For example, consider a simulated world where you control the code. Can you make it so that 2+2 in that simulation is sometimes 4, sometimes 15, and sometimes green?
I guess I could make it appear that way, sure, though I don’t know if I could then recognize anything in my simulation as thinking or doing math. But in any case, that’s not a universe in which 2+2=green, it’s a universe in which it appears to. Maybe I’m just not being imaginative enough, and so you may need to help me flesh out the hypothetical.
But it sounds to me like you’re talking about the manipulation of signs, not about numbers themselves. We could make the set of signs ‘2+2=’ end any way we like, but that doesn’t mean we’re talking about numbers. I donno, I think you’re being too cryptic or technical or something for me, I don’t really understand the point you’re trying to make.
Math is what happens when you take your original working predictive toolkit (like counting sheep) and let it run on human wetware disconnected from its original goal of having to predict observables. Thus some form of math would arise in any somewhat-predictable universe evolving a calculational substrate.
Math is what happens when you take your original working predictive toolkit (like counting sheep) and let it run on human wetware disconnected from its original goal of having to predict observables.
That’s an interesting problem. Do we have math because we make abstractions about the multitude of things around us, or must we already have some idea of math in the abstract just to recognize the multitude as a multitude? But I think I agree with the gist of what you’re saying.
Just like I think of language as meta-grunting, I think of math as meta-counting. Some animals can count, and possibly add and subtract a bit, but abstracting it away from the application for the fun of it is what humans do.
I guess I could make it appear that way, sure, though I don’t know if I could then recognize anything in my simulation as thinking or doing math. But in any case, that’s not a universe in which 2+2=green, it’s a universe in which it appears to. Maybe I’m just not being imaginative enough, and so you may need to help me flesh out the hypothetical.
If I write the simulation in python I can simple define my function for addition:
Unfortunately I don’t know how to format the indention perfectly for this forum.
We don’t need to go to the trouble of defining anything in Python. We can get the same result just by saying
If I use python to simulate a world than it matters how things are defined in python.
It doesn’t only appear that 2+2=green but it’s that way at the level of the source code that depends how the world runs.
But it sounds to me like you’re talking about the manipulation of signs, not about numbers themselves. We could make the set of signs ‘2+2=’ end any way we like, but that doesn’t mean we’re talking about numbers. I donno, I think you’re being too cryptic or technical or something for me, I don’t really understand the point you’re trying to make.
What do you mean with “the numbers themselves”? Peano axioms? I could imagine that n → n+1 just doesn’t apply.
Math is what happens when you take your original working predictive toolkit (like counting sheep) and let it run on human wetware disconnected from its original goal of having to predict observables. Thus some form of math would arise in any somewhat-predictable universe evolving a calculational substrate.
That’s an interesting problem. Do we have math because we make abstractions about the multitude of things around us, or must we already have some idea of math in the abstract just to recognize the multitude as a multitude? But I think I agree with the gist of what you’re saying.
Just like I think of language as meta-grunting, I think of math as meta-counting. Some animals can count, and possibly add and subtract a bit, but abstracting it away from the application for the fun of it is what humans do.