If you take a functional perspective, these are all equivalent:
f1 = 1+1, f2 = 2, f3 = 1+1+1-1
When you run, say, a Java Virtual Machine on various kinds of hardware, the fundamental chipset instructions it translates to may all be different, but the results are still equivalent.
When you upload your brain, you’d expect the hardware implementation to differ from your current wetware implementation—yet as long as the output is identical, as long as they are indistinguishable when put into black boxes, you probably wouldn’t mind (cf. Turing tests).
Now, when you go for a perfect correspondence between two functions, by necessity their compressed representation of the relevant parts of the function (relevant for the output) has to be isomorphic.
The example you provided reduces to “def predictable(): return 42”. These are the parts relevant to the output, “the components involved in that decision” (I should have stressed that more).
If you predict the output of predictable() perfectly, you are simulating the (compressed) components involved in that decision—or a functionally equivalent procedure—perfectly.
If you take a functional perspective, these are all equivalent:
f1 = 1+1, f2 = 2, f3 = 1+1+1-1
When you run, say, a Java Virtual Machine on various kinds of hardware, the fundamental chipset instructions it translates to may all be different, but the results are still equivalent.
When you upload your brain, you’d expect the hardware implementation to differ from your current wetware implementation—yet as long as the output is identical, as long as they are indistinguishable when put into black boxes, you probably wouldn’t mind (cf. Turing tests).
Now, when you go for a perfect correspondence between two functions, by necessity their compressed representation of the relevant parts of the function (relevant for the output) has to be isomorphic.
The example you provided reduces to “def predictable(): return 42”. These are the parts relevant to the output, “the components involved in that decision” (I should have stressed that more).
If you predict the output of predictable() perfectly, you are simulating the (compressed) components involved in that decision—or a functionally equivalent procedure—perfectly.