He is before all things, and in him all things hold together. — Colossians 1:17


Contents



Abstract

Since the first essay of this topology, one verb has done more work than it has ever been made to explain. Does Time need Me, or do I need Time? established that the Now, having no reserves of its own, must be held open by what is not itself in time — the self-subsisting I AM WHO I AM — and every essay since has leaned on that sustaining without once saying what it is. The word was left as a metaphor: God sustains the Now the way attention holds a thought. This essay retires the metaphor and, in retiring it, states the definition of the Lemniscate that the five-essay temporal sequence has earned. Two things inherited from the early language must be corrected. First, the adverb: to say the Now “continuously depends” on God places succession on the wrong side of the relation, smuggling time back into the Ground it was meant to escape — the succession belongs to the receiving creature, not to the grounding. Second, the grammar: “God sustains the Now” is malformed, because the Now is not a being that could be the object of an operation; it is the invariant form of a continuant’s reception of actuality. From these a third correction follows, and it is the essay’s center: to sustain is not to conserve against decay but to constitute. The derivative has no autonomous existence that could lapse and so require propping; constitutive dependence has no otherwise. The Lemniscate is then defined, in its mature form, not as a picture of time but as a per-continuant topology of temporal actualization, grounded in no element of its own figure — not the loops, not even the crossing — but in the Non-Derivative, who is not a point on the figure but the reason there is a figure to trace. The essay closes on the lived datum the whole abstraction exists to name: no one authors his own next moment.


I. The Word Still Owed

A topology that has made the auditing of its own debts a matter of method (The Now’s Not-Yet) cannot go on indefinitely spending a word it has never earned. The word is sustain. Does Time Need Me? reached it honestly and left it standing as an image: God sustains the Now the way attention holds a thought — withdraw the attention and the thought does not fall, it ceases. The image was chosen well, and against the worse images it corrected — the hand holding a cup, the force pushing a present forward — it was right. But it was an image, and it did a peculiar thing under its own weight: it made the sustaining epistemic. Attention is a mode of knowing. To say God sustains the Now as attention holds a thought is to make the ground of being sound like a knower keeping an object in view, and the corpus does not mean that. It means something ontological, and it has never said what.

The other essays inherited the unpaid word and put it to load-bearing use. What Is the Past? argued that nothing lived is lost because the past is not separately preserved but carried inside the present, which is itself sustained, at every instant, by the one ground that holds the Now open. What Is the Future? grounded the openness of the horizon in that same ground. What Is the Now?, correcting the topology’s largest overreach, relocated the sustaining from a single cosmic slice to every point of actualization along every continuant’s history at once, and mapped it — rightly, and with the modesty of a resonance rather than a proof — onto Aquinas’s doctrine of divine immensity. Each of these essays said where the sustaining reaches, or how many crossings it holds, or what depends on it. None said what the verb means. What Is the Now? located the sustaining. It did not cash it. This essay cashes it, and in doing so completes the figure whose grounding the verb names.


II. Where the Sequence Has Arrived

Five results are presupposed here, argued elsewhere, recalled and not re-derived. The invariance of the Now: a condition does not travel, and the Now is a condition; what we experience as flow is the succession of actualizations, not the motion of the crossing (Does Time Need Me?). Condensation: every present gathers its predecessor rather than succeeding it, constituted by inheritance and reception together, with grace as reception’s highest case (The Weight of the Present). Closure: the past is confluence that has ceased receiving, deposited as trace into the constitution of what now is, subtracted from nowhere (What Is the Past?). Asymptote: the future is the horizon faced at every scale and entered at none, open because uncondensed, receding at exactly the rate the present advances (What Is the Future?). And the correction that reshaped the figure: there is no single universal Now spanning all separated events; the Now is a per-continuant relation, one crossing per worldline, and what God sustains is not one slice but the uncountable multitude of crossings, each held entire and undivided (What Is the Now?).

That last result did something to the Lemniscate that has not yet been stated as a definition. It multiplied the figure. There is no longer one lemniscate for the cosmos to trace; there are as many as there are continuants. The figure survived the multiplication — the axis that enters it from outside was never traveling within the plane to reach a privileged node, and so loses nothing by finding many — but the corpus has not paused to say what the figure now is, once it is one-per-continuant and once the verb that grounds it is about to be made precise. That is the first task.


