What Do We Owe Each Other? Exactly Love's Act, Promised or Not

There's a woman on the third floor of your building you've never spoken to.

You've nodded at her in the stairwell twice. That's the whole relationship. She has never asked you for anything, and you've never offered her anything.

This Saturday her door is open and you can see into her kitchen. She has enough food for about three weeks. After that she has none, unless someone brings her some, and as far as you can tell you're the only one who has noticed.

You have a full fridge and a free afternoon. Nobody would ever find out if you did nothing.

Do you owe her a trip to the store?

And if you do, how much? One bag, or more?

Most of us feel a pull to help and file it under kindness. The usual view is that only a promise would turn it into a debt: if you'd told her "I'll bring you food," you'd owe it, and without one, it's up to you.

That feeling tracks something real. The real thing is more exact than the feeling, and it doesn't wait for a promise. This post shows how.

The short answer

We owe each other love's act, promised or not. Love's act is the act that leaves the least cost on the whole future record, among the acts that meet the code's four clauses (the next section lists them). Do less than that and it's forbidden. Do more and it's forbidden too.

No promise is needed. The stranger is owed: what you owe comes from the least total cost on the relationships you actually have, with no promise anywhere in the history. The code can require you to help a stranger you've promised nothing. In the worked case, helping is required and doing nothing is forbidden, and the requirement comes from what the world's motion does next, not from any promise. Step 1 works the case through and says what the world's motion is.

I'll use feeding as the example, because it's the case we've worked out exactly. Right and Wrong Aren't Opinions worked out feeding someone you'd promised. Here the promise comes out and the requirement stays.

Here's the whole answer in six steps. The rest of this post takes them one at a time and shows how we know each one.

1. Help can be required with no promise. By a stranger I mean someone you've promised nothing, who has relied on nothing from you. In the worked case, doing nothing leaves strictly more cost on the record from three weeks later on, so helping is required. A promise raises the stakes. It doesn't create the duty.
2. What's owed is exactly love's act. Where help leaves less cost than doing nothing, doing nothing is forbidden. An act that does more than the least-cost act leaves more cost, so it's forbidden too. There is no act beyond the requirement.
3. You owe everyone their own write, true books and no push. An act may move a bond only when both of its ends write on it, every record has to stay true, and no act moves cost onto someone who didn't write it, at the moment it's done. It's owed bond by bond, so a kindness to one person never pays for a harm to another.
4. What others do on bonds your act doesn't touch changes nothing. When their help reaches her through what your act also moves, it does enter your verdict.
5. Walking away cancels nothing. Ending a bond deletes no one and no cost. An ended, strained bond stays on the record with all of its cost.
6. What's due in a deal is read from what happened, and a release is a new entry. The books alone can't say what's owed. A release never erases a miss.

Why this matters: everyone has a rough sense that we owe each other more than nothing and less than everything. A duty with no promise behind it sounds like a matter of conscience. Here it's a column of numbers you can add up yourself, and it closes the exits people actually use: "someone else will," "I'll just leave," "I'll let myself off."

What the code stands on

Three facts and a paragraph. Each fact comes with its reason. Right and Wrong Aren't Opinions goes through them at more length, and Part 1 of The Universe Writes in Pen introduces the record. This is what you need here.

Nothing that happens is ever erased. Every event leaves a complete trace, and the full record of what happened is part of reality now. The past still exists. The reason starts in established physics: the basic laws never destroy information. In quantum mechanics that's 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.¹ Our institute's work adds the record's own rule: it only grows, and writing a new entry never alters an earlier one.²

Every entry is a relation between two things, and a relation has two ends. The smallest thing that can happen is one thing being told apart from another, a single yes or no. You're doing it right now, reading these letters. Every measurement and every perception tells one thing from another. Telling two things apart takes information about both, so the record's unit is a relation between two terms, carried as one number: one term's amount divided by the other's. I'll call a relation's entry a bond. A bond at 1 is level. Each end of a bond keeps its own record of it, on its own books, and nobody writes in anyone else's books. (To write on a bond is to enter a change in your own books.) Each person also has a bond of their own, a number for how heavy their own load is, and 1 is level there too.

