This essay develops a metaphysical account of time in which the present (the Now) is treated as an invariant condition of actualization rather than a moving moment within a temporal sequence. Against the common assumption that time flows and the present passes, the argument proposes that the Now is a singular, non-extended point at which all events are continuously actualized. What is experienced as temporal flow is not the movement of the Now itself but the succession of events occurring within (...) it. -/- Time, in this framework, is not a substance but a dependent condition, arising only where change occurs within space and matter. The Now, as the condition of all actualization, cannot sustain itself and therefore points to a non-temporal ground that holds it open. This leads to a philosophical account of divine presence understood not as a being within time, but as the sustaining source of the Now itself. -/- The essay further argues that the singularity of the Now implies the singularity of the self: identity is constituted not by possible alternatives but by actualization within the one shared present. The resulting framework—referred to as a lemniscatic topology of time—offers a unified account of temporality, agency, and metaphysical grounding. (shrink)

The self does not fall into chaos — it falls into a better-organized lie. -/- This essay argues that sin, addiction, and moral collapse do not disintegrate the structure of the self but relocate its center. Within the Gaitan Topology, when the self abandons the crossing point — the locus of divine presence, the eternal I AM — it constructs an alternate lemniscate around a false center. -/- Six modes are examined: deferral (Lope de Vega, Dante, Barrie), desire as asymptotic (...) approximation (Moore-Penrose pseudoinverse), pride as self-axialization (non serviam), fusion as self-dissolution (Papini's Heloise) in becoming a satellite, epistemic error as collectively reinforced illusion (Andersen's The Emperor's New Clothes), and trauma as structural damage to the curve itself (CCC, nn. 2280–2283). -/- Each false center carries the seed of its own rupture. Scaled collectively, overlapping alternate lemniscates produce what the essay calls Legion of Legions — the institutionalization of displacement in social immorality, governmental corruption, and corporate capture. -/- Against every mode, the divine self-disclosure I AM WHO I AM stands as the only stable center: pure presence without reference, the crossing point that does not move while everything else does. (shrink)

If mercy is always present at the Now, grounded in Christ's continuous presence at every crossing point, what does Calvary actually do? If David could receive mercy centuries before the Incarnation, if the righteous before Christ could genuinely encounter the ground of mercy at the Now — what changes at the Cross? -/- This essay proposes a structural interpretation of human existence centered on the Now as the invariant condition of actualization. Through a lemniscate model (Figure I), it distinguishes between (...) two modes of being: presence (without succession) and succession (the experience of time as before and after). Within this structure, the will operates at the crossing point, where divine address, human response, and mercy converge. -/- Through the figures of Adam, Cain, and David, the essay develops a “geometry of the will,” identifying distinct orientations—deflection, resistance, and return—at the moment of encounter. Mercy is interpreted not as a temporal response to repentance, but as a structural condition always present in the Now, grounded in the continuous presence of Christ as the axis that intersects every act of actualization. -/- The essay further distinguishes between the permanent availability of mercy and the historical opening of its consummation, arguing that the Cross does not introduce mercy, but renders fully accessible, within the created order, the communion toward which mercy is ordered. As illustrated in Figure I, human existence is not a movement along time, but a continuous passage through a crossing point where will, mercy, and divine presence coincide. (shrink)

This essay proposes that the serpent's biblical punishment — "on your belly you shall go" (Genesis 3:14) — is topological: a condemnation to an incomplete lemniscate that loops without crossing, circulates without arriving, and operates exclusively in future tense. Within the Gaitan Topology, the serpent's curve is the geometry of drift — the counterfeit of the lemniscate's geometry of presence. -/- The essay traces this counterfeit geometry through the mimetic chain, in which the serpent's original vertical promise ("you will be (...) like God") is horizontalized into an endless loop of borrowed identities. The figure of Legion (Mark 5:9) is read as the collapse of the "I" into plurality — a self possessing knowledge without traction. -/- The essay identifies flat sight as the precondition for mimetic absorption, rereads Genesis 3:6 as the archetype of abandonment without opposition, and introduces the concept of "the first extraction" — the act by which Eve converts presence into object, gift into possession, encounter into acquisition. A new section on the other as a vector of displacement extends the topology from time into relation. Companion to The Topology of Presence: Four Planes of Existence on the Lemniscate. (shrink)

This essay proposes a structural interpretation of the final states of human existence through the lens of the Now as the invariant point of actualization. It argues that Heaven, Purgatory, and Hell are not spatial destinations but distinct modes of existing in relation to the crossing point where will, mercy, and divine presence converge. -/- Heaven is described as the Now fulfilled—dwelling at the crossing without succession. Purgatory as a state oriented toward the Now yet unable to actualize from within (...) itself. Hell as the inverted Now—permanent existence at the crossing point in refusal of what it contains. -/- In this framework, the end of time does not signify annihilation but the cessation of succession, revealing the definitive orientation of the will toward or away from the presence that has always been given. (shrink)

This essay introduces the concept of “One Day” as a temporal structure of displacement within the broader framework of the Ghost Zone. It argues that certain forms of anticipation—commonly expressed through phrases such as “one day” or “you will see”—do not function as genuine hope but as mechanisms that relocate the self away from the present moment, where life alone can be encountered. -/- Drawing on a topological model of presence, the essay proposes that the future, when treated as a (...) site of fulfillment, operates not as a domain of realized experience but as a field of projection. In this structure, the individual’s activity—often disciplined, creative, and sustained—becomes oriented toward a limit that is indefinitely approached but never reached. The result is a form of continuity without arrival, in which life is simulated through internal completion rather than entered through actual encounter. -/- The analysis further examines the relation between this temporal displacement and formative absence, suggesting that the deferred future often functions as an address to an absent witness rather than as a response to present reality. Through phenomenological description, theological reflection, and structural comparison, the essay distinguishes between hope as presence-oriented trust and deferral as future-oriented displacement. -/- By situating “One Day” within the broader dynamics of asymptotic movement and the Heroic Illusion, the text contributes to a unified account of experiential non-arrival. It concludes by reaffirming the ontological status of the present as the only locus of contact, where life is not projected but received. (shrink)