III. The Mature Lemniscate

Set down first what the figure is not, because the whole history of the image invites the errors. The Lemniscate is not a picture of time as a substance that moves. Nothing traces it from outside; no point travels its loops; the crossing does not slide from past toward future. And it is not one figure. It is the shape of a single continuant’s temporal actualization, and there are exactly as many as there are beings that undergo one. This multiplication is one of temporal histories within a single created order, not of worlds or realities: the many crossings are many lives, not many universes.

Now the figure, part by part. The crossing is the continuant’s Now — zero-thickness, not a moment but the standing relation between that continuant and the whole of what is actual for it (What Is the Now?). It is where condensation occurs: where inheritance, gathered entire, meets the reception of what is newly given. The left loop is not the past. It is memory — the interior’s act of reading the condensed, curving out from the crossing and returning, selective and fallible precisely because it is an act. The right loop is not the future. It is anticipation — the act of projecting over the horizon, fallible in the same way and for the same reason. The loops are epistemic; the crossing is ontological. What the loops perform, the crossing constitutes. And temporal order is not laid along the loops like a track; it arises from the asymmetric condensation of successive crossings — the later gathers the earlier, the earlier did not gather the later — so that the figure’s order is internal to its actualizations and not a line they are strung upon.

The Lemniscate is the topology of a continuant’s temporal actualization: a zero-thickness crossing — the Now — at which an inherited constitution, condensed entire, meets an open horizon of reception; flanked by two epistemic loops, memory reading what has closed and anticipation projecting what has not yet arrived; its order generated by the asymmetric condensation of successive crossings rather than by any motion within the figure; and grounded, as a whole, in no element of itself but in the Non-Derivative upon which its every actualization depends.

One objection to the figure must be met here rather than deferred, because it is the sharpest one available and the later essays have armed it. A lemniscate has loops, and loops have extent — area, a swept region, a magnitude. But What Is the Past? and What Is the Future? labored to deny exactly this of the past and the future: the past is no region behind, the future no territory ahead; neither has extent, because neither is a place. Does the figure not re-spatialize precisely what the doctrine de-spatialized? It would, if the loops were the past and the future. They are not, and the correction the corpus already made is what saves the figure. The loops are the acts — memory and anticipation — and acts do have reach: a memory extends and returns, an anticipation projects farther or less far, and this reach is real and belongs to the performance. What has no extent is the past itself, the future itself, and the Now — and none of these is a loop. The past is condensed into the crossing; the future is faced at the crossing; the Now is the crossing. The figure gives spatial expression only to the reach of these epistemic performances, and leaves dimensionless what the doctrine requires to be dimensionless. The loops were never the territories. They were always the traversals.


IV. The Adverb on the Wrong Side

Now the verb. Begin with the smallest correction, because it is the one most easily missed and the one that quietly undoes everything if left in place. The corpus, following its first essay, speaks of the Now as continuously dependent — receiving its existence, at every instant, from the Ground. Read the adverb literally and it does damage. Continuously is a temporal word: it names a succession, an at-every-instant, a keeping-on. Attach it to the grounding relation and the Ground acquires a schedule. A God who performs the depending-relation instant by instant, holding this crossing and then the next and then the next, is a God with a when — which is exactly the God Does Time Need Me? denied when it placed I AM WHO I AM outside the sequence altogether, on pain of an infinite regress of Nows in which to exist. The sustaining-hand was painted out of the picture; the adverb smuggled it back in, invisible, doing the same work under a better word.

The correction is not to delete the succession but to move it. The succession is real. It is simply on the other side of the relation. The creature continuously receives; the Ground does not continuously give. There are not many acts of grounding, one per crossing, strung along a divine timeline; there is one non-successive act of giving being, under which a continuant’s crossings arise successively because the continuant, not the Ground, is the thing that runs in a line. Move the adverb one term to the left — from the grounding to the receiving — and the last mechanism drops out. God grounds, tenselessly and non-successively; the creature receives, continuously and in series. The creature’s dependence is continuous because its temporal actuality is successive; this does not entail a succession of divine acts answering, one for one, to that succession. What Is the Now? already saw the shape of this when it insisted that the Now is indexed to a continuant while actuality is not made relative by that indexing. The same asymmetry holds for the verb: the succession is indexed to the receiver, and the grounding is not.


