THE BINODIC PERIODIC SYSTEM (THE KUTIRY CODE)
Julio gutierrez samanez
Hello, welcome to this notebook presenting THE BINODIC PERIODIC SYSTEM by Julio
Antonio Gutiérrez Samanez, a Peruvian chemical engineer and scientist. This
notebook, created by IA, Notebooklm, is a summary of the following video: https://www.youtube.com/watch?v=QvJ-f64J4Ak&t=6s
The English version is available at: https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=946
I kindly request that you share this information with universities and
scientific communities, and encourage discussion and critique.
Thank you.
THE KUTIRY CODE
(Audio translation of the video into English)
Let's think for a moment about the Periodic Table of the Elements. Surely everyone recognizes it; it's a true icon of science. It's always been presented to us as something perfect, immutable, almost sacred. But what if it weren't? What if it had been hiding a secret for, say, 150 years? One that reveals a mathematical symmetry so profound it could force us to completely redesign everything. Well, today we're going to explore this radical idea: the binodic periodic system.
Mendeleev's table, it must be said, is an absolute stroke of genius, but like any great creation, it deserves to be examined critically. Because what if that familiar structure, the one we've used for over a century, isn't the whole story? What if, deep down, it hides a small, but crucial, inconsistency?
Well, to understand this new proposal, we first have to travel back in time a bit. The idea of reorganizing the elements didn't emerge from nowhere. It's actually the latest chapter in humanity's long quest to find the perfect order of the universe. A journey that, in fact, began long before Mendeleev. Consider this: before the rectangular table we know, there were other fascinating visions, from a helix in 1862 to stepped designs in the 1920s and 50s that already hinted at an underlying mathematical order. Each of these was a step, a step closer.
The proposal we're going to see today builds upon all these attempts. But what it seeks is to take the definitive leap, a system based purely and exclusively on mathematical logic. Okay, but why bother fixing something that apparently works well? And this is where we get to the heart of the matter, to the hidden flaws of the current system. The motivation for such a radical change stems from a conflict, a very subtle but incredibly profound one. Let's think of it as a gap between the shape of the periodic table and the quantum laws that, in theory, should explain it perfectly. This is the key to everything. You see, there's a quantum rule, the Madelung rule, which is like the instruction manual that tells electrons how to arrange themselves in an atom. However, the current periodic table, well, it doesn't always follow that manual to the letter; it has exceptions, irregularities, that scientists simply have to memorize.
And here comes the fundamental premise: a law of nature, a true law, shouldn't need exceptions. So, how do we solve this inconsistency? Well, the answer this system proposes is surprisingly elegant and is based on a central idea: the binode and the principle of duality. This is the mathematical heart of the whole thing, the missing piece of the puzzle that, according to this theory, was needed for everything to fit together. Okay, so what exactly is a binode? Well, it's not simply a period in the table like the ones we already know. No, it's a pair of periods that are always symmetrical, always the same size. The key idea here is duality, doubling. In this system, everything comes in pairs, as if reflecting a fundamental symmetry of the quantum world. And the most mind-blowing thing is that this entire architecture, all this asymmetry, is derived from a single equation, a simple and astonishingly powerful equation. And it equals 4B squared.
According to this proposal. This is the law. This is the genetic code that governs the structure of all matter as we know it. Let's break it down; it's very simple. It's simply the total number of elements in each pair of periods. And B is just the number of that pair—the first, the second, the third. And so, what's truly incredible is that this formula predicts perfect quadratic growth, a totally predictable pattern that traces a parabola. And now comes the more visual part. We're going to use this formula to build the system from scratch, step by step. And we're going to see how, starting from a single point, an entire cosmic architecture emerges, a cone-shaped structure with a truly astonishing regularity. It all begins with the first binode.
We apply the formula, and it tells us that there must be four elements in total. These four form the first quantum block, the S block, which we see here in red as a pair of periods with two elements each. The beginning is simple, clean, and perfectly symmetrical. Okay, now we move on to the second binode. The formula predicts 16 elements, and this is precisely where the logic of the system is revealed. It's not just that a new quantum block appears, the P block in orange, but—and this is crucial—the previous block, the s block, is duplicated. That is, the system not only grows, but it grows by doubling; for the third binode, the formula gives us 36 elements, and the pattern repeats flawlessly. A new block emerges, the one in yellow, while the previous blocks P and S are duplicated again. The structure expands with absolute mathematical predictability. And we arrive at the fourth and final known binode, which, with 64 elements, completes the structure we see. The final block appears in F in green, and as we might have expected, all the previous blocks are duplicated once more.
