The Immutable Past · What Is
What Is a First Time
A first time is treated as an event with more in it than the ones that follow. Nothing in the event is different. Derived from the two halves of the Arrow Theorem’s antecedent rather than from either half of what it concludes, a first time turns out to be a reading taken where expectation holds no term — which is why nothing is lost at the second time, and why no first time can be arranged.
The count the ordinary account cannot produce
2
A first time needs two unlike facts, and either one on its own gives nothing at all.
One of the two is about the world: what happened is in the record, and no present operation produces a different assignment. The other is about you: a record updates expectation forward, and the update does not re-open. Neither of them carries a direction. Together they carry one, and it is the only direction a first time has ever had.
Contents
- Three ordinary cases the usual account cannot hold
- Where it actually sits — the two unlike terms, and the removal test
- What a first time is, then — and the magnitude I cannot derive
- Nothing is lost at the second time
- Anticipation is work on the denominator
- What it costs, stated without softening
- The circumference is not the list
- On an ordinary Tuesday
Everybody keeps a short list. The first time you heard the record that rearranged a year of your life. The first time you stood on a harbour wall at four in the morning with the tide out. A first kiss, a first flight, the first house whose key was yours. The list is short, it is mostly closed, and nearly everyone believes the same thing about it — that those events held something the later ones did not.
That belief is not naive. It is the plainest reading of the evidence, and the evidence is that the second time was worse. Say it fairly: the ordinary account puts the specialness inside the event. There was more in it. Some richness was present then, and it has since drained out of the world, or out of us, and the later instances are thinner copies of a fuller thing.
It cannot survive three ordinary cases, and I would rather put them up front than build to them.
Case 01 · The first time that carried nothing
Most first times pass without a mark. The first time you drove down a particular road. The first pear. The first cup of coffee, which is generally unpleasant and which almost nobody remembers as a threshold. If firstness were a property that events carry, then every first would arrive charged, and nearly none of them do. The word picks out a position; the charge arrives separately, or does not arrive.
Case 02 · The song you heard four times before you heard it
Almost everyone has one. It played in a shop, then in somebody’s car, then behind a conversation, and then one afternoon it opened and became a fact about your life. Under the ordinary account you were present at the first time and it did not take — which is already the admission that the event was not where the thing was.
Case 03 · The fourth attempt that beat the first
Oysters. A difficult record. A city in the rain. If the first time were maximal by construction, an acquired taste would be a contradiction rather than the ordinary route into most of what people end up loving. The account has to explain not a rare anomaly but the usual way in.
Three cases, one shape. In each of them the event stayed exactly where it was and the reading moved. So a first time is not a kind of event, and its charge is not a substance. It is a position in something else, and the foundation is specific about what.
Where it actually sits
R3 is the Arrow Theorem, and the thing to notice first is that it is a conditional. Immutable numerators and forward-only denominators give time a direction and make surprise additive. This series has already spent both halves of that consequent — one piece on why pressing undo is not a subtraction, another on why a run of wins arrives in the hand as a single quantity rather than as a tally.
This piece is running at neither. It is running at the if: the two unlike things that have to hold before there is any direction to have. I want to be explicit about that, because a piece that quietly ran at the direction again would just be the undo argument in a new coat. The antecedent is a conjunction, and a first time is the plainest ordinary word I have found for what a conjunction of that shape produces.
Take the two terms separately, because their unlikeness is the whole hinge.
The first term is about the record. P0 in its precise form says the records admit exactly one consistent assignment, and that no present operation produces a different one. R2 is the same fact stated as an operating rule: marks are added and nothing is edited. There is no host in this term at all. It would hold in a world with nobody in it.
The second term is about you. R2’s other clause: a record updates expectation forward, and that update does not re-open. P4 puts expectation in the denominator of R, and R8 says the host meets only the quotient — never the actual on its own, never the expectation on its own. This term is defined only where somebody is standing. It says nothing at all about what happened.
Now remove them one at a time. That is the test a conjunction admits, and it is the one this piece runs.