This monograph is the second in a series built around the lemniscate — the mathematical figure-eight curve — as a contemplative heuristic for understanding human temporal existence. Proceeding from the geometric framework established in the first volume, it descends into the interior: into what it means to inhabit time from within, as a person who moves through the curve's two loops, approaches the crossing point, and either passes through or turns away. -/- Across nine chapters organized at five levels of (...) interiority — cosmic, philosophical, social, scriptural, and existential — the work develops three central claims. First, that the crossing point of the lemniscate is the only location where human agency operates: the infinitesimal gap between today and tomorrow where freedom lives and grace arrives. Second, that unrealized possibilities are not abandoned by Providence but return at later crossing points in transformed form — the harmonic echo, grounded scripturally in Ecclesiastes 3:15, Genesis 50, and Revelation 21:5. Third, that a specific condition — the Ghost Zone — displaces millions of people from the real plane of existence into a fabricated parallel topology, silently and without drama, with roots in generational abandonment and accelerating rapidly through the attention economy and misused technology. -/- The scriptural figures — Nathanael, Peter, Nicodemus, the adulterous woman, and the name changes of Abram, Jacob, Simon, and Saul — appear as persons in motion rather than fixed types. The literary witnesses — J.M. Barrie, John Milton, Lope de Vega, Giovanni Papini (Giudizio Universale), Ruben Dario, and Luis de Gongora — arrive not as authorities but as those who have stood at or near the crossing and left behind language that allows the moment to be recognized from within. The monograph concludes with a recognition: that the four movements of the Rosary — Joyful, Sorrowful, Glorious, Luminous — correspond structurally to the lemniscate's two loops, its crossing point, and its second loop's transformation. The geometry was already being prayed. (shrink)

A working essay in theological anthropology proposing a four-quadrant ontological framework (the Gaitan Topology) mapped onto the lemniscate. The essay develops a topology of presence organized around the crossing point of the figure-eight as the site of the Now, grace, and encounter. It introduces the grammatical axis (God's present tense versus the serpent's future tense), the reference/residence distinction, the phenomenology of presence, three mechanics of deferral, and the Ghost Zone as a state of existential displacement. Companion to The Lemniscate of (...) Time: A Topology of Memory, Possibility and Memory. (shrink)

Este ensayo sostiene que Martin Heidegger recuperó correctamente la pregunta por el Ser, pero que el horizonte temporal no basta como fundamento ontológico. Concediendo la fuerza fenomenológica de su análisis de la finitud, el arrojamiento y el ser-para-la-muerte, el texto distingue entre el problema de la inteligibilidad y el problema del sustento. En lugar de un modelo basado en el horizonte, propone una explicación centrada en el Ahora como condición invariante de actualización. Finalmente, relaciona este marco con las tradiciones metafísicas (...) clásicas de Aristóteles, Tomás de Aquino y la fórmula del Exodo: “YO SOY EL QUE SOY. (shrink)

This essay develops a structural account of time as a non-uniform condition arising from actualization, introducing the concept of temporal density to describe variations in the depth of change. It distinguishes between two orders of change—physical and ontological—and situates the human will at the invariant crossing point (the Now), where orientation is decided. -/- Through an analysis of fall, habit, and fixation, the essay argues that the will is formed across time by repeated responses, generating a kind of structural inertia (...) that shapes the capacity to turn. Human life is described as a finite passage through a lemniscate of temporal succession, in which each crossing of the Now is complete yet not indefinitely repeatable. -/- The essay concludes that time is not a neutral medium but a finite field of actualization: while it cannot be extended, each moment fully contains the possibility of reorientation. The finitude of time and the completeness of each Now are thus shown to be structurally inseparable. (shrink)

Si la misericordia siempre está presente en el Ahora, fundamentada en la presencia continua de Cristo en cada punto de cruce, ¿qué hace realmente el Calvario? Si David pudo recibir misericordia siglos antes de la Encarnación, si los justos antes de Cristo pudieron encontrar genuinamente el fundamento de la misericordia en el Ahora — ¿qué cambia en la Cruz? -/- Este ensayo propone una interpretación teológica de la existencia humana en la que el Ahora es comprendido como el lugar invariante (...) de la actualización, donde acontece el encuentro entre Dios y la criatura. A partir de un modelo en forma de lemniscata (Figura I), se distinguen dos modos de existencia: la presencia, propia de la comunión no fragmentada, y la sucesión, propia de la experiencia temporal marcada por el antes y el después. -/- En este marco, la voluntad humana se sitúa en el punto de cruce, donde la interpelación divina —manifestada en las preguntas dirigidas a Adán y Caín— convoca a una respuesta. A través de las figuras de Adán, Caín y David, el ensayo desarrolla una “geometría de la voluntad”, en la que se revelan tres orientaciones fundamentales: la deflexión, la resistencia y el retorno. La misericordia se comprende no como una reacción posterior al arrepentimiento, sino como una condición permanente inscrita en el Ahora, fundada en la presencia continua de Cristo, eje que sostiene y atraviesa todo acto de actualización. -/- Asimismo, se distingue entre la disponibilidad constante de la misericordia y la apertura histórica de su plenitud. En esta perspectiva, la Cruz no introduce la misericordia en la historia, sino que, desde el interior de la creación, abre el acceso pleno a la comunión definitiva con Dios. Como se muestra en la Figura I, la existencia humana no consiste en un transcurrir lineal en el tiempo, sino en un paso continuo por el punto de encuentro donde convergen la voluntad, la misericordia y la presencia divina. (shrink)

This essay introduces the Ghost Zone—a parallel interior topology in which the self functions at a remove from reality, either through rehearsed success or anticipated defeat. Drawing on phenomenological observation, it examines how displacement of the experiential center shapes presence, relationship, and the capacity for encounter. Part I of The Ghost Zone Series, a conceptual extension of the lemniscate framework developed in the author's forthcoming monograph.

