Hence, finding new axioms and using them to prove new sets of statements is an endless problem. Similar infinite problems exist in computability “Does program X halt?” and computational complexity “What is the Kolmogorov compexity of string X?” as well as topology “Are 2 structures which have properties X, Y, Z… in common homeomorphic?”.
Aren’t these single problems that deal with infinities rather than each being an infinite sequence of problems? Would that kind of infinity bring about any sense of excitement or novelty more than discovering say, the nth digit of pi?
It’s probably worth noting that my moral opinions seem to be in disagreement with many of the people around here, as I place much less weight on avoidance of suffering and experiencing physical bliss and much more on novelty of experience, helping others and seeking truth than the general feeling I get from people who want to maximize qualies or don’t consider orgasmium morally repugnant.
Out of curiosity, if we did run out of new exciting truths to discover and there was a way to feel the exact same thrill and novelty directly that you would have in those situations, would you take it?
Aren’t these single problems that deal with infinities rather than each being an infinite sequence of problems? Would that kind of infinity bring about any sense of excitement or novelty more than discovering say, the nth digit of pi?
The n-th digit of pi is computable, meaning there exists a deterministic algorithm that runs in finite time and always gives you the right answer. The n-th busy bever number is not, meaning that discovering it will require new advancements in mathematics to figure it out. I’m not claiming that you personally will find that problem interesting (although mathematicians certainly do). I’m claiming that it is likely that whatever field you do find interesting probably has similar classes of problems with a literally inexhaustible supply of interesting problems.
Out of curiosity, if we did run out of new exciting truths to discover and there was a way to feel the exact same thrill and novelty directly that you would have in those situations, would you take it?
No. I would consider such a technology abhorrent for the same reason I consider taking a drug that would make me feel infinitely happy forever abhorrent. I would literally prefer death to such a state. If such a mindset seems unfathomable to you, consider reading the death of Socrates since he expresses the idea that there are things worse than death much more eloquently than I can.
Aren’t these single problems that deal with infinities rather than each being an infinite sequence of problems? Would that kind of infinity bring about any sense of excitement or novelty more than discovering say, the nth digit of pi?
Out of curiosity, if we did run out of new exciting truths to discover and there was a way to feel the exact same thrill and novelty directly that you would have in those situations, would you take it?
The n-th digit of pi is computable, meaning there exists a deterministic algorithm that runs in finite time and always gives you the right answer. The n-th busy bever number is not, meaning that discovering it will require new advancements in mathematics to figure it out. I’m not claiming that you personally will find that problem interesting (although mathematicians certainly do). I’m claiming that it is likely that whatever field you do find interesting probably has similar classes of problems with a literally inexhaustible supply of interesting problems.
No. I would consider such a technology abhorrent for the same reason I consider taking a drug that would make me feel infinitely happy forever abhorrent. I would literally prefer death to such a state. If such a mindset seems unfathomable to you, consider reading the death of Socrates since he expresses the idea that there are things worse than death much more eloquently than I can.
What reasons are those? I can understand the idea that there are things worse than death, but I don’t see what part of this makes it qualify.
Can you imagine why taking a drug that made you feel happy forever but cut you off from reality might be perceived as worse than death?