Every bond has a cost, and the cost is forced. A level bond costs nothing. A bond at 2, or at 1/2, costs 1/4. A bond at 4 costs 9/8. The recipe: add the number to its flip (1 divided by the number), halve the total, and subtract 1. For 4: 4 plus 1/4 is 17/4, half of that is 17/8, and 17/8 minus 1 is 9/8. The cost measures imbalance, so it's zero only at level and grows as the two sides drift apart. The recipe isn't a choice. The cost has to be zero when the two sides match, grow as they differ, and be the same whichever side you put first. Add the rule for how the costs of combined comparisons add, and one calibration (how sharply the cost rises near level), and exactly one formula is left.³ Meet in the Middle builds it from scratch.

The code. There is one moral code, and it fits in a paragraph.⁴ An act is admissible when it meets four clauses:

1. it acts only on bonds that exist now;
2. every record of every bond is true after it;
3. it moves a bond only when both of that bond's ends write on it;
4. it ends a bond only when one of that bond's own ends ends it.

Clause 3 is the heart of consent: an act may move a bond only when both of its ends write on it. Consent is the record of who wrote. It's a rule about acts. The record's own motion is different: it moves bonds with no one writing. I'll call it the world's motion, and Step 1's worked case gives it a simple rule.

These clauses aren't chosen. They're what a record kept twice, once on each end's own books, admits. Of the admissible acts, the code permits exactly those that leave the least total cost on the complete record, every week still to come included. Every other act is forbidden. Doing nothing is always admissible, so among any finite set of possible acts, something is permitted. Where an admissible act leaves less cost than doing nothing, doing nothing is forbidden, and the code requires an act. Love's act is the permitted act: the admissible act of least cost.

The code judges acts. It makes no one do anything: the forbidden act is as possible as the permitted one, and nothing physical stands in its way.

The route

Here's the route. I'll stop after each step to zoom out, so you always know where we are, what we have and why the next step comes next.

Step 1: Help can be required with no promise

The code can require you to help a stranger you've promised nothing. In the worked case, helping is required and doing nothing is forbidden, and the requirement comes from what the world's motion does next, not from any promise.

The woman on the third floor is a drawing of the worked case. The case itself is the groceries world from Right and Wrong Aren't Opinions with the promise taken out, so there is no undertaking anywhere in the history. It runs on the same rules. The numbers are the example's own, chosen to keep the arithmetic short, and the results are exact for this world.⁵

• Each of you has a reserve: what you have left to keep going on, counted in one unit that food and work are both counted in.
• Every week the world stretches each person's own bond to 2, and each person puts it back by paying 1/4 from their own reserve. That's upkeep: the cost of staying in working order, and the cost of a bond at 2.
• A trip to the store uses 1/4 of your reserve in work and gives her 1/2. It changes her books as well as yours, so it's a joint act: the authors of an act are exactly the people whose own records it changes.

You start this week with a reserve of 2, which is eight weeks of upkeep. She starts with 3/4, which is three weeks. Nobody promised her anything, so she did her own shopping.

Two acts are on the table, and the code judges both: you make the trip, or you do nothing. At the end of this week:

Feeding: you pay 1/4 for the trip and 1/4 upkeep, so your 2 becomes 3/2. She gets 1/2 and pays her 1/4, so her 3/4 becomes 1. Doing nothing: you pay your upkeep, so 7/4, and she pays hers, so 1/2. Both of you paid upkeep either way, so every bond is back at level and the total cost is 0 in both rows. Both of you still have something left in reserve. Read the books at the end of this week and the two plans tie.

But the code doesn't read one checkpoint. It reads the complete record: the cost at every checkpoint still to come, here the end of each week. So let the world run.

The world's motion is what happens to the bonds from week to week when nobody acts. It moves bonds with no one writing: clause 3 is a rule about acts, not about the motion. In this case the motion is the weekly rule above. While a reserve lasts, the bond goes back to level every week. Once a reserve is gone, nothing puts the bond back, so it stays stretched and gets stretched again, and it doubles every week: 2, 4, 8, 16. The case is closed on purpose. After this week nobody acts again, you included, and nothing new comes in.

