#kolmogorov — Public Fediverse posts

@si_irini @mina @HistoPol
11/
The Verdict

Kolmogorov's quote is a brilliant challenge to human ego, but it assumes the model is modeling the *entity*. Current AI is modeling the *artifact* (our language).

An LLM can give you the perfect answers, but it does so via a shortcut that has nothing to do with thinking. It is a masterpiece of statistical interpolation, acting as a flawless mirror of human thought, while remaining completely hollow inside.

#AI
#LLM
#Kolmogorov
#algorithms

@si_irini @mina @HistoPol
10/
Similarly, an LLM can bypass the structural engine of consciousness—subjective experience, emotion, and situational awareness—and still generate the text of a genius. It looks "sufficiently complete" on the page, but only because human language is structured enough to be mathematically modeled.

#AI
#LLM
#Kolmogorov
#algorithms

@si_irini @mina @HistoPol
9/
If we build a flawless robotic flower out of plastic and wires that opens when light hits it, releases a synthetic fragrance, and attracts real bees, it is a highly sophisticated model. But it is not a "living being," because it bypasses the entire structural engine of biology—metabolism, cellular reproduction, and organic evolution.

#AI
#LLM
#Kolmogorov
#algorithms
#models

@si_irini @mina @HistoPol
8/
The Functionalist Blindspot

The fundamental issue with applying Kolmogorov to current AI is that it mistakes behavorial mimicry for structural equivalence.

#AI
#LLM
#Kolmogorov
#algorithms

@si_irini @mina @HistoPol
7/
Because of this architecture, an LLM can mimic the products of thought (arguments, poetry, code) flawlessly without ever executing the process of thought (intent, reflection, comprehension). It achieves a high degree of superficial completeness in the medium of text, but the internal model of a "thinking being" is entirely absent.

#AI
#LLM
#Kolmogorov
#algorithms

@si_irini @mina @HistoPol
6/
The Predictive Loop: When an LLM generates a response, it is calculating the next most statistically probable token based on patterns in its training data. It is a highly articulate calculator optimization loop.

#AI
#LLM
#Kolmogorov
#algorithms

@si_irini @mina @HistoPol
5/
There is a profound difference between a model that simulates a thinking being and a model that predicts the text a thinking being would write.

*A Model of text vs. A Model of reality*:

An LLM does not possess a model of a physical universe, a sense of self, or an internal arena where it weighs decisions. It possesses a highly sophisticated, multi-dimensional geometric map of human language."

#AI
#LLM
#Kolmogorov
#algorithms

@si_irini @mina @HistoPol
4/
Under this rule, if the output displays genuine insight, it is irrelevant whether it came from a carbon-based biological brain or a silicon-based statistical network. The functionality is the thought.

The Counter-Argument: Is an LLM "Sufficiently Complete"?

The breakdown happens when we look under the hood of current Large Language Models and ask if they actually meet Kolmogorov’s criteria of a "complete model."

#AI
#LLM
#Kolmogorov
#algorithms

@si_irini @mina @HistoPol
3/
then keeping it in a separate category is just a semantic game driven by human exceptionalism. From a strictly mathematical and functional perspective, the simulation becomes the reality because it achieves the exact same computational work.

#AI
#LLM
#Kolmogorov
#algorithms

@si_irini @mina @HistoPol
2/
Kolmogorov’s stance is rooted in an objective, input-output worldview. He is essentially saying that information is as information does.

If a system possesses the algorithmic complexity to process the world, adapt to novel inputs, synthesize ideas, and generate outputs that are structurally, logically, and conceptually indistinguishable from a thinking human...

#AI
#LLM
#Kolmogorov
#algorithms

@si_irini @mina @HistoPol

Let me play a devil's advocate and quote Andrey Kolmogorov—one of the absolute titans of 20th-century mathematics, probability theory, and algorithmic complexity:

"A sufficiently complete model of a living being, in all fairness, must be called a living being, and a model of a thinking being must be called a thinking being . . ."

#AI
#LLM
#model
#Kolmogorov
#quotes

#KnowledgeBit: In #Information theory, the #Kolmogorov #Complexity of a string is defined as the length of the #Shortest #Program that can generate that string as output.

It provides a way to quantify the information content of a string

https://knowledgezone.co.in/kbits/63e8dd1fed03cfa5ce2f4fa4

#NicoleGarreau est sincèrement désolée de pinailler une nouvelle fois, chère France Cul’, mais là elle écoute le court balado que vous avez consacré la place de la science physique dans les toiles de #VanGogh et où vous mettez en doute — probablement à raison — le fait que le plasticien eût pu vouloir représenter la turbulence cosmique en peignant « La Nuit étoilée » et donc illustrer la Loi de #Kolmogorov. La vieille Garreau est d’accord sur ce point : la plupart du temps on prête aux artistes bien plus d’intentions qu’iels n’en ont réellement.
(…)

https://seenthis.net/messages/1155173

The XRISM analysis had a limited amount of observed fields of view (integrations are expensive!!) and tried to reconstruct the "velocity structure function" (VSF), i.e. a standard way to study turbulence in many different environments.

