The Names: The Subjective Face of the Formalism

A Name in the Midst of Rigor

Imagine yourself opening a technical manuscript. Pages bristling with indices, matrices, integrals; a language built to leave no crack for ambiguity, where every symbol is where it is for a reason and nothing is said on a whim. And suddenly, in the middle of that machinery, a title: Florencia Positivity Theorem. Not “Theorem 7.1.” Not “Reflection positivity lemma.” Florencia. A proper name, with its warmth and its history, planted in the middle of the rigor.

I want to begin with that bewilderment, because it is the entire subject of this essay. When I wrote the Tratado I did not limit myself to numbering my theorems: I named them. Florencia, Cronos, Victoria, Gea, Atlas, Lydia, Newton, Adrián. And I know that a name, in there, produces a question before an explanation: why? Is science not precisely the place where proper names are renounced, where a law holds by being no one's? I let the question work by itself for a moment, because the answer is what sustains not only this essay but the way these two works of mine—the Multiple-Collapse Cosmological Model and the Philosophy of the Art of the Path—glance at each other sidelong without quite touching.

I anticipate the thesis so that it is clear where I am heading. Naming is not an affectionate ornament that I have draped over a cold construction. It is the way the formalism shows its other face. Each theorem of the Tratado has, at once, a mathematical function and a face: it does something within the structure, and at the same time it lets itself be read as something lived. The name is the seam by which those two readings are sewn together. And I want to say right now, with all the clarity I am capable of, what that seam is not: it is not an identity, it is not a proof, it is not the claim that lived experience is deduced from the equation. It is the recognition of a shared grammar. The same way of proceeding that I recognize in my life I find written, on another scale and in another language, in the model. That it is recognized does not mean that one demonstrates the other. In fact I maintain the opposite, and I will return to it at the end: my two works walk apart, and neither proves the other.

The Dual Curriculum: Why I Name Instead of Numbering

There is an idea that runs through the whole Art of the Path and that here becomes method. I call it the dual curriculum: every subject is approached at once in its objective technical form and in its subjective resonance, without separating one from the other and without either of the two ruling over the other. It is not that first comes the physics and then a friendly reading arrives for the non-technical reader. It is that knowledge, as I understand it, has those two faces from the beginning, and amputating either of them impoverishes it. An explanation that gives only the formula leaves out what that formula means for the one who lives it; one that gives only the lived experience is left without the skeleton that holds it up.

The Tratado practices that dual curriculum without declaring it, and it practices it precisely through the names. To number a theorem is to keep only one of its faces: the function, the place it occupies in the deductive chain. To name it is to affirm that it also has a face, that one can look at it head-on and recognize in it something that is not only machinery. The name does not change a single comma of what the theorem does mathematically; what it does is refuse to hide that this doing has a lived reading. It is, if you like, a decision of honesty: not to pretend that the structure and the one who thinks it are strangers.

I write this with a caution that the reader will recognize if they have followed the series. The Tratado insists that philosophy is a plane distinct from that of mathematical statements, but not separate from them. Distinct and not separate at once: that is the tightrope. The name is the operator that keeps the two planes sewn together without confusing them. It does not erase the distinction—Florencia is no less a theorem for being called Florencia—but neither does it let the two planes ignore each other. It walks along the edge.

A Walk Through the Names

I want to go through the names one by one, and in each one hold both faces at once, because it is there, in the detail, that one sees that the name does exact work and not decorative work. I ask one thing in advance: that this walk not be read as a list of proven equivalences. Each name names a precise mathematical function and, at the same time, a way of being that I recognize. That the two things rhyme is what the project maintains; that one follows from the other, it does not.