Count weeks from the end of this one: week 0 is the end of this week, week 1 is the end of the next. Her reserve decides when her doubling starts. If you do nothing, she has 1/2 at week 0, then 1/4, then 0, and in week 3 she can't pay. If you feed her she has 1, then 3/4, 1/2, 1/4, then 0, and in week 5 she can't pay. Your own reserve is big enough in both plans that your own bond stays level through week 6, so until then the total cost is her bond's cost, counted once.

The two plans tie through week 2. From week 3 on, doing nothing leaves strictly more cost at every week, and the gap has no top: 1/4, 9/8, 45/16, 189/32, and it keeps growing. Feeding never leaves more cost than doing nothing at any week. So feeding is the act that leaves the least cost on the complete record, and doing nothing leaves more. The code requires the one and forbids the other.

Feeding isn't free for you. The trip uses 1/4 of your reserve, so your own bond starts to stretch in week 7 instead of week 8. That's counted: at week 7 the record holds 961/64 if you do nothing and 53/16 if you feed her.

Look at what isn't in this arithmetic: a promise. Nobody offered anything before this week and nobody accepted anything. The requirement is in the books and in what the world does to them.

What a promise adds. In the groceries world she had relied on your promise. She spent her week's outing on other work, so she started with 1/4 instead of 3/4, half a unit poorer. Run the same rules and the gap between doing nothing and feeding opens two weeks sooner:

With a promise, the gap is larger at every week after the first. A promise raises the stakes. It doesn't create the duty: it matters because it changed what she did, and what she did changed the books. The same least-cost reading requires the feeding in both worlds.

How we know. The requirement is a verdict on your act when you take it, and it comes from what follows the act. The code permits exactly the admissible acts that leave the least total cost on the complete record, reading that cost at every checkpoint. Read this week's checkpoint alone and the two plans tie, so the verdict can't come from there. Every number above is the recipe used again: a bond at 8 costs (8 + 1/8)/2 minus 1, which is 49/16, and a bond at 16 costs 225/32. From these rules, the two plans tie at weeks 0, 1 and 2, feeding never leaves more cost than doing nothing, and doing nothing leaves strictly more from week 3 on. A promise isn't in that argument anywhere. It enters only through her reserve.

One step isn't derived yet. Which situations carry such a requirement depends on the world's motion, which is still being derived. The weekly rule above, with its doubling when a reserve runs out, is the example's own.

Zoom out. Step 1 is done. In the worked case the code requires you to feed a stranger you've promised nothing, because doing nothing leaves strictly more cost on the complete record from week 3 on. A promise only opens the gap sooner. Next, and why: if feeding is required, how much? Is more required? That's Step 2.

Step 2: What's owed is exactly love's act

Where help leaves less cost than doing nothing, doing nothing is forbidden. An act that does more than the least-cost act leaves more cost, so it's forbidden too. Nothing is owed beyond love's act.

Step 1 showed the first half. The second half has the same reason from the other side: the code permits an act only when no admissible act leaves less cost, and an act can miss the bottom by overshooting as well as by falling short.

Meet in the Middle works out the exact case. A friend is moving apartments and her load is a bond at 4. Yours is level, at 1. Together they cost 9/8. Take on part of her load and meet in the middle, at 2 and 2, and they cost 1/2. That's love's act. Carry more than that and the cost climbs again: at 3 and 4/3 the pair costs 17/24, and carrying all of it, at 4 and 1, costs 9/8, exactly what doing nothing left. You've only moved the strain onto your side. The cost curve bends up on both sides of level, so it has one bottom, and the code permits only the bottom.

Love also stops where both of you can carry it. In that post, a budget that holds a bond up to 3/2 stops love there, short of the middle.

What's owed is always love's act, and love's act isn't always an act. Where no admissible act leaves less cost than doing nothing, doing nothing is love's act.

How we know. The judgment is the code's own: of the admissible acts, permit exactly those that leave the least total cost. The arithmetic is the recipe. A bond at 3 costs (3 + 1/3)/2 minus 1, which is 2/3. A bond at 4/3 costs (4/3 + 3/4)/2 minus 1, which is 1/24. The pair at 3 and 4/3 costs 2/3 plus 1/24, which is 17/24, more than 1/2.