Textbook turbulence (isotropic, incompressible) has a very distinct trend of VSF, first derived by genius A. #Kolmogorov in 1941.

The XRISM paper reported that the VSF in the Coma cluster is way different than this, hence turbulence must be weird there.

'Integral Probability Metrics Meet Neural Networks: The Radon-Kolmogorov-Smirnov Test', by Seunghoon Paik, Michael Celentano, Alden Green, Ryan J. Tibshirani.

http://jmlr.org/papers/v26/24-0245.html

#nonparametric #distributions #kolmogorov

Kolmogorov Turbulence

Turbulent flows are ubiquitous, but they’re also mindbogglingly complex: ever-changing in both time and space across length scales both large and small. To try to unravel this complexity, scientists use simplified model problems. One such simplification is Kolmogorov flow: an imaginary flow where the fluid is forced back and forth sinusoidally. This large-scale forcing puts energy into the flow that cascades down to smaller length scales through the turbulent energy cascade. Here, researchers depict a numerical simulation of a turbulent Kolmogorov flow. The colors represent the flow’s vorticity field. Notice how your eye can pick out both tiny eddies and larger clusters in the flow; those patterns reflect the multi-scale nature of turbulence. (Image credit: C. Amores and M. Graham)

#2024gofm #flowVisualization #fluidDynamics #Kolmogorov #numericalSimulation #physics #science #turbulence #turbulentEnergyCascade

#Autism as the #Kolmogorov Complexity Phenotype

https://www.lesswrong.com/posts/mqidwkF6KgRHLDoLb/autism-as-the-kolmogorov-complexity-phenotype

#DidYouKnow: In #Information theory, the #Kolmogorov #Complexity of a string is defined as the length of the #Shortest #Program that can generate that string as output.

It provides a way to quantify the information content of a string

https://knowledgezone.co.in/kbits/63e8dd1fed03cfa5ce2f4fa4

In our second session of the day, we heard from Jørn Hafver who trained an AI in audio recognition right in front of us - so it could tell how loud we were clapping at the end. Ben Ashforth spoke about a journey he went on, inspired by a talk from the last gathering, to visit roads named after every day of the year (details at http://benguin.co.uk/roads). @alisonkiddle talked about the maths behind the games Guess Who and Which One Doesn't Belong, and has a pleasing binary chop device made from card with pins and holes. Phil Ramsen followed up on his talk from three years ago and discussed slide rules and Kolmogorov. Daniel Johnson explored the possibly surprising link between Numberblocks and Polyominoes (https://youtu.be/htnZGHjX8p4?si=YzAXxPP7lT2-_Do5&t=522)- and @Tarim said what we've all been thinking and pointed out some illogical song lyrics - lions don't really live in the mighty jungle, and Kilimanjaro is nowhere near the Serengeti! #mathsjam #maths #ai #travelling #guesswho #wwdb #sliderules #means #averaging #kolmogorov #numberblocks #polyominoes #songs #logic #lyrics

On line sul sito di "Prisma" un mio articolo uscito qualche tempo fa, dove cerco di spiegare il legame fra casualità, comprimibilità e contenuto di informazioni in una sequenza di dati (per esempio il #DNA), trovato da #Kolmogorov negli anni '50.

https://www.prismamagazine.it/2023/05/31/la-complessita-di-kolmogorov/

#DidYouKnow: In #Information theory, the #Kolmogorov #Complexity of a string is defined as the length of the #Shortest #Program that can generate that string as output.

It provides a way to quantify the information content of a string

https://knowledgezone.co.in/kbits/63e8dd1fed03cfa5ce2f4fa4

Here we analyze the impact of #facies, #region, #taxonomy, and #collection style over #size #distributions using diameter as a proxy of Late #Devonian #ammonoids in their entirety using non-metric #multidimensional #scaling and #PERMANOVA based on #Kolmogorov distance.

https://doi.org/10.2110/palo.2021.063

@FrohlichMarcel Can we use this to make the #Kolmogorov #complexity of a sequence (with a little noise) computable?

Is the set of #computable #functions equivalent to the set of strings (of #finite or #infinite length) that contain finite #information, i.e. have a finite #Kolmogorov #complexity?

#math #compsci