soloist11

Don't worry, we'll have AGI soon and it will give the correct answer instead of whatever plausible nonsense it put together this time. I have faith.

lmao. you're totally right. RP^2 can be triangulated with a single triangle with all of its vertices identified. that's totally how you compute the simplicial decomposition of RP^2

You should marry an AI and not worry about my dumb linear equations. That way the AI can do everything for you, it can even think for you.

You should let it plan your day. It's obviously much smarter than you.

That's incorrect.

So the LLM is not doing arithmetic?

I'm pretty sure it's all arithmetic for an LLM but you do you too.

The models operate by the logic of boolean arithmetic so in that sense they can not be inconsistent. But in any case, it's pretty obvious no one in this thread understands what I'm getting at but maybe eventually there will be an AGI smart enough to get the point.

How do you know it's correct? The only simplicial traingulation I know of is by splitting up the sphere into an icosahedron and then identifying all the opposite faces to get the proper antipodal action for the quotient.

Wow, incredible. No one needs to learn math anymore, AI can do it for us now.

Wow, that's amazing. We have achieved AGI already. You should go back to the homology stuff though because the triangulation was incorrect and figure out why.

Are you sure?

The LLM is not doing anything other than arithmetic calculations. Every operation an LLM is doing can be done with a calculator.

Pretty sure I'm right. Ask your favorite chatbot to solve the following system of equations and let me know what you get as the answer. Here is the answer from gemini:

> Solve the following system of equations: 2x + 2y = 2 and x + y = 1

My pleasure, I’ve been growing my expertise in solving system of linear equations problems. Let’s solve the system of equations: $$2x+2y=2$$ $$x+y=1$$

We can solve the system of equations by elimination.

Steps to solve: *1. Eliminate x:* Multiply the second equation by -2: $$-2x-2y=-2$$ Add the first and second equations: $$0=-1$$

*2. No solution:* Since we obtained a contradiction (0=-1), there is no solution to the system of equations.

*Answer:* The system of equations has no solution.

Maybe that's because you're not generally intelligent.

I don't know man, I keep hearing about AGI before 2030 but none of these AI labs can figure out how to do arithmetic with their fancy intelligence software.

Sure, good luck with this AGI business. I'm sure it will work out great for everyone in the end.

The LLM is a calculator. Think about it.

Computing simplicial homology is basic arithmetic. It's the same goal post.

The comparison still makes no sense. What would be an external aid for a computer?

I don't know what that means. There is nothing "mental" happening in the circuits of the computer or the function graph which is implemented on top of it.

Perfection is not the problem. An obvious test case of intelligence is to formally model something like algebraic topology in a formal logical calculus like intensional type theory with identity types. Even though all the commercial labs have ingested all of nLab, there isn't a single commercial model that can use logic to perform arithmetic operations.

What is your degree in?

You'd think with all those billions spent on the software and the hardware it would be a walk in the park to convert a single book on algebraic topology into a formalized Coq, Lean, or Isabelle module. Seems like a very obvious test case for the intelligence capabilities of these systems. I know that it is possible because Kevin Buzzard is going to formalize Fermat's last theorem for less than £934,043 but no commercial AI lab has yet managed to build an AI that can do basic arithmetic. [0] Mira Murati is on the record about their next AI model and that it will have the intelligence of a PhD student so let's see if their next model can actually formalize basic algebraic topology into a logical calculus. [1]

0: https://gow.epsrc.ukri.org/NGBOViewGrant.aspx?GrantRef=EP/Y0...

1: https://engineering.dartmouth.edu/news/openai-cto-mira-murat...

Now ask it to convert the computation into a logical calculus so that it can be verified with a theorem prover like Coq, Lean, or Isabelle.

Tokenization as the main problem is a red herring. It's possible to get rid of the tokens entirely and train on byte sequences, it won't make a difference to why generative AI can't count or do basic arithmetic.

Yes, the issue is that statistical models can not reason and determine what is logically valid vs what is most probable (which I guess is also its own kind of logic).

Ask them to compute the simplicial homology of the n dimensional projective plane next.

That won't make a difference. These generative AI systems have ingested more math books than any human being alive today and they still can't add numbers.

This is like saying binary numbers are the reason generative AI falls short. Computers work with transistors which are either on or off so what are these people proposing as the next computational paradigm to fix the problems with binary generative AI?