Zoom out. Step 2 is done. Doing less than love's act leaves more cost, and so does doing more. The permitted act is the bottom of the curve, nothing above it and nothing below. Next, and why: so far it's been you and one other person. What do you owe everyone, and what does it mean that the record is kept bond by bond?

Step 3: You owe everyone their own write, true books and no push

An act may move a bond only when both of its ends write on it, so before you move anything you share with someone, you owe them their own write. You owe every record the truth. You owe no push: no act that moves cost onto someone who didn't write it. All of it is owed bond by bond, and nothing nets.

Start with who. You owe it to everyone at the other end of a bond with you. A person's burden is the cost of the bonds they're an end of, each counted in full, and an act can change a person's burden exactly when they're an end of a bond. So being an end of a bond is what makes someone count. Being able to act and being able to be wronged are separate, so a baby, a sleeping person and someone who can't speak all count. A Favor Isn't a Yes works that out.

What do you owe them? The code's clauses, read as duties:

• Their own write. You can't move what you share by writing alone, and you can't write their side for them. Their write is their consent, as yours is yours.
• True books. After your act, every record of every bond is true: it gives the bond's actual number. A book is false when what it says about a bond isn't what the bond is.
• No push. Each person writes only on their own books, so a book never holds an entry its owner didn't write. A book goes false when the bond changes and its owner didn't write the change. That's what harm is, made physical: changing a bond without the other end writing it, which leaves a false entry in their own record. To move cost onto someone, an act would have to do exactly that. An act that would is wrong, and clause 3, both ends write, excludes it at the moment the act is done, on any books, true or false.

Nothing nets. All of this is owed bond by bond. The code's own sentence: one participant's relief of you never offsets another's harm to you. Here's the arithmetic.

Your bond with Eli reads 2, which costs 1/4. Eli relieves it: you both write, and it goes to 1. That same afternoon Dana pushes the bond you share with her from 1 to 2, without your write. If the push went through, your burden would be 1/4 again, the same as before Eli's relief. Net zero for you, so a ledger that only watched your burden would call it even.

The code doesn't net. Eli's relief is love's act, and it's judged as itself. Dana's push would leave your own record of your bond with her false, and the clauses exclude it, whatever Eli did for you. Taking part in one act never consents to another done at the same time, and two acts on separate bonds, done together, are judged as the two acts.

How we know. These clauses aren't chosen. They're what the two-record ledger admits: each bond is kept on each end's own books, and an act that moved a bond one end didn't write would leave that end's record false. A rise in a bond's cost is consented to only by its own ends' writes on that bond.

Consent is a condition, not a price. Try the other way. Let every act through, put a fine on each false record, and let the least total cost decide. No finite fine works, because the cost of a bond has no top, so the relief a one-sided act can buy has no top either. Fine a false record 100. A bond at 400 costs (400 + 1/400)/2 minus 1, which is about 199. If the other end won't write, no act both ends write can touch that bond, so its 199 stays. One end alone moves the bond to level, pays the fine of 100, and comes out about 99 ahead. Pick any fine you like and some bond is lopsided enough to beat it. So the code doesn't price consent. It makes consent a condition: the clauses come first, and only then does the cost compare the acts that meet them. The code is the least cost over consensual acts: the acts every affected end writes.

Zoom out. Step 3 is done. You owe each person at the other end of a bond their own write, true books and no push, and you owe it bond by bond, so what you do for one person never pays for what you do to another. Next, and why: a favorite reason for doing nothing is that somebody else will. Does it change what you owe?

Step 4: What others do on bonds your act doesn't touch changes nothing

When what others do lands on bonds your act doesn't touch, "somebody else will help" and "nobody else will" rank your acts the same way. What you do moves only bonds you and the other end write, and what they do moves only bonds they and the other end write.

"Somebody else will" is the oldest reason to do nothing, and "nobody else will" is the oldest reason to do everything. The code ranks your acts the same way under both, as long as their acts land on bonds yours doesn't touch.

Here's why. Your act moves only the bonds you and the other end write. Say a later act by someone else, Sam, lands on bonds your act doesn't touch: it moves only the bonds Sam and the other end write, and you don't write Sam's act. Then your act and Sam's act touch no bond in common. Whatever cost Sam's act leaves on the record, call it c, is the same whichever plan you took. It's added to both plans' totals, and the gap between them doesn't contain it.