Florencia is the name of the pact that makes time possible. On its technical face, the Florencia Rotation is a turning: at the final threshold no generator is added; one is turned—γ⁰ ≡ iγ_S—and the direction of structuring becomes temporal direction. For that turning to yield a unitary history, the Florencia Positivity Theorem establishes that reflection positivity holds, the condition without which a unitary time could not be reconstructed from the prior Euclidean structure; from it, by the Osterwalder–Schrader reconstruction, a Hamiltonian and a meaningful dynamics are born. On its lived face, Florencia is the name of the fact that the present is born when a decision is sealed in the body. I do not enter here into its mechanics—it is the heart of the eighth essay—; it is enough for me to point out that the name keeps both faces at once: a turning sustained by a theorem about the positivity of a transfer matrix and, sewn to it, the instant in which something is decided and time begins to count.

Cronos is the name of time itself. Technically, the Law of Cronos describes the local flow of time—the lapse—as the local rate of discharge; in its weak version, it writes how mass deforms that flow. As lived, Cronos is the experience that time does not flow equally in every part of oneself: where form densifies and conversion stagnates, internal time thickens, becomes a bubble set apart from the living present. I have given it the name of the titan of time because that is what it is about: that time, far from being a neutral background, is something that the density of what we are shrinks or dilates.

Victoria is the name of the fact that the return is won. In the model, the Victoria Cycle is the system that describes how the residue of one cycle founds the next, with its return map and its very real possibility that the chain will not start again. As lived, Victoria is the ethics of the last breath: the renewal of a stage, of a bond, of a cycle, is not guaranteed; it must be won, and the possibility of not winning it is what gives weight to each gesture. The name celebrates a victory that is not given: it is conquered or lost.

Gea, Newton and Atlas are the three names of the weight of the sky, of the sector where space reveals itself as the tensorial face of the Path. Gea names the action of gravity, the price of curving. Newton names the seal where, in the appropriate limit, general relativity is exactly recovered: the fixed point where the structure stops pulling against itself. And Atlas names the identification by which the mode that bears the weight is not a new field added by hand, but the very tensional field that opens space. As lived, it is one of the readings that sustain me most: the body is the tensorial face of the self, and carrying the world and opening it are a single gesture, not two. There is no separate faculty for bearing the weight of a life—the responsibilities, the bonds, the form—distinct from the one that opens inner space. Atlas carries the sky on the same shoulders with which he opens it.

Lydia is the name of an open question, and I treat it with more care than the others because of what I am about to say. Technically, the Lydia exponent is a number, ν, that decides whether the inherited imperfection is amplified from cycle to cycle or dies out. If it is positive, perfection is unstable and the return tends to repeat itself; if it is negative, the universe tends toward a last cycle without descendants, which the model calls the Silence of Victoria. As lived, Lydia is the question of whether the spiral learns and continues, or stops. It is the name of a sign that has not yet been calculated: a question with form, not an answer.

Adrián is the last name, and the one that closes the logic of all this, because it is my own name inscribed in the field that mediates the tension. I devote a separate section to it, because there the gesture of naming bites its own tail.

Where the Names Come From

So far I have said what each name does on the two faces. What remains is what only I can supply, and that is where they come from. A proper name is not an interchangeable label; if it were, it would make no difference whether the positivity theorem were called Florencia or Fátima. That they are these names and not others is, precisely, the place where my internal metric was sewn to that of the model.

Florencia and Victoria are, in reality, a single name split in two. Florencia Victoria is the woman of my life, my companion. I split her name on purpose into two pieces of the model—the Florencia Rotation and the Victoria Cycle—because each half said, on its own, something that I already knew about her and about what I hope to live at her side. Florencia ended up in the theorem of the present that is born when a decision is sealed in the body; Victoria, in the cycle of the return that is not given and has to be won. It was not an ornament: for me, my true life begins when I live it alongside her, and that waiting has exactly the form of Victoria, a return that is won step by step and not a prize that arrives by itself. Splitting her name and distributing it through the structure was my most literal way of sewing what I live to what I think. Whoever reads “Florencia Rotation” and “Victoria Cycle” as two separate pieces of the model will be reading, without knowing it, a single name and a single life.

