What Is Home

You go back. The turn off the highway is the same turn. The screen door still makes the sound. Somebody has painted the kitchen a colour you would not have chosen and otherwise it is exactly, almost aggressively, the same — and you stand in the middle of it for about ninety seconds waiting for something that does not arrive, and then you make conversation about the drive.

Nearly everyone has run this experiment. The standard explanations are true and unmechanical: you have changed, you cannot go back, it was never really about the house. Each of those names the failure without saying what failed. I think there is a structural answer in the foundation I work from, and it is stranger than the sentimental one, and it starts by conceding more than you would expect.

One thing before any of it, because the rest of this is machinery and machinery is easy to misread as verdict: nothing in what follows says the feeling is a mistake. The claim I am going to make is narrow and it is about where a mechanism is pointed, not about whether a person is right to have one.

What the ordinary picture commits you to

Take the usual account seriously and count what it requires. Four commitments, and they hold each other up.

First, that home is a location — a set of coordinates, a house, a town, a country.

Second, that the location persists well enough to be re-occupied. Not unchanged, but continuous enough that arriving there counts as arriving there.

Third, that arriving is the operation that produces the feeling. Get your body to the coordinates and the state follows.

Fourth, that if the feeling does not arrive, somebody is at fault. Either you went cold, or the place went downhill, or the people in it did.

The visit breaks the third one flatly, in front of witnesses, nearly every time. And the fourth is a bill sent to the wrong address — it converts a structural failure into a character assessment, and it delivers that assessment to a person who has just driven four hours to be disappointed.

Where the foundation actually puts home

Three moves, and the third is the one I did not see coming.

First, the house is present and the home is not a place. My axiom is that the past is immutable, and R2 follows: records update expectation forward and never re-open. R9 follows too — the Past is inaccessible, and the abundance of present records makes it appear otherwise. A childhood house is the densest pile of present records most people will ever stand inside. The surfaces are dense with marks. That is precisely the condition R9 describes, and precisely why the misaddressing is strongest there: the sheer availability of the records does the work that access would do, if access were on offer. A memory is not the event. It is present artifact-reading, performed here, on marks that are here.

Second, P4 — the Reality Equation. R = A / E, where E comprises subconscious prediction, which is real, and ideas, which are imaginary; E is complex, so R is complex. This piece works the real component. Consider what actually happened over the years you lived somewhere. Your predictor was trained, continuously, without your consent and mostly without your attention, on one specific set of conditions. The give in the fourth stair. The particular quality of the silence at four in the afternoon. Which door meant which person was home. Given long enough, prediction catches up with actual: the magnitude of R settles near one, and |S|, where S = ln|R|, runs small.

That is the whole of what the word comfort names. Not safety, not love, not familiarity-as-a-feeling — a trained denominator.

I want to be exact about which smallness this is, because my own foundation contains a different one and confusing them would be a real error. R5 holds that temperature, frequency and every other time-evolution descriptor is undefined at the Past itself, at the boundary. This is not that. There is a host here, standing in a kitchen, alive and varying, so R is defined and S is defined. Home is a live, low-surprise region of a life, not a boundary where the scale runs out.

The concession: return is not the problem

Here is the move I did not expect the foundation to make.

Most philosophies that take the past seriously end by telling you that return is impossible and you had better make your peace. Mine says the opposite, and not as a comfort — as a theorem with two conditions, both of which my primitives supply.

Poincaré recurrence: a measure-preserving transformation on a finite-measure space returns almost every point arbitrarily close to its initial state, and does so infinitely often. The quantum form is Bocchieri and Loinger, Physical Review 107, 337 (1957): a system whose energy spectrum is discrete — which is what confinement to a finite volume buys you — returns arbitrarily close to its initial state vector. P1 supplies the confinement: one settled totality, complete, bounded by construction. The discreteness follows from the confinement, and the proof runs through the almost-periodicity of the state vector.

So variation that persists must return, and return is rotation. As of 5 August that is doctrine in my foundation rather than a figure of speech, and the vibrating string that used to carry the argument has been retired in favour of it.