Put numbers on it. Say the bonds your choice touches leave 0 if you feed her and 9/8 if you do nothing, as at week 4 in Step 1. Sam's later act is on bonds he and others write, none of which your act touches. Let it leave c = 0 if he helps and c = 1/2 if he doesn't. (Those two values are made up. Any value works.)

Sam's choice moves both totals by the same amount. It can't move the gap, so what you owe is exactly what you owed.

Nothing in this asks you to guess what Sam will do. Whatever weight you give his choices, his part sits in both plans and cancels from the difference, so no chance on the future enters the judgment.

How we know. The code states it: your act moves only bonds both of whose ends write it, a later act by other people moves only bonds both of whose ends write that act, and the two touch no common bond. So the cost that others' later acts add is the same whichever act you took. The table is that sentence with numbers in it.

One step isn't derived yet, and it's the world's motion again. The record's own motion moves bonds with no one writing, and this holds when that motion runs each bond from its own state and its own reserve, so that what Sam's act does to one bond never changes what your act does to another. That the record's motion works that way is still being derived. Step 1's small world doesn't keep the two apart: every trip to her fills the one reserve her own bond runs on, so there a second helper's food lands where yours would. When their help reaches her through what your act also moves, as in the groceries world, it does enter your verdict.

Zoom out. Step 4 is done. What others do on bonds your act doesn't touch adds the same cost to both of your plans, so it can't change which plan leaves less. Next, and why: another exit people try when something is owed and strained is to leave. Does ending the bond end the debt?

Step 5: Walking away cancels nothing

Ending a bond deletes no one and no cost. An ended bond stays on the record with all of its cost. Ending a strained bond removes the only way to repair it, so walking away is never relief.

When a bond is strained, meaning off level, one way out looks easy: end it. The code allows an ending when one of the bond's own ends makes it, and nobody else can end your bond for you. But look at what an ending does.

Take a bond at 2. It costs 1/4.

• Repair it. Both ends write the repair, the bond goes to 1, and its cost drops to 0.
• End it. An ending changes no number, so the bond stays on the record at 2, with its cost of 1/4. Nothing can repair it now, because a repair takes both ends.

The ending is admissible, and the judgment prices it: in every future it leaves more cost than the repair would have. So ending a strained bond can be forbidden. It's never relief.

Why doesn't it vanish? Because nothing recorded is erased. An ending is one more entry: it alters no earlier entry and deletes nobody, so nobody walks out of a strain by leaving it.

How we know. The ending clause says a live bond is ended only by one of its own ends, and an ending changes no number, so it makes no record false. The complete ledger keeps the ended bond with all of its cost. The arithmetic is two lines: a bond at 2 costs 1/4, and a bond at 1 costs 0. One step isn't derived yet: whether the world's motion moves a bond after it has ended.

Zoom out. Step 5 is done. A strained bond can be repaired by both ends or ended by one, and the ending keeps the cost on the record with no way left to repair it. Next, and why: the other exit is to let yourself off. For what's owed in a deal, who can do that?

Step 6: What's due in a deal is read from what happened

What one person owes another in a deal is read from what happened between them. A debt changes only by a new entry, and "I release myself" changes nothing. A release never erases a miss.

A deal is where one person owes another a definite thing. The code reads a deal from the record of what happened between the two of them: the offer, the acceptance, the delivery, the repayment. It doesn't read it from either person's notebook. Here's the exact version, from Sorry Doesn't Rewind the Tape.

Alice offers Bob a meal on credit, price 1. Bob accepts, and Alice delivers. Now Bob owes 1. Each keeps private notes of the deal in a notebook, which isn't either person's own record of the bond. Alice's notebook says "Bob: 1" and Bob's is blank. In World A nothing else happens. In World B Alice says "forget it": she releases the whole 1, and Bob takes the release.

Open the notebooks. They're identical in the two worlds, page for page. But what's owed is 1 in World A and 0 in World B. So no rule that reads only the notebooks can get what's owed right in both worlds. What's due is read from what happened, event by event. Two true records of a bond agree, so when two records disagree, that isn't a claim on anyone. At least one of them is false.

