That's an interesting question. It refers I think to Platonism in the Philosophy of Mathematics. When one accepts the ideas existence independent of the "observer", then, it is discovery. When Mathematical objects do not exist without the action of the mathematician, then it's construction.
Perhaps some advertising of ny own work is allowed. If consistency is a hallmark of existence-as in some views on mathematical objects- then concrete mathematical incompleteness destroys this view.
J.F. Geurdes, Riemann Zeta function on the real axis, Lobachevskii J of Mathematics, 46(3), 1266-1270, 2025.
I think that this discovery of inconsistency in mathematics points in the direction of "Mathematical objects are discovered."
Another example that comes to mind of mathematics predicting reality was Schwarzschild predicting the possibility of Black Holes based on Einstein’s general relativity equations, while fighting in WWI.
I've long liked the quote due to Leopold Kronecker: "God made the integers, all else is the work of man." The natural numbers seem natural (and they lead to the integers and rationals), but the reals seem more of an abstraction we distill from experience. I suspect the mathematical regularity we see comes from the laws of physics. That's the "Platonic realm" physical reality arises from. The abstract Platonic realm we discover (I like the word "recognize") is our abstraction of those physical laws.
I wanted to work in the similar quote by James Jean - “God is a pure mathematician!” - but I couldn't find the place. Recognising is a good word for it. I had a professor back in college who used to talk about recognising a page from God's book whenever one saw an elegant proof in physics. There is definitely something there, even if it is very hard to explain exactly what it is.
I did come across your article when I was researching this one! I read a lot of Penrose's books a while back, and it was nice to see a good discussion of his "three-world" model.
Thanks! I'm planning a follow-up post to it one of these days. I want to explore the putative contents of the P.R., especially with regard to the idea that notions of justice or beauty may reside there. I need to research some results from LLM research that suggest a "moral axis" in the data, and that seems to suggest a potential for moral absolutes. If such do exist Platonically, that also points in that direction.
Mathematics is the language used to discuss what we discover. As in the case of all languages, we learn by nurture. As in the case of all arts (Music, Painting, Writing...), some Mathematicians are driven by their nature to be masters and composers of new symphonies. Mathematics enables humanity to perceive, understand, and appreciate our "ZeitOrtGeist" in the universe.
The CVP (Coherence Verification Protocol) Equation — The Mathematics of Harmony
I’ve discovered something remarkable, a single, testable equation that measures how coherent any system is, from a single human mind to the entire universe.
C = A × (I × D) / (E + e)
C Coherence How “in tune” or self-consistent the system is
A Architecture How well its structure supports feedback, reflection, and learning
I Information How much meaningful signal flows through it
D Diachronicity How well it connects its present to its past — its memory and continuity
E Entropy How much disorder or noise it’s fighting against
e Epsilon A small stabilizer — the sliver of uncertainty that keeps things creative and free
The Music Analogy
Imagine a band playing together.
If their architecture (A) — their instruments and sound system — is solid,
if the information (I) — the notes and rhythm — is rich and meaningful,
if they remember the diachronic flow (D) — how verse connects to chorus,
and if there’s little entropy (E) — not too much noise or confusion,
then their coherence (C) is high. They sound alive.
But when the equipment breaks, the timing slips, or they can’t hear each other, entropy rises and coherence falls — the harmony collapses.
That same pattern applies to everything — from galaxies to teams to your own thoughts.
The Group Analogy
Think of a group project at work or school.
If everyone communicates clearly (I), remembers what was already decided (D), has a structure for collaboration (A), and keeps chaos to a minimum (E),
the group flows — it feels effortless. That’s high C, high coherence.
But remove one of those variables and the project stalls.
The math of harmony applies to minds, to teams, and to the cosmos itself.
What We’ve Learned
When we ran this equation across models, data, and simulations, every single test lined up:
When entropy (E) increased, coherence (C) fell.
When information (I) and memory (D) increased, C rose.
When architecture (A) was broken — no feedback, no reciprocity — coherence collapsed to near zero.
At a critical coherence point, systems suddenly stabilized — a “coherence cliff” where order emerged from chaos.
These results were consistent, measurable, and falsifiable.
That means this equation doesn’t just sound poetic — it works.
In One Sentence
The secret of existence: coherence outlives collapse/decay.
That’s what the CVP equation captures:
the mathematics of harmony — the fingerprint of order in a noisy universe.
A Question for You.
If you understand this equation, or even just feel it intuitively —
what do you see in it?
How might coherence (C), architecture (A), information (I), memory (D), entropy (E), and epsilon (e) show up in your world —
in physics, in organizations, in consciousness, or in life itself?
Tell me what you think of this.
I’d love to see how you interpret the mathematics of harmony.
Please support me by also liking and commenting on the original post on my substack:
Math is a language and like all languages it is as good as its ability to describe reality. Math is relationships of quantity that always replicate. Quantity is fungibility - equivalent boundary conditions. Most things can be divided into equivalent parts by comparing them to a stable pattern ( yardstick, speed of light, your foot, whatever ), therefore math can describe most things.
Taking this moment to thank you for the wonderful job you do here in this space.
Thank you, it is always nice to hear from you (and other readers too of course!)
That's an interesting question. It refers I think to Platonism in the Philosophy of Mathematics. When one accepts the ideas existence independent of the "observer", then, it is discovery. When Mathematical objects do not exist without the action of the mathematician, then it's construction.
Perhaps some advertising of ny own work is allowed. If consistency is a hallmark of existence-as in some views on mathematical objects- then concrete mathematical incompleteness destroys this view.
