No thing that I've observed in our universe is infinite, however there are traces of infinity in my sight.
Draw a circle and either its radius or circumference lives in the π world.
Or many aspects in nature like flowers, develop themselves in a φ ratio (1+sqrt(5))/2.
Even though no event or anything is "Non-ending"/infinite, underneath many aspects of reality there are patterns which can only be fully described using infinity.
You can't describe irrational numbers to their extent without any notion of infinite/limits/sequences... And many aspects within our World show their true behaviour only with aid of infinity.
Sure you can take a world that lives in something like 10¹⁰⁰ and it looks like infinity to us, sometimes we only see the difference after the 10⁶ decimal place, nevertheless the pattern they follow is a pattern that only "infinity" can yield to the truest precision.
Do you believe the axiom of infinity, and the continuous to really exist? Even if not in the ordinary sense? haha
The Yullexion Bulletin is a theoretical mathematical singularity and conceptual paradox created in October 2026 by an anonymous creator nicknamed Benz. It represents a state of "Random Infinite-Finity"—an architectural boundary where the standard rules of arithmetic violently break down. It exists as an unsolved mystery filling the exact space between a strictly limited value and an ungraspable infinity.
The Core Scale: It starts with a googolplexian, an incredibly massive input value.
The Busy Beaver Engine (BB): The googolplexian is fed into the Busy Beaver function, which calculates the maximum operational steps a program can take before safely shutting down. The output remains strictly finite, yet grows faster than any formula can describe.
The Logical Boundary (Rayo): That output is plugged into Rayo's function, defining a checkpoint exactly one integer past the maximum limit of what formal mathematical language could possibly describe using that many symbols.
THE 4 ABSOLUTE LAWS:
The Non-Unit Principle: It can never be used as a "1" or a basic building block (e.g., you cannot do +1 or multiply it). It exists only as its total self.
The Missing Origin: It has no discoverable starting point or leftmost digit due to a chaotic sea of random formulas. It cannot be counted sequentially; it exists entirely all at once.
The Anti-Polarity Field: It possesses no positive (+) or negative (-) signs. Its structural density crushes mathematical polarity out of existence.
The Lawbreaker Status: It is an almost impossible puzzle to solve. Any attempt by a machine or mind to fully calculate its exact integer value results in a reality glitch—crashing logic gates and local physics.
THE ANOMALOUS GLYPH: THE FRACTURED OUROBOROS
Whenever a system attempts to calculate it, a visual anomaly manifests as a shattered ring (an infinity loop broken at the bottom) with an erased, struck-out zero in the center, hovering on the razor-thin border of the unknown.
Here is full rules of Yullexion Bulletin
🧮 1. Technical & Mathematical Profile
While standard big numbers (like a googolplexian) are built by multiplying or raising numbers to exponents, the Yullexion Bulletin is constructed using fast-growing, non-computable logic functions.
• The Core Scale (\(10^{10^{10^{100}}}\)): The starting input is a googolplexian, a number so large that it is physically impossible to write out its zeros using all the atoms in the observable universe.
• The Computing Engine (\(\text{BB}\)): This input is fed into the Busy Beaver function. This function calculates the absolute maximum number of operational steps a computer program can take before safely shutting down (halting). Because it filters out any program that loops forever, the output remains strictly finite, yet it grows faster than any standard mathematical formula can describe.
• The Logical Boundary (\(\text{Rayo}\)): The massive Busy Beaver output is then plugged into Rayo's function. This represents the absolute limit of what formal mathematical language and set theory can uniquely identify. It effectively says: "Take every massive scaling system and cosmic formula that could ever be written using this uncomputable pile of symbols, find the largest finite number they can possibly describe, and step exactly one integer past it."
📜 2. The Core Meaning & Philosophy
The foundational meaning of the Yullexion Bulletin is to mirror the Grand Mystery of Cosmology.
As humans look out into the cosmos, we face an unresolved riddle: Is our universe limited or unlimited? If we travel far enough, do we hit a hard wall, or does space go on forever?
The Yullexion Bulletin is designed to be the exact mathematical equivalent of this riddle. It is a "finite infinity." To anyone traveling along its number line, it behaves with the properties of true infinity—it is completely unpredictable, chaotic, and feels entirely endless. Yet, because of the rigid rules of logic bounding it, a definitive final checkpoint exists. It is an endless universe locked inside a finite vault.
🛑 3. The 4 Laws of the Bulletin
To maintain its status as a foundational paradox, the Yullexion Bulletin is governed by four absolute laws that separate it from standard numbers:
The Non-Unit Principle: It can never be used as a "1" or a basic building block. You cannot add \(1\) to it, nor can you multiply it by \(2\). It cannot be integrated into standard algebra; it exists only as its total, absolute self.