This essay introduces the concept of the Heroic Illusion as an upward expression of a broader condition of displaced presence previously described as the Ghost Zone. Whereas the latter designates a structural non-arrival within lived experience, the Heroic Illusion names the internal construction of fully resolved moments—recognition, coherence, and completion—that precede and displace actual encounter. -/- The analysis proposes that these constructions do not operate along the temporal axis of lived experience, but rather along an orthogonal dimension in which internally (...) consistent but non-intersecting events are generated. As such, the subject may exhibit functional participation in reality while remaining partially exterior to the moment in which action and relation occur. -/- The essay further advances the notion of a “counterfeit orthogonal” to describe the structural imitation, from within the subject’s own interiority, of forms of interruption that in other contexts would be understood as originating beyond the subject (e.g., grace). This imitation preserves the form of arrival while lacking its source, thereby sustaining a system that appears complete but cannot be shared. -/- By articulating this structure, the essay situates the Heroic Illusion not as a pathological distortion, but as a precise response to conditions in which essential forms of recognition were not originally received. However, because it does not intersect with lived time, it cannot generate actual encounter, and therefore contributes to a persistent displacement of presence. -/- This text forms part of a broader series examining the conditions, mechanisms, and possible interruption of such displacement. (shrink)

El yo no cae en el caos — cae en una mentira mejor organizada. -/- Este ensayo sostiene que el pecado, la adicción y el colapso moral no desintegran la estructura del yo sino que reubican su centro. Dentro de la Topología Gaitan, cuando el yo abandona el punto de cruce — el locus de la presencia divina, el eterno YO SOY — construye una lemniscata alterna alrededor de un centro falso. -/- Se examinan seis modos: el aplazamiento (Lope de (...) Vega, Dante, Barrie), el deseo como aproximación asintótica (pseudoinversa de Moore-Penrose), la soberbia como autoaxialización (non serviam), la fusión como autodisolución (la Eloísa de Papini) y la transformacion del ser en un satelite, el error epistémico como ilusión colectivamente reforzada (El Traje Nuevo del Emperador de Andersen), y el trauma como daño estructural en la curva misma (CIC, nn. 2280–2283). -/- Cada centro falso porta la semilla de su propia ruptura. A escala colectiva, las lemniscatas alternas superpuestas producen lo que el ensayo denomina Legión de Legiones — la institucionalización del desplazamiento en la inmoralidad social, la corrupción gubernamental y la captura corporativa. -/- Frente a cada modo, la autorrevelación divina YO SOY EL QUE SOY se erige como el único centro estable: presencia pura sin referencia, el punto de cruce que no se mueve mientras todo lo demás sí lo hace. (shrink)

Este ensayo propone que el castigo bíblico de la serpiente — «sobre tu vientre caminarás» (Génesis 3:14) — es topológico: una condena a una lemniscata incompleta que gira sin cruzar, circula sin llegar y opera exclusivamente en tiempo futuro. Dentro de la Topología Gaitan, la curva de la serpiente es la geometría de la deriva — la falsificación de la geometría de la presencia de la lemniscata. -/- El ensayo traza esta geometría falsificada a través de la cadena mimética, en (...) la cual la promesa vertical original de la serpiente («seréis como Dios») se horizontaliza en un bucle interminable de identidades prestadas. La figura de Legión (Marcos 5:9) se lee como el colapso del «Yo» en pluralidad — un ser que posee conocimiento sin tracción. -/- El ensayo identifica la vista plana como precondición de la absorción mimética, relee Génesis 3:6 como el arquetipo del abandono sin oposición, e introduce el concepto de «la primera extracción» — el acto por el cual Eva convierte la presencia en objeto, el don en posesión, el encuentro en adquisición. Una nueva sección sobre el otro como vector de desplazamiento extiende la topología del tiempo a la relación. Compañero de La Topología de la Presencia: Cuatro Planos de Existencia sobre la Lemniscata. (shrink)

This essay develops a theological and phenomenological account of why the center of human experience—the crossing point in the Gaitan Topology—does not deplete, in contrast to the self-sustaining but ultimately exhausting loops of displacement. Building on prior analyses of the Ghost Zone, temporal deferral, and asymptotic movement, the text examines how hope, when detached from the present, becomes the sustaining mechanism of a structure that never arrives. -/- Through a series of structural comparisons, the essay argues that fulfillment is determined (...) not by the content of what is received but by the position from which it is received. Off the center, every satisfaction generates renewed lack, producing cycles of thirst that perpetuate themselves through anticipation. At the crossing point, the same conditions yield a different structure: reception without depletion, where what is given does not exhaust because it is grounded in presence. -/- This principle is developed through scriptural and narrative figures, including the Samaritan woman, the widow of Zarephath, Penelope, and Esther, each of whom embodies a distinct relation to hope, fulfillment, and non-arrival. The analysis introduces the concept of topological relativity, according to which identical experiences produce opposite effects depending on their relation to the center, and distinguishes between hope as present-tense habitation and hope as deferred projection. -/- The essay concludes that the non-depletion of the center is not a property of the self but of its source. The present, when inhabited, is sustained by the Eternal Present, understood not as a temporal moment but as the ontological ground of being, where the human “I am” participates in the inexhaustible reality of the divine “I am.” . (shrink)