J.F. Geurdes, Riemann Zeta function on the real axis, Lobachevskii J of Mathematics, 46(3), 1266-1270, 2025.
I think that this discovery of inconsistency in mathematics points in the direction of "Mathematical objects are discovered."
Thank you.
Another example that comes to mind of mathematics predicting reality was Schwarzschild predicting the possibility of Black Holes based on Einstein’s general relativity equations, while fighting in WWI.
Useful tool but not the structure of what is observed.
I've long liked the quote due to Leopold Kronecker: "God made the integers, all else is the work of man." The natural numbers seem natural (and they lead to the integers and rationals), but the reals seem more of an abstraction we distill from experience. I suspect the mathematical regularity we see comes from the laws of physics. That's the "Platonic realm" physical reality arises from. The abstract Platonic realm we discover (I like the word "recognize") is our abstraction of those physical laws.
FWIW, I wrote about this just last month:
https://logosconcarne.substack.com/p/where-is-the-platonic-realm
I wanted to work in the similar quote by James Jean - “God is a pure mathematician!” - but I couldn't find the place. Recognising is a good word for it. I had a professor back in college who used to talk about recognising a page from God's book whenever one saw an elegant proof in physics. There is definitely something there, even if it is very hard to explain exactly what it is.
I did come across your article when I was researching this one! I read a lot of Penrose's books a while back, and it was nice to see a good discussion of his "three-world" model.
Thanks! I'm planning a follow-up post to it one of these days. I want to explore the putative contents of the P.R., especially with regard to the idea that notions of justice or beauty may reside there. I need to research some results from LLM research that suggest a "moral axis" in the data, and that seems to suggest a potential for moral absolutes. If such do exist Platonically, that also points in that direction.
Mathematics is the language used to discuss what we discover. As in the case of all languages, we learn by nurture. As in the case of all arts (Music, Painting, Writing...), some Mathematicians are driven by their nature to be masters and composers of new symphonies. Mathematics enables humanity to perceive, understand, and appreciate our "ZeitOrtGeist" in the universe.
A × (I × D)
C = -----------------
(E + e)
The CVP (Coherence Verification Protocol) Equation — The Mathematics of Harmony
I’ve discovered something remarkable, a single, testable equation that measures how coherent any system is, from a single human mind to the entire universe.
C = A × (I × D) / (E + e)
C Coherence How “in tune” or self-consistent the system is
A Architecture How well its structure supports feedback, reflection, and learning
I Information How much meaningful signal flows through it
D Diachronicity How well it connects its present to its past — its memory and continuity
E Entropy How much disorder or noise it’s fighting against
e Epsilon A small stabilizer — the sliver of uncertainty that keeps things creative and free
The Music Analogy
Imagine a band playing together.
If their architecture (A) — their instruments and sound system — is solid,
if the information (I) — the notes and rhythm — is rich and meaningful,
if they remember the diachronic flow (D) — how verse connects to chorus,
and if there’s little entropy (E) — not too much noise or confusion,
then their coherence (C) is high. They sound alive.
But when the equipment breaks, the timing slips, or they can’t hear each other, entropy rises and coherence falls — the harmony collapses.
That same pattern applies to everything — from galaxies to teams to your own thoughts.
The Group Analogy
Think of a group project at work or school.
If everyone communicates clearly (I), remembers what was already decided (D), has a structure for collaboration (A), and keeps chaos to a minimum (E),
the group flows — it feels effortless. That’s high C, high coherence.
But remove one of those variables and the project stalls.
The math of harmony applies to minds, to teams, and to the cosmos itself.
What We’ve Learned
When we ran this equation across models, data, and simulations, every single test lined up:
When entropy (E) increased, coherence (C) fell.
When information (I) and memory (D) increased, C rose.
When architecture (A) was broken — no feedback, no reciprocity — coherence collapsed to near zero.
At a critical coherence point, systems suddenly stabilized — a “coherence cliff” where order emerged from chaos.
These results were consistent, measurable, and falsifiable.
That means this equation doesn’t just sound poetic — it works.
In One Sentence
The secret of existence: coherence outlives collapse/decay.
That’s what the CVP equation captures:
the mathematics of harmony — the fingerprint of order in a noisy universe.
A Question for You.
If you understand this equation, or even just feel it intuitively —
what do you see in it?
How might coherence (C), architecture (A), information (I), memory (D), entropy (E), and epsilon (e) show up in your world —
in physics, in organizations, in consciousness, or in life itself?
Tell me what you think of this.
I’d love to see how you interpret the mathematics of harmony.
Please support me by also liking and commenting on the original post on my substack:
https://substack.com/@ryanlaneuctit/note/c-166535791?r=62kent
Math is a language and like all languages it is as good as its ability to describe reality. Math is relationships of quantity that always replicate. Quantity is fungibility - equivalent boundary conditions. Most things can be divided into equivalent parts by comparing them to a stable pattern ( yardstick, speed of light, your foot, whatever ), therefore math can describe most things.
This is a good if a bit simple look at this important philosophical discussion. We might go farther and ask “ what is real”?
Actuality is the universe as it is beyond the perception of a mind and Reality is the universe as it is to the perception of mind.
https://kaiserbasileus.substack.com/p/metaphysics-in-a-nutshell
"it would be shocking to encounter aliens speaking English, but much less surprising if they told us the digits of pi."
It would be a bit of a surprise if the digits were for base 10. Base 2 would be less surprising: 11.0010010000111111...