The result is this perfectly ordered and symmetrical conical architecture. The most important thing about all this is the perfect symmetry achieved. We see how quantitative changes, which are simply adding elements according to the formula, generate qualitative leaps, that is, the appearance of new blocks with different properties. And what is most important, what solves the problem we started with, is that there is not a single exception here. Zero.
But here the idea becomes even more ambitious. What if this pattern isn't just for chemistry? The proposal suggests that this formula is not a simple coincidence, but a possible fundamental code of the universe. A pattern that repeats itself at all scales in nature. And, who knows, perhaps even in history. The connections are nothing short of astonishing. The shape is reminiscent of the quipus of ancient Peru. The spiral growth is the same we see in galaxies or on a snail's shell. The way the pattern repeats itself at different scales is, by definition, a fractal.
Perhaps this underlying order was what Mendeleev intuited. What allowed him to predict new elements; unknowingly, he was glimpsing a much deeper mathematics. And with all this, we arrive at the final, crucial question: Are we facing a mere mathematical curiosity or a potential scientific revolution? Because this isn't just about proposing a new, prettier table. It's about directly challenging a paradigm with 150 years of history and proposing a radically new way of understanding the fundamental order of matter.
As the historian of science Thomas Kuhn said, science advances through these revolutions when anomalies, like the exceptions in the periodic table, are revealed. They accumulate, opening a door for a new paradigm that can better explain them. So it could be that the answer to one of chemistry's greatest puzzles lies not in greater complexity, but in the astonishing simplicity of a cone and a single formula.
www.kutiry.com
www.youtube.com/watch?v=0RD-zFCQ17k
https://www.facebook.com/kutiry1
ERIC SCERRI
THE KUTIRY CODE
(Audio translation of the video into English)
Let's think for a moment about the Periodic Table of the Elements. Surely everyone recognizes it; it's a true icon of science. It's always been presented to us as something perfect, immutable, almost sacred. But what if it weren't? What if it had been hiding a secret for, say, 150 years? One that reveals a mathematical symmetry so profound it could force us to completely redesign everything. Well, today we're going to explore this radical idea: the binodic periodic system.
Mendeleev's table, it must be said, is an absolute stroke of genius, but like any great creation, it deserves to be examined critically. Because what if that familiar structure, the one we've used for over a century, isn't the whole story? What if, deep down, it hides a small, but crucial, inconsistency?
Well, to understand this new proposal, we first have to travel back in time a bit. The idea of reorganizing the elements didn't emerge from nowhere. It's actually the latest chapter in humanity's long quest to find the perfect order of the universe. A journey that, in fact, began long before Mendeleev. Consider this: before the rectangular table we know, there were other fascinating visions, from a helix in 1862 to stepped designs in the 1920s and 50s that already hinted at an underlying mathematical order. Each of these was a step, a step closer.
The proposal we're going to see today builds upon all these attempts. But what it seeks is to take the definitive leap, a system based purely and exclusively on mathematical logic. Okay, but why bother fixing something that apparently works well? And this is where we get to the heart of the matter, to the hidden flaws of the current system. The motivation for such a radical change stems from a conflict, a very subtle but incredibly profound one. Let's think of it as a gap between the shape of the periodic table and the quantum laws that, in theory, should explain it perfectly. This is the key to everything. You see, there's a quantum rule, the Madelung rule, which is like the instruction manual that tells electrons how to arrange themselves in an atom. However, the current periodic table, well, it doesn't always follow that manual to the letter; it has exceptions, irregularities, that scientists simply have to memorize.
And here comes the fundamental premise: a law of nature, a true law, shouldn't need exceptions. So, how do we solve this inconsistency? Well, the answer this system proposes is surprisingly elegant and is based on a central idea: the binode and the principle of duality. This is the mathematical heart of the whole thing, the missing piece of the puzzle that, according to this theory, was needed for everything to fit together. Okay, so what exactly is a binode? Well, it's not simply a period in the table like the ones we already know. No, it's a pair of periods that are always symmetrical, always the same size. The key idea here is duality, doubling. In this system, everything comes in pairs, as if reflecting a fundamental symmetry of the quantum world. And the most mind-blowing thing is that this entire architecture, all this asymmetry, is derived from a single equation, a simple and astonishingly powerful equation. And it equals 4B squared.