Este ensayo propone un marco ontológico de cuatro cuadrantes — la Topología Gaitan — mapeado sobre la lemniscata (∞), en el cual el punto de cruce de la figura del ocho funciona como el sitio del Ahora, la gracia y el encuentro. Dos planos ocupan la curva temporal (la vida moral consciente, donde el arrepentimiento es posible, y la no-existencia visible, donde el mal es real pero impermanente); dos se sitúan fuera de ella (el Presente Eterno que sostiene el punto (...) de cruce, y la no-existencia eterna — el infierno entendido no como aniquilación sino como el modo de ser en el que los condenados nunca están muertos sino eternamente muriendo). -/- El ensayo desarrolla un eje gramatical: Dios habla en tiempo presente ("Yo soy el que soy"), la serpiente en tiempo futuro ("Seréis como Dios"), y la Caída es estructuralmente un cambio de tiempo verbal de la presencia al desplazamiento. -/- Otras contribuciones incluyen la distinción referencia/residencia (la memoria y la anticipación como herramientas versus como habitaciones rivales), tres mecánicas del aplazamiento (lúcido, condicional y por deber), la fenomenología de la presencia (la infancia como Edén fenomenológico, "no nos quedamos sin tiempo — nos quedamos sin presencia"), y la Zona Fantasma como estado de desplazamiento existencial enraizado en la ausencia de presencia durante la niñez. Compañero de La Lemniscata del Tiempo: Una Topologia de la Memoria, la Posibilidad y la Gracia. (shrink)

Este ensayo desarrolla una concepción metafísica del tiempo en la que el presente (el Ahora) es tratado como una condición invariante de actualización, y no como un momento en movimiento dentro de una secuencia temporal. Contra el supuesto común de que el tiempo fluye y el presente pasa, el argumento propone que el Ahora es un punto singular y no extendido en el que todos los eventos son continuamente actualizados. Lo que se experimenta como flujo temporal no es el movimiento (...) del Ahora en sí mismo, sino la sucesión de eventos que ocurren dentro de él. -/- El tiempo, en este marco, no es una sustancia sino una condición dependiente, que surge únicamente donde el cambio ocurre dentro del espacio y la materia. El Ahora, como condición de toda actualización, no puede sostenerse a sí mismo y apunta, por tanto, a un fundamento no temporal que lo mantiene abierto. Esto conduce a una concepción filosófica de la presencia divina entendida no como un ser dentro del tiempo, sino como la fuente sustentante del Ahora mismo. -/- El ensayo argumenta además que la singularidad del Ahora implica la singularidad del yo: la identidad no está constituida por alternativas posibles sino por la actualización dentro del único presente compartido. El marco resultante — denominado topología lemniscática del tiempo — ofrece una explicación unificada de la temporalidad, la agencia y el fundamento metafísico. (shrink)

Este ensayo desarrolla una explicación teológica y fenomenológica de por qué el centro de la experiencia humana—el punto de cruce en la Topología de Gaitán—no se agota, en contraste con los bucles autosostenidos pero finalmente exhaustivos del desplazamiento. Partiendo de análisis previos sobre la Zona Fantasma, la deferencia temporal y el movimiento asintótico, el texto examina cómo la esperanza, cuando se desvincula del presente, se convierte en el mecanismo que sostiene una estructura que nunca llega. -/- A través de (...) una serie de comparaciones estructurales, el ensayo sostiene que la plenitud no está determinada por el contenido de lo recibido, sino por la posición desde la cual se recibe. Fuera del centro, toda satisfacción genera una nueva carencia, produciendo ciclos de sed que se perpetúan mediante la anticipación. En el punto de cruce, en cambio, las mismas condiciones producen una estructura distinta: recepción sin agotamiento, donde lo dado no se consume porque está arraigado en la presencia. -/- Este principio se desarrolla mediante figuras escriturales y narrativas, incluyendo la mujer samaritana, la viuda de Sarepta, Penélope y Ester, cada una de las cuales encarna una relación distinta con la esperanza, la plenitud y la no-llegada. El análisis introduce el concepto de relatividad topológica, según el cual experiencias idénticas producen efectos opuestos dependiendo de su relación con el centro, y distingue entre la esperanza como habitación en tiempo presente y la esperanza como proyección diferida. -/- El ensayo concluye que el no-agotamiento del centro no es una propiedad del yo, sino de su fuente. El presente, cuando es habitado, está sostenido por el Presente Eterno, entendido no como un momento temporal sino como el fundamento ontológico del ser, donde el “yo soy” humano participa de la realidad inagotable del “Yo Soy” divino. (shrink)

Este ensayo introduce el concepto de «Un Día» como una estructura temporal de desplazamiento dentro del marco más amplio de la Zona Fantasma. Argumenta que ciertas formas de anticipación —comúnmente expresadas a través de frases como «un día» o «ya verás»— no funcionan como esperanza genuina sino como mecanismos que reubican al ser lejos del momento presente, donde únicamente la vida puede ser encontrada. -/- Apoyándose en un modelo topológico de la presencia, el ensayo propone que el futuro, cuando es (...) tratado como sitio de realización, opera no como un dominio de experiencia realizada sino como un campo de proyección. En esta estructura, la actividad del individuo —a menudo disciplinada, creativa y sostenida— se orienta hacia un límite que es indefinidamente aproximado pero nunca alcanzado. El resultado es una forma de continuidad sin llegada, en la cual la vida es simulada a través de completación interna en lugar de ser entrada a través del encuentro real. -/- El análisis examina además la relación entre este desplazamiento temporal y la ausencia formativa, sugiriendo que el futuro diferido funciona a menudo como una dirección hacia un testigo ausente más que como una respuesta a la realidad presente. A través de descripción fenomenológica, reflexión teológica y comparación estructural, el ensayo distingue entre la esperanza como confianza orientada a la presencia y el aplazamiento como desplazamiento orientado al futuro. -/- Al situar «Un Día» dentro de las dinámicas más amplias del movimiento asintótico y la Ilusión Heroica, el texto contribuye a un relato unificado de la no-llegada experiencial. Concluye reafirmando el estatus ontológico del presente como el único locus de contacto, donde la vida no es proyectada sino recibida. (shrink)

This essay develops a concise philosophical argument concerning contingency, explanatory termination, necessary being, and divine hiddenness. It argues that an infinite regress of existentially dependent realities does not adequately account for existence and that a necessary ground of being offers a more coherent explanatory terminus than a brute contingent universe. Drawing on the classical theist tradition, the essay further examines divine simplicity, timelessness, and the limits of empirical methods in addressing metaphysical questions.

