The key detail you're missing is that the problem must be written down. All details must be specified, so that you can unambiguously tell how well it's being so

The key detail you're missing is that the problem must be written down. All details must be specified, so that you can unambiguously tell how well it's being solved. Yes, you can write down a problem inspired by a specific stick. And yes, the written down problem will of course inevitably differ in the details from the real stick. Normally you'd think of these small differences as small errors in the description. But as soon as you try to argue the stick is computing the written-down problem, they become errors in the stick because they affect its ability to implement the problem you wrote down.