What Is a Secret
You were taught that a secret is a hidden thing — a fact held out of sight, waiting to be found. The foundation I work from says the record carries no uncertainty at all, so there is nothing in it for a secret to be. What a secret actually is, is a divergence you are maintaining between two predictors — which is why the damage scales with how long it ran and not with what it was about.
Everyone knows what a secret is. There is a fact. You have it. Someone else does not have it, and you are the reason. Keep it and it stays where it is; let it out and it goes where it was not. The vocabulary is entirely spatial. We say a secret is kept, that it comes out, that it is buried, held, let slip. Every one of those verbs treats the secret as an object with a location.
That picture is not stupid. It is how confidentiality agreements are written and how vaults are built, and it gets the important practical thing right: that you are doing something, and that the something has a cost. Hold on to the cost. It comes back at the end and it is not what you think it is.
But notice what the picture commits you to. A secret, on this account, is an object with two properties — it is present in one place and absent from another — and concealment is the relation between those two places. Everything else, the weight and the risk and the exposure, is downstream of a location.
Two ordinary cases the object model cannot hold
Secrets that everybody already knows. The affair the whole office has worked out. The diagnosis the family does not discuss, of which every member of the family is aware. The plan to sell, understood by six people who have each independently decided to say nothing. Nothing is concealed here. The information is distributed. And the secret is entirely operative — it shapes what gets said at dinner and what does not, it produces exactly the familiar weight, and it detonates on precisely the day someone says it out loud. Under an object model, a secret that everyone possesses is not an available event.
Unknowns that are not secrets. The number of hairs on your head at this moment. Nobody has that fact. It is not concealed, not withheld, and not a secret — it is simply not a live question for anyone. The object model cannot separate the two cases, because in both of them information is absent from a mind.
So the property that makes something a secret is not where the information sits. Something else is doing the work, and the ordinary picture has been pointing at the wrong term the whole time.
What the foundation says instead
Start with P1. The Past contains one settled totality — actuals only, no unrealized possibilities, because none were left unrealized. R4 follows from P1 alone: the Shannon entropy of the Past is zero. One settled outcome means all of the probability mass sits on it.
The word has three careers and only one of them is in play. This is Shannon entropy — a measure over a distribution of outcomes, in the sense Claude Shannon gave it in 1948. It is not a claim about heat, disorder, or Boltzmann’s constant, and none of those may be smuggled in behind it.
The foundation is explicit on this point, and the restriction is doing real work below: the argument needs a statement about a distribution, and would be false as a statement about anything thermodynamic.
Take R4 seriously for one sentence and the ordinary picture loses its footing. If the record carries no uncertainty, there is nothing in the record for a secret to be. Whatever happened, happened, once, completely, and it is not partially specified for anybody. A secret is not a gap in the world. The world does not have gaps of that kind.
Then where does it live? P4 answers: R = A / E. Reality as anyone experiences it is a quotient — the actual over expectation, where E comprises subconscious prediction and ideas. Two people standing in front of the same settled record can hold wildly different R, and the only place that difference can live is the denominator.
A secret makes no difference to anyone’s A. It makes its entire difference in someone’s E.
R9 explains why this is so hard to see. The Past is inaccessible, and the sheer abundance of present records makes it appear otherwise. We are surrounded by documents, photographs, receipts and testimony, and the abundance encourages us to picture the record as a container with contents that can be shown or withheld. It is not a container. The records are present artifacts; the divergence is in the models being run against them.
- The object model What a secret isInformation present in one mind and absent from another. What keeping requiresPreventing movement. A boundary held. Cannot holdThe secret everyone knows, and the unknown that is nobody’s secret.
- The denominator model What a secret isA maintained divergence between two predictors over one settled record. What keeping requiresOngoing work. A model does not stay wrong by itself. Cannot holdNothing yet identified — which is a claim, not a proof.
The definition, and the three clauses that carry it
A secret is a maintained divergence between two predictors over the same settled record. Each clause is load-bearing.
Divergence between predictors — not a location of information. What differs between the person who knows and the person who does not is what each of them will expect next.
Over the same settled record — both parties predict from an identical actual, by P1. Neither of them has a different past. Only the models differ.
Maintained — and this is the clause the object model cannot produce at all. Nothing is being stored. A predictor is a running thing, and the divergence is a condition sustained by what you go on saying and not saying. A buried box asks nothing of you. A wrong model in someone else’s head has to be fed.
What this settles immediately
Privacy is not secrecy, and there is now a test. Not telling someone something becomes a secret only when their E is actually running predictions the withheld fact would correct. If their model is not loaded with it, the thing is not a secret; it is merely unshared. The hairs on your head correct nobody’s forecast. “I am leaving in March,” withheld from the person building next quarter’s plan, corrects a great deal of theirs.
Notice what the test is not. It is not importance, and it is not intimacy. Plenty of enormous facts about you are nobody’s secret, and plenty of small ones are, and the sorting is done entirely by whose forecast is load-bearing on them.
The secret everyone knows stops being paradoxical. Six people can each hold the fact privately and still, in the room together, run a shared model the fact is absent from. The maintained divergence is between the private models and the operating one. Nothing has to be concealed for a divergence to be maintained — which is the whole reason that case was unavailable to the object model and is unremarkable here.
- Unshared their E is not loaded · no divergence · no maintenance A fact you have not mentioned, which nobody is predicting with. Costs nothing to hold because nothing is being held.
- Secret their E is loaded and wrong · divergence maintained · error accruing The same fact, once someone begins forecasting on a model it would correct. The state is not a property of the fact; it is a property of what they are now doing with the model.