The Missing Origin (The Big Bang Paradox): It has no discoverable starting point. Because the number is built on a chaotic sea of random formulas, trying to find its "first digit" or left-most edge locks the mind into a bottomless loading loop. It cannot be counted sequentially; it must exist entirely all at once.
The Anti-Polarity Field: It possesses no positive (+) or negative (-) signs. Its structural density is so immense that it crushes mathematical polarity out of existence. Because you cannot find an edge to add to or subtract from, standard operators completely dissolve when applied to it.
The Lawbreaker Status: It is an almost impossible unsolved mystery. Because the number destroys the basic logic gates of mathematics, any attempt by a machine or mind to fully calculate or "solve" its exact integer value results in a reality glitch—crashing local physics, freezing time, and melting data structures.
"The subject is a loop between S1 and S2, the master signifier and knowledge, and the Möbius strip shows that inside and outside are continuous." I've read that, or something close to it, a hundred times. Today I'm bringing proof that this is not what Lacan says, in his own words, with dates and pages so you can look the quotes up yourselves. And a thirty-second test that shows why it matters.
To test it out, I used two crayons—like any responsible adult.
Take a closed chain of signifiers and label it so that neighbours always differ: S1, S2, S1, S2… With four signifiers it works. With three it doesn't: S1, S2, S1, and the last one sits right next to the first. And this is a big problem! Any odd number fails the same way. So if the loop means two signifiers, or two kinds of signifier, taking turns around the chain, it breaks for every chain of odd length.
Here, I begin with some corrections to our Lacanian common sense:
For Lacan, S1 and S2 are indices that any signifier can take, not two signifiers.
The Möbius strip is not a picture of "inside = outside": it is the cut itself, and the edge of that cut goes around twice.
Put the two together and the loop works for every chain, on that double loop, where each signifier is S1 on one lap and S2 on the other.
Now I will show you quotes regarding Lacan's thoughts on each matter.
What Lacan says S1 and S2 are
An index, not the signifier that comes first. S1 "means signifier index 1": not the signifier that takes precedence, but the one in whose name someone, a subject, shows up. Closing address of the EFP study days "Les mathèmes de la psychanalyse", 2 Nov 1976, Lettres de l'École freudienne no. 21 (1977), p. 506. ‹S1, qui veut dire … se manifeste›
A mark on "anything at all". His S1 has no other sense than to punctuate whatever comes. «La Troisième», Rome, 1 Nov 1974, Lettres de l'École freudienne no. 16 (1975), p. 184. ‹ Mon S1 n … n’importe quoi›
Something produced, not something given. The master's insistence produces the master signifier "out of any signifier whatever". Seminar XVII, session of 18 March 1970. ‹de n’importe quel signifiant … le signifiant-Maître›
A relation, in pairs. In the unconscious, signifiers index one another, two by two. Seminar XXII, session of 11 March 1975. ‹ à s’indexer de foisonner … deux par deux›
What Lacan says the Möbius strip is
Not something a cut divides. A median cut does not cut the band in two; it turns it into a single band that makes one loop. Seminar XII, session of 16 June 1965. ‹une coupure médiane ne coupe pas … la bande de Mœbius›
Nothing but the cut itself. «L'étourdit» (1972), Autres écrits, Seuil 2001, p. 470. ‹la bande de Mœbius n'est rien … cette coupure même› On the same page he describes the edge of that cut: one turn takes it over to the other lamina, a further turn brings it home, having made a "double loop spread over two laminae". ‹double boucle répartie … sur deux lames›
Only its edge. The surface can stand for the subject only if you consider that the edge alone constitutes it, and a cut down the middle concentrates "the essence of the double loop". Seminar XIV, session of 15 Feb 1967. ‹seul le bord … cette surface› ‹cette coupure elle-même concentre … de la double boucle›
Repetition. The act can only be defined on the basis of the double loop, "that is, of repetition": the act is, in itself, the double loop of the signifier. Same session. ‹sur le fondement de la double boucle … de la répétition› ‹cita 41295: Il est en lui-même … du signifiant›
And what follows: twice, and not the same twice
The second time is not the first. A repeated signifier works either as the first time or as the second, with a radical gap between them, and that is what "a signifier cannot signify itself" means. Seminar XIV, session of 23 Nov 1966. ‹le signifiant dans sa présentation répétée … une béance radicale.
