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Really? I also value the evidence that numerical simulations provide, and if I didn't know of the problem at hand, the simulation would indeed convince me of the correct answer. But has one really understood something just because one has become comfortable with its behavior?

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I would say it was more so the process of implementing that same logic forces you to understand it, and then seeing that logic pan out is a confirmation of what was learned in implementation.

Much like you can understand the math of a lever and see levers working, but precalculating that x can lift y with a z long lever, and then building it, reinforces the logic you used in precalculation and binds the abstract to the real.

I was able to predict how simulation would go when i saw the program that i wrote. When i saw the simulation confirm my prediction it was so much more convincing then any other method. If the logic was to complex for me to understand then i would only see the behavior and not much more.

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