plug in the “initial conditions”, and “time” as inputs into the equation, and then you get your answer.
For three bodies, however, the situation is a lot more complicated and it winds up not being possible to come up with such nice equations, and so the only way to find out how the three bodies behave, is by simulating them. With simulation, you use the laws of gravity as your “rules” and “step through time” by approximating how the positions and velocities evolve after a very small time step, and then you use those newfound positions and velocities as the initial conditions for the next iteration of the simulation. You repeat this process hundreds, or thousands, or billions of times. The smaller the time-step, the more accurate your simulation will be, but the more iterations it will take to get your answer.
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