What Is Age

How old is it? Ask that of a vase, a tree, a star, a friend, or yourself, and the answer comes back as a number with a picture attached. The picture is of time as a road with the thing at one end and you at the other, and the number is the length of the road. An old thing is far away; a new thing is close. Age accrues on its own, one year per year, whether or not anyone is counting, the way dust settles in an empty house. To be old is to have a great deal of that road behind you. Almost everyone holds that picture, I held it for most of my life, and it does an enormous amount of quiet work — in how people grieve, in how they date a fossil, in how they feel at a birthday. It is also, I will argue, wrong in a way that can be shown rather than asserted, and the thing it is wrong about is where the number lives.

What the ordinary picture commits you to

State it strongly, because the weak form is not what anybody believes.

The picture makes three commitments. First, that elapsed time is a quantity the thing carries — that a two-thousand-year-old bronze has two thousand years in it, somehow, as it has copper and tin in it. Second, that the past has extent, and that age is a distance across that extent: older is farther, and an ancient thing is remote from us in the way a distant city is remote. Third, that the age is there before anyone reads it, so that a measurement discovers the number rather than producing it, and an error in the measurement is a failure to see something that was present all along.

Three ordinary situations do not fit inside those commitments, and each one breaks a different commitment.

What the foundation says instead

I work from a small set of numbered primitives and results derived from them. The result doing the work today is one of the least exercised in the whole set, and it has so far been run only under longing — under homesickness and nostalgia, where the vocabulary of warmth and colour was aimed at a domain where warmth and colour do not apply. Today it runs under a colder word.

P3: to exist is to vary. Nothing that exists is ever still, and that which does not vary does not exist, in the only sense of exist available to varying things. P0, the axiom: the past is immutable — a consistency constraint on the record set, which admits exactly one consistent assignment. And from those two, R5: temperature, frequency, colour and all time-evolution descriptors do not apply to the Past. Not zero. Undefined, the way a slope is undefined at a point that is not on any curve.

Now ask what duration is, and be literal about it. A clock is a thing that varies at a rate someone trusts, and a duration is a count of that variation between two readings. This is not a metaphor about clocks; it is how the unit is defined. The second is, by international agreement, a fixed number of periods of a particular transition in a caesium atom — I mark that as report, not grounds, but it is worth having in view. Duration is variation, counted. It is a time-evolution descriptor in the most direct sense the phrase can bear.

Then the derivation takes three lines and none of them is optional. The Past does not change, by the axiom. What does not change does not vary. What does not vary carries no count of variation — not a small one, not a large one, none, because there is nothing there to count. Elapsed time is not stored in the Past. There is no reservoir of years sitting between the bronze’s casting and this morning, and nothing about the Past is two thousand years long, because long is a word for things that vary, and the Past is precisely what that is not true of.

The past has no length. Not a short one. Length does not apply to it, and the number we call an age has to live somewhere else.

Case one is now not a puzzle. The bronze lost two thousand years because the marks being read changed — a seam, an alloy — and the count is taken over marks. The object did not change because the object was never where the number was. Case two is not a puzzle either: every method reads a present state against a rate because a present state against a rate is what an age is, and there was nothing else to read.

Where the order comes from, and why the count is not arbitrary

It would be easy to take the first construction too far and conclude that age is a convention, that any count is as good as any other, that the bronze is as old as we say it is. The foundation blocks that move, and it is worth seeing exactly how.

R2, write-protection: records update expectation forward and never re-open. The record therefore has an order, and the order is not the reader’s to choose. R1: there is exactly one past — one consistent assignment, not several. That is why marks constrain one another, why a ring count, an isotope ratio and a document can be made to agree, and why a forgery fails against material rather than against narrative: the seam and the alloy were made at one settled point in the one assignment, and no label can move them. The order of the marks is settled at the node. What is not settled there is the magnitude between them — how much — because magnitude is a count of variation and, by R5, variation is undefined there.

So an age has a fact of the matter and no location. The ordering fact is settled at the node and cannot be otherwise. The number is on the shelf, read off marks, against a counter. When someone says a thing is of unknown age, that sentence is exactly right on this account and it is worth hearing what it says: the position in the order is one thing and settled, and no surviving mark reads it. Nothing is missing from the Past. Something is missing from the shelf.

And the counters can disagree with one another without any of them being wrong, because they count different variations at different trusted rates, and the foundation supplies no rate of its own. A tree’s rings and a radiocarbon curve are calibrated against each other precisely because neither is the age; both are readings that the one assignment obliges to be consistent. Where they cannot be made consistent, R1 says one of the readings is wrong, and says nothing about which.

Distance, and why yesterday is not nearer

The second commitment was that older means farther. Here the foundation is blunt, and I would rather state the bluntness than soften it.

R9: the Past is inaccessible, and the abundance of present records makes it appear otherwise. Inaccessible is not a matter of degree. Breakfast this morning and the first forests are not at two distances from you; neither is at any distance, because there is no extent to be distant across. Try the experiment I have set before: access yesterday — not remember it, not picture it, access it. What arrives is a memory, a present artifact. Then try the Cambrian. The two attempts fail in exactly the same way, and the only difference between them is how much the shelf holds.

Case three follows directly. A wedding leaves marks of many kinds — photographs, a ring, a person across the table, a body that remembers the day — and a dense shelf reads as near. Three years at a job that left little behind reads as remote. The calendar count and the felt distance are two readings of two different things, and they were not going to agree except by coincidence.