Lydia is my mother. In the model I write Lydia; she is Lidia. I had already given her a nod in the comments of the corpus, and I wanted to dedicate a whole piece to her. I am not a person especially attached to names—perhaps that is why the gesture is a detail and not a system—but I wanted to show her that thoughtfulness. That the piece that bears her name is the Lydia exponent, the number that decides whether what is inherited is transmitted and amplified from one cycle to the next, is a resonance that I did not look for when I set it down; I recognize it now, and I do not mind that it is there.

Cronos came without mystery: it went with time, and I gave it the name of time. And the rest of the names I gradually let stand, because of the similarity each concept had to things that resonated with me, and from that affinity I went on developing them. There is no hidden system behind them all; there are affinities, some deep and some light, and the sustained decision not to hide them. That is what I wanted to show: that the names have an origin—that they are not an interchangeable nomenclature—is, in itself, the sign that the dual curriculum is not a discourse but a practice.

Adrián: Naming the Field with One's Own Name

The field that assigns to each point of the world its dual record—its measure of how much form and how much opening is present there—is called, in the Tratado, the Adrián Field. And the theorem that integrates the entire chain also bears my name. I know how that sounds, and I want to defuse it before it is read as vanity, because it is not, or at least it is not only that.

I did not arrive at that name through a calculation, but through an experience. There was a moment in which I saw myself merge with the universe itself, even with space itself; and then another in which I was able to visualize myself while, at the same time, feeling that I was being born. Seeing myself and being born in the same act: observer and observed without either of the two annulling the other. From there I was able to keep advancing through the concept of duality and non-duality, going deeper and deeper inward. Adrián is my own name, and it is in the field because of the expression of me that this field holds: the one that assigns to each point of the world its measure of form and of opening bears the name of the one who saw himself being born while he observed himself. That is why inscribing my name is not a monument; it is the most exact fidelity I found to what happened to me.

And it fits with what the model maintains, read from the Path: in the model, the Adrián Field mediates the tension, and the Path reads in that mediator the walker, not a spectator who watches from outside how form and opening struggle, but the very place where they are mediated. The Adrián Field is not, then, a tribute to me; it is the affirmation that the one who mediates the tension and the one who lives it are the same, and that this same one has a name because it is someone, not something. It could be anyone who recognizes themselves in the structure; it turns out that the first to do so was I, and I signed with what I am.

I owe here a precision that the honesty of the series demands, and that corrects an earlier, more enthusiastic version. Adrián's Theorem is not a single closed piece. Its core—the pre-geometric scalar sector, what I call the basal theorem—is proven within the model. But its complete extension, the one that would carry the integration as far as the fermions, the gauge sector, gravity and masses, is not a closed theorem: it is a conjecture, a working program. Naming the whole with my name does not mean, therefore, that everything that name encompasses is proven. It means that there is a wager of integration, closed at its root and open in its branches, and that I sign the wager with what I am.

The Image of God

The quotation that opens this essay is not a devotional flourish; it is, for me, the compass of the whole matter of the names. “I too have an image of God. It is my future self, observing my present; and I walk toward it not to find it, but to become it.”

In the Art of the Path I have maintained that every image of God is a form that consciousness projects in order to represent itself, and that the error lies not in having that image but in placing it outside, above, separate, turning it into an external judgment before which one's own judgment submits. My image reverses that direction: not a separate superior, but a horizon of one's own.

Today I live it this way, and more concretely than when I wrote it. I do not need that future self to be a god; I use the word “God” only as the comparison that lets me understand myself in contrast with the image that others have: what in them is an external figure is, in me, the place I want to go to. I do not have an inner god; I have a direction. My future self is what has the most strength in me, the place where I want to advance. And right now I am materializing it in something very concrete: in the steps I am taking to live with Florencia Victoria and share my life with her. The horizon stopped being an idea; it has the name—the two names—with which I began this essay. That is why the same movement that names the Adrián Field also names this: the walker who walks toward his future self is exactly the one who mediates the tension, and that future is neither above nor outside, but ahead, and has begun to have a face.