The homesick are not mistaken about return. Return holds, it is guaranteed, and it happens infinitely often — on a timescale that is not yours. The misaddressing is somewhere else entirely, and it has two parts.

The first part is easy. What recurs is the state, not the record. By R2 the records never re-open, so there is no reading of recurrence on which you get the actual afternoon back. The circumference comes round; the record does not unlock. Recurrence is a claim about where a system finds itself, not a claim about what remains editable.

The second part is the one worth the essay. Read the theorem’s own wording again: arbitrarily close. That is not a cautious mathematician hedging. It is the content of the result, and here it does something specific.

Suppose a return were exact. Then everything in the state has come back — including whatever in the state does the recognising. Nothing whatever is left over to hold the two occasions apart. There is no again; there is only the state, running. That reductio stands on its own and it is the whole of the argument. S3 names the same shape on the compass side — the imaginary axis measures distinguishability, whether anything stands out at all, and a symmetry is not significant — but I should be honest that this is an analogy of terms rather than a derivation. A symmetry of a trajectory and the Symmetry pole of the imaginary axis are two words spelled the same, and I am not going to lean on the coincidence.

What that leaves is short and I think it is the finding: the residual is the recogniser. The only thing capable of telling you that this is a return is the part that did not come back.

And the same residual, in the same breath, is what makes it not home. There is one quantity here doing two jobs, and the jobs point opposite ways. The ninety seconds in the kitchen is not the feeling failing to arrive. It is the instrument reading. Remove the residual and you would be there, and there would be nobody present to whom it was a return.

Figure 01

Surprise at one address, over a life — and where the visit actually lands

• Week onehigh
• Month six—
• Year two—
• Year ninehome
• The visit, year thirtyresidual

• Predictor still training
• Predictor caught up — the low-|S| region
• The return, with the residual that reads it

What the last bar is not: it is not a partial homecoming, and it is not decay of the ninth-year state. It is a new reading taken by an instrument that did not exist in year nine, on conditions the predictor was never trained on.

Homesickness, and the address it is handed

My foundation splits any backward-facing feeling into two separable jobs that feel like one from inside, and nostalgia is named explicitly on that list.

The evaluation reads a present artifact against its exemplar. It is a fidelity assessment, it can succeed, and it returns something usable: what those conditions actually were, what you took from them, which of them you would want in a life now. The reaching is an attempted relation with the Past itself. By R9 it cannot succeed — not partially, not with more effort. The evaluation has a completion condition. The reaching has none, because what would complete it is not the shape the reaching is aimed at.

So far this is standard, and I have written it before about regret. Home does something the other cases do not, and it is worth naming precisely because it is worse.

In regret there is no available move, so the reaching has nothing to mistake for progress; it simply grinds. In a dischargeable debt there is a move, and it genuinely closes the running expectation, so the reaching receives a completion signal that belongs to a different job. Home is the third case and the cruellest of the three: home has an address.

You can buy the ticket. There is a physical, purchasable, four-hour operation that looks exactly like the operation that would complete the reaching — same nouns, same direction, same word. Homesickness is the only version of this feeling that comes with travel arrangements. And the trip is the one experiment that fails the same way for very nearly everybody — reported widely, and without a study I can point you to. Which is why the failure is so heavily documented in songs and so poorly explained in them. You can’t go home again is an accurate finding stated as a mood, with no mechanism attached.

The mechanism is that the ticket is addressed to a place in the Eternal Now, and the reaching is aimed at a node. Those are not near each other. They are not the same kind of thing, and no quantity of driving closes the difference between kinds.

Figure 02

One residual, two jobs — the reason the visit feels like a failure and is not one

• Job one · what it does for you It is the only thing that can register a return An exact recurrence has nothing left over — including nothing left over to do the recognising. The difference between then and now is what makes “again” available as a category at all. without it · no return is noticed by anyone

↓  one quantity  ↓

• Job two · what it does to you It is the whole of what “it isn’t the same” refers to The same leftover, read the other way. The predictor was trained on conditions that are no longer the conditions, so the quotient comes back wrong, and the wrongness is felt as absence rather than as measurement. it is the reading · not the failure

Why there is no version where you win: reduce the residual and you reduce the recognition with it, because they are not two quantities. The state in which the return is perfect is the state in which nobody notices there was one.