V. The Now Is Not a Thing to Be Sustained

The second correction is harder, because it touches a sentence the corpus has repeated as if it were obviously well-formed: God sustains the Now. Grammatically the sentence is transitive — an agent, an operation, an object — and that grammar is the whole trouble. It forces three items into view: God, an act of sustaining, and a Now that receives the act. It pictures precisely the arrangement the corpus is trying to leave, in which sustaining is something done to a thing that would otherwise not persist.

But the Now is not a thing. It has no thickness, no substance, no reserves — the first essay was emphatic — and a point of zero extension is not the kind of item that can be the object of an operation, held the way an object is held. What, then, is being sustained? Not the Now, as though the Now were a fragile entity kept from collapse. What depends on the Non-Derivative is actuality itself — the being-actual of whatever is actual — and “the Now” is not a second thing that also depends; it is the name for the invariant form that this dependence takes for a temporal continuant. To be actual at all, for a creature, is to receive actuality non-autonomously, from what one is not. The Now is what that reception looks like from inside a being that receives it serially: the standing crossing, the same in kind at every instant, at which the creature is given to be. God grounds actuality. “The Now” is the invariant form that grounding wears from within the grounded.

This dissolves the transitive picture rather than improving it. The sentence should not be repaired into “God sustains the Now by X”; it should be re-read. To be actual is to be grounded in the Non-Derivative; the Now is the invariant form under which a temporal creature undergoes that grounding. There are not three items — God, act, Now — but two terms of one relation of dependence: the Non-Derivative, and the derivative actuality that is nothing except as received. The Now is not a party to the relation. It is the relation’s shape, on the side of the one who is held.


VI. Sustaining Is Constitution, Not Conservation

The two corrections converge on the third, which is the essay’s center and the point at which the metaphor is not replaced but dissolved. The whole search for a mechanism of sustaining — does God sustain by thought, by attention, by a holding-open — rests on a picture no one has stated because stating it would refute it: the picture of a gap. It supposes that the Now, left to itself, would tend to close; that its persistence is an achievement wrung from a native tendency to lapse; that sustaining is the continuous defeat of that tendency, the propping-open of what would otherwise fall shut. Every candidate mechanism is an answer to the question how is the closing prevented? — and the question is malformed, because constitutive dependence has no otherwise.

A derivative actuality is not a thing that exists and then, precariously, keeps existing against a pull toward non-being. It has no existence from itself — none — except as received. There is therefore no autonomous persistence for a decay to threaten and no interval across which a propping would have to hold. The Now is not held open against a tendency to close, because it has no tendency of its own in either direction; it has no of-its-own. The word has carried three senses that must not be run together: physical preservation, the keeping of a thing from breaking or decaying; temporal continuation, the persistence of a thing from one instant to the next; and ontological conservation, the dependence of a being upon its source for being-actual at all. The first two presuppose a thing already secured in existence, and neither is what is meant here. To sustain, made precise, is not to conserve something against its own dissolution. It is to constitute: to be that upon which a thing’s being-actual wholly consists, such that the thing is not first there and then maintained, but is, in the same undivided respect, given-to-be and dependent. What is constituted is the creature’s being-actual — its esse — not its essence, its identity, its content, or its own secondary causality, all of which remain genuinely the creature’s: God constitutes its being-actual, without supplying what it is or acting in its place. The creature has no esse from itself; that, and no more, is the claim. Remove the ground and nothing decays, because nothing was standing on its own to begin with to start falling. There is not even an instant of ceasing — the first essay saw this and stated it better than it knew: not a falling, not a delay, not a transition; it simply is not. Nothing here removes the creature’s own causal agency; secondary causality remains genuinely creaturely at the crossing.

Here the tradition should be received with care, because it reached this before the topology did and reached it more soberly. Aquinas treats the conservation of things in being not as a second act performed after creation — not a maintenance grant renewed each instant — but as the very continuation of the one act by which God gives existence, an act, he is careful to say, without motion and without time. The topology adds nothing to that but a vocabulary, and should say so plainly. What Aquinas calls conservation being one act with creation, not a sequel to it, is exactly what the corrected adverb of the previous section required: no succession on the Ground’s side, because there is no second act, and no nth act, but one. And where the Thomistic language can sound as though something is being kept from lapse — were God to withdraw His action, all would fall to nothing — the point is not that creatures strain against a decay God perpetually counters, but that their non-being, were the dependence to cease, would be immediate and total precisely because their being was never their own to slow the loss of. The “would fall to nothing” is the logical face of non-autonomy, not a rate of decay. I do not presume to improve on the doctrine; I mean only to show that the topology, followed honestly, arrives where it already stood, and that the arrival disciplines the metaphor the corpus had been using in its place.


