4 ms·
> What about this one This is not the kind of thing Aaronson is actually asking about. He's not asking about a function f that outputs 1 if God exists or 0 if
by pdonis 2y ago
> What about this one
This is not the kind of thing Aaronson is actually asking about. He's not asking about a function f that outputs 1 if God exists or 0 if God doesn't exist. He's asking about a label f that refers to the function f1 (that just outputs 1) if God exists or the function f0 (that just outputs 0) if God doesn't exist. To me the question is not about computability at all, it's about labels.
- layer8 2y ago> He's not asking about a function f that outputs 1 if God exists or 0 if God doesn't exist. Because that’s not a function in the mathematical sense. The output of a mathematical function can only depend on its inputs, and the function in question is not given any inputs, hence it’s necessarily a constant function, and constant functions are trivially computable.
- pdonis 2y ago> the function in question is not given any inputs As the problem was posed, the function does take an input; it's defined as a function from {0, 1} to {0, 1}. However, as I pointed out in another comment upthread, the function makes no use of its input so it could just as well be defined with no inputs. (Indeed, even if you read the question as asking about a function f that outputs 1 if God exists or 0 if God doesn't exist, it doesn't seem like whether or not God exists is supposed to be an input.)