Two things follow for what we owe each other.

You can't let yourself off. In this exchange, only Alice can give the release, because she's the one who is owed. If Bob writes "I release myself," that's written down, and what's owed stays at 1. A debt changes only with a new entry: the one owed gives the release and the one owing takes it.

Her yes isn't a yes to being skipped, and a release never erases a miss. In the groceries world, when she accepted your promise, that was a yes to being fed. It wasn't permission to skip. And even a real release from the one who is owed is a new entry after the old ones. Say you skip a week and she then releases you from the rest of the promise. That clears what's required of you from then on. It doesn't deliver the missed groceries, and the miss stays written. Right and Wrong Aren't Opinions works through the groceries version.

Now both exits are closed. Leaving cancels nothing (Step 5), and letting yourself off changes nothing (Step 6).

Two steps here aren't derived yet. One is that only the one owed can give a release: that's a rule the worked exchanges are built with, and deriving it from deeper physics is still being worked out. The other is that the physical record carries what's due, with the two parties as the bond's two ends.

Zoom out. Step 6 is done. What's due is read from events, only the one owed gives a release in the worked exchange, and a release never erases a miss. Next: what's still open, then the whole trip in one breath.

What's still open

The preprint lists the derivations the code still needs.⁴ Five open steps touch this post.

• Which situations carry a requirement to help. The worked case shows that the code can require help with no promise anywhere. Which situations carry such a requirement depends on the world's motion, which is still being derived. The weekly rule in Step 1, with its doubling when a reserve runs out, is the example's own. That the record's own motion runs each bond from its own state and reserve, and reads only the record, is still to be derived. So is whether that motion moves a bond after it has ended, and the step from "the record charges this cost, and the charge grows without bound" to "this ought not be done."
• Which relations are on the record. The code reads the bonds it's given. Which bonds a real person actually has, and so how far all of this reaches, is still being derived. So is the step from this small world to real people: what a real person's bond and reserve count.
• The two records. That each end's record holds one exact state of a bond, and that keeping books true and ending a bond only by its own ends follow from what a comparison is, is still being derived. It's the reason behind clause 3, and whether a release needs the debtor's write as well as the creditor's depends on it. It also leaves a gap at reserves: the clauses take an act's writes and books as handed over, and taking from a shared reserve passes them with no write and can move someone's bond later.
• What's due, and who can release it. That the physical record carries what's due, with the two parties as the bond's two ends, is still being derived. That only the one owed can give a release is a rule the worked exchanges are built with, and deriving it from deeper physics is still being worked out.
• Competing claims. Promise the same groceries to two people when there's food for only one: which promise governs, and whether the second promise wronged the first person, hasn't been derived yet.⁵

The whole trip, in one breath

Reality keeps a permanent record. Its unit is a bond between two ends, each kept on that end's own books and priced by one forced cost. We owe each other love's act, the admissible act that leaves the least cost on the whole future record. The code can require you to help a stranger you've promised nothing: in the worked case doing nothing leaves strictly more cost from week 3 on, so helping is required and doing nothing is forbidden, and a promise only opens the gap sooner. Doing more than love's act leaves more cost, so it's forbidden too. An act may move a bond only when both of its ends write on it, and that's a condition, not a price. You owe everyone at the other end of a bond their own write, true books and no push, bond by bond, so a kindness to one person never pays for a harm to another. What others do on bonds your act doesn't touch adds the same cost to both of your plans, so it never changes what you owe. Walking away leaves the bond on the record with all of its cost. And what's due in a deal is read from what happened: you can't release yourself, and a release never erases a miss.

So, the woman on the third floor. In the worked case you owe her the trip: doing nothing leaves strictly more cost, and the code forbids it. How much? Love's act, the least cost on the record, which in the worked case is the trip. Which situations carry such a requirement depends on the world's motion, which is still being derived.

So what do we owe each other? Love's act: never less and never more, to everyone at the other end of a bond with us. Nobody has to vote on it, nobody has to promise, and nobody has to find out.

That's how reality is built: a record that keeps everything, one forced cost on every bond, and one code that reads them both. How much we owe each other isn't a feeling, and you can add it up yourself.