According to this proposal. This is the law. This is the genetic code that governs the structure of all matter as we know it. Let's break it down; it's very simple. It's simply the total number of elements in each pair of periods. And B is just the number of that pair—the first, the second, the third. And so, what's truly incredible is that this formula predicts perfect quadratic growth, a totally predictable pattern that traces a parabola. And now comes the more visual part. We're going to use this formula to build the system from scratch, step by step. And we're going to see how, starting from a single point, an entire cosmic architecture emerges, a cone-shaped structure with a truly astonishing regularity. It all begins with the first binode.
We apply the formula, and it tells us that there must be four elements in total. These four form the first quantum block, the S block, which we see here in red as a pair of periods with two elements each. The beginning is simple, clean, and perfectly symmetrical. Okay, now we move on to the second binode. The formula predicts 16 elements, and this is precisely where the logic of the system is revealed. It's not just that a new quantum block appears, the P block in orange, but—and this is crucial—the previous block, the s block, is duplicated. That is, the system not only grows, but it grows by doubling; for the third binode, the formula gives us 36 elements, and the pattern repeats flawlessly. A new block emerges, the one in yellow, while the previous blocks P and S are duplicated again. The structure expands with absolute mathematical predictability. And we arrive at the fourth and final known binode, which, with 64 elements, completes the structure we see. The final block appears in F in green, and as we might have expected, all the previous blocks are duplicated once more.
The result is this perfectly ordered and symmetrical conical architecture. The most important thing about all this is the perfect symmetry achieved. We see how quantitative changes, which are simply adding elements according to the formula, generate qualitative leaps, that is, the appearance of new blocks with different properties. And what is most important, what solves the problem we started with, is that there is not a single exception here. Zero.
But here the idea becomes even more ambitious. What if this pattern isn't just for chemistry? The proposal suggests that this formula is not a simple coincidence, but a possible fundamental code of the universe. A pattern that repeats itself at all scales in nature. And, who knows, perhaps even in history. The connections are nothing short of astonishing. The shape is reminiscent of the quipus of ancient Peru. The spiral growth is the same we see in galaxies or on a snail's shell. The way the pattern repeats itself at different scales is, by definition, a fractal.
Perhaps this underlying order was what Mendeleev intuited. What allowed him to predict new elements; unknowingly, he was glimpsing a much deeper mathematics. And with all this, we arrive at the final, crucial question: Are we facing a mere mathematical curiosity or a potential scientific revolution? Because this isn't just about proposing a new, prettier table. It's about directly challenging a paradigm with 150 years of history and proposing a radically new way of understanding the fundamental order of matter.
As the historian of science Thomas Kuhn said, science advances through these revolutions when anomalies, like the exceptions in the periodic table, are revealed. They accumulate, opening a door for a new paradigm that can better explain them. So it could be that the answer to one of chemistry's greatest puzzles lies not in greater complexity, but in the astonishing simplicity of a cone and a single formula.
Julio Gutiérrez Samanez
Hi Eric.
Reviewing your last message, I've tried to answer your questions, as you can read below in italics.
On December 21st, you wrote:
Hi Julio,
How are you?
I tried to post a reply to your recent post. Did it go through?
I ask because I didn't see it and couldn't even find it in my "Sent" folder. So this is a second, shorter attempt.
I was saying that I really liked your video and your way of presenting the periodic table abstractly, ignoring anomalies and specific details about the elements interpreted as "simple substances."
(I think the periodic table is essentially a continuous relationship of protons, like a mathematical series. I believe there are no anomalies in the Z series of atomic numbers because, by definition, they are whole numbers. Furthermore, by definition, we know that the number Z of protons must be exactly equal to the number of electrons; that is, in any given atom, the number of protons must equal the number of electrons. So, regarding the number of these particles (electrons), there are no anomalies. The anomalies arise in the "position" occupied by some electrons, which doesn't correspond to the place predicted by the theory. This occurs in about twenty atoms. I don't know if the number of electrons in atoms conceived as "simple substances" is different from that of atoms conceived as "basic substances." If, as you say, DIM focused on the "abstract" sense of element, this sense can only be the element defined by its atomic weight and then by its atomic number, a property that admits no anomalies).
As Mendeleev emphasized that the periodic table focuses primarily on the abstract sense of "element."
On this point, I recently co-authored an article on structural realism in the context of the periodic table, which is currently under review at a philosophy of science journal.
Here is a preprint.
Finally, have you built a 3D model of your conic representation of the elements, as seen in the video?
(I haven't yet made a physical 3D model, as I'm not sure it should be a conic representation (where the spirals aren't truly continuous), but rather a spiral representation on a paraboloid. I hope AI will come to my aid.)
What would a conic representation look like if the arrangement weren't based on binods, but on the usual single-period representation?
