Well, in this case you shouldn’t need the experiment if you can just calculate the results mathematically.
How do you know you did not forget some salient features of the real-life problem when constructing your proof? There is a good chance that modeling it would expose a previously missed angle of the problem.
How do you know you did not forget some salient features of the real-life problem when constructing your proof?
I fully agree that in the case of applying a mathematical model to the real world, it is worthwhile to test the predictions in case there is a false hidden assumption. However, what we are talking about here is applying a mathematical model to a computer simulation, any false assumptions that have come in will have done so in the step from real world to computer simulation rather than from computer simulation to mathematical analysis, the only assumption made in the analysis is that your computer works and your code is not buggy.
There is a good chance that modeling it would expose a previously missed angle of the problem.
This is false, the mathematical analysis is a complete solution of the problem as stated. Arguing that a salient feature may have been missed is like arguing the same for any mathematical proof, i.e. silly.
How do you know you did not forget some salient features of the real-life problem when constructing your proof? There is a good chance that modeling it would expose a previously missed angle of the problem.
I fully agree that in the case of applying a mathematical model to the real world, it is worthwhile to test the predictions in case there is a false hidden assumption. However, what we are talking about here is applying a mathematical model to a computer simulation, any false assumptions that have come in will have done so in the step from real world to computer simulation rather than from computer simulation to mathematical analysis, the only assumption made in the analysis is that your computer works and your code is not buggy.
This is false, the mathematical analysis is a complete solution of the problem as stated. Arguing that a salient feature may have been missed is like arguing the same for any mathematical proof, i.e. silly.