Yet another classic, at last found its way to my library.

I'm wondering. If #computability and #unsolvability theories are mostly concerned with the existence of algorithms for classes of problems, if one could prove or disprove such a thing (class of theorems?) starting from #geometry.

I'll explain. I've recently understood (Steenrod et al, "First concepts of topology") that #topology is mostly concerned in proving existence theorems. The subject matter of this book sounds, in a way, like an attempt to prove such theorems. So naturally I came to wonder if anyone had attempted tackling them with topological means and tools instead. I haven't looked to see if this question even makes sense, but my humble instinct says that maybe yes, and that most likely at least someone has worked on it in the past.

[Up and Atom] on the unsolved problem of whether NP-Complete problems can be decided in polynomial time
https://youtu.be/ctwX--JEzSA
#mathematics #ComputerScience #computability #ComplexityTheory #NPComplete

Why #AI systems are always special and limited.
Why every learning algorithm is special and has systematic blind spots.
What would Artificial General Intelligence be (and what not)? How could it be achieved? Would it be useful?
Why we don't have to fear #AGI and #Superintelligence.
Why will the current line of AI research not lead to AGI?
Why Intelligence cannot be formalized and requires #creativity.
https://againstprofphil.org/2023/03/05/artificial-but-not-intelligent-a-critical-analysis-of-ai-and-agi/
#Philosophy #Longtermism #Computability #ComputerScience

@patrickcmiller
[Up and Atom] videos on #computability
https://youtu.be/t37GQgUPa6k
https://youtu.be/PLVCscCY4xI

#YouTube #TuringMachines #HaltingProblem #Decidability

An interesting and apparently naive question:

Is the Kolmogorov complexity of any string equally low?
https://math.stackexchange.com/questions/4335542/is-the-kolmogorov-complexity-of-any-string-equally-low

No matter what encoding scheme you specify, there will always be, for all n, some string of ≤n bits which requires ≥n bits to encode. This follows inexorably from the pidgeonhole principle.

#complexity #pattern_recognition #kolmogorov #compression #computability

Interesting - Noise can break non-computability:

Noise vs computational intractability in dynamics

by Mark Braverman, Alexander Grigo, Cristóbal Rojas
2018

https://arxiv.org/pdf/1201.0488.pdf

https://www.arxiv-vanity.com/papers/1201.0488/

#computability #noise #dynamicalSystems #TuringCompleteness

André Malraux working on musée imaginaire or, why PowerPoint is not thinking or, why serial computing is mathematically incompetent.

Nagging me for sometime now has been Peirce's remark that mathematics is fundamentally diagrammatic, especially in equations. You can't orientate yourself to it as a stepwise procedure.

#AndréMalraux #MuséeImaginaire #art #mathematics #PowerPoint #computability #PropositionalCalculus @philosophy

So, I think I need some help from #mathstodon and the wider community with understanding of #computability and #recursiveenumeration.

If you go to

http://jdh.hamkins.org/alan-turing-on-computable-numbers/

there is a wonderful article by Dr. Joel David Hamkins, a mathematician whose work I deeply admire.

However, if you scroll down to the comments, you will notice a comment from Nathan Harvey (that’s me!) contesting some of the claims of the article. In particular, Dr. Hamkins makes the claim that with Turing’s original definition of computable numbers and functions, addition is not a computable function. He appears to view computable functions as consumers of the output of the programs that represent the reals, not as consumers of the programs themselves, and I give an example where the analysis changes and make reference to Turing’s definition.

But! I can be wrong here. Dr. Hamkins is the real stuff. I just keep coming back, after spending time to consider his points and trying to reframe them to ensure I understand, thinking that my point wasn’t refuted or even really addressed. And as I read the responses, I fail to see any comments about my example or my point about the difference between consuming outputs of the computation versus the actual program, … and I keep thinking the point is getting missed. But that’s dangerous territory that can lead one to crankdom and obstinate ignorance. I don’t want to do that to myself.

So if there are any mathematicians who enjoy the area of computable functions and want to give it a quick read, I would appreciate any comments on my point. Even if it’s just a comment “No, Nate, you’re wrong and deeply misguided” with no further explanation. After one or two of those from other mathematicians, I’ll take the L and shrink off to read more books on the topic.

And if you don’t know the answer but have followers who work in that or related areas of math, a boost would be appreciated. This is an area of math that is deeply interesting to me and I thought I understood it well, but self-taught people are known to go off the rails.