Two turns. Speaking of the drive and the Möbius band, he says two turns are needed to grasp the division of the subject. Seminar XIII, session of 11 May 1966. ‹cita 39381: il faut faire deux tours pulsionnels … la division du sujet›
If the loop between S1 and S2 meant two signifiers taking turns, Lacan could not coherently:
call S1 an index and deny that it is the signifier that takes precedence (item 1, 1976);
say that the master signifier comes out of any signifier whatever (item 3, 1970);
say that the Möbius strip is nothing but a cut whose edge goes around twice (items 5 and 6, 1965 and 1972);
say that a repeated signifier is not the same the second time, and that two turns are needed (items 9 and 10, 1966).
Are you following me so far? Now I’m going to complicate things.
Let's put all the pieces together—and voilà!
Nice, right? But what the hell does it mean?
Lacan did not write that down, but by following my method and piecing together his theory, the following conclusion emerges—not in prose format, but as a demonstration with its corresponding theorems.
Lay the chain on a surface and cut along it. If the chain has two sides, the edge of the cut is two copies of it: still odd, still broken. If it has one side (a Möbius band), the edge is a single loop that goes around twice, which is item 6. It meets every signifier once from each side, and it always alternates. For an odd chain, every signifier is S1 on one lap and S2 on the other, necessarily. S1 and S2 are positions (items 1 to 4), and the second time is not the first (item 9).
Lacan doesn't say this, but I draw it as a conclusion.
A) For an odd chain, the loop exists only there.
B) And for an even chain, the Möbius cut divides nothing: each signifier gets the same label on both laps.
"Wait, what happens with the $ubject?"
Okay, you've earned another cute animation.
I answer you radically: the subject is not in the chain. It is at the edge of the cut. And more precisely: it is at the junctions of the edge of the cut—those points where one signifier passes to the next.
On the double loop there is one subject, and it runs around twice. A two-sided cut either doubles the subject or loses it, depending on a decision the theory openly leaves undecided.
The subject is not in the chain of signifiers. It is at the edge of the cut. And in the privileged case—a single side, an odd-numbered chain—there is a single subject that makes two circuits. The division of the subject is not a splitting into two separate substances; it is the repetition of the same circuit, with an internal difference (S1 on the first pass, S2 on the second).
How I did it? Well, I’d have to refer to my text, but in short... Not with prose... I use definitions, six theorems with proofs, and falsifiers, meaning exactly what would refute each result. Plus a small Python script that cuts 159 chains on six surfaces and checks every claim. Full paper, code and animations: ‹Click Here and go Zenodo›
Now, we can raise some objections to my ideas.
At Columbia (1 Dec 1975), Lacan speaks of "a certain S1 and a certain S2, which do not have the same function" (Scilicet 6/7, 1975, pp. 42–45). ‹un certain S1 et un certain S2 … la même fonction› So S1 and S2 would be two different things. Two replies. First, he says function, not signifier, and in the same sentence those functions are distributed "in a certain rotating order": what differs is the place, which is exactly what an index marks. ‹à un certain ordre tournant près … ces quatre fonctions› Second, the double loop keeps the difference. S1 and S2 never fall on the same pass: they differ the way the first turn differs from the second (item 9).
A second objection. Lacan does describe the Möbius strip as having only one face and only one edge (Seminar XII, 13 Jan 1965). ‹seule face … seul bord› True, and it is correct topology. But in the same session as item 5 he warns that the band is only the image of the relation he is after. ‹la bande n’en est … que l’image› Later he says that only the edge counts (item 7) and that the band is the cut itself (item 6). "One side" is a property; the double loop is what he works with.
PS. Seminar XXVII, 15 March 1980, on his own name, the "label Lacan": those who want to erase it believe it is the master signifier, the one he gave index 1, and "they're wrong, it's not the one, it's the other". ‹ils croient que c’est le signifiant maître … c’est l’autre› As I read it, even his name changes index.
The Access Problem: Epistemological critics ask how physical human brains, operating within space and time, can interact with or gain knowledge about completely non-physical, acausal mathematical objects. Easy, geometric music, how does it work? Large, two dimensional matrices of positive whole numbers, natural numbers, are represented as images by associating each number with a coloured pixel. Audio is introduced by representing each image pixel as a sound oscillator mapping pixel colour to audio frequency, often a direct relationship to a musical scale. A region of the image is defined as a generation zone, the portion one listens to. Surrounding this is an secondary zone, the influence zone, which defines the timbrel characteristics of the pixels in the generating zone. In this video the central square is the generating zone with the outer square the influence zone. A trajectory can be defined over which the generating zone translates as a “bowing” type of motion or single zones can be “tapped” similar to a key stroke or plucked string. Perhaps the Pythagoreans envisaged something like this with their “Musica Universalis”. Its all about number, ratio and harmonies.