Remove the record term. Suppose what happened could be unmade. Then firstness becomes a revisable assignment: unmake the earlier instance and the later one takes its place. First would be a label somebody could rearrange. The striking thing is not that this would be difficult. It is that nobody has ever been in a position to attempt it. Nobody has arranged a second first time by going back and tampering with the first, and the reason is not effort.
Remove the expectation term. Suppose the denominator could be put back the way it was. The record sits exactly where it sat, entirely undisturbed, and nothing whatever follows from it. The next instance is read against the same expectation the first was read against, and it comes out the same. Every occasion is a first occasion, and the word has nothing left to pick out.
Two unlike facts, neither with a direction inside it, and the one-way street of firstness sits in neither of them and in both.
That is what running at the antecedent means, and it generalises past this subject. The two terms are individually direction-free, so any ordinary word for a one-way phenomenon can be tested by pulling each term out in turn. If the phenomenon survives either removal, the word was about something narrower than the conjunction. If it survives neither, the word is about the conjunction itself, and a great deal of confusion about it is the confusion of looking for a single cause.
Marked construction 01 · Consequence, not a numbered result
The antecedent of the Arrow Theorem is a conjunction of two direction-free terms, so the removal of each term in turn is a usable diagnostic: a one-way phenomenon that survives either removal is not about the conjunction, and one that survives neither is.
Traceable to R3 read as a conditional, and to the two terms as the foundation already states them in P0, R2, P4 and R8. It adds a method and no claim, and nothing below rests on the method being novel. Filed as CONSEQUENCE, not offered as a new result.
Figure 01
Four worlds, and only one of them has a first time in it
- Neither term “The record is open and expectation resets.” Nothing is fixed and nothing accumulates. No order among marks, no persisting reading. No first and no last. Not even a sequence to be first in.
- Record term only “What happened is settled, and expectation resets.” Marks stand in a settled order. Every reading of them is taken fresh, against an expectation that carries nothing forward. Endless first times. The word picks out nothing, because every occasion reads as one.
- Expectation term only “Expectation runs forward, and the record is editable.” Readings accumulate, but the marks they were taken from can be unmade after the fact. Firstness is a label to be rearranged. A second first time is a clerical operation.
- Both terms “The record is settled and expectation runs forward.” The conjunction the foundation actually asserts. Neither term contributes a direction; the pair does. Exactly one first time per description, unrepeatable, and unavailable to any operation anybody has.
What a first time is, then
R8 says the host meets only the quotient. So a first time is not an event at all — it is a reading, taken when an actual arrives at a description the denominator holds no term for. Part III gives the magnitude of a mark as surprisal, how far the actual departed from the prediction, and P7 says when a description is available to be predicted under: naming makes the relationship conscious, and expectation carries terms at the descriptions under which something has been named. Before the first, there is no term at that description. The quotient comes out large because the denominator is thin there, and not because the actual is rich.
Which is the answer to all three cases at once. The pear was a first time with no charge because the description was too close to a dozen others you already held terms for — another sweet fruit, read against a denominator that was ready. The song opened on the fifth hearing because that was the first time it arrived under a description you had a term to be wrong about. The oysters got better because the fourth attempt was the first reading taken at a description fine enough to register what was there.
Now the soft place, which I would rather name than let a reader find.
Marked construction 02 · Consequence, with a gap I cannot close
The first reading at a description is not the first point on a curve of shrinking readings. It is the curve’s boundary, because the denominator holds no term there rather than a small one — and the foundation supplies no expression for the magnitude of a term’s absence, so the claim that the first reading is the largest available at that description is my position and not a derivation.
P4 defines R wherever a host stands and puts its magnitude above zero, so there is no question of a reading failing to happen. What the primitives carry no expression for is how thin expectation is at a description nothing has yet been read under. The foundation gives the direction; it does not give the size of the first step, and the reason I believe the first step is the largest is that first times feel large, which is exactly the kind of reason this document exists to refuse.
