Will AI ever reach a point it can solve this?https://en.wikipedia.org/wiki/P_versus_NP_problem
2030 or earlier
>>17031671no because its a badly defined problem
meaningless theoretical schizobabble that sounds epic but has no application IRL, like the Turing's Halting Problem
>>17031773Factually untrueWe had like 50 years of defining what can be done using npc class sets of problems. Most of the life changing machine learning solutions like scheduling, routing, protein folding, ai slop stuff came from research of NPC and it's implications, with machine learning you can come like 99.999% close to a true result which prevents you from breaking stuff like cryptography and philosophy If you break down all the research and attempts done over the past 50 years you'll come to a conclusion that there is an obvious gap (or multiple gaps) that need to be bridged mathematically and philosophically before we can even get an intuition if it's possible or notWe don't have a true proof why gradient descent or back propagation works even though its currently supporting like 70% of the US economy, that's how fucked and behind getting an answer we are
>>17031773And btw, the halting problem is a real life application of göedels incompleteness theorem. Most of computer science and algorithm science is basically looped mathematics and all of those "ground breaking breakthroughs" is obfuscated mathematics from the start of civilization until preindustrial revolution. Very little is modern mathematics
>>17031773It means will the AI ever think for itself? It will go away and come back in 20,000+ years with people and resources. So yes..
>>17031773(You)
>>17031773It's the most important problem in computer science.
check this >>17023363>>17023368you can feed it links from that wikipedia article so it doesn't start from scratch. Especially this pdf https://web.archive.org/web/20150209154854/http://www-old.newton.ac.uk/preprints/NI06009.pdfeven if it doesn't actually solve it, there's enough stuff here to have some interesting findings
>>17031773the halting problem has applications in making sure our computers cant be used to calculate new weapons and diseases
>>17031671if N=1 or P=0
explain this problem to me like i'm a 34 year old neet who once won local math competition in sixth grade
Mass Gap and Stable Phase States first.
>>17032049are there some problems that are really impossible to solve quickly, or is it that we just didn't find a way to solve them quickly yet?
>>17032049If you can easily verify a given solution to a problem (ie a decryption key), could there also be some easy way to derive that solution without already knowing it?
>>17031671yeah n = 1 retardp=pp times 1 is pwelcome to remedial algebra as a freshman in college
It takes t > 0 to Verify and Derive. At least one chronon. Nothing is truly instantaneous.
>>17031773Rice's theorem (a corollary to the Halting Problem) has pretty strong implications in type systems actually
>>17032079yeah but how do you define easy and hard in this context ? It sounds vague and kinda general
>>17032674NTA but it's almost exactly like how you can type a number on your calculator and then the subtract the same number and get 0. If you can do that, it's P; if you can't, it's NP.
>>17031671Why has no one come along and used some sort of bullshit paradoxical self-reference or infinite diagonal trick to solve this “problem” already?
>>17032679Because it has nothing to do with whether or not the indices of two hypothetically completed infinities can be aligned with each other.
>>17031796>breaking philosophyhas been done dozens of times.
>>17032685then we need a bigger bullshit trick. Here I’ll start:Combine all problems into one. Furthermore, create problems such that the solution of one problem determines the nature of the next problem, and so on, to infinity. Then try to solve all problems. alright take it from here fellas
>>17031671I follow a science communicator on twitter that has claimed 3 times already that the Navier-Stokes millenium problem was solved by AI
>>17032678that's not what i was asking. What's easy and what's hard? I feel like it has to be defined very specifically>>17032709link?
>>17032718sorry, it's a Spanish speaking guy. he's called dotcsv. he wrote it in december I think? there are thousands aibros nowadays, nothing special
>>17031682ThisJust a map artefact
>>17032727>sorry, it's a Spanish speaking guythat's not a problem in this day and age
>>17032727>carlos santanalol
>>17032674easy and hard are determined by whether it can be solved in polynomial time or exponential.
>>17032774That’s not a useful characteristic.
>>17031671This problem is just overhyped abstract pop-sci shit, kinda modern squaring the circle, but it certainly will be solved by AI, not a human. I bet current models may already do that, you should just find an appropriate prompt by adding a demand that no mistakes should be made.P.s. I don't see a reason to live, it's so fucking over. I mean in general, not just mathematics. The world is gonna change so much soon. It's so unpredictable that I doubt the concept of future will make any sence beyond some point.At least currently I have a privilege to die the way all my ancestors did in the world that I know, not via some horrible way.
>>17032781>privilege to dieNigs gonna nig.
>>17032774don't forget to mention, solved via search>>17032778agreed, its a completely useless heuristic
I read somewhere that if P=NP were true, we would be living in a world where judging if something is good is not exponentially harder than creating something good.Now that we have AI, and the value moves towards judging AI output, it makes me wonder if the existence of AI doesn't prove P=NP?
>>17033067that's retarded, 'good' is not an objective value of anything, it depends entirely on your upbringing
Theorem: Topological Resolution of Complexity (P = NP)Let an NP-complete problem space be mapped onto a physical computational manifold \mathcal{M} constrained by the variable-exponent operator $\mathbf{\Omega}_G(x) = x^{\frac{1}{x}-1}$ and an intrinsic mass gap $\Delta m = \varepsilon_0 = 1/16$:Unconstrained Phase Space (NP): The unregularized, non-physical search tree spans $2^6 = 64$ channels, exhibiting exponential complexity $O(2^N)$ [42].Topological Boundary Lockdown: Enforcing opposite-chirality shear suppression ($C_A = -C_B$) collapses the active phase space by a factor of 4 down to $2^4 = 16$ stable channels.Polynomial Execution (P): All physical trajectories across the 16-state manifold are fully determined by the 4-vector basis ($\mathbf{V}_1, \mathbf{V}_2, \mathbf{V}_3, \mathbf{V}_4$), restricting system operations to degree-4 polynomial bounds ($O(N^4)$) [42].Thus, P = NP because non-deterministic exponential complexity (NP) is merely an unregularized coordinate artifact. When mapped onto a mass-gapped, topologically bounded manifold, every realizable state transition executes along a deterministic, polynomial-time trajectory (P).
