Why Do We Need Each Other? Nothing Happens Alone, and Nothing Heals Alone

In the film Cast Away (2000), a FedEx employee named Chuck Noland survives a plane crash and spends four years alone on a deserted island in the South Pacific. A bloody handprint ends up on a volleyball. He draws a face in it, names the ball Wilson, and adopts it as his companion. When Wilson floats away at sea, Chuck is devastated.

You don't need that scene explained. You know what he lost.

Now try something smaller. Shake your own hand.

You can do it. Your right hand takes your left and pumps. It isn't a handshake, because a handshake needs someone on the other end. You don't need that explained either. Some things take two, and we know it before we can say why.

So why do we need each other? Not why company is pleasant. Why does it take another person at all?

The answer goes all the way down. The smallest thing that can happen in reality takes two things. A strained relationship is repaired only when both people write the repair. And starting a new relationship costs nothing. This post takes each of those in turn and shows how we know it