Open, and left open
- The question
- Can the foundation supply a magnitude for a reading taken at a description the denominator holds no term at — or is such a reading not a reading at all?
- Why it is load-bearing here
- If the magnitude is underived, then the direction of firstness stands and its steepness does not. Everything in this piece about the second time being read against a term the first installed survives; anything that implies a first time is the best available at that description is carrying weight it has not earned.
- What would close it
- Either a magnitude for a reading at an unnamed description, derived from the primitives rather than from the observation that first times feel large — or a demonstration that no reading can be performed where the denominator holds no term, in which case a first time is not a reading and this derivation is wrong at the root. Both are amendments to the foundation and neither is mine to make.
- Until then
- Read every sentence below as a claim about direction. Where a sentence sounds like a claim about size, it is the marked construction above and not a result.
Nothing is lost at the second time
This is the result the argument exists for, and it is both the relief and the cost.
The ordinary account says something was present at the first time and has since drained away. R2 forbids that description. Marks are added; the record is not edited and does not shrink. The numerator did not get smaller between the first time and the second, and nothing left the world in the interval. What happened is that something was added — a term the denominator did not hold before, installed by the first reading, and not removable, because the update runs forward and does not re-open.
So the second time is not a diminished copy of the first. It is a reading taken against a denominator the first one built. That is a different sentence, and it has different consequences.
Another piece in this series works the case where marks accumulate into a run and each successive reading of the same actual comes out smaller. That argument is about a sum taken over many marks and about what a run does to expectation as it lengthens. This one is about the single step from no term at all to one term, which is not a point on that curve — it is what makes there be a curve. The resemblance is real and worth naming rather than hoping a reader misses it; the difference is that a run is something you are inside, and a first time is the edge you crossed to get there.
An ordinary evening
You put on the record for somebody who has never heard it, and you watch their face instead of listening. They say it is good. It is good. What you were waiting for does not arrive, and on the way home you decide the record has aged, or that they have no ear, or that you have lost something.
The record is the same object it was. There are two readings in that room and one actual, and the foundation has an expression for each reading and none for the arithmetic between them.
Anticipation is work on the denominator
People try to spend first times well. Save the good bottle. Do not watch it yet. Ration the album to one side a week. Read everything about the city before going.
The last of those is the only one doing anything, and what it is doing is not saving. A description read about in advance is a description the denominator now holds a term at. When the actual arrives, the reading is taken against that term. Rationing the album changes when the reading happens and not how it comes out. If you have been holding a bottle for four years, whatever you were protecting was never in the bottle.
Two things this is not. It is not a budget, and there is no stock of anything being drawn down — the quotient is a quotient, and nobody is being charged. And nothing is in transit: the Future is a node, pure potential, and there is no reservoir up ahead from which a first time is issued. Whether a forward-facing feeling breaks into parts the way a backward-facing one does is an open question in this foundation, recorded as open, and I am not going to touch it in passing here.
Figure 02
One description, five steps, and only the last one is irreversible
- The description is nameableThe circumference is infinite and no enumeration closes it, so there is no fixed list of available descriptions to be working through. This step restates S1.
- The description gets namedNaming makes the relationship conscious and creates nothing, per P7. Until this step the thing is not something expectation could hold a term at, which is why an illegible experience is not a first time and does not read as one.
- The actual arrives and a reading is takenP4 and R8: the host meets the quotient, and the denominator holds no term at this description. The direction of what follows is settled here; the size of the reading is the marked construction above and is not reported.
- The mark enters the recordOne consistent assignment, add-only, no present operation producing a different one. P0 with R2. This step is the first of the antecedent’s two terms doing its work.
- The denominator now holds a termR2’s other clause: forward-only, and it does not re-open. This is the second term, and it is the step nobody has an operation for. Every later reading at this description is taken against it.
What it costs
Here is the part that consoles nobody, and I would rather state it flatly than dress it.
