Michael Nelson

[Michael Nelson @mnelso32]

Goldbach's Conjecture, CW Complexes, and Minimal Free Resolutions:

A thread on a ring I’m studying whose structure encodes partitions of integers into odd primes.

🧵(0 <= N <= 15)

[Michael Nelson @mnelso32]

@littmath Curious how you factor in long-term memory? Current models reason well but are largely stateless. Human taste/judgment (like Grothendieck developing his 'yoga' over years) relies on a continuously evolving, cumulative intuition. Can a stateless architecture truly replicate that?

[Michael Nelson @mnelso32]

@IAmTimNguyen I think the issue that he would bring up though is that forming the right questions is generally harder than solving certain problems that were already asked (by people who knew the right questions to ask). I agree with you though that it still opens up more opportunities.

[Michael Nelson @mnelso32]

@MIC_btc @MatBabiak @exec_sum Nope, always look at the market cap over time. It hasn't recovered yet.

[Michael Nelson @mnelso32]

@exec_sum Has it though?

[Michael Nelson @mnelso32]

@davidmbudden You're still using the same Z_red that you and he already both agreed represents a trivial class because it's a complete intersection. This is a geometric constraint. No additional combinatorial/algebraic argument you make will ever fix that problem.

[Michael Nelson @mnelso32]

@davidmbudden @littmath @MaleManlpulator @nEquals001 @nitbean The issue I think is that he doesn't know what he's betting against. It might help if you both got a trusted third party to understand what the bet is actually on. He gets this with CMI on the other bet, but this is lacking on your new proposed bet.

[Michael Nelson @mnelso32]

@davidmbudden @NinaTheGayCat @AcerFur But you never showed H is the stabilizer of [Z_red]! You showed it was the stabilizer of Z_red (without the brackets). These are totally different things! You are not working with cohomology classes here. For all we know, your [Z_red] could be trivial like @NinaTheGayCat said.

[Michael Nelson @mnelso32]

@davidmbudden @AcerFur You argument is flawed here. You said H is the stabilizer of Z_red, but this doesn't mean it's the stabilizer of [Z_red] as @NinaTheGayCat pointed out. This isn't just "semantic", it's two different actions.

[Nina the Cat @NinaTheGayCat]

@davidmbudden There is an error in the proof of nonvanishing, specifically in Step 1 of Theorem 5.3. Even though H is the stabilizer of the cycle Z_red, there is no reason why it should also be the full stabilizer of the class [Z_red]. For all we know, [Z_red] could be trivial.

[Michael Nelson @mnelso32]

@DiracDeltaFunk @AntiDisentarian @joejanizek I feel like the key thing that LLMs lack that human brains have is memory; LLMs are limited to a finite context window (a now moment). I think what we call "deep intuition" is heavily related to how human memory works, and I don't think LLMs alone can ever achieve that.

[Michael Nelson @mnelso32]

@quinnswm @DiracDeltaFunk @t0tientqu0tient It's an algebra homomorphism if you use shuffle product on C[x]. In other words, they are thinking about the divided power polynomial algebra (which should be denoted C<x> not C[x]).

[Michael Nelson @mnelso32]

@dasalazarr @willccbb If you type in https://t.co/OY04B3zRAI in the URL it seems to work.

[Michael Nelson @mnelso32]

15) Assuming these are all supported on regular CW complexes, then showing G->S is an isomorphism is equivalent to showing these CW complexes are all path connected!

[Michael Nelson @mnelso32]

Goldbach's Conjecture, CW Complexes, and Minimal Free Resolutions:

A thread on a ring I’m studying whose structure encodes partitions of integers into odd primes.

🧵(0 <= N <= 15)

[Michael Nelson @mnelso32]

14) More generally, for n large enough (depending on d), the k-complex F_n,d should be supported on a regular CW complex of dimension d-1. Note that minimality of F already implies F_n,d has length <= d-1.