VII. What the Word Names From Inside

None of this earns its place as metaphysics until it is shown to be the description of something lived, because a concept in this topology is required to illuminate the human condition from inside it, not to hover above it. So set the apparatus down and ask what sustaining names before it is a doctrine.

It names this: I do not author my own continuance. I did not make the moment I am in, and I am not making the next one. It arrives. I find myself already within it, given to be, without having produced the being by which I am there to notice. This is not an inference; it is the most constant datum there is, and the most overlooked, because it never varies. Every breath is received before it is drawn. The self that would have to sustain itself is not underneath its own existence, holding it up; it is on top of it, carried. The Monad That Receives: On Leibniz, Indivisibility, and the Possibility of Relation found that to receive is not to acquire a second thing beside a first but an alteration wholly within the one act of an indivisible subject — and the receiving of one’s own next actuality is the limiting case: what is received is not a content added to a self, but the self’s very being-there to receive anything at all.

This is what the abstraction is for. “Derivative actuality depends on Non-Derivative Being” becomes the muralist’s suspicion made flesh only when it is read as the transcription of the moment’s arrival — the un-self-caused givenness of a further Now I did not manufacture. Whoever has felt existence as a thing handed to him rather than a thing he holds has already met, without the vocabulary, everything the vocabulary is trying to say. The concept does not replace the experience. It is the experience, stated so that its structure can be seen.


VIII. The Grammar of the Ground

Two things remain to be placed: the Ground relative to the figure, and the claim relative to what it is a claim about. The figure first. The standing temptation of any center-and-figure image is to promote God to the center point — to make the Non-Derivative the crossing, the still node the loops turn around. The corpus posted the guard early: God holds the figure because He is not inside it at all, not even as its center; the Now, though it is the created point of contact, is not God. This essay hardens the guard into a consequence of the verb. If sustaining is constitution and not an operation performed at a location, then the Ground is not at any point of the figure, not even the privileged one, because there is no point at which the constituting happens as an event among the figure’s events. The Ground is not the crossing. It is why there is a crossing to be.

And because the figure is now per-continuant and uncountably many, this is the only picture that will serve: not one Ground occupying one central node, but one Ground that is the reason each of the uncountable crossings is, present to each — as the tradition said of immensity — entire and undivided, according to that crossing’s own mode, without being spread across them as one medium among many (What Is the Now?). The three levels the corpus distinguished hold this exactly: Presence, God’s mode of being; the Now, the created condition of actualization; the present, the creature’s actuality. Sustaining runs down the levels as dependence, not as an act crossing a distance — the present is because of the Now, the Now is grounded in Presence, and none of the three is God descending into the figure to do something at a spot within it. The Now is not a cause set between God and the creature, a third thing through which being is relayed; it is the condition — the form — under which the creature’s received actuality is temporally instantiated. The relation has two terms, not three.

The claim second, and with the method note this corpus keeps. What is offered here is a philosophical proposition about the meaning of ontological dependence, not a doctrinal pronouncement. It is a proposition about conservation alone — the dependence of creatures upon God for their being — and does not attempt to derive from that dependence a theory of providence, or of the determination of future free acts; the open horizon What Is the Future? defended therefore stands untouched. Scripture speaks of a holding-together — in him all things hold together, upholding all things by the word of his power, in him we live and move and have our being — and this essay does not exegete those texts so much as offer the philosophy a reader might carry back to them: a content for the word uphold that does not make God a cosmic strut. The philosophical Ground named here is no rival to, and no narrowing of, the God the Church confesses as Creator: creation and its conservation are the inseparable work of the one Triune God — Father, Son, and Spirit — in whom, as the epigraph has it, all things hold together. Whether the account is adequate to what those texts intend is a further and humbler question than the one settled here. And the lineage is a resonance, not a credential. That the ground of a being might be that which is not a categorical item alongside it — present as the condition of the finite rather than as a member of it — is a thought de Lubac and Rahner pursued far past where this essay stands, and I invoke them as company on the road, not as authorities I have earned the right to enlist. The topology’s claim rests on its own structural coherence, as the first essay said of all its witnesses, and not on their names.