Este ensayo desarrolla un argumento filosófico conciso sobre la contingencia, la terminación explicativa, el ser necesario y el ocultamiento divino. Sostiene que una regresión infinita de realidades existencialmente dependientes no explica adecuadamente la existencia y que un fundamento necesario del ser ofrece un término explicativo más coherente que un universo contingente asumido como hecho bruto. Inspirado en la tradición teísta clásica, el ensayo examina además la simplicidad divina, la intemporalidad y los límites de los métodos empíricos frente a las preguntas (...) metafísicas. (shrink)

This essay examines Martin Heidegger’s concept of Das Man through literature, theology, and contemporary social life. It argues that anonymity, conformity, and relational fragility arise where the first person singular is displaced by impersonal collective forms. Through readings of Hans Christian Andersen, Franz Kafka, Lope de Vega, and biblical anthropology, the essay proposes that authentic communion requires selves first gathered into presence.

Este ensayo examina el concepto de Das Man de Martin Heidegger a través de la literatura, la teología y la vida social contemporánea. Sostiene que el anonimato, la conformidad y la fragilidad relacional surgen allí donde la primera persona del singular es desplazada por formas colectivas impersonales. Mediante lecturas de Hans Christian Andersen, Franz Kafka, Lope de Vega y la antropología bíblica, el ensayo propone que la comunión auténtica requiere yos previamente reunidos en la presencia.

Este ensayo propone una interpretación estructural de los estados finales de la existencia humana a partir del Ahora como punto invariante de actualización. Sostiene que el Cielo, el Purgatorio y el Infierno no son destinos espaciales, sino modos distintos de existir en relación con el punto de cruce donde convergen la voluntad, la misericordia y la presencia divina. -/- El Cielo se presenta como el Ahora consumado — la permanencia en el punto de cruce sin sucesión. El Purgatorio como un (...) estado orientado hacia el Ahora, pero incapaz de actualizarse desde sí mismo. El Infierno como el Ahora invertido — existencia permanente en el punto de cruce en rechazo de lo que en él se ofrece. -/- En este marco, el fin del tiempo no implica aniquilación, sino el cese de la sucesión, revelando la orientación definitiva de la voluntad hacia o en contra de la presencia que siempre ha estado dada. (shrink)

Este trabajo desarrolla una lectura ontológica de la estructura decimal. Sostiene que la notación decimal contiene dos lógicas simultáneas: incremento lineal del valor y recurrencia cíclica de la forma simbólica. El cero retorna en cada frontera decimal, los dígitos se repiten entre magnitudes y el valor posicional registra acumulación mediante repetición estructurada. Interpretada mediante la imagen de la lemniscata, la representación decimal se convierte en un modelo de tensiones filosóficas entre identidad y cambio, progreso y retorno, y extensión infinita frente (...) a forma recurrente. El ensayo no cuestiona los fundamentos aritméticos; propone una interpretación metafísica de la estructura representacional. (shrink)

El Es y el SOY Presencia, Identidad y el Fundamento que Sostiene es un ensayo metafísico sobre la estructura de la existencia humana, la naturaleza del presente y el fundamento de la realidad contingente. Sostiene que la experiencia vivida se organiza mediante memoria, anticipación y un umbral presente de decisión en el que lo posible se vuelve actual. -/- Este umbral, descrito como la micro-brecha, es presentado como el lugar fenomenológico de la libertad, la responsabilidad y la orientación moral. Utilizando (...) la lemniscata (figura de ocho) como modelo simbólico de la temporalidad, el ensayo explora cómo la identidad no está determinada solo por actos aislados, sino también por la dirección acumulada de la voluntad y por relaciones que constituyen al yo mediante el encuentro, la obligación y el amor. -/- Frente a las visiones que consideran el tiempo como último o autosuficiente, la obra propone que la actualidad contingente no explica plenamente su propia persistencia, lo que apunta hacia un fundamento no derivado del ser. Dentro de la tradición bíblica, ese fundamento es contemplado a través del nombre divino revelado en el Éxodo: “YO SOY EL QUE SOY”. Integrando fenomenología, ontología, reflexión literaria e interpretación teológica, el ensayo presenta la persona como realidad comunitaria, relacional y orientada hacia una fuente sustentadora más allá de la sucesión temporal. (shrink)

Este ensayo examina el contraste entre los modelos kármicos de reciprocidad moral y la doctrina cristiana de la gracia mediante el marco del “punto de cruce”, entendido como el momento presente donde se sitúan la agencia, el arrepentimiento y la transformación. Se argumenta que los sistemas regidos exclusivamente por retorno, proporción y consecuencia no pueden explicar plenamente el perdón, la misericordia ni la posibilidad de un comienzo verdaderamente nuevo. Inspirándose en parte en la comprensión de Agustin de Hipona sobre la (...) voluntad herida y la necesidad de la gracia, el ensayo interpreta las figuras de David, Pablo, la mujer sorprendida en adulterio y María Magdalena como estudios de caso de una realidad donde la consecuencia es real, pero no agota lo posible. La tesis central sostiene que un mecanismo puede devolver lo enviado, pero solo una fuente personal puede ofrecer lo no merecido. (shrink)

Este ensayo reexamina el famoso cogito de René Descartes (“pienso, luego existo”) argumentando que el pensamiento no revela el fundamento del ser, sino únicamente la actividad de la conciencia temporal. Apoyándose en Agustin de Hipona, Tomas de Aquino y la tradición contemplativa, el texto desarrolla una visión metafísica en la que la sensación, la pasión y el pensamiento discursivo pertenecen a la vida corporal y temporal, mientras que el modo más profundo del alma es la aprehensión directa de la realidad. (...) La muerte es interpretada no como extinción del yo, sino como la remoción de la interferencia cognitiva mediante la cual el alma conoce sin mediación. El ensayo propone una inversión de la fórmula cartesiana: no pienso, luego existo, sino pienso porque existo. (shrink)