Some hashtags to meet the right eyes:
#math #mathematics #metamathematics #constructivism #Turing #formallanguages

Some attags, not to get their direct response (unless interested themselves in doing so), but if they find the discussion respectful and the topic interesting, a boost might benefit the discussion:
@ProfKinyon @MartinEscardo @BartoszMilewski

A #TuringTest for #FreeWill by #SethLloyd

https://www.youtube.com/watch?v=5wyJlUUEpSE&ab_channel=FQXi

#Turing #AlanTuring #Philosophy #PhilosophyOfScience #Computing #Computability #HaltingProblem #TheHaltingProblem #Probability #QM #QuantumMechanics #Randomness #UniversalComputer #UniversalTuringMachine #TuringCompleteness #SelfReference #Recursion

Here's a fun post about Chaitin's Constant over on Cohost:

https://cohost.org/chronos-tachyon/post/492184-empty

Chaitin's Constant is the probability that a random computer program halts, assuming that your process for selecting random computer programs is biased so that long programs are exponentially less likely to be selected than short ones.

It's a great example of why I think that uncomputable real numbers don't exist.

#GregoryChaitin #ChaitinsConstant #HaltingProblem #computability

#SeanCarroll - Is #Information the Foundation of #Reality ?

https://www.youtube.com/watch?v=SRd0IY23baA&ab_channel=CloserToTruth

#Science #Physics #Philosophy #PhilosophyOfScience #PhilosophyOfPhysics #Computation #Computability #InformationTheory #CloserToTruth #RobertKuhn

#SethLloyd - Is #Information the Foundation of #Reality ?

https://www.youtube.com/watch?v=a35bKt1nuBo&ab_channel=CloserToTruth

#Science #Physics #Philosophy #PhilosophyOfScience #PhilosophyOfPhysics #Computing #Computability #UniversalComputation #ItFromBit #BitFlipping #QM #QuantumMechanics #QuantumPhysics #QuantumComputing #QuantumComputer #QuantumComputers #Qubit #Qubits #CloserToTruth #RobertKuhn

#RodneyBrooks - Is the #Cosmos a #Computer ?

https://www.youtube.com/watch?v=M0v-NUaFo48&ab_channel=CloserToTruth

#Science #Physics #Computing #Computability #Computation #Information #PhilosophyOfScience #Metaphysics #CloserToTruth #RobertKuhn

#SethLloyd - Theorem of Human #Unpredictability

https://www.youtube.com/watch?v=AIWemQthcZg&ab_channel=SeriousScience

#Philosophy #Science #PhilosophyOfScience #FreeWill #HumanUnpredictability #Information #Computability #HaltingProblem #TheHaltingProblem #Programming #AI #ArtificialIntelligence #Recursion #SelfReference #Goedel #KurtGoedel #Incompleteness #IncompletenessTheorem

📆 Special Days on #Combinatorics and Arithmetic for Physics will happen on November 28th-29th at the IHES. There are co-organized by Gerard H. E. Duchamp (@LipnLab), M. Kontsevich, G. Koshevoy, S. Nechaev, and K. A. Penson.
💡 The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on #computability. Problems are drawn mainly from theoretical physics: e. g. renormalization, combinatorial physics, geometry, evolution equations.
🔗 https://indico.math.cnrs.fr/event/8730/

📆 Special Days on #Combinatorics and Arithmetic for Physics will happen on November 28th-29th at the IHES. There are co-organized by Gerard H. E. Duchamp, M. Kontsevich, G. Koshevoy, S. Nechaev, and K. A. Penson.
The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on #computability. Problems are drawn mainly from theoretical physics: e. g. renormalization, combinatorial physics, geometry, evolution equations.
🔗 https://indico.math.cnrs.fr/event/8730/

Hello!

After a few days figuring out Mastodon with the help of the folks at QOTO, I will formally introduce myself in order to pin this in my profile :)

My name is Abde and I am a computer scientist. My main domain is #NumericalCalculus and #ParallelComputing. I am currently a PhD student at the Université Libre de Bruxelles (#belgium) and working on porting numerical solvers for simulations on the GPU using #CUDA. You may find my first paper here: https://etna.math.kent.edu/vol.55.2022/pp687-705.dir/pp687-705.pdf

Other research interests are #complexity #computability #graphtheory #geometry #discretemath

I also work as a #VirtualReality developer. My current professional interests are #simulations #numericalcalculus #geometry. We also contribute in several #opensource projects. Most of my work is done in #Unity3D, so feel free to ask any questions!

As a hobby I do some #gamedev and also #musicproduction. I will share some snippets of what I do here, but for now I am focusing in crafting my art by producing #housemusic in #bitwig.

Please enjoy! I am not the most active but I am looking to build my Mastodon network, so feel free to follow and I will follow back :)

#introduction #mastodon #newcomer #developer #music #programming

On #computability, overlooked epistemic issues of #BigData & #AI #DeepLearning, and how everything is connected to #Fluxus, #ConceptualArt, #football, non-participation artists and the #Unabomber.

Filippo Lorenzin interviewed me on my contribution to the book "Pattern Discrimination":

https://wwwunderkammer.net/2018/11/26/disrupt-by-the-rules-interview-with-florian-cramer/