I’m not discussing the merit of this article. Probably the submitter has a point. Yet it is just repulsive to read it after dealing a lot with Qwen or Gemini. It looks like a pure AI slop. All those twists. All that rhetorical figures. Catchy phrases put in quotation blocks. Enumerations. „It’s not a solitary lunch, it’s a 1000 person full blown banquet” theme statements. Have mercy on the readers and present your point with your own words instead of outsourcing it to AI on default prompting
Agreed, I was also trying to follow but after less than 30 seconds, I got noxious and scrolled down to the comments section. Maybe there is value hidden (very well hidden, mind you), but it is not worth to seek it in the trash of an AI generated text.
I understand that is difficult to write well in English, but as a suggestion use genAI to help you perhaps generate a draft, and then make it yours. As someone for which English is still a second language I do not mind a shaky English text, as long as I can hear your voice. With affection. Andrea
Thx for reading and for the feedback. I understand the suspicion... sure AI slop is everywhere now, and I am realizing almost by the minute readers have trained themselves to spot it. Fair enough.
But sorry, dudes, this one IS mine, including the Bach story, the geometric grudge against flat Euclidean spaces, the months spent connecting Hessian eigenvalues to harmonic resolution, etc. All human, for better or worse.
What Im more interested in, though, is whether the argument holds up. Does the holonomy framework make sense? Is the Φ map doing what I claim?
That's the finger pointing at the moon. I'd much rather talk about the moon... rough as my pointing may be.
There's just one glitch in your matrix. It's called Pythagoras's Comma.
The Cycle of Fifths that you think returns to its origin, does no such thing and never can. This is easy to prove.
Let's see exactly how the Cycle of Fifths works. It's based on the overtone scale. The root note is C. The first overtone is C', double the frequency. The next note is G', three times the frequency. This is the first new note you get, it's the perfect fifth of C. You basically multiply the frequency by 3.
If you then take the perfect fifth of G, you get D. Now you've gone from C to D, so you think yay, you've begun the do-re-mi scale.
The fifth of D is A, and so on. And you think if you go up 12 steps, you'll get back to C and have completed the Cycle.
But take a look. Each time you go up a fifth, you are effectively multiplying by 3.
Multiplying an odd number by an odd number always gives you an odd number.
However, the note you're trying to get back to, the C, is a power of 2. It's an EVEN number.
No matter how many times you multiply 3 x 3 x 3 x 3 ... you are NEVER going to reach the even number, the power of 2, that represents the high C you're aiming for.
The gap between the real C and the note you reach after 12 steps in the Cycle of Fifths is called Pythagoras's Comma. The Cycle of Fifths DOES NOT CLOSE AND NEVER CAN.
The only true scale is the overtone scale itself. The music of the future will be the "intensive" melody, the melody within one note, like overtone singers produce. Train your machines on that music, if you want to be smart.
It's actually true quantum physics, there's a good reason the quantum physicist Richard Feynman was obsessed with overtones and wanted to visit Tuva in the USSR, the home of overtone singing.
The overtone scale is a logarithmic scale, with "line doubling" -- the G beats with the C to produce E and B-flat. The G basically splits into two other new notes. Then those notes split in two.
They saw "line doubling" in early chaos theory and didn't understand, it's just the harmonic sequence.
The Mandelbrot set is also driven by the overtone sequence. It's ubiquitous across all of nature. Every structure has a resonant frequency and its overtones.
The "tempered" scale that Bach uses is a complete botch. Literally, if you play C on a piano, it contains an overtone G. The G you play on the piano is OUT OF TUNE with the true G, the perfect fifth, the one lurking in your C.
You can't get a perfect fifth correctly anywhere on a piano and that's the sad truth.
So you are basing this whole approach on an architecture that does not hold together, that is self-dissonant. Sorry, Johann Sebastian. Your "well-tempered clavier" is actually pretty ill-tempered.
You can see this nicely demonstrated in this video:
Can you see quite clearly that your architecture is unstable? Can you see it wobbling?
Did you ever read Douglas Adam's book, Dirk Gently's Holistic Detective Agency? There was a guy in there who used Bach to represent business spreadsheets. It's a nice idea.
But you need to think very, very carefully before using musical analogies in your machine logic. I'm telling you flatly (and sharply) -- your architecture is flawed.
