A Favor Isn't a Yes

You come home from a week away and your bedroom is a different color.

Your roommate painted it while you were gone. It's a nicer color than the one you picked. Honestly, it's better. You stand in the doorway and like it more than you expected to.

So: did you say yes?

You didn't. Nobody asked. And yet part of you wants to say "I'm happy, so it's fine," while another part has noticed that something got skipped. Notice what's strange here. If she'd painted it a color you hated, you'd know exactly what to say, and it wouldn't be "thanks." The question only gets slippery because you like it.

Both parts of you are tracking something real. There's an exact reason a favor feels different from a yes. It's built into the way reality keeps its permanent record of every event.

The short answer

No. A favor isn't a yes.

Any event between people has two separate facts: who wrote it, and whether they came out better. In the record, saying yes is writing your own side of the relationship. Being better off doesn't write it. Nothing that happens to you writes it, however good it is. And nobody else can write it for you.

Here's the whole answer in five steps. The rest of this post takes them one at a time. Each step gives its reason, then works it through with a small example.

1. Every relationship is written twice. Each person keeps their own record of it. If the two records disagree, at least one is false. And an act is allowed to change a relationship only when both people in it write on it.
2. Better off is not a yes. You can like how things came out without writing a word, and you can write something and come out behind.
3. The numbers forget who signed. The numbers that sum up how things came out never contain the consent. It sits on its own line of the record, "who wrote this."
4. A yes has a content and a moment. A later yes doesn't reach back to an earlier entry. A yes covers what you were shown, not what was kept back.
5. Who can be wronged, and who says yes. Anyone at the end of a relationship can be wronged, whether or not they can speak. And nobody signs for you.

Why this matters: "it was for your own good" is an excuse everyone has heard. People use it for everything from surprise makeovers to a boss who "helps" by taking over your project. The record shows exactly why it never works as a yes. It also settles who can be wronged. A sleeping person, a baby and someone who can't speak up can't bargain or explain, and every one of them can still be wronged.

Here's the route. I'll end each step with one line on why the next step comes next, so you always know where we are.

Two facts this post stands on

Each comes here with its reason. Part 1 of this series covers the permanent record and the smallest event in more depth.

First, the past still exists. Every event leaves a complete trace, and none is ever erased. That full record of what happened is part of reality now.

The reason is in known physics. The basic laws of physics never destroy information. In quantum mechanics this is called unitarity. The present fixes the past exactly, and running the laws backward recovers every earlier state. That's why physicists treat the black hole information problem as a real problem: losing information would break the laws.

Second, the record is kept as each person's own books. The smallest thing that can happen is one thing being told apart from another. You're doing it right now, reading these letters: every measurement and every perception tells one thing from another. A comparison needs both of the things it compares, so the record's basic unit is a relationship between two ends. Each end keeps its own record of it. Each person writes only in their own books. An act is a change written on the actor's books, or on both sides' books when two people act together. So when you act, your act is the entry. The authors of an act are exactly the people whose own records it changes, so who wrote is something you can read off the books. Consent is the record of who wrote. Nobody else can write in your book.

Step 1: Every relationship is written twice

Every relationship has two ends: the two people in it. Each keeps their own book, so the record of the relationship is written twice. (The books are a drawing. The two records are real: each end of a relationship holds its own.) And an act is allowed to change a relationship only when both people in it write on it. You'll see why below, and what it means when someone changes one alone.

Here's how it works, with small numbers. Alice has cooked Bob two dinners, and Bob has cooked her one. That's two against one: a ratio of 2. The ratio is the state of the relationship between them: how far it is off balance, with 1 at balance. Read from Bob's end, the ratio is 1/2, and that changes nothing. (Dinners keep the numbers small. Which physical quantity holds the state of a real relationship is one of the two open steps at the end.)

What one person owes another is read from the record of what happened between them: the offer, the acceptance, the delivery, the repayment. Here the deliveries set the state. Both books record the same thing: the relationship's state. Here both say "2 to 1." A record is true when it gives the relationship's actual state, so both of these are true. Two true records agree. So when two records disagree, that isn't a claim on anyone. It means at least one of them is false.

A relationship that's off balance isn't free. It has a cost, and the cost measures the imbalance. The cost has to meet three requirements: it's zero only at balance, it grows with the mismatch, and it's the same from either end. Here's the recipe: take the ratio, add its flip (the ratio turned upside down), halve that, and subtract 1.

• Balanced, 1 to 1: (1 + 1) / 2 - 1 = 0. No cost.
• 2 to 1: (2 + 1/2) / 2 - 1 = 1/4. The cost is 1/4.
• 1 to 2: (1/2 + 2) / 2 - 1 = 1/4 again. Doubling and halving cost exactly the same.

The record uses this same recipe for every relationship, and it isn't a choice. Those three requirements, one rule for how the costs of combined comparisons add up, and one calibration (how sharply the cost rises near balance) leave exactly one formula, and this recipe is it.¹

Your burden is the total cost of the relationships you're in. So both people in a relationship carry its whole cost: at 2 to 1, that's 1/4 on Alice's burden and 1/4 on Bob's. The record's own total counts each relationship once, not once per person, so this one adds 1/4 to it. A burden isn't blame: both people carry it, whoever caused the imbalance.