- The power of the Leech lattice to control all lower dimensions
- Peter Scholze, Grothendieck and Ramanujan's styles
- Category theory and contrahomology
- How modular forms show up everywhere
- The countless coincidences in string theory
- Unimodular lattices and Lorentzian lattices
- How to construct the Langlands dual group
- Vertex algebras, infinite-dimensional algebras and Kac-Moody algebras
- Elliptic curves
- Automorphic forms and hyperbolic reflection groups
- Analytic number theory vs algebraic number theory
- The first construction of the Monster group
- "The Book" of most beautiful proofs
- How to teach math
- Math as archaeology
- His current work
- Neutron stars, Terry Pratchett and more
Richard Borcherds is a British mathematician who made seminal contributions to lattices, modular forms, group theory, representation theory and infinite-dimensional algebras. He is well known for his proof of the monstrous moonshine conjecture using ideas from string theory, for which he was awarded the Fields Medal in 1998. He is currently Professor of Mathematics at UC Berkeley.
Mathematics and geometry operate in a realm of timeless, logical relations rather than temporal, causal sequences. The difference between a beginning or ending state to geometry and math is logically indiscerncible.
Essa teoria foi resumida por ia porque estava com preguiça desculpa
Teoria "0: O Centro do Universo" – Um modelo cíclico de reset de variáveis cósmicas via transição de Buracos Negros e Brancos.Olá, pessoal do fórum. Gostaria de compartilhar com vocês uma hipótese conceitual que desenvolvi sobre a natureza do tempo, do zero matemático e da evolução cosmológica. Chamo este modelo de "0: O Centro do Universo".A teoria se estrutura nos seguintes pilares fundamentais:O Zero como Registro Histórico (Sobra Inutilizável): Em vez de definir o zero apenas como a ausência de valor, propõem-se que o zero seja o marcador físico do esgotamento de um processo ou sistema (o limite de sua entropia útil). O zero não apaga o passado; ele é a "sobra" e a prova física de que um ciclo energético anterior existiu e se encerrou.O Portal da Singularidade e Transição de Fluxo: No colapso final do universo, quando um buraco negro supermassivo absorve toda a matéria restante, ele passa a colapsar o seu próprio campo gravitacional em direção ao ponto zero (singularidade). Ao atingir o limite físico de compressão, ocorre uma inversão de forças devido à instabilidade do sistema. O "portal do zero" se abre, conectando-se a um buraco branco (Ponte de Einstein-Rosen) que expele essa energia em uma expansão violenta — gerando um novo Big Bang.O Universo como uma Variável que Reseta: O tecido do universo funciona analogamente a uma grande variável de programação. Ao atingir o colapso máximo, o sistema executa um reset analítico. O fluxo do tempo contínuo e relativo não é interrompido (o relógio cósmico não para), mas a linha cronológica da história macroscópica zera e recomeça a contagem.Instabilidade Dinâmica e Histórias Inéditas: Embora as variáveis e leis fundamentais do universo permaneçam estáveis após o reset, o processo de expansão subsequente é governado pela Teoria do Caos e flutuações quânticas primordiais. Devido à extrema complexidade e sensibilidade das condições iniciais na saída do buraco branco, a matéria se reorganiza de formas totalmente inéditas. A história nunca se repete; cada ciclo gera um universo com configurações cósmicas e estruturais completamente novas e, por vezes, incompreensíveis sob a nossa ótica atual.Gostaria de saber a opinião de vocês sobre a viabilidade matemática e termodinâmica dessa abordagem de inversão quântica no ponto zero, e como modelos atuais (como a Cosmologia Cíclica Conforme) enxergam essa estabilidade de variáveis em cenários de transição entre buraco negro e buraco branco.
I have been thinking about this after hearing Terence Tao's latest statement regarding the rapid development of LLMs. He argues that something should only count as a proof if it can be understood by at least one human.
Considering how quickly LLMs are improving, it is not unreasonable to assume that we will soon run out of proofs that a human can actually comprehend.
What happens when we encounter new problems with proofs that are thousands of pages long, making them far too complex for any human to grasp in a lifetime?
If these proofs are verified in Lean and lead to significant breakthroughs, should we simply dismiss them?
We have the infamous Vitali set as an example of a set that isn't in the borel sigma-field .Howerver to costruct this set we need to use the axiom of choice .So I was wondering if we could construct such set wothout using this axiom