Firstness runs one way. The descriptions you have already read something under are descriptions at which no reading of yours will ever again be the first, and there is no operation, effort, discipline, substance or interval that recovers one. The count only moves in one direction. That is not a shortage anybody imposed and not a rationing scheme anybody administers; it is what two unlike facts amount to when they happen to point the same way.
Two things are not part of that, and both need saying in plain words.
The first is any suggestion of accounts being squared. Nothing here says a first time is owed to anybody, that one already taken is repaid somewhere else, or that a person who has had fewer of them is due more. There is no such arithmetic in this argument and I am not importing one to soften the ending.
The second is the layer of self-reproach that usually sits on top of this — that you should have been more present, that you wasted it, that a better-attending person would have got more out of it. That layer needs the quotient to have been yours to set, and it was not. Expectation is not a dial. What P5 makes revisable is the response to a readable condition, and R13 puts responsibility with the host for the marks it makes — which is a real and demanding thing, and is not the same as control over how a reading comes out. There was never an operation to fail to perform, so there is nothing there to have failed at.
The circumference is not the list
There is one thing on the other side of the ledger, and it is structural rather than consoling.
What is finite here is the naming, not the circle. S1 is explicit that the circumference is infinite and that no enumeration closes it, while the descriptions actually named at any moment are finite. So the supply of first times available to a person is bounded by their list of descriptions — and a list is the one object in this whole argument that can be added to.
I want to be careful not to turn that into a technique, because it is not one. Another piece in this series makes the point that most of what has not been named is not readable and generates nothing, and that what a person can actually buy is legibility rather than interest. A new description is not a first time. It is the precondition for one, and most new descriptions produce nothing at all. That is the honest expected return.
And I have no evidence about why people report fewer of these later in life, and I am not going to invent any. What the foundation gives is narrower and better: the bound is on the naming and not on the circumference, and the naming is the only part of this within anybody’s reach.
Figure 03
Three moves people make, and which term each one reaches
- Acts on the naming, which is the movable part
- Acts on the denominator, before the actual arrives
- Acts on when the reading happens, and on nothing else
If what you want back is a particular one
Some of the first times on a person’s list are attached to somebody who is gone, or to a body that worked differently, or to a year nobody can visit. Nothing above is addressed to that, and none of it is an argument that the wanting is a mistake. The argument here is about why the direction exists. It is not a claim that the feeling is invalid, and understanding a mechanism is not what stops it running.
There is no schedule for this and no reading of it makes the thing smaller. If what you are carrying is looping rather than aching — if it runs every day on the same track and does not move — then a metaphysics is the wrong tool and I will not offer it as though it were the right one. That is work for a person, not a page.
On an ordinary Tuesday
Five things fall out of this that do not need the marked constructions to be right.
- Stop saving them. Holding something back does not preserve a first time, because there is nothing there to preserve; the only thing rationing changes is when the reading happens. Open the bottle, watch the film, play the record. The waiting was not doing the work you thought it was doing.
- Know which thing you are doing when you read up in advance. A trailer, a review, a friend’s full account — each of them installs a term at the description before the actual gets there. This is not an argument for avoiding all of it. Sometimes the term is exactly what makes a thing legible enough to be read at all, which is the oysters case. It is an argument for knowing which of the two you are doing.
- Do not grade a second time against a first. They were read against two different denominators, so the comparison is not between two events at all. When somebody says the sequel was worse, that sentence has two candidate meanings and almost nobody says which one they mean.
- A first time cannot be handed over. Taking somebody to the place that opened for you puts them in front of the same actual carrying their own expectation. You can give the actual. The reading is not transferable, and the flatness when it lands flat is not their failure or yours — it is a comparison the foundation has no expression for, and I am not going to pretend otherwise.
- Name one thing this month you have never had a description for. Not to manufacture a first time, which is not on offer, but because the bound in this whole argument is on the naming and not on the circle. Most attempts will produce nothing. That is the honest rate, and it is still the only movable part.
Nothing was taken from you at the second time. A term was added, by a reading that happened once, and the direction that follows from it is the only direction anybody has ever had.