Este monográfico es el segundo de una serie construida en torno a la lemniscata — la curva matemática en forma de ocho — como heurística contemplativa para comprender la existencia temporal humana. Partiendo del marco geométrico establecido en el primer volumen, desciende hacia el interior: hacia lo que significa habitar el tiempo desde dentro, como una persona que se mueve a través de los dos lazos de la curva, se aproxima al punto de cruce y lo atraviesa o se aleja (...) de él. -/- A través de nueve capítulos organizados en cinco niveles de interioridad — cósmico, filosófico, social, escritural y existencial — el trabajo desarrolla tres afirmaciones centrales. Primera, que el punto de cruce de la lemniscata es el único lugar donde opera la agencia humana: la brecha infinitesimal entre hoy y mañana donde vive la libertad y llega la gracia. Segunda, que las posibilidades no realizadas no son abandonadas por la Providencia sino que regresan en puntos de cruce posteriores en forma transformada — el eco armónico, fundamentado escrituralmente en Eclesiastés 3:15, Génesis 50 y Apocalipsis 21:5. Tercera, que una condición específica — la Zona Fantasma — desplaza a millones de personas del plano real de la existencia hacia una topología paralela fabricada, silenciosa y sin drama, con raíces en el abandono generacional y acelerada rápidamente por la economía de la atención y la tecnología mal utilizada. -/- Las figuras escriturales — Natanael, Pedro, Nicodemo, la mujer adúltera y los cambios de nombre de Abram, Jacob, Simón y Saulo — aparecen como personas en movimiento más que como tipos fijos. Los testigos literarios — J.M. Barrie, John Milton, Lope de Vega, Giovanni Papini (Giudizio Universale), Rubén Darío y Luis de Góngora — llegan no como autoridades sino como quienes han estado en el cruce o cerca de él y han dejado atrás un lenguaje que permite reconocer ese momento desde dentro. El monográfico concluye con un reconocimiento: que los cuatro movimientos del Rosario — Gozosos, Dolorosos, Gloriosos, Luminosos — corresponden estructuralmente a los dos lazos de la lemniscata, su punto de cruce y la transformación de su segundo lazo. La geometría ya se estaba rezando. (shrink)

Este trabajo pregunta si la resistencia es constitutiva de la identidad. Sostiene que los seres llegan a ser lo que son mediante el contacto sostenido con las condiciones de su existencia, y que los sistemas económicos y tecnológicos contemporáneos redirigen cada vez más esas presiones en lugar de abolirlas. La selección natural darwiniana se interpreta no como un ideal moral, sino como un modelo de honestidad estructural: la supervivencia bajo restricción real revela lo que un ser verdaderamente es. En contraste, (...) las formas modernas de “selección artificial” privilegian la compatibilidad con sistemas de mantenimiento sobre la transformación genuina. -/- Mediante análisis del Barco de Teseo, la sustitución ecológica, la cultura antienvejecimiento, la espiritualidad mercantilizada y el modelo lemniscático de la temporalidad, el trabajo desarrolla el concepto del “Ahora Deshabitado”: un presente cada vez más lleno de formas que persisten mientras carecen de la profundidad interior generada por el paso genuino, la pérdida y la reconstitución. Se propone una lectura teológica del Ahora como dependiente de un fundamento autosustentado, presentada como modelo interpretativo y no como conclusión presupuesta. (shrink)

Este ensayo desarrolla una interpretación estructural del tiempo como una condición no uniforme que surge de la actualización, introduciendo el concepto de densidad temporal para describir las variaciones en la profundidad del cambio. Distingue entre dos órdenes de cambio —físico y ontológico— y sitúa la voluntad humana en el punto de cruce invariante (el Ahora), donde se decide la orientación. -/- A través del análisis de la caída, el hábito y la fijación, el ensayo sostiene que la voluntad se forma (...) a lo largo del tiempo mediante respuestas repetidas, generando una especie de inercia estructural que condiciona la capacidad de girar. La vida humana se describe como un tránsito finito a través de una lemniscata de sucesión temporal, en la que cada cruce del Ahora es completo pero no indefinidamente repetible. -/- El ensayo concluye que el tiempo no es un medio neutro, sino un campo finito de actualización: aunque no puede extenderse, cada momento contiene plenamente la posibilidad de reorientación. La finitud del tiempo y la plenitud de cada Ahora se muestran así como estructuralmente inseparables. (shrink)

This paper asks whether endurance is constitutive of identity. It argues that beings become what they are through sustained contact with the conditions of their existence, and that contemporary economic and technological systems increasingly redirect rather than abolish such pressures. Darwin’s concept of natural selection is interpreted not as a moral ideal, but as a model of structural honesty: survival under real constraint reveals what a being actually is. By contrast, modern forms of “artificial selection” privilege compatibility with maintenance systems (...) over genuine transformation. -/- Through analyses of the Ship of Theseus, ecological replacement, anti-aging maintenance culture, commodified spirituality, and the lemniscate model of temporality, the paper develops the concept of the “Uninhabited Now”: a present increasingly filled by forms that persist while lacking the interior depth generated through genuine passage, loss, and reconstitution. A theological reading of the Now as dependent on a self-sustaining ground is proposed as one interpretive model rather than as a presupposed conclusion. (shrink)

This essay reexamines René Descartes’ famous cogito (“I think, therefore I am”) by arguing that thinking reveals not the ground of being, but only the activity of temporal consciousness. Drawing on Augustine of Hippo, Thomas Aquinas, and contemplative theology, the paper develops a metaphysical account in which sensation, passion, and discursive thought belong to embodied temporal life, while the soul’s deeper mode is direct apprehension of reality. Death is interpreted not as the extinction of selfhood, but as the removal of (...) cognitive interference through which the soul knows without mediation. The essay proposes an inversion of the Cartesian formula: not I think, therefore I am, but I think because I am. (shrink)