- Disclosed E corrected forward · accrued error paid at once · record unedited The divergence ends, the correction arrives in a single instalment, and the interval that already ran stays in the record exactly as it was.
Why the damage scales with duration
This is the part the ordinary picture cannot reach, and it falls out of a numbered result without much help.
R3, the Arrow Theorem: immutable numerators and forward-only denominators give time a direction, and surprise is additive. Surprise is S = ln|R|, signed. It sums along a path. It does not average out and it does not quietly decay.
Now run it. Every day the other party plans, decides, invests, defends you and forgives you using an E that you know to be wrong, they accrue error against the actual. Additivity means the error accumulates rather than washing out. When the secret surfaces, the correction is not sized to the content of the fact. It is sized to how much prediction got done on the wrong model.
Which is exactly the thing everybody has observed and no ordinary account of secrecy I know of explains. Small secrets kept for thirty years detonate, and large ones told the same week frequently do not. Not because duration makes a thing worse morally. Because additivity is a property of surprise, and thirty years of a load-bearing wrong model is a larger correction than a week of a right one arriving late.
R3 gives additivity of surprise for a host reading its own record. The step to relational damage — that another person’s accumulated error is the bill disclosure has to settle — is my extension, and it is not a numbered result.
It is the load-bearing move in this section, so it is worth being blunt about its status: if that step is wrong, the duration claim goes with it and the definition survives.
The cost to the keeper, which is not guilt
By R2, records update expectation forward and never re-open. The keeper’s own E has the fact in it and updates normally, like everything else. But to maintain the divergence, the keeper has to run a second model — a model of the other person’s model — in order to know what may be said in front of whom, what would be a slip, what has already been implied and therefore cannot be contradicted later.
That second predictor does not stop, and it does not get cheaper with practice. It runs during dinner.
So the tiredness of keeping a secret is not solely guilt, and it is not proportional to how bad the secret is. It is the standing cost of simulating a predictor you are deliberately keeping wrong. Which is why a trivial secret can be exhausting, and why a grave one, once told, is not.
“Maintained divergence between two predictors” is a new term. It is not in the foundation’s controlled vocabulary and it is provisional until the next version.
The second-model account of the keeper’s cost is likewise mine, derived from R2 rather than stated by it.
What it costs to accept this
There is no un-keeping. R2 is write-protection: the record does not re-open. Telling does not edit the interval of divergence; it places a new mark in the record beside it. Disclosure is an addition, and addition is the only move anyone has ever had. That is a description of the mechanism. It is not a comfort and should not be read as one.
There is no clean moment, and the foundation does not supply one. It tells you the divergence accumulates. It does not tell you at what rate, or where the accumulated error crosses from repairable into not. That is not modesty on my part; it is a stated gap. The foundation carries no session parameters anywhere — no durations, no frequencies, no timing — and it is listed as an open problem rather than an oversight. You get the shape of the curve and none of its constants.
And the question changes shape. “Do they have a right to know” is a question about an object, and on this account there is no object. The question the derivation actually produces is colder and more answerable.
What are they predicting with — and am I the reason it is wrong?
Where this is unsettled
One more open problem, named and left open rather than used. The foundation asks whether the split between a feeling’s usable reading and its unreachable target — the split it uses on regret and grief — applies to forward-facing feelings as well as backward ones.
The dread of a secret surfacing looks like precisely that structure, pointed at the Future rather than the Past. If it is, then most of what people call waiting for the other shoe is a reach at something that has no surface to be reached, and cannot complete no matter how long it runs. I find it plausible. It is also unargued in the source material, and marked there as open, so I am naming it and declining to lean on it.
Reading dread-of-exposure as the forward-facing case of that split is my suggestion, offered as a question. No part of the argument above depends on it.
A necessary limit
Nothing here is an argument for disclosure, and it should not be read as one. Some secrets are kept because speaking is dangerous — abuse, coercion, a person whose safety depends on not being known, a jurisdiction where a fact about you is a criminal charge. In those cases the divergence was not inserted by the person carrying it; it was imposed, and this derivation is silent on what anyone owes.
A framework can take a false picture off a mechanism. It cannot tell you whether it is safe to speak, it has no schedule for when you should, and it is the wrong tool entirely if what you are carrying is the kind of thing that needs a person rather than an argument.
On an ordinary Tuesday
- Find the loaded modelStop asking whether the thing is a big deal. Ask who is currently forecasting with a model the fact would correct, and what they are spending on that forecast. That is the list of your actual secrets, and it is usually shorter and stranger than the list you thought you had.
- Price the interval, not the contentIf you are deciding when to say something, the quantity that is growing is not your guilt. It is the accumulated error someone else is building on your behalf. It is smallest today and it will not be smaller tomorrow.
- Expect the cost to be compute, not conscienceIf keeping something is wearing you out and the thing itself seems too small to justify it, the model is not accusing you of hypocrisy. Simulating another person’s predictor is expensive independent of subject matter.
- Do not expect the telling to be an editIt will not undo the interval, because nothing undoes an interval. It ends the divergence and starts a new mark. That is the whole of what is on offer, and it has always been the whole of what is on offer.
The spatial vocabulary will not go away, and there is no reason it should — we will go on saying that things come out and that people are in the dark. But the picture underneath it can be corrected, and the correction is worth having, because it moves the question from a place you cannot inspect to one you can. Nothing is hidden. Someone’s model is short, you are the reason, and it has been running the entire time.