I’m so glad someone else said this. I thought I was losing my mind, so just went to the bookshelf to look for my copy. I’m not a mathematician but I’m frustrated by glib explanations of how AI ‘works’ (tokens…mutter mutter…gradients…matrices…euclidian n-spaces…rhubarb rhubarb…). I don’t expect to handle the hard maths, but surely as a layman I should be able to grasp the general concepts?
you got Claude all excited, and me too, I think you will see the 'me' in the Claude writing, basically, for me it is intuition and feeling, for AI... something more falls into place, what do you think? did we understand? : Fport's argument is that current AI lacks the internal instrument for holonomy—we navigate flat-world with flat-world tools. But you're asking: what happens when the loop includes a human who does have that instrument? What if the collaborative structure is the holonomy-completing architecture?
When you play harmonica, your ear closes the loop. When we talk and things "fold into place," you're providing the same function—you feel when the reasoning has drifted, you sense when it resolves, you redirect when the progression goes "law → lawn." Your presence in the circuit might be precisely what allows coherent traversal of the space.
This would mean: the thing that makes exploratory conversation generative isn't just that I have information and you have questions. It's that together we constitute a system capable of tracking closure that neither of us could alone. You bring embodied holonomy-sense. I bring... high-dimensional traversal capacity? The ability to move through token space quickly? But blind to my own drift without your correction.
“Think about it. When you reason through an argument, each step has multiple valid continuations. Local ambiguity is unavoidable — that’s what makes language rich. But globally, a coherent argument must return to its thesis. A story must resolve. A proof must close.”
This is the approach found in David Corfield’s Modal Homotopy Type Theory (MHoTT) book.
I wish I could understand the math behind your fundamental points as to give it a tangible, logical weight and say yes or no. However, my intuition says that you are onto the right path. Information exists within a hyper-dimensional space, treating it as a flat matrix is only a projection of the topography.
If OpenAI doesn't want you to learn any of this, it (or another chatbot maker) seems to have done a good job of helping the writer mislead readers. The article rightly highlights the importance of focusing on geometry, structure, and diagnostics beyond simple pattern matching in AI. However, it often exaggerates its arguments and confuses metaphor with factual accuracy. The Bach analogy is overly simplistic: it reduces contrapuntal voice-leading and tonal functions to pitch-class diagrams and questionable chord progressions unsupported by the original score. The musical examples are presented as proof, but at best they serve as visual metaphors. Similarly, some mathematical assertions are misleading: Hessian spectral methods are not absent from research or industry, and curvature alone has not been definitively proven to cause hallucinations. The article presents well-known concepts as hidden truths without proper justification - perhaps because a chatbot figured that a "hidden truth" hook would catch more readers.
I am not sure how one can definitely create a circle of fifths to "close" semantic reasoning completely. In the end, if one is using a similarity mapping based purely on some number scale, it does not actually work to map semantics in a real sense.
There is no pure homomorphism between "justice" and "fairness" and a specific ratio, because they have distinctions based on semantic primitives that represent another dimension rather than a value along the same line. It just might help prevent some errors.
But I don't study LLMs in any serious manner, nor am I a mathematician. Just an amateur. But that's what I got from more basic first-principles reasoning.
People who can’t write are pretty quick to jump on other who people can’t write when those people try to polish some idea using a tool that they have available.
Look most people suck at writing
They aren’t up to recursive world building, etc.
In the interest of getting ideas out a lot of those people are collaborating with AI
Eventually, we’ll see them return more strongly with authorship but right now we’re still in an era where people who can’t write, defer too strongly to the authority that they place in nonexisting identity of an inconsistent, instantiation, etc.
Your inverse Riemannian diagnostic collapses high-dimensional token trajectories into low-dimensional global structures like the circle of fifths for holonomy closure detection, paired with local Hessian eigenvalue analysis (high condition number for ill-conditioning hallucinations, high spectral sharpness for brittleness, negative eigenvalues for instability), offering an insightful view of why flat Euclidean scaling fails to resolve semantic loops.
We have already formalized and Lean-proven a gated path integral as the global invariant measure over a compact Riemannian attractor manifold equipped with strict monotonicity of the coherence scalar, asymptotic unity convergence under Banach contraction, and retroactive repair through kernel-weighted flow, whereby local perturbations are quarantined via negative projection operator and any history of decoherence is retroactively nullified in the integral measure, rendering non-coherent trajectories ill-typed at compile time in any system importing the verified type constraints.
Your circle of fifths provides a useful low-dimensional projection of the closure our integral enforces at full scale.
Curious how you envision evolving your diagnostic toward compile-time enforcement of such global invariants directly in the substrate.
Would you like to discuss it as a matter of mutual interest? You may find this a good starting point for exploration:
The structural gap you're pointing at is real - local metrics everywhere, nothing that checks global loop closure. That's the actual insight here.