This essay examines the contrast between karmic models of moral reciprocity and the Christian doctrine of grace through the framework of the “crossing point,” the present moment as the sole locus of agency, repentance, and transformation. It argues that systems governed exclusively by return, proportion, and consequence cannot fully account for forgiveness, mercy, or the possibility of a genuinely new beginning. Drawing in part on Augustine of Hippo’s account of the wounded will and the necessity of grace, the essay interprets (...) the figures of David, Paul, the woman caught in adultery, and Mary Magdalene as case studies in a reality where consequence is real but does not exhaust what is possible. The central claim is that a mechanism may return what was sent, but only a personal source can offer what was not earned. (shrink)

The Is and the AM: Presence, Identity, and the Ground that Holds is a metaphysical essay on the structure of human existence, the nature of the present, and the grounding of contingent reality. It argues that lived experience is organized through memory, anticipation, and a present threshold of decision in which potential becomes actual. -/- This threshold, described as the micro-gap, is presented as the phenomenological site of freedom, responsibility, and moral orientation. Using the lemniscate (figure-eight) as a symbolic model (...) of temporality, the essay explores how identity is shaped not only by isolated acts but by the accumulated direction of the will and by relations that constitute the self through encounter, obligation, and love. -/- Against accounts that treat time as ultimate or self-sufficient, the work proposes that contingent actuality does not fully explain its own persistence, pointing instead toward a non-derivative ground of being. Within the biblical tradition, this ground is contemplated through the divine name revealed in Exodus: “I AM WHO I AM.” Integrating phenomenology, ontology, literary reflection, and theological interpretation, the essay presents personhood as communal, relational, and oriented toward a sustaining source beyond temporal succession. (shrink)

This essay argues that Martin Heidegger correctly recovered the question of Being, but that temporal horizon does not suffice as ontological ground. Granting the phenomenological force of Heidegger’s analysis of finitude, thrownness, and Being-toward-death, the paper distinguishes the problem of intelligibility from the problem of sustenance. In place of a horizon-based model, it proposes a center-based account in which the Now functions as the invariant condition of actualization. The argument then relates this framework to classical metaphysical accounts in Aristotle, Thomas (...) Aquinas, and the Exodus formula “I AM WHO I AM. (shrink)

This paper develops an ontological reading of decimal structure. It argues that decimal notation contains two simultaneous logics: linear increase in value and cyclical recurrence in symbolic form. Zero returns at each decade boundary, digits repeat across magnitudes, and place value records accumulation through structured repetition. Interpreted through the image of the lemniscate, decimal representation becomes a model for philosophical tensions between identity and change, progress and return, and infinite extension versus recurring form. The essay does not challenge arithmetic foundations; (...) it proposes a metaphysical interpretation of representational structure. (shrink)

This monograph proposes the lemniscate (∞) as a contemplative framework for understanding the relationship between time and eternity in Christian theology. Drawing on Scripture, patristic sources, medieval scholasticism, and modern theology, it explores how Christ's Incarnation, death, and Resurrection open a "crossing point" where temporal succession intersects eternal presence. The work addresses sacramental theology (particularly Eucharistic presence), liturgical time (the Church's calendar as participation in eternity), prayer and prophecy (as temporal access to the crossing point), and eschatology (three destinations and (...) bodily resurrection). It engages objections from philosophy (spatial metaphors for temporal realities), theology (concerns about mechanism and semi-Pelagianism), and science (thermodynamics, cosmology, entropy). Published under Creative Commons BY-NC 4.0 for free educational use. 223 pages, 40,433 words. (shrink)

Book Description (Blurb): Cognitive Design for Artificial Minds explains the crucial role that human cognition research plays in the design and realization of artificial intelligence systems, illustrating the steps necessary for the design of artificial models of cognition. It bridges the gap between the theoretical, experimental and technological issues addressed in the context of AI of cognitive inspiration and computational cognitive science. -/- Beginning with an overview of the historical, methodological and technical issues in the field of Cognitively-Inspired Artificial Intelligence, (...) Lieto illustrates how the cognitive design approach has an important role to play in the development of intelligent AI technologies and plausible computational models of cognition. Introducing a unique perspective that draws upon Cybernetics and early AI principles, Lieto emphasizes the need for an equivalence between cognitive processes and implemented AI procedures, in order to realise biologically and cognitively inspired artificial minds. He also introduces the Minimal Cognitive Grid, a pragmatic method to rank the different degrees of biologically and cognitive accuracy of artificial systems in order project and predict their explanatory power with respect to the natural systems taken as source of inspiration. -/- Providing a comprehensive overview of cognitive design principles in constructing artificial minds, this text will be essential reading for students and researchers of artificial intelligence and cognitive science. (shrink)

In this paper, I argue for a novel defence of the view that attributes are numerically distinct for Spinoza, which, contrary to paradigmatic objectivist readings, does not contradict his substance monism nor commit him to the view that the only substance has more than one essence. I show that Spinoza offers three overlooked arguments for attribute unity that are consistent with my interpretation. Next, I turn to the perspectivist interpretations of Spinoza’s theory of attributes, dominant in Spinoza scholarship today, under (...) which each attribute is one way in which the whole essence of the only substance can present itself to the intellect. I contend that my interpretation has two advantages over these readings: it can accommodate Spinoza’s arguments of attribute-essence symmetry and essence-modes proportionality. (shrink)

In this paper we identify and characterize an analysis of two problematic aspects affecting the representational level of cognitive architectures (CAs), namely: the limited size and the homogeneous typology of the encoded and processed knowledge. We argue that such aspects may constitute not only a technological problem that, in our opinion, should be addressed in order to build arti cial agents able to exhibit intelligent behaviours in general scenarios, but also an epistemological one, since they limit the plausibility of the (...) comparison of the CAs' knowledge representation and processing mechanisms with those executed by humans in their everyday activities. In the fi nal part of the paper further directions of research will be explored, trying to address current limitations and future challenges. (shrink)

