#godel — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #godel, aggregated by home.social.
-
🎩 Ah, the saga of Gödel: the #genius mathematician who proved the #incompleteness of his own dining habits, 🤦♂️ and yet managed to make his passing a #logic puzzle unsolvable by any mere physician. 🍽️ 'Personality disturbance' is just scientist-speak for 'too brilliant to remember to eat.'
https://iain.so/infinities-impossibilities-and-the-man-in-the-white-linen-suit #Gödel #DiningPuzzle #Brilliance #HackerNews #ngated -
🎩 Ah, the saga of Gödel: the #genius mathematician who proved the #incompleteness of his own dining habits, 🤦♂️ and yet managed to make his passing a #logic puzzle unsolvable by any mere physician. 🍽️ 'Personality disturbance' is just scientist-speak for 'too brilliant to remember to eat.'
https://iain.so/infinities-impossibilities-and-the-man-in-the-white-linen-suit #Gödel #DiningPuzzle #Brilliance #HackerNews #ngated -
“Gödel presented his #CompletenessTheorem on 6 September 1930 at conference in Königsberg (today known as Kaliningrad in Russia). #Hilbert was at a different conference in Königsberg and gave a grand speech on 8 September, in which he famously rejected the idea that there are limits to human knowledge. “We must know. We will know,” he said – words that were eventually engraved on his tombstone.
There is just one problem with Hilbert’s rallying cry to mathematicians – Gödel had already destroyed all hope of it the day before. Not on 6 September, when he presented his completeness theorem, but on 7 September. During a discussion with fellow logicians that day, #Gödel let slip that he had identified the possibility of “undecidable” statements – ones that cannot be proven true given a certain set of axioms, but crucially cannot be proven false either. This was the genesis of an idea that would limit the horizons of #mathematics forever.”
#Proof / #MathematicalObjects / #JacobAron <https://newscientist.com/article/2522297-the-man-who-ruined-mathematics/> (paywall) / <https://archive.md/s18W0>
-
“Gödel presented his #CompletenessTheorem on 6 September 1930 at conference in Königsberg (today known as Kaliningrad in Russia). #Hilbert was at a different conference in Königsberg and gave a grand speech on 8 September, in which he famously rejected the idea that there are limits to human knowledge. “We must know. We will know,” he said – words that were eventually engraved on his tombstone.
There is just one problem with Hilbert’s rallying cry to mathematicians – Gödel had already destroyed all hope of it the day before. Not on 6 September, when he presented his completeness theorem, but on 7 September. During a discussion with fellow logicians that day, #Gödel let slip that he had identified the possibility of “undecidable” statements – ones that cannot be proven true given a certain set of axioms, but crucially cannot be proven false either. This was the genesis of an idea that would limit the horizons of #mathematics forever.”
#Proof / #MathematicalObjects / #JacobAron <https://newscientist.com/article/2522297-the-man-who-ruined-mathematics/> (paywall) / <https://archive.md/s18W0>
-
What Do Gödel's Incompleteness Theorems Mean?
https://www.quantamagazine.org/what-do-godels-incompleteness-theorems-truly-mean-20260518/
#HackerNews #Gödel #Incompleteness #Theorems #Mathematics #Philosophy #Logic #Science
-
What Do Gödel's Incompleteness Theorems Mean?
https://www.quantamagazine.org/what-do-godels-incompleteness-theorems-truly-mean-20260518/
#HackerNews #Gödel #Incompleteness #Theorems #Mathematics #Philosophy #Logic #Science
-
creates semantic nodes and clusters #KURT #GÖDEL aepiot.com/advanced-sea... Do you like aéPiot semantics? Donate to the aéPiot semantic platform: www.paypal.com/donate?busin...