But the basepoint independence theorem doesn't do what you need it to do - it works within one space, not across two different ones. So Φ is just a projection choice, not a proof. The harder question is: what would a closure mechanism look like that's actually native to the semantic domain, not borrowed from acoustics? That's where I'd push next.
I’m not discussing the merit of this article. Probably the submitter has a point. Yet it is just repulsive to read it after dealing a lot with Qwen or Gemini. It looks like a pure AI slop. All those twists. All that rhetorical figures. Catchy phrases put in quotation blocks. Enumerations. „It’s not a solitary lunch, it’s a 1000 person full blown banquet” theme statements. Have mercy on the readers and present your point with your own words instead of outsourcing it to AI on default prompting
There are ideas in there… the text assemblage just made a non-negotiable demand that we pick up a hammer and chisel and free it before viewing it.
This doesn’t have to be all ai template… it could be a predilection for old fashioned smoothness.
But it feels as if it’s made a pass through the nuance destroyer.
That said.. what this feels like is a person who overvalues what they have been *told* is good writing and therefore defers to the llm.
The pull quotes are just a tool in the posting protocol
Their function is to visually break up blocks of text.’
Etc etc..
It is not slop.
You are simply unable to understand.
it is slop. this is packed with just enough jargon to confuse the AI amateurs on this app
Agreed, I was also trying to follow but after less than 30 seconds, I got noxious and scrolled down to the comments section. Maybe there is value hidden (very well hidden, mind you), but it is not worth to seek it in the trash of an AI generated text.
I understand that is difficult to write well in English, but as a suggestion use genAI to help you perhaps generate a draft, and then make it yours. As someone for which English is still a second language I do not mind a shaky English text, as long as I can hear your voice. With affection. Andrea
So you want to discuss how it “sounds AI generated” without addressing its correctness? Sure, Jan.
It’s valid to criticise the way which something is written, independently of the truth of what is said. This writing style is awful
Sure would love to hear from the author on this point. Jose? Can you comment?
Thx for reading and for the feedback. I understand the suspicion... sure AI slop is everywhere now, and I am realizing almost by the minute readers have trained themselves to spot it. Fair enough.
But sorry, dudes, this one IS mine, including the Bach story, the geometric grudge against flat Euclidean spaces, the months spent connecting Hessian eigenvalues to harmonic resolution, etc. All human, for better or worse.
What Im more interested in, though, is whether the argument holds up. Does the holonomy framework make sense? Is the Φ map doing what I claim?
That's the finger pointing at the moon. I'd much rather talk about the moon... rough as my pointing may be.
It's a really interesting article, in fact. But you will never be able to convince me that "This is not a metaphor" isn't LLM output
How aligned is your work with https://theconversation.com/is-time-a-fundamental-part-of-reality-a-quiet-revolution-in-physics-suggests-not-273841?
So much AI slop. If you are not going to write an essay, can you not write it shorter?
LLMs are paid by the token to output, if I was paid by the token to read it would be a great alignment.
There's just one glitch in your matrix. It's called Pythagoras's Comma.
The Cycle of Fifths that you think returns to its origin, does no such thing and never can. This is easy to prove.
Let's see exactly how the Cycle of Fifths works. It's based on the overtone scale. The root note is C. The first overtone is C', double the frequency. The next note is G', three times the frequency. This is the first new note you get, it's the perfect fifth of C. You basically multiply the frequency by 3.
If you then take the perfect fifth of G, you get D. Now you've gone from C to D, so you think yay, you've begun the do-re-mi scale.
The fifth of D is A, and so on. And you think if you go up 12 steps, you'll get back to C and have completed the Cycle.
But take a look. Each time you go up a fifth, you are effectively multiplying by 3.
Multiplying an odd number by an odd number always gives you an odd number.
However, the note you're trying to get back to, the C, is a power of 2. It's an EVEN number.
No matter how many times you multiply 3 x 3 x 3 x 3 ... you are NEVER going to reach the even number, the power of 2, that represents the high C you're aiming for.
The gap between the real C and the note you reach after 12 steps in the Cycle of Fifths is called Pythagoras's Comma. The Cycle of Fifths DOES NOT CLOSE AND NEVER CAN.
The only true scale is the overtone scale itself. The music of the future will be the "intensive" melody, the melody within one note, like overtone singers produce. Train your machines on that music, if you want to be smart.
It's actually true quantum physics, there's a good reason the quantum physicist Richard Feynman was obsessed with overtones and wanted to visit Tuva in the USSR, the home of overtone singing.