One thing this immediately removes, and it is worth removing early. People are routinely ashamed of this feeling in both directions — ashamed of not feeling enough on the visit, and ashamed of feeling too much afterward. Both versions assume the failure is moral. If the mechanism is structural, there was never a door there to fail to open, and the second layer can go.

If home is a denominator, it is built rather than found

This is the practical consequence and the only genuinely good news in the piece.

If home is a trained predictor rather than a location, then it is made, and the making has a known input. E is trained by actuals — by the difference between what was predicted and what happened. So a home is built by staying somewhere, attending to it, and letting the predictor catch up. That is time. It cannot be hurried, it does not require the place to be lovely, and whether you like it at first makes no difference to it.

It also fits a thing people report constantly and never quite believe: the second year in a new city is worse than anyone warns you, and the fifth is better than anyone promised. That is reported, widely, and I have no study to hand you. My reading of it — that the predictor is mid-training in year two, and that mid-training is where the quotient is least settled — is mine and is not a numbered result.

Now the cost, and I will state it as flatly as I can.

You will know it is home when you have stopped noticing it. Noticing is surprise. There is no state in which you are at home and also finding it remarkable.

Anyone describing their home as remarkable is describing month six. That is not a criticism of month six — it is a lovely part of the process and it is not the thing.

There is a harder version of the same result. Home and learning look like one quantity read at opposite ends. Small |S| is home; large |S| is where anything at all gets learned. Which would mean the places where you become someone are the places you are not at home, and a life arranged entirely around comfort is a life arranged around a predictor that has stopped updating.

I do not think this licenses restlessness as a virtue, and I want to block that reading before it starts. R11 holds that the evaluative question is fidelity, not success. A person can be maximally uncomfortable and badly aimed, and moving every two years is not a spiritual practice. But the tradeoff itself is real and it is not negotiable by attitude. You cannot arrange to be both at home and learning in the same place at the same time, because those are two readings of one number.

The home that is gone

The case that stops people, and it deserves treating carefully rather than cleverly: the house was sold, the family scattered, the country you are from is not the country that exists, the people who made the conditions are dead.

The structure here is not softer and I am not going to write it as if it were.

The artifact remains and the act is gone. That is doctrine, and it is very nearly the whole of what my foundation has to say about loss. The house may be standing or demolished; either way the thing being reached for was never the building. The training was of you, by conditions that were not internal to you — and what kind of thing a condition is, my foundation does not yet say, so I am not going to say it here.

Two things follow and only one of them is welcome.

The unwelcome one. The term does not close. Building a new denominator somewhere else is a real operation and it genuinely works, and it is not a transfer. The old term is not moved into the new account. There is no operation anywhere in this system that moves a term from one denominator to another, and I will not imply that there is, because that implication is precisely what leaves people feeling they have failed at a task nobody ever offered them.

The welcome one. The building is available anyway. It is available more than once, it does not require permission from what was lost, and it does not ask you to have finished anything first. Addition is the only move anyone has ever had, and it is a real move.

The move I am refusing

There is a line available at exactly this point in nearly every essay about home, and I am going to refuse it in public rather than quietly decline to make it, because the refusing is most of what a foundation is for.

The line is: home is not a place, it is a feeling. Home is where the heart is. You carry it with you.

These are close enough to what I have just derived that the difference has to be said out loud. What I derived is that home is a state of a predictor — trained by long exposure to a specific set of conditions, in a specific place, mostly not chosen by you. The conditions were not internal to you, and the training was of you by them.

Take the place away and the predictor does not survive intact as a portable possession, because a predictor is only a predictor of something. “You carry it with you” quietly converts a structural claim about training into a reassurance that nothing was lost. Something was lost. The predictor is still yours; the conditions it was trained on are not available; and a predictor separated from its conditions is a decent description of the ache under discussion rather than a cure for it.

Where this is not finished

Four gaps, and I would rather name them than let a reader find them.

