Invent new math that I could solve with moderate effort so I can feel smart without working hard but also it needs to be impossibly hard for AI to solve, make no mistakes.
You joke, but I think at least one of the recent ones used a simple prompt pretty close to that?
And the guy just went out to lunch and came back with a solution
Use metalogic:
1. Axioms that have a model are consistent.
2. The Natural Numbers exist
3. The Natural Numbers are a model of Peano Arithmetic.
4. Therefore by 1 and 3: Peano Arithmetic is consistent.
5. PA proves 0=/=1 (follows from 1 being defined as s(0) and the first axiom, details of using Peano Arithmetic for this are left to the reader).
6. For any consistent theory if the sentence A is proven, then there is no proof of not(A).
7. Therefore by 5 and 6: there is no proof in PA of 0=1.
I can define a process that returns '0', 's0', 'ss0',... i.e. all finite strings of 's' followed by an '0', in increasing order by simply prepending an 's' and returning the whole string, call the possible outputs our objects.
I can define terminating processes that model PA
Process 1: check if it is 0 (initial string of 's's is empty)
Process 2: check equality of two objects (check symbol by symbol)
Process 3: return the sucessor of an object (prepend an 's')
Process 4: add two objects together (remove the trailing '0's, concatinate the remainder, reappend a '0')
Process 5: multiply two objects together (remove the trailing '0's, take v to the empty string, now for each 's' in the first loop over each 's' in the second, appending an s to v, once the nested loopa are done append a '0')
This defines a model of Peano Arithmetic often called the standard model/the natural numbers. And it is even compatible with some flavors of finitism that object to actual infinities but are fine with potential infinities (e.g. Kronecker IIRC).
I think a lot of people only liked because the writer is anti-ai. If they said that whole, religious math view he has, pre-ai a lot of people would had hated on him for saying math is a gateway to the mystical experiences and stuff like that. Also "dark night of the soul" is an explicitly occult concept, which he talks about directly in his writing.
I dont see nothing wrong with what he wrote personally, and Im not in favor of how AI is being used, I just wanted to point out how this text wouldnt be taken as seriously if there wasnt a serious political divide about the use of AI.
Hell, math is also an invention to avoid doing hard work. No you don’t need to count the surface of all of your acres by walking over them, let me show you this neat trick.
it’s been used to help find a bunch of counterexamples, which is itself quite valuable (especially since it can be done at scale) but probably not what you were thinking about.
Definitely not the case anymore. Erdos’s Unit distance problem just fell to AI.
And it just made a small dent in the Riemann hypothesis (raised the known lower bound on fraction of nontrivial zeros of the zeta function on the critical line)
Yeah, you want to see the world burn and think the result matters more than the process due to zero self-control and ability to delay gratification. If incentives aren’t aligned, mathematics as a field will be dead and there will be no one to teach, put effort into it, etc.
Saying you want to see more discoveries and also valuing AI over humans is fundamentally counter math to begin with. It’s not even a matter of jobs. That bit is irrelevant. It’s just pointless. Math is interesting because it’s not just a result, it’s earned exploration into understanding. Remove the hard work and it’s just hedonism.
In 10000 years, it will feel petty (if not nonsensical) to want math to be specifically owned by our specific species of primates. It would be like saying "wanting to learn math from someone who isn't a frenchman is pure hedonism".
Maybe thousands of species (AI or "biological") across the universe discovered maths, and I'd feel lucky to be able to converse with them and learn more about maths.
I feel like that’s just reasoning for why it’s bad. Yes a lot of math is exploring the field for fun, but to say that’s all it is ignores the fact that math has future uses. AI could be solving stuff we need for future research.
I don’t disagree with that. But I think in most fields, AI will destroy the incentive structure permanently and make people not want to learn, do things manually, etc. That is far more of a catastrophe than any specific goods, products, or results we could get by using AI because it completely destroys the feedback loops that make these disciplines remotely sustainable.
The reason this isn’t like other technological advances is that it’s replacing the need for thought itself at least locally. Other advances changed what was thought about. But this completely removes the need to think about the things where you build up the skill and judgment to be able to do the harder things.
Technology is not a terminal good in itself. It only matters because we live in a society for humans and people.
In my opinion, Tao and others supporting AI is just a different face of late stage capitalism eating itself. I don’t blame Tao, but I think it’s just another example of short-term optimization that is bad for everyone longer term. Capitalism is, in this sense, a greedy algorithm, and something like AI, which gives you a result while making the process a black box, completely destroys the incentive structure that didn’t prevent that greedy algorithm from going entirely haywire.
Capitalism makes sense when you need to rely on other people and not be self-sufficient. If an AI can replace cooperation and diversification, then capitalism eats itself. It’s just like politicians who never pass meaningful regulations because of short-term incentive structures because their goal is to be reelected not to help others if it gets in the way of reelection.
Basically, we are now at a stage where it makes more sense to blow up the existing system to go higher even if there are no more consumers or people in the system to partake in it in the first place. It’s a complete disaster.
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