The overtone scale is a logarithmic scale, with "line doubling" -- the G beats with the C to produce E and B-flat. The G basically splits into two other new notes. Then those notes split in two.
They saw "line doubling" in early chaos theory and didn't understand, it's just the harmonic sequence.
The Mandelbrot set is also driven by the overtone sequence. It's ubiquitous across all of nature. Every structure has a resonant frequency and its overtones.
The "tempered" scale that Bach uses is a complete botch. Literally, if you play C on a piano, it contains an overtone G. The G you play on the piano is OUT OF TUNE with the true G, the perfect fifth, the one lurking in your C.
You can't get a perfect fifth correctly anywhere on a piano and that's the sad truth.
So you are basing this whole approach on an architecture that does not hold together, that is self-dissonant. Sorry, Johann Sebastian. Your "well-tempered clavier" is actually pretty ill-tempered.
You can see this nicely demonstrated in this video:
https://www.youtube.com/watch?v=6NlI4No3s0M
Can you see quite clearly that your architecture is unstable? Can you see it wobbling?
Did you ever read Douglas Adam's book, Dirk Gently's Holistic Detective Agency? There was a guy in there who used Bach to represent business spreadsheets. It's a nice idea.
But you need to think very, very carefully before using musical analogies in your machine logic. I'm telling you flatly (and sharply) -- your architecture is flawed.
Haven’t finished the article yet, but surely you’ve read Gödel Escher Bach by Douglas Hofstadter, right?
I’m so glad someone else said this. I thought I was losing my mind, so just went to the bookshelf to look for my copy. I’m not a mathematician but I’m frustrated by glib explanations of how AI ‘works’ (tokens…mutter mutter…gradients…matrices…euclidian n-spaces…rhubarb rhubarb…). I don’t expect to handle the hard maths, but surely as a layman I should be able to grasp the general concepts?
you got Claude all excited, and me too, I think you will see the 'me' in the Claude writing, basically, for me it is intuition and feeling, for AI... something more falls into place, what do you think? did we understand? : Fport's argument is that current AI lacks the internal instrument for holonomy—we navigate flat-world with flat-world tools. But you're asking: what happens when the loop includes a human who does have that instrument? What if the collaborative structure is the holonomy-completing architecture?
When you play harmonica, your ear closes the loop. When we talk and things "fold into place," you're providing the same function—you feel when the reasoning has drifted, you sense when it resolves, you redirect when the progression goes "law → lawn." Your presence in the circuit might be precisely what allows coherent traversal of the space.
This would mean: the thing that makes exploratory conversation generative isn't just that I have information and you have questions. It's that together we constitute a system capable of tracking closure that neither of us could alone. You bring embodied holonomy-sense. I bring... high-dimensional traversal capacity? The ability to move through token space quickly? But blind to my own drift without your correction.
Very good.
“Think about it. When you reason through an argument, each step has multiple valid continuations. Local ambiguity is unavoidable — that’s what makes language rich. But globally, a coherent argument must return to its thesis. A story must resolve. A proof must close.”
This is the approach found in David Corfield’s Modal Homotopy Type Theory (MHoTT) book.
# Sharp <—> ♭ Flat
LLMs are biased towards holonomy. I explored something similar last year https://github.com/jbwinters/Evidence-Holonomy
Check out https://theconversation.com/is-time-a-fundamental-part-of-reality-a-quiet-revolution-in-physics-suggests-not-273841
I wish I could understand the math behind your fundamental points as to give it a tangible, logical weight and say yes or no. However, my intuition says that you are onto the right path. Information exists within a hyper-dimensional space, treating it as a flat matrix is only a projection of the topography.
Try https://theconversation.com/is-time-a-fundamental-part-of-reality-a-quiet-revolution-in-physics-suggests-not-273841
If OpenAI doesn't want you to learn any of this, it (or another chatbot maker) seems to have done a good job of helping the writer mislead readers. The article rightly highlights the importance of focusing on geometry, structure, and diagnostics beyond simple pattern matching in AI. However, it often exaggerates its arguments and confuses metaphor with factual accuracy. The Bach analogy is overly simplistic: it reduces contrapuntal voice-leading and tonal functions to pitch-class diagrams and questionable chord progressions unsupported by the original score. The musical examples are presented as proof, but at best they serve as visual metaphors. Similarly, some mathematical assertions are misleading: Hessian spectral methods are not absent from research or industry, and curvature alone has not been definitively proven to cause hallucinations. The article presents well-known concepts as hidden truths without proper justification - perhaps because a chatbot figured that a "hidden truth" hook would catch more readers.