IX. A Formal Statement

Two sentences, offered as the definitions this essay exists to fix.

The Lemniscate is the per-continuant topology of temporal actualization: a zero-thickness crossing at which inheritance, condensed entire, meets an open horizon of reception, flanked by the two epistemic loops of memory and anticipation, ordered by the asymmetric condensation of successive crossings and not by any motion within it, and whose every actualization is ontologically dependent upon the Non-Derivative, which is no element of the figure.

To sustain is to constitute: to be that upon which a derivative actuality radically and non-successively depends for its being-actual, such that the actuality is not first and then maintained but is, in one undivided respect, given-to-be — the ground giving, without succession and without motion; the creature receiving its actuality, continuously and in series; and no gap between them across which anything could be held, because the derivative had nothing of its own to hold.


X. Coda

The first essay asked whether time needs us or we need time, and answered that neither is primary and both are held. It named the holder and left the holding unexplained, because the question that day was who, not how. The how has now been answered in the only way the topology permits: not by finding the mechanism, but by dissolving the demand for one. There is no thought by which God thinks the Now, no hand by which He holds it, no attention by which He keeps it in view, because there is no gap between the Now and its ground for any of these to bridge. The Now is not sustained the way a weight is carried or a thought is entertained. It is constituted, if an image may be allowed, the way a shadow is cast — not held up by the light against a tendency to fall, but simply not there, at all, in the light’s absence, and not because the light did anything further than be the light.

We do not author our continuance. That is the whole of it, felt from inside; and stated from outside, it is that derivative actuality receives its being, without remainder and without interval, from the Non-Derivative that does not receive its own. The figure is traced once per creature, forward, singular. Its crossing is dimensionless. Its ground is not a point upon it. And the sustaining that the corpus has named since its beginning is not, and never was, an act performed upon the Now. It is the standing of the whole figure in the One who is not inside it —

I AM WHO I AM.


References

  • The Holy Bible. Revised Standard Version, Second Catholic Edition. Ignatius Press, 2006. (Colossians 1:17; Hebrews 1:3; Acts 17:28; Exodus 3:14.)
  • Aquinas, Thomas. Summa Theologiae. Translated by Fathers of the English Dominican Province. Christian Classics, 1981. (I, q. 8, on immensity; I, q. 104, on the conservation of things in being.)
  • Augustine of Hippo. Confessions. Translated by Henry Chadwick. Oxford University Press, 1991. (Book XI.)
  • de Lubac, Henri. The Mystery of the Supernatural. Translated by Rosemary Sheed. Herder & Herder, 1998.
  • Rahner, Karl. Foundations of Christian Faith. Translated by William V. Dych. Crossroad, 1978.
  • Gaitan, Oscar. Does Time Need Me, or Do I Need Time? The Ontology of the Now, the Invariance of Presence, and the Ground of Being. 2026.
  • Gaitan, Oscar. The Lemniscate of Time: A Topology of Memory, Possibility, and Grace. 2026.
  • Gaitan, Oscar. The Weight of the Present: On Condensation, Grace, and the Continuity of Becoming. 2026.
  • Gaitan, Oscar. The Monad That Receives: On Leibniz, Indivisibility, and the Possibility of Relation. 2026.
  • Gaitan, Oscar. When Is the Present? On the Invariant Now and Temporal Actuality. 2026.
  • Gaitan, Oscar. What Is the Past? On Closed Confluence, Condensation, and the Being of What Has Been. 2026.
  • Gaitan, Oscar. What Is the Future? On the Asymptotic Horizon, Open Reception, and Eternal Presence. 2026.
  • Gaitan, Oscar. What Is the Now? On Simultaneity, the Single Point, and the Closing of the Figure. 2026.
  • Gaitan, Oscar. The Now’s Not-Yet: On the Future, the Past, and the Debts the Topology Owes. 2026.


Further Reading

Book

  • The Lemniscate of Time: A Geometric Meditation on Eternity and Temporal Succession
    ISBN: 9798248842360
    Zenodo: DOI: 10.5281/zenodo.18684516


Selected Essays