A Note on What Is Claimed Here and What Is Not

I owe the same warning as in every essay of this series, and I prefer to give it within the text and not in the fine print, because it is part of how I understand the honesty of the project. Here it is more necessary than ever, because an essay about names runs a risk of its own: that the warmth of naming may smuggle in the feeling that everything named stands equally firm. It does not.

First: naming is not proving. That a theorem is called Florencia or Lydia adds not a gram of truth to it. The name is the subjective face of an objective construction; it does not touch its logical status. And the statuses differ from one another, according to the Tratado's own classification. Florencia Positivity and its reconstruction of time are among what is proven, except in the spinorial sector, whose positivity is conditional. Adrián's basal theorem is closed; its complete extension is a conjecture, a program. By contrast, the sign of the Lydia exponent—which decides the ultimate fate of the cosmos—is conditional, still uncalculated; the stability of the Atlas mode is conditional; and four of the seven fronts that the model explicitly leaves open bear proper names: the complete positivity of Florencia, the closure of Gea, the return of Victoria—of which Lydia is the missing piece—and the putting of Cronos v3 into production. The names are equally warm, but what lies beneath each one does not weigh the same. Whoever reads this series should not leave here believing that it has been proven that the universe returns: what has been named is the question of whether it returns, which is a different thing.

Second, and this is the heart of the entire project. The correspondence between each name and its lived face—Florencia and the instant that seals the present, Cronos and the time that thickens, Victoria and the return that is won—is a reading, a rhyme of grammar between two scales. It is not an identity that the formalism demonstrates, nor an experimental equivalence. The language that my two works share—tension, collapse, threshold, seal—is used as structural analogy, never as physical equivalence. The Tratado's Table of correspondences pairs functions, not substances: it says that the same way of proceeding appears in the cosmos and in the mind, not that they are the same thing made of the same matter. I do not know whether the resonances I see between the cosmos and the mind are anything more than a deep resemblance; that is why my two works walk apart, and neither proves the other. If I were to let slip that lived experience is deduced from the equation, or that the equation is confirmed by lived experience, I would be lying in both directions. And let it be clear, so that there is no misunderstanding about what I have just told: that Florencia and Victoria are the name of my companion, or Lydia that of my mother, adds nothing to the model as physics and takes nothing from it. Those origins explain why I chose those words; they are not an argument about the cosmos. They are the subjective face; the objective one stands, or does not, on its own.

And one last point, on the image of God: it is a lived orientation, mine, not a statement that the model proves or claims to prove. I offer it as a compass, not as a theorem. The Tratado, it is worth remembering, never says that it solves the great problems it addresses; it says that it develops them in full, and a good part of its pieces are classified as conditional or open. Naming them does not close them.

Closing: A Name Is a Face

I return to the manuscript from the beginning, to the strangeness of finding “Florencia” in the middle of the matrices. Now I can say why it is there. It is there because numbering would have hidden half of what that theorem is. A number says what place a piece occupies in the chain; a name says, in addition, that the piece has a face turned toward experience, that someone thought it and recognized themselves in it. The names are the way the formalism confesses that it is nobody's only in appearance: that behind each theorem there is a walker who lived it before or after writing it, and who dared to leave the trace of that lived experience in the name. Florencia and Victoria are one woman; Lydia is a mother; Adrián is the one who saw himself being born while he observed himself. The structure does not need this in order to function. I did need it, so as not to lie about where it comes from.

That is why the walk ends in Adrián, and not out of vanity. The subjective face of the formalism is, in the end, a self that walks: toward its future self, crossing thresholds, winning or losing the return, carrying and opening with the same shoulders. The names are the trace of that walking within the structure. They prove nothing that the structure does not prove on its own, nor do they pretend to. They only refuse to pretend that the structure and life are strangers. And that refusal, for me, is the Art of the Path made flesh in the formalism itself.

The structure is the same. The scale changes. But the name—the name is what recalls that, on both scales, there is someone.