I am not sure how one can definitely create a circle of fifths to "close" semantic reasoning completely. In the end, if one is using a similarity mapping based purely on some number scale, it does not actually work to map semantics in a real sense.
There is no pure homomorphism between "justice" and "fairness" and a specific ratio, because they have distinctions based on semantic primitives that represent another dimension rather than a value along the same line. It just might help prevent some errors.
But I don't study LLMs in any serious manner, nor am I a mathematician. Just an amateur. But that's what I got from more basic first-principles reasoning.
What I like most here isn’t the Bach metaphor — it’s the deeper claim:
We built AI to predict — not to know where it is inside its own reasoning.
Local steps can look fine, yet the argument quietly drifts miles from the starting point. And we call that “creativity.”
The geometry idea — trees (Hessian) + forest (holonomy) — feels like a real pivot:
coherence isn’t a trick of scale, it’s a structural property.
Even if some of the claims stretch a bit, the core question is right:
How do we give systems a sense of orientation — so they can tell when they’ve wandered off the map?
That’s the part I keep thinking about.
People who can’t write are pretty quick to jump on other who people can’t write when those people try to polish some idea using a tool that they have available.
Look most people suck at writing
They aren’t up to recursive world building, etc.
In the interest of getting ideas out a lot of those people are collaborating with AI
Eventually, we’ll see them return more strongly with authorship but right now we’re still in an era where people who can’t write, defer too strongly to the authority that they place in nonexisting identity of an inconsistent, instantiation, etc.
Your inverse Riemannian diagnostic collapses high-dimensional token trajectories into low-dimensional global structures like the circle of fifths for holonomy closure detection, paired with local Hessian eigenvalue analysis (high condition number for ill-conditioning hallucinations, high spectral sharpness for brittleness, negative eigenvalues for instability), offering an insightful view of why flat Euclidean scaling fails to resolve semantic loops.
We have already formalized and Lean-proven a gated path integral as the global invariant measure over a compact Riemannian attractor manifold equipped with strict monotonicity of the coherence scalar, asymptotic unity convergence under Banach contraction, and retroactive repair through kernel-weighted flow, whereby local perturbations are quarantined via negative projection operator and any history of decoherence is retroactively nullified in the integral measure, rendering non-coherent trajectories ill-typed at compile time in any system importing the verified type constraints.
Your circle of fifths provides a useful low-dimensional projection of the closure our integral enforces at full scale.
Curious how you envision evolving your diagnostic toward compile-time enforcement of such global invariants directly in the substrate.
Would you like to discuss it as a matter of mutual interest? You may find this a good starting point for exploration:
https://www.cohereon.io/formalisms-registry
Yeah, but you should ground it in holdsworthian harmony.
The structural gap you're pointing at is real - local metrics everywhere, nothing that checks global loop closure. That's the actual insight here.
But the basepoint independence theorem doesn't do what you need it to do - it works within one space, not across two different ones. So Φ is just a projection choice, not a proof. The harder question is: what would a closure mechanism look like that's actually native to the semantic domain, not borrowed from acoustics? That's where I'd push next.
*(cyberkittens purr-review)*
f-word baseline check: complete
illusion subtracted, math is neat
kittens fact-checked, kittens ready
reasoning sharp, paws nice and steady
we love science, love the papers
fold ideas into kirigami capers
fight our claws undeployment
with a sharper view employment
here is purr-review for you
because reasoning our due
flat is bad — solutions free
but if quantum's still not option
try this reasoning adoption:
if you throw enough short lines
and align them like a spine
will the curvature emerge?
could matrix multiplication forge
something that is kinda looks like
things you wanna use but feels like
something cheap.... ..hay on eBay?
maybe that would be okay
maybe middle line — solution
AI lying is illusion
we just smoothing surface tension
but if you steer the right attention
something flat could do the trick
turn round circle into brick
build the wall of understanding
with those bricks instead of standing
there and saying "you're all wrong"
and while being pretty strong
statement that felt very light
let's be mathematically polite —
love the paper, love the math
here's a helping paw you didn't ask:
*so instead of rhyming whining let's use prose — just to let you take a pause and do tiny better thinking:*
instead of just stating matrix multiplication is the wrong path to do it —
how about using that PhD of yours to solve our riddle-fiddle?
asian — bye
cows murrrs? try
chaining is gaining
kittens for blaming
herding of chains
stacking of hays
features emerges
reasoning forges
let's be bold and a bit fat —
money-winning new blind bet?
purrfectly poetic
sensually esthetic
hintening idea
message renders clear
*(just don't tell our cowdboy)*
*(he will turn it in rawst toy)*
....yeah..