Now watch the books.

Say Alice writes in her own book, "Bob owes me two," and Bob writes nothing. The relationship hasn't moved, because Bob didn't write. It's still 2 to 1, and Bob still owes one dinner, not two. So Alice's book now says something untrue: her record is false. Writing it wasn't allowed, because it leaves a record false. Bob's record and his burden are unchanged. And it isn't a claim on Bob. Alice can make her own book true again by correcting it.

Why can't Alice's entry move the relationship? Because of how the books work. Bob didn't write, so his book still shows the old state. If the relationship had moved anyway, his record would now be false, and nobody else can write in his book to fix it. That rule comes from the record itself, not from any person: after every allowed act, every record of every relationship stays true.² So an act is allowed to change a relationship only when both people in it write on it. That holds for each act, at the moment it's done.

What about someone who changes a relationship anyway, without the other person's entry? To do that, an act would have to make the other person's own record false. That's exactly what harm is: a false entry in someone else's own record (Step 5). The rule that an allowed act leaves every record true is the rule against it.

Carol is a third person. She can vouch for Alice and talk them both into a better mood. What she can't do is change Alice and Bob's relationship: she isn't an end of it. She writes on her own relationships.

So how do Alice and Bob settle it? Bob cooks the dinner he owes, and both write it. Call that a joint record: both ends write the same entry at once. Now it's two against two: ratio 1, cost 0. Bob can't settle it by writing alone. Bringing a relationship to balance changes it, so both ends write the repair.

This isn't a rule somebody made up for people. It follows from how the record is kept: each person writes only in their own book, an allowed act has to leave every record true, and each record holds the relationship's one exact state. That last part is still being derived; it's the first open step at the end.

Next, and why: your roommate wrote and you didn't, and you like the result, so we ask what being better off does to "yes."

Step 2: Better off is not a yes

Any event has two separate facts: who wrote it, and whether you came out better. Each one has an exact meaning in the books.

• Wrote it. The entry is in your book, and you wrote it. In the record, this is consent: you wrote your own side.
• Better off. How you came out. In the books, that's your burden going down; if it went up, you're worse off. You can also judge it by your own measure, as you do the paint.

Consent is the first one, and only the first. It's the part of a yes that the record carries: who wrote it. Whether you were free when you wrote isn't an entry in the record. Step 4 says what the record does and doesn't hold about how a yes was given.

Here's how it works, with small numbers: two scenes.

Scene 1. A yes, and worse off. Alice and Bob start balanced: 1 to 1, cost 0. They write a new deal together: Alice will cook Bob a dinner. She does, and both write it, so the relationship is now 2 to 1. The cost is 1/4, and each of them carries all of it. Both wrote, so both said yes. And each one's burden went up, from 0 to 1/4. The cost isn't about who got the dinner. It measures how far the relationship is off balance, and both of them are in it.

Scene 2. No yes, and you like it. Back to your bedroom. Your roommate wrote, and you didn't. You came out ahead, by your own measure. Your "wrote it" box is empty. Did you say yes? No. Do you like the paint? Yes. Those are different facts on different lines of the record, and neither one answers the other.

And an act is allowed to change a relationship you share only if you write on it too. If her repaint did move one, your own record of it would now be false. Liking the color doesn't change that.

Read down the scenes. Alice and Bob wrote, and both came out behind. You wrote nothing and came out ahead, by your own measure. "Better off" and "wrote it" come apart in both directions. You can be better off without saying yes, and you can say yes and be worse off.

Doesn't it count that you like the color? Liking it is a fact about how you came out, not something you wrote. And a better outcome doesn't make an act allowed: the rule that an allowed act leaves every record true comes before any count of costs.

Does that make your roommate a bad person? The record doesn't say that. It speaks to the act: without your entry, that change isn't allowed. Favorable effects matter. They just can't stand in for a yes.

Next, and why: if no outcome writes your side, then no number about how things came out can contain the consent, and Step 3 checks that.

Step 3: The numbers forget who signed

From the books you can work out numbers that sum up how things came out: each relationship's ratio and cost, and each person's burden. None of them says who wrote. Events with different authors can leave every ratio, every cost and every burden the same. So consent can't be read from these numbers. It sits on its own line of the record: who wrote this.

Here's how it works, with small numbers: two deals of the same size.

Give Alice two relationships, one with Bob and one with Carol. Each starts balanced, at 1 to 1.

Run 1. Alice and Bob sign a deal: each cooks one dinner for the other. Both write it, so the Alice-Bob relationship reads 2 to 2. The Alice-Carol one stays at 1 to 1.

Run 2. Alice and Carol sign the same deal. Now the Alice-Carol relationship reads 2 to 2, and the Alice-Bob one stays at 1 to 1.

In both runs, every relationship is balanced before and after. Every ratio is 1, every cost is 0 and every burden is 0: the same in both runs.