MultiSearch Tag Explorer -
"L'accomplissement de Kurt Gödel dans la logique moderne est singulière et monumentale – en fait, c'est plus qu'un monument, c'est un jalon qui restera visible loin dans l'espace et le temps." – John von Neumann (1903-1957)
#citation #mathématiques #maths #math #Gödel -
"Kurt Gödel's achievement in modern logic is singular and monumental – indeed it is more than a monument, it is a landmark which will remain visible far in space and time." – John von Neumann (1903-1957)
#quote #mathematics #maths #math #Gödel -
"L'accomplissement de Kurt Gödel dans la logique moderne est singulière et monumentale – en fait, c'est plus qu'un monument, c'est un jalon qui restera visible loin dans l'espace et le temps." – John von Neumann (1903-1957)
#citation #mathématiques #maths #math #Gödel -
"Kurt Gödel's achievement in modern logic is singular and monumental – indeed it is more than a monument, it is a landmark which will remain visible far in space and time." – John von Neumann (1903-1957)
#quote #mathematics #maths #math #Gödel -
“For what man in the natural state or course of thinking did ever conceive it in his power to reduce the notions of all mankind exactly to the same length, and breadth, and height of his own? Yet this is the first humble and civil design of all innovators in the empire of reason.”*…
A “theory of everything” (a Grand Unified Theory on steriods)– a (still hypothetical) coherent theoretical framework of physics containing and explaining all physical principles– is the holy grail of physicists. Natalie Wolchover checks in on the most recent front-runner in the hunt…
Fifty-eight years after it first appeared, string theory remains the most popular candidate for the “theory of everything,” the unified mathematical framework for all matter and forces in the universe. This is much to the chagrin of its rather vocal critics. “String theory is not dead; it’s undead and now walks around like a zombie eating people’s brains,” the former physicist Sabine Hossenfelder said on her popular YouTube channel in 2024.
String theory is a “failure,” the mathematical physicist and blogger Peter Woit often says. His complaint is not that string theory is wrong — it’s that it’s “not even wrong,” as he titled a 2006 book. The theory says that, on scales of billionths of trillionths of trillionths of a centimeter, extra curled-up spatial dimensions reveal themselves and particles resolve into extended objects — strands and loops of energy — rather than points. But this alleged substructure is too small to detect, probably ever. The prediction is untestable.
A further problem is that uncountably many different configurations of dimensions and strings are permitted at those tiny scales; the theory can give rise to a limitless variety of universes. Amid this vast landscape of solutions, no one can hope to find a precise microscopic configuration that undergirds our particular macroscopic world.
These issues are profound indeed. Yet in my experience, the typical high-energy theorist in a prestigious university physics department still thinks string theory has a good chance of being correct, at least in part. The field has become siloed between those who deem it worth studying and those who don’t.
Recently, a new angle of attack has opened up. An approach called bootstrapping has allowed physicists to calculate that, under various starting assumptions about the universe, a key equation from string theory naturally follows. For some experts, these findings support the notion of “string uniqueness,” the idea that it is the only mathematically consistent quantum description of gravity and everything else.
Responding to one bootstrap paper on her YouTube channel, mere weeks after the “undead” comment, Hossenfelder said it was “string theorists do[ing] something sensible for once.” She added, “I’d say this paper strengthens the argument for string theory.”
Not everyone agrees, but the findings are reviving an important question. “This question of ‘Does string theory describe the world?’ has just been so taboo,” said Cliff Cheung, a physicist at the California Institute of Technology and an author of the paper discussed by Hossenfelder. Now, “people are actually thinking about it for the first time in decades.”
Getting wind of this work, I wanted to drill down on the logic and examine how the string hypothesis is faring these days…
And so she does: “Are Strings Still Our Best Hope for a Theory of Everything?” from @nattyover.bsky.social in @quantamagazine.bsky.social. Eminently worth reading in full.
Compare/contrast with: “Where Some See Strings, She Sees a Space-Time Made of Fractals.”
* Jonathan Swift, A Tale of a Tub
###
As we grapple with Godel, we might spare a thought for Hermann Rorschach; he died on this date in 1922. A psychiatrist and psychoanalyst, his education in art helped to spur the development of a set of inkblots that were used experimentally to measure various unconscious parts of the subject’s personality. Rorschach knew the human tendency to project interpretations and feelings onto ambiguous stimuli and believed that the subjective responses of his subjects enabled him to distinguish among them on the basis of their perceptive abilities, intelligence, and emotional characteristics. His method has come to be known as the Rorschach test, iterations of which have continued to be used over the years to help identify personality, psychotic, and neurological disorders.