A central objection to objectivist interpretations of Spinoza’s theory of attributes is their alleged inconsistency with his commitment to the simplicity of God’s essence. This paper offers a novel response to this objection. I begin by outlining two main arguments for the claim that, for Spinoza, God’s essence must be simple: his alignment with a longstanding tradition that treats simplicity as a necessary divine property, and his endorsement of the principle that parts are by nature prior to their wholes. I (...) then introduce a distinction, available within Spinoza’s framework, between integral and metaphysical parts. I argue that while Spinoza is committed to the view that God’s essence cannot have integral parts, he is not committed to denying it metaphysical parts. This reading not only addresses the simplicity objection but also clarifies Spinoza’s definition of ‘attribute’ and strengthens the case for both structural and constitutive forms of objectivism. (shrink)

In this article we present an advanced version of Dual-PECCS, a cognitively-inspired knowledge representation and reasoning system aimed at extending the capabilities of artificial systems in conceptual categorization tasks. It combines different sorts of common-sense categorization (prototypical and exemplars-based categorization) with standard monotonic categorization procedures. These different types of inferential procedures are reconciled according to the tenets coming from the dual process theory of reasoning. On the other hand, from a representational perspective, the system relies on the hypothesis of conceptual (...) structures represented as heterogeneous proxytypes. Dual-PECCS has been experimentally assessed in a task of conceptual categorization where a target concept illustrated by a simple common-sense linguistic description had to be identified by resorting to a mix of categorization strategies, and its output has been compared to human responses. The obtained results suggest that our approach can be beneficial to improve the representational and reasoning conceptual capabilities of standard cognitive artificial systems, and –in addition– that it may be plausibly applied to different general computational models of cognition. The current version of the system, in fact, extends our previous work, in that Dual-PECCS is now integrated and tested into two cognitive architectures, ACT-R and CLARION, implementing different assumptions on the underlying invariant structures governing human cognition. Such integration allowed us to extend our previous evaluation. (shrink)

We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of the combination of prototypical concepts. The proposed logic relies on the logic of typicality ALC + TR, whose semantics is based on the notion of rational closure, as well as on the distributed semantics of probabilistic Description Logics, and is equipped with a cognitive heuristic used by humans for concept composition. We first extend the logic of typicality ALC + TR by typicality inclusions of the (...) form p :: T(C) v D, whose intuitive meaning is that “we believe with degree p about the fact that typical Cs are Ds”. As in the distributed semantics, we define different scenarios containing only some typicality inclusions, each one having a suitable probability. We then exploit such scenarios in order to ascribe typical properties to a concept C obtained as the combination of two prototypical concepts. We also show that reasoning in the proposed Description Logic is EXPTIME-complete as for the underlying standard Description Logic ALC. (shrink)

An ontology of Leibnizian relationalism, consisting in distance relations among sparse matter points and their change only, is well recognized as a serious option in the context of classical mechanics. In this paper, we investigate how this ontology fares when it comes to general relativistic physics. Using a Humean strategy, we regard the gravitational field as a means to represent the overall change in the distance relations among point particles in a way that achieves the best combination of being simple (...) and being informative. (shrink)

Paul Watzlawick argued that reality is not discovered but constructed through communication. This paper extends his radical constructivist framework to the digital age, tracing how information technologies have progressively automated the construction of what Watzlawick called "second-order reality" - the domain of meaning, value, and significance. The analysis follows three technological regimes. Search engines transferred epistemic authority from human judgment to algorithmic ranking, making relevance a function of network topology rather than truth. Social media fragmented shared reality into parallel epistemic (...) bubbles, where narrative resonance supplants factual accuracy. Large Language Models complete this trajectory: they produce fluent, coherent discourse without comprehension, intention, or reference - making "hallucination" not a malfunction but the default mode of a system that generates meaning without anchoring it to anything beyond statistical probability. The paper introduces the concept of algorithmic constructivism to characterize this new condition, and warns of its anthropological consequence: epistemic atrophy. As sense-making is progressively delegated to automated systems, humans risk losing the capacity to distinguish negotiated meaning from algorithmic simulation - and with it, the ability to construct reality through genuine communicative exchange. (shrink)

The goal of this essay is twofold. First, it provides a quick look at the foundations of modern relational mechanics by tracing its development from Julian Barbour and Bruno Bertotti's original ideas until present-day's pure shape dynamics. Secondly, it discusses the most appropriate metaphysics for pure shape dynamics, showing that relationalism is more of a nuanced thesis rather than an elusive one. The chapter ends with a brief assessment of the prospects of pure shape dynamics in light of quantum physics.

Any account of Spinoza's understanding of attribute must be able to satisfy his definition criterion; that is, it must coherently accommodate the elements involved in his definition of attribute as “what the intellect perceives of a substance as constituting its essence” (E1d4). But this is not enough. There are several available readings that satisfy this criterion and are mutually incompatible. To know what Spinoza means we must supplement his definition criterion with a criterion aiming at consistency with other principles in (...) his system. With the definition and consistency criteria in the backdrop, the aim of this paper is to offer a critical overview of the current state of the debate on Spinoza's theory of attributes. (shrink)

La activista, filósofa política y profesora emérita de la Universidad de Berkeley Wendy Brown participó en el Festival de las Ideas con una conversación con el periodista Jesús García Calero sobre la pérdida de valores. En esta entrevista el profesor de la UCM Antonio Sánchez Domínguez repasó las ideas que recoge en su extensa obra ensayística, cuyo último título es "Tiempos nihilistas" (Lengua de Trapo y Círculo de Bellas Artes, 2023), donde defiende la construcción de una izquierda crítica y (...) empoderada que sea capaz de volver a seducir a la gente. (shrink)