Did Bob sign? In Run 1, yes. In Run 2, no. A rule that reads only the numbers must give the same answer for both runs, since the numbers are the same. No such rule can tell which run it's looking at. One pair of runs is enough to show that.

So where is the consent? In the entries themselves. Whenever something is written, the books that change are the books of the people who wrote it. In Run 1, Bob's book changed. In Run 2, it didn't. The record keeps that line: who wrote this. The numbers throw it away.

How things came out is one fact. Who wrote it is another. The record keeps both, in separate columns, and no amount of staring at the first column finds the second.

Next, and why: a yes also has a content and a moment, which answers "but you agreed later!" and "but you signed it!"

Step 4: A yes has a content and a moment

A yes is tied to four things: who said it, which entry it answers, its content (what it covers) and its moment (when it was said). Two exact things follow.

A later yes doesn't reach back.

Take Alice's entry from Step 1: "Bob owes me two," in her own book, with Bob writing nothing. As in Step 1, the relationship hasn't moved, and Bob's record is still true. Alice's entry stays what it was: a record Bob never wrote.

A week later, Alice and Bob shake on a bigger deal. Bob's handshake is real. It's his, and it's a yes to that deal only. The extra dinner, the second one in Alice's entry, was never part of that deal. A handshake can't reach back and make Bob the author of Alice's entry.

If Bob agrees to owe a second dinner, they write it together, now. That's a new yes, with its own moment.

What does the record know about why Bob shook on the bigger deal? Nothing. A pressured yes and a free yes are the same kind of entry. The record holds what each person wrote and the order they wrote it in: her entry first, his handshake after. Whether her entry is why he shook isn't an entry.

A yes covers what you were shown.

Dan, a drummer, lands a gig.

His manager keeps her own copy of the contract. It says Dan owes her a commission of one night's pay. The copy she puts in front of Dan says half a night's pay. Dan signs the one he was shown. In his book he writes 1/2.

Now the two records disagree. Hers says 1, a night's pay. His says 1/2, half a night's pay. True records always agree, so when two disagree, at least one is false. Dan said yes to half a night's pay. That's what he wrote. He never wrote the other half.

An honest deal is a joint record: both write the same number, and the records agree. The record shows the mismatch and which number each side wrote. It doesn't show what the manager meant. The 1/2 is in it. The motive isn't.

Next, and why: if consent is writing your own side, who can be wronged, and who can sign for whom?

Step 5: Who can be wronged, and who says yes

Anyone at the end of a relationship can be wronged. Nobody can say yes for you.

Start with who can be wronged. The record doesn't ask who's smart enough to bargain or who can speak up. It asks one thing: is this person an end of a relationship?

An act can change your burden exactly when you're an end of a relationship. So being an end of a relationship is what makes you count. The capacity to act and the capacity to be wronged are separate: each occurs without the other.

Turn it around, and a person with no relationships at all isn't an end of anything, so no act can change their burden. No cleverness enters. No savings, no speech, no ability to act. A baby, a sleeping person, someone who can't speak: each is at the end of relationships, so each can be wronged.

Harm is a false entry in someone else's own record. The rule that an allowed act leaves every record true forbids any act that would make one. "Can be wronged" names exactly this capacity: being an end of a relationship. This step asks only who can be wronged, and the answer is everyone who is an end of a relationship.

Now, who says yes? Your side of a relationship is written by you or by nobody. The books have exactly two kinds of entry: your own, in your own book, and a joint record that both ends write. There's no third kind, no entry "on behalf of." A friend, a boss or a roommate can write their own side of any relationship they're in. They can't write yours. So their yes is theirs. "I'll sign for you" leaves your side blank.

What if she knew you'd love it? Painting the room was her entry. Your side is still blank.

Next: what's still open, then the whole trip in one breath.

What's still being worked out

Two steps are still being worked out. The first is that each person's record holds one exact state of the relationship. That's being derived from what a comparison of two records returns, and it's the step that makes "both must write" hold, for a favor too: it's why one person isn't allowed to change a shared relationship alone, even to help. The second is what physically carries the two records: which quantity, held at each end, gives the state of a real friendship, a real debt or a real paint job. The sizes in this post, a few dinners and one night's pay, are chosen to keep the arithmetic small. The structure holds for any sizes. Only the cost numbers change.

The whole trip, in one breath

Every relationship is written twice, once in each person's book. If the two records disagree, at least one is false. An act is allowed to change a relationship only when both people in it write on it, so no lone entry is an allowed change to it. Who wrote an event and whether they came out better are two separate facts. Consent is the first: in the record, saying yes is writing your own side, and no outcome writes it for you. The numbers about how things came out forget who signed, so consent lives on its own line, who wrote this. A yes has a content and a moment: a later yes doesn't reach back, and a yes covers what you were shown. Anyone at the end of a relationship can be wronged, and nobody writes your side but you.

That's how reality keeps its record. Each person writes only on their own books, so every relationship is held in two copies, one in each person's hands, and every entry has a line for who wrote it. A favor can leave you better off and still not be a yes, and the record has a line for each.