That I can run or emulate a program usually doesn’t much imply that I understand it very much. If I have a exe I need to decompile it or have its source provided to me and even then need to study it quite a bit. If I run it through pen and paper I am not guaranteed to gain more insight than running it via an external computer.
There is also the distinction of a specific program or what a program could be. For example “programs will halt” is wrong althought the question of this or that program haling can right or wrong. There are not many properties that you can deduce from a program from it simply being a program. “Programs have loops” can be a good inductive generalization about programs “found in the wild” but it is a terrible description of a general program.
That I can run or emulate a program usually doesn’t much imply that I understand it very much. If I have a exe I need to decompile it or have its source provided to me and even then need to study it quite a bit. If I run it through pen and paper I am not guaranteed to gain more insight than running it via an external computer.
There is also the distinction of a specific program or what a program could be. For example “programs will halt” is wrong althought the question of this or that program haling can right or wrong. There are not many properties that you can deduce from a program from it simply being a program. “Programs have loops” can be a good inductive generalization about programs “found in the wild” but it is a terrible description of a general program.