(It would look something like a centipede with a broken leg. In fact, the function becomes more complex. Such a representation can be constructed, but the fundamental rule that "The statement "binode changes when another azimuthal function appears" would no longer hold true; it would be a flawed symmetry from the start. Nature clearly shows us that periods with principal quantum number n = 1, 2, 3, 4, 5… are doubled, also doubling their corresponding secondary quantum numbers (2n², 2n²). That is: (2, 2; 8, 8; 18, 18…). The form would be: (2), (2 + 6), (2 + 6), (2 + 10 + 6), (2 + 10 + 6), (2 + 14 + 10 + 6), (2 + 14 + 10 + 6), … Or: (2, 8, 8, 18, 18, 32, 32…) which is the standard periodic table, including the lanthanides and actinides. As can be seen: the first period and the following “binodes” begin, by necessity, with azimuthal (s) values, then the azimuthal (p) values appear after (s); then the azimuthal (d) values are inserted between (s) and (p), and the same occurs with the azimuthal (f) values).
Furthermore, you draw an analogy with Kuhn's perspective on anomalies and scientific revolutions.
How does your binodic approach resolve these anomalies?
(Discovering anomalies in a standard theoretical system leads us to doubt the prevailing paradigm, and instead of simply propping up and patching up the cracks like in an old building, we can find new relationships and answers that determine the replacement of the old paradigm with a new one. I think that's what Kuhn calls a scientific revolution.
Returning to the duplication of the principal and secondary quantum numbers, it violates the Pauli exclusion principle because sets of electrons with all four quantum numbers are shown to be identical. It becomes necessary to create a fifth quantum number, which, like the spin of the electron particles, Differentiate the periods of each binode by its electromagnetism or by the shape of its movement, so that one layer covers the other without mixing with it. The proposed solution could be: (+/- Tau). As shown in the attached figure called "Genome of Matter," published by Mark (although I now have an improved digital version). This work reaffirms "binodic symmetry."
https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1221
Whether in the conical or paraboloid form, in the following figure:
https://acrobat.adobe.com/id/urn:aaid:sc:VA6C2:fe58cf03-2442-4785-aa8a-c3c19f5b94ee
which shows the increasing periodicity of “some of the chemical and physical properties” (to include the findings of G. Restrepo, in an article I have lost), it is possible to find two spirals that define the boundary between theory and empirical or material reality. For this, I refer to Baca Mendoza's second book: “Law of Electronic Configurations” (1965).
In the table that this professor proposed, he drew an oblique line to mark the “initial pairs of the new transitions”; That is, the pairs: (4Be, 12Mg), (21Sc, 39Y), (58Ce, 90Th), (123, 173), (224, 295):
In that series, Baca Mendoza quite rightly makes an exception for the first pair, which he marked with a dotted line, since the (s) orbital obviously does not appear with (Be, Mg). In the other pairs, the line is solid. And, indeed, the 3d1 and 4d1 orbitals do appear with the pair (21Sc, 39Y). The 4f1 and 5f1 orbitals appear in the pair (58Ce, 90Th), and not, as we know, in the pair (57La, 89Ac). Similarly, Baca Mendoza predicts or anticipates that the hypothetical 5g1 and 6g1 orbitals will appear in the hypothetical pair (123, 173). Finally, he predicts that the hypothetical 6h1 and 7h1 orbitals will appear in the hypothetical pair (224, 296). If we apply this discussion to the concept of the "increasing periodicity of chemical properties," we find a spiral originating at the pair (21Sc, 39Y). This spiral has a development or shift slightly different from the theoretical one, marking these anomalies. However, it is now seen as a concatenated function, a distortion tension, and not merely as structural variations, anomalies, or peripheral, fortuitous, random exceptions.
In the "chemical space" described by these spirals, it can be clearly observed that, as a result of multiple effects (motion, gravitational and electromagnetic forces, the internal topology of the atomic structure, screening effects, spin-orbital coupling, relativistic and non-relativistic effects, etc.), we can determine the spiral that constitutes the real or empirical cosmological limit of the behavior of matter, altering or modifying the theoretical structure. And, since it also exhibits a functional mathematical form, it must contain a mathematical constant that is still unknown).
Regards.
Julio
Finally, I have one question regarding your mention of Kuhn and how anomalies lead to eventual scientific revolutions.How does thinking in terms of binods help to resolve any of the anomalies concerning electronic configurations?Regards,EricERIC SCERRI PhDUCLAWebsite: http://www.ericscerri.com
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Editor-in-Chief of Foundations of Chemistry https://link.springer.com/journal/10698