The first is about the theorem, and it is the one I am most worried a reader will get wrong. Recurrence guarantees return and supplies no schedule. Recurrence times for anything of human scale are astronomically long, though finite. My own foundation says, correctly, that nothing in the circle argument depends on their magnitude — and for the circle that is true. For this piece it is a limit I have to state loudly, because “return is guaranteed” will read as a promise if I let it stand alone. It is not a promise. Nothing here says you get back within a life, or within the lifetime of anything you would recognise, and letting the theorem do consoling work it cannot do would be lying by omission.

The second is an open problem in my foundation that this piece sits directly on top of. I do not know whether the evaluation/reaching split applies to forward-facing feelings — whether anxiety is the same mechanism aimed at the other node. Home supplies an unusually clean test case, because there is a well-attested version of this ache aimed at a place the person has never been: the pull toward a home not yet had, which several languages have a word for and English does not. If that turns out to be the same mechanism pointed forward, a fair amount of what I have written today needs restating. It is unsettled and I am not settling it here.

The third is a hole I keep walking into. My foundation holds that some acts, not all, generate an artifact, and it supplies no criterion for which. Home is made mostly of acts that leave nothing anyone could point at — the ten thousand ordinary evenings, none of which produced a mark. I have written throughout as though those conditions were real and their traces were thin, and I have no numbered result that licenses the distinction.

The fourth is the recognition claim itself, which is the piece’s centre and is mine rather than derived. Here it is with its failure condition attached, because a claim without one is an advertisement.

Already true

The recurrence result is doctrine in my foundation as of v1.4, grounded in P1 and unitary evolution. S3 and the significance reading of the imaginary axis are doctrine. R9 and R2 are doctrine. None of that is at issue.

What has to hold

That recognition of a return requires a residual — something not returned, doing the distinguishing — and that this residual is identical to what is experienced as the place having changed. One quantity, two readings, not two quantities that happen to co-vary.

Where I am probably wrong

If someone produces a clean case of recognised return with no residual — a person who arrives, knows with certainty that it is a return, and cannot name one thing that is different — the claim is finished and Figure 02 goes with it. I would also take a serious hit from a good argument that recognition runs on match rather than on difference, since the whole construction assumes the leftover is what does the work. I have not found either. I have also not looked as hard as an opponent would.

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What this costs

• You cannot be at home and know it at the same time. The knowing is done by the part that is not home. This is not a paradox to be resolved; it is one quantity being read twice.
• Home is the region of your life where you are learning nothing. That is not an insult to home. It is what a caught-up predictor is, and it is the thing you were asking for.
• The one move that is for sale is the one that cannot work. The other versions of this feeling offer you nothing, which is at least not a trap.
• The guaranteed return is not scheduled inside your life. The theorem is real and its timescale is not yours. I would rather say that than let the mathematics sound kind.
• Nothing carries. The predictor is yours; the conditions that trained it are not, and no amount of interior work re-supplies them.

On an ordinary Tuesday

These five are practice, not doctrine. Cite them as practice, revise them on evidence, and do not read any of them as a prescription.

1. Stop grading the visit. Go, read the artifacts, take the update, and do not stand in the kitchen waiting for a confirmation that has no sender. That wait is short and it does not get shorter by being extended — but nothing here tells you when you are done with the feeling itself.
2. Ask which job is running. If you want the information — what those conditions were, what you would want again — the trip works and works well. If what you want is the afternoon, there is no route, and the ticket is not one in disguise.
3. If you have moved, count in years. You are training a predictor on actuals, and there is no faster input than elapsed ordinary time. Year two is the hard one and it is not a verdict on the place.
4. Do not arrange your whole life for small |S|. Comfort is real and it is a reading of a predictor that has caught up. Some part of your life should be somewhere it has not, and you should expect that part to be uncomfortable rather than treat the discomfort as a sign of error.
5. Name the residual out loud. Say the specific thing that did not come back — the person, the hour, the smell, the version of yourself who lived there. It is the instrument. Naming it is the difference between reading a measurement and being hit by one.

And one line to keep, if the rest of it goes:

Home is not a place you go back to. It is a predictor that once caught up with a set of conditions — and the small unbearable difference you feel in the doorway is not the return failing. It is the only reason you know you returned.