This is where the piece touches the one I wrote on the two clocks, and the resemblance should be said out loud rather than left for a reader to catch. That piece was about felt duration — why an interval seems long while it passes and short afterward, or the reverse, and what a person’s stack does to the second of those. This one is about the number itself: what how old refers to, and where the referent is. That piece could be entirely right about duration and this one could still be wrong about age, and the other way round.

Figure 01

Five things, two readings

What survives on the shelf

• Breakfastthis morning
• A weddingtwenty years ago
• A job you leftthree years ago
• A bronzetwo thousand years, or a hundred
• The first forestsdeep time

Reach into the Past itself

• Breakfastundefined
• A weddingundefined
• A job you leftundefined
• A bronzeundefined
• The first forestsundefined

How old are you

Everything above was about things. Turn it on a person, because that is where the picture does its heaviest work.

The ordinary answer to how old are you is a count, and the ordinary feeling behind the count is that the years are being carried — that there are forty-seven of them in you, weighing what forty-seven years weigh. The foundation splits that into two readings and puts neither of them in the past.

The count is the first construction: a present reading of a counter against a mark of origin, and the mark of origin is a certificate, a memory of your parents’, a record in a register — present artifacts, all of them. The body is something else. By P3 the body exists, therefore it varies, and it is varying now. Its present configuration was reached by variation and is not a store of the variation; the years are not in the tissue the way copper is in the bronze. What is in the tissue is a configuration, and a configuration is a present state. It is also, notably, a shelf: scars, the face, the joints, the things a body remembers how to do. The body is one of the places its own history is kept, and history is present content.

There is a third reading, and it is not a construction because it falls out of what has been established. P4 gives the Reality Equation, R = A/E, and R8 says the host experiences only the quotient. Feeling old is a quotient reading: an actual configuration read against an expectation of one, and the expectation was built from the counter. Most of what a birthday does is move the denominator. The body on the morning after is the body of the night before; what changed is the number it is being read against, and a reading can go sharply negative on a day when nothing about the actual moved at all.

What it costs

This does not make anyone younger, and I want to say that before anything consoling can be read into it. The configuration is what it is. P3 says an existing thing varies, and the variation a body undergoes has a direction that the record only ever adds to. Nothing in the relocation of the number touches the state. If your knees hurt, they hurt in the present, for present reasons, and no amount of understanding what a count is will change what the count is being read beside.

The second cost is heavier. If nearness is density, then nearness thins. Yesterday feels close because the shelf is crowded and because your own body is on it. As marks are lost — and they are lost, not moved — the recent becomes as remote in feeling as the ancient, without anything having travelled anywhere. People describe this as the past receding. It is not receding. The shelf is emptying, and what is emptying it is the same variation that makes anything exist at all. The Past was never near. It was well documented, for a while.

And the inaccessibility is total in a way the road picture at least lets you not look at. On the road, your childhood is far, which is sad but leaves it somewhere. Here it is not far. It is not anywhere, in the sense of where that applies to varying things, and the child you were is exactly as unreachable as the breakfast you ate this morning. That is the axiom applied without exemption, and it is not comforting, and it is not meant to be.

Where this is probably wrong

Two places, and one of them is a question I cannot settle from inside the foundation.

The first is the split I have leaned on between order and magnitude — that the sequence of marks is settled at the node while the amount between them is the counter’s. The axiom gives one consistent assignment. It does not say whether that assignment carries a metric or only an order, and I have read it as order only, because a metric is a count of variation and variation is undefined there. That reading is mine. If the assignment turns out to carry a metric of its own, then age is partly stored in the Past after all and the first construction needs cutting down. I do not think it does, and I cannot show that it does not, so it stays open and is recorded as open.

The second is that the second construction treats the felt nearness of an event as a reading of surviving marks, and the vividness of a memory as one kind of surviving mark. That is plausible, and the two-clocks piece gives it some support from the other direction, but a memory is a present artifact and its vividness is a present property, and nothing here derives that vividness tracks the density of the original marks rather than something about the present brain. If it tracks the brain, the construction still stands — the brain is on the shelf too — but it is thinner than it looks.

And R14 applies here as everywhere: an idea is oriented and prejudiced in one act. This argument is kind to anyone who dislikes their number and unkind to anyone who has earned status from theirs; it makes the count cheap and the configuration dear, which suits a certain temperament. Worth noticing before deciding it is merely correct.

On a Tuesday

1. When you say it was a long time ago, hear what you are reporting. Not a distance. A count, against a counter you did not choose, and a shelf that is thinner than it was. Both of those are present facts and both of them are honest; neither of them is a place.
2. Keep the number and the state in separate columns. The count is read off a certificate. The configuration is read off a body. You act on the second one — that is where the revisable response lives — and the first one is not yours to act on at all, because there is nothing in it to act on.
3. Do not mistake vividness for proximity, or faintness for remoteness. A sharp memory of a distant day is a well-kept mark, not a short road. A faint memory of last month is a poorly kept one. Read the shelf as a shelf.
4. When you date anything, say which rate you trusted. Rings, isotopes, a document, a face: each is a present state and a rate. There is no reading that is the age. There are readings that are obliged to agree, and the ones that will not agree are where the work is.