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PK2 comments on Does Your Morality Care What You Think? - Less Wrong
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Question for Obert: Suppose there are intelligent aliens in a galaxy far far away... There is a pretty good chance they will discover math. They might use different symbols and they might represent their data differently but they will discover math because the universe pretty much runs on math. To them 2 + 3 will equal 5. Would they discover morality? Would their 'morality' be the same thing as our 'morality' here? Does morality converge into one thing like math does, no matter where you start from?
There are some aliens here on earth already. Chimpanzees. They're pretty alien. Do they have math?
If superintelligent aliens found us, would they think we had math?
The universe runs on math? Really? I'd say the universe runs on the universe. We model how the universe runs using math. The map is not the territory.
By "aliens", I think PK2 meant "intelligent aliens able to build a technological civilization". And for that, you do need "maths".
As for the universe "running on maths", he added "pretty much", which is not very precise, but can mean something like "it really seems like the universe is running on maths", which is true. Our map of the universe relies on maths and is very accurate (making very accurate prediction on the universe itself), so any other accurate map of the universe has to include something which will look very much like maths. Two very accurate maps of the same territory will share many similar characteristics.
Do you think our map of the universe will seem very accurate to super intelligent beings? Does a chimpanzees map of the universe seem very accurate to you? Does our math "include something which will look very much like" a Chimp's map?
A better map doesn't necessarily include recognizable representations of a poorer map.
It's just human vanity to believe that our concepts will be some subset of the concepts that a superintelligent being uses. Sure, if they were very motivated to bother, they could figure out our concepts and represent them in theirs, just as we can represent a Chimp's knowledge with our concepts. But that a far cry from saying that their concepts will include something which will look very much like maths, anymore than our concepts include things very much like a Chimp's concepts. Or a banana slug's concepts.