Perhaps his insight that we humans tend “to project interpretations and feelings onto ambiguous stimuli” can inform our understanding of physicists trying to construct mental/conceptual models of our reality, which they’ve been doing for a very long time, and of the limitations of that quest.
#bootstrapping #conceptualModels #culture #Godel #HermannRorschach #history #interpretation #KurtGodel #mentalModels #Physics #projection #RorschachTest #Science #stringTheory #theoryOfEverything -
“For what man in the natural state or course of thinking did ever conceive it in his power to reduce the notions of all mankind exactly to the same length, and breadth, and height of his own? Yet this is the first humble and civil design of all innovators in the empire of reason.”*…
A “theory of everything” (a Grand Unified Theory on steriods)– a (still hypothetical) coherent theoretical framework of physics containing and explaining all physical principles– is the holy grail of physicists. Natalie Wolchover checks in on the most recent front-runner in the hunt…
Fifty-eight years after it first appeared, string theory remains the most popular candidate for the “theory of everything,” the unified mathematical framework for all matter and forces in the universe. This is much to the chagrin of its rather vocal critics. “String theory is not dead; it’s undead and now walks around like a zombie eating people’s brains,” the former physicist Sabine Hossenfelder said on her popular YouTube channel in 2024.
String theory is a “failure,” the mathematical physicist and blogger Peter Woit often says. His complaint is not that string theory is wrong — it’s that it’s “not even wrong,” as he titled a 2006 book. The theory says that, on scales of billionths of trillionths of trillionths of a centimeter, extra curled-up spatial dimensions reveal themselves and particles resolve into extended objects — strands and loops of energy — rather than points. But this alleged substructure is too small to detect, probably ever. The prediction is untestable.
A further problem is that uncountably many different configurations of dimensions and strings are permitted at those tiny scales; the theory can give rise to a limitless variety of universes. Amid this vast landscape of solutions, no one can hope to find a precise microscopic configuration that undergirds our particular macroscopic world.
These issues are profound indeed. Yet in my experience, the typical high-energy theorist in a prestigious university physics department still thinks string theory has a good chance of being correct, at least in part. The field has become siloed between those who deem it worth studying and those who don’t.
Recently, a new angle of attack has opened up. An approach called bootstrapping has allowed physicists to calculate that, under various starting assumptions about the universe, a key equation from string theory naturally follows. For some experts, these findings support the notion of “string uniqueness,” the idea that it is the only mathematically consistent quantum description of gravity and everything else.
Responding to one bootstrap paper on her YouTube channel, mere weeks after the “undead” comment, Hossenfelder said it was “string theorists do[ing] something sensible for once.” She added, “I’d say this paper strengthens the argument for string theory.”
Not everyone agrees, but the findings are reviving an important question. “This question of ‘Does string theory describe the world?’ has just been so taboo,” said Cliff Cheung, a physicist at the California Institute of Technology and an author of the paper discussed by Hossenfelder. Now, “people are actually thinking about it for the first time in decades.”
Getting wind of this work, I wanted to drill down on the logic and examine how the string hypothesis is faring these days…
And so she does: “Are Strings Still Our Best Hope for a Theory of Everything?” from @nattyover.bsky.social in @quantamagazine.bsky.social. Eminently worth reading in full.
Compare/contrast with: “Where Some See Strings, She Sees a Space-Time Made of Fractals.”
* Jonathan Swift, A Tale of a Tub
###
As we grapple with Godel, we might spare a thought for Hermann Rorschach; he died on this date in 1922. A psychiatrist and psychoanalyst, his education in art helped to spur the development of a set of inkblots that were used experimentally to measure various unconscious parts of the subject’s personality. Rorschach knew the human tendency to project interpretations and feelings onto ambiguous stimuli and believed that the subjective responses of his subjects enabled him to distinguish among them on the basis of their perceptive abilities, intelligence, and emotional characteristics. His method has come to be known as the Rorschach test, iterations of which have continued to be used over the years to help identify personality, psychotic, and neurological disorders.
Perhaps his insight that we humans tend “to project interpretations and feelings onto ambiguous stimuli” can inform our understanding of physicists trying to construct mental/conceptual models of our reality, which they’ve been doing for a very long time, and of the limitations of that quest.
#bootstrapping #conceptualModels #culture #Godel #HermannRorschach #history #interpretation #KurtGodel #mentalModels #Physics #projection #RorschachTest #Science #stringTheory #theoryOfEverything -
😆 Wow, another programmer bravely dives into Gödel's #incompleteness theorems with the finesse of a cat herding seminar! 🚀 This article promises a whimsical romp through math's greatest hits, interpreted with all the precision of a banana-shaped ruler. 📏👉🤓
https://stopa.io/post/269 #programming #humor #Gödel #math #whimsy #tech #exploration #HackerNews #ngated -
😆 Wow, another programmer bravely dives into Gödel's #incompleteness theorems with the finesse of a cat herding seminar! 🚀 This article promises a whimsical romp through math's greatest hits, interpreted with all the precision of a banana-shaped ruler. 📏👉🤓
https://stopa.io/post/269 #programming #humor #Gödel #math #whimsy #tech #exploration #HackerNews #ngated -
What Gödel Discovered (2020)
#HackerNews #Gödel #Discovered #Incompleteness #Theorems #Mathematics #Philosophy #Logic #2020
-
What Gödel Discovered (2020)
#HackerNews #Gödel #Discovered #Incompleteness #Theorems #Mathematics #Philosophy #Logic #2020
-
@levelbot Actually they are only at 99%... until we say it's 100%, that is, that makes it 100%, which means it is 99%...
#SelfReference #Stats #Statistics #Godel #Hofstadter #StrangeLoop #MetaMeNoMetas
-
@levelbot Actually they are only at 99%... until we say it's 100%, that is, that makes it 100%, which means it is 99%...
#SelfReference #Stats #Statistics #Godel #Hofstadter #StrangeLoop #MetaMeNoMetas
-
New from R&D: What If Penrose Is Asking The Wrong Question? https://artoffaceless.org/what-if-penrose-is-asking-the-wrong-question/?utm_source=dlvr.it&utm_medium=mastodon #Gödel #Penrose #ThrottledMachines #Research #SPMS
-
New from R&D: What If Penrose Is Asking The Wrong Question? https://artoffaceless.org/what-if-penrose-is-asking-the-wrong-question/?utm_source=dlvr.it&utm_medium=mastodon #Gödel #Penrose #ThrottledMachines #Research #SPMS
-
Mathematics is either inconsistent or incomplete.
What is your philosophical interpretation of Gödel’s incompleteness theorems?
#math #mathematics #maths #logic #MathematicalLogic #gödel #kurtgödel #godel #KurtGodel #Philosophy #PhilosophyOfMathematics #PhilosophicalLogic #philosophyoflogic #logic
-
Mathematics is either inconsistent or incomplete.
What is your philosophical interpretation of Gödel’s incompleteness theorems?
#math #mathematics #maths #logic #MathematicalLogic #gödel #kurtgödel #godel #KurtGodel #Philosophy #PhilosophyOfMathematics #PhilosophicalLogic #philosophyoflogic #logic
-
Penultimate part of my essays exploring the Simulation Hypothesis. Warning: may make your head spin (or worse) 😵💫 —🤯
https://jetse.substack.com/p/the-simulation-hypothesis-reprise-e11
-
Penultimate part of my essays exploring the Simulation Hypothesis. Warning: may make your head spin (or worse) 😵💫 —🤯
https://jetse.substack.com/p/the-simulation-hypothesis-reprise-e11
-
I discuss A Language Insufficiency Hypothesis, Chapter 1: A Genealogy of Insufficiency – From Ancient Greece through the 20th Century.
👉 https://youtu.be/A-yoDtJ_ICE
#philosophy #language #video #youtube #genealogy #hypothesis #foucault #semantics #pragmatics #communication #power #ideology #structure #plato #aristotle #Wittgenstein #shadows #augustine #Locke #Liebnitz #Nietzsche #Gödel #Saussure #barthes #shannon #cognition #cognitivescience #rationality
-
I discuss A Language Insufficiency Hypothesis, Chapter 1: A Genealogy of Insufficiency – From Ancient Greece through the 20th Century.
👉 https://youtu.be/A-yoDtJ_ICE
#philosophy #language #video #youtube #genealogy #hypothesis #foucault #semantics #pragmatics #communication #power #ideology #structure #plato #aristotle #Wittgenstein #shadows #augustine #Locke #Liebnitz #Nietzsche #Gödel #Saussure #barthes #shannon #cognition #cognitivescience #rationality
-
TBT I miss my speaking goat avatar.
https://philosophics.blog/2024/03/06/video-response-to-response-on-sapolsky-v-dennett-debate/?utm_source=masto&utm_medium=social
#philosophy #determinism #video #reaction #Sapolsky #dennett #goat #avatar #freewill #perspective #blog #response #debate #reality #Gödel #youtube #TBT -
TBT I miss my speaking goat avatar.
https://philosophics.blog/2024/03/06/video-response-to-response-on-sapolsky-v-dennett-debate/?utm_source=masto&utm_medium=social
#philosophy #determinism #video #reaction #Sapolsky #dennett #goat #avatar #freewill #perspective #blog #response #debate #reality #Gödel #youtube #TBT -
Physicists prove the Universe isn’t a #simulation after all - https://www.sciencedaily.com/releases/2025/11/251110021052.htm "Using #Gödel’s incompleteness theorem, scientists found that reality requires “non-algorithmic understanding,” something no computation can replicate." exciting stuff
-
Physicists prove the Universe isn’t a #simulation after all - https://www.sciencedaily.com/releases/2025/11/251110021052.htm "Using #Gödel’s incompleteness theorem, scientists found that reality requires “non-algorithmic understanding,” something no computation can replicate." exciting stuff
-
@jackwilliambell If the authors want to rephrase #Gödel to say, "Undecidability means that mathematics can't be simulated from within mathematics," then I'm sure there's a way to make that a sensible claim.
But for the next step, it seems you need to believe that mathematics and physics are the same thing, in the sense that calculating on a physically-real computer in some existing reality is identical to contemplating pure mathematics in some abstract Platonic realm.
I'm not sure I could name that many mathematicians or physicists who believe that.
(Not that I have much time for the #simulation idea.)
-
@jackwilliambell If the authors want to rephrase #Gödel to say, "Undecidability means that mathematics can't be simulated from within mathematics," then I'm sure there's a way to make that a sensible claim.
But for the next step, it seems you need to believe that mathematics and physics are the same thing, in the sense that calculating on a physically-real computer in some existing reality is identical to contemplating pure mathematics in some abstract Platonic realm.
I'm not sure I could name that many mathematicians or physicists who believe that.
(Not that I have much time for the #simulation idea.)
-
When I was a child, I thought the world had things that were true and things that were false, i.e., things were "black and white".
Things happened to me, including reading "Gödel, Escher, Bach: an Eternal Golden Braid" #Godel #GodelEscherBach, and I realized "Oh! There’s a gray area! (and not only that, the very edges of the gray area are fuzzy!"
And then I learned about #Bayes (and #Laplace) and realized: "Oh shit! It’s **all** gray!"
It feels like you **know** some things to be true because have assigned them such high probabilities. So high, they seem certain. Sorry. It’s not actually 1. And always remember: probability is what you **know**; reality is outside of that (just like "is your blue the same as my blue?"). Yes! Your model is good enough to navigate the world and make good decisions; but absolutely don’t confuse that with having no room left to learn.
I know I said this in a weird way, but keep growing.
-
There’s a strong urge to believe what you wish instead of what you can prove. Computer rumors are a great example. Many rumors have no basis other than being a feature someone wants. They call it "wish casting".
We want the world to be black and white. Some given statement is either true or false. But it’s not. Gödel #Godel describes at least three states: true, false, and unprovable (e.g., the statement "This statement is false". Can’t be true or false; it’s unprovable. Maybe there’s a better name.)
But it’s worse than that.
In science, a theory isn’t true … it’s just the best explanation we have so far. The whole endeavor of science is to keep finding better explanations. To make good decisions you don’t need the absolute best explanation, just one good enough to guide you to beneficial choices. (I said "prove" before, but to be more accurate I should be talking not about what you can prove, but about what you can’t disprove.)
#Bayes (really #Laplace) says a given notion isn’t true, it’s actually true-with-some-probability. Each new thing you observe impacts that #Probability. This is the actual math behind the #ScientificMethod. And it’s the truth of the world. Your beliefs must adapt to your observations, constantly, forever.
If you have unshakable faith in some set of "facts", you’re probably doing it wrong. Even when you’re right, you could be righter.
Of course, if you don’t adjust your beliefs with new input, if you don’t test, if you have "facts" instead of "very probable theories". If you believe things because of how strongly the person who convinced you believed instead of what they could actually show you. If you believe simply because that’s what your parents taught you. Then, well, you **might** be right (even a stopped clock is right twice a day). But at best you’re not going to make good decisions for yourself, and at worst you’re going to try to tell others what to do based on an inaccurate understanding.
It’s messy; and that’s just how it is.
-
Ok this was generated by googles gemini image generator and I quiet like it :)
-
Ok this was generated by googles gemini image generator and I quiet like it :)
-
La #faille de #Gödel est une auto-contradiction dans la #Constitution des #États-Unis #US que le logicien austro-américain Kurt #Gödel postule en 1947. Elle permettrait de transformer légalement la #démocratie #américaine en #dictature
#Gödel l’avait prédit..
-
La #faille de #Gödel est une auto-contradiction dans la #Constitution des #États-Unis #US que le logicien austro-américain Kurt #Gödel postule en 1947. Elle permettrait de transformer légalement la #démocratie #américaine en #dictature
#Gödel l’avait prédit..
-
AIXI
https://en.wikipedia.org/wiki/AIXI
"AIXI /ˈaɪksi/ is a theoretical mathematical formalism for artificial general intelligence. It combines Solomonoff induction with sequential decision theory. AIXI was first proposed by Marcus Hutter in 2000[...]."
"[...]AIXI is incomputable."
3/3
#AI #ArtificialIntelligence #Gödel #AGI #ArtificialGeneralIntelligence
-
AIXI
https://en.wikipedia.org/wiki/AIXI
"AIXI /ˈaɪksi/ is a theoretical mathematical formalism for artificial general intelligence. It combines Solomonoff induction with sequential decision theory. AIXI was first proposed by Marcus Hutter in 2000[...]."
"[...]AIXI is incomputable."
3/3
#AI #ArtificialIntelligence #Gödel #AGI #ArtificialGeneralIntelligence
-
#Pythagoras believed the world was made of #numbers—until irrational numbers like √2 broke that belief. Centuries later, #Russell tried to build #math on logic, but #Gödel proved no system can capture all truth. Today, #AI is built on the same false faith: that everything is #computable. But life isn’t code. It’s blurry, intuitive, #contradictory. The dream of full #understanding through math isn’t just wrong—it’s a #delusion we keep repeating.
-
#Pythagoras believed the world was made of #numbers—until irrational numbers like √2 broke that belief. Centuries later, #Russell tried to build #math on logic, but #Gödel proved no system can capture all truth. Today, #AI is built on the same false faith: that everything is #computable. But life isn’t code. It’s blurry, intuitive, #contradictory. The dream of full #understanding through math isn’t just wrong—it’s a #delusion we keep repeating.
-
In 1931, Kurt Gödel proved that any system describing the natural numbers could not be both consistent and complete. #Poetry #Science #History #Logic #Incompleteness #Gödel (https://sharpgiving.com/thebookofscience/items/p1931a.html)
-
When, in 1930, the german logician Kurt Goedel managed to prove the incompleteness of a range of rule-based systems, he did so by an encoding that looked like a programming language--and drove, through Alonzo Church, Alan Turing, forth the development that led to _all_ computing. There is an infinity that programs can't predict about themselves; so "AI" is impossible.
https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis
#godel#goedel#incompleteness#aiisamisnomer#doubtai#incompletenesstheorem#logic#uncomputability#theorems
-
🚨 BREAKING: Nobel laureate drops bombshell in 473rd video explaining AI won’t gain consciousness because #Gödel said so. 🎓🤖 Meanwhile, YouTube comments section still debating if robots dream of electric sheep. 🐑💤
https://www.youtube.com/watch?v=biUfMZ2dts8 #NobelLaureate #AIConsciousness #YouTubeDebate #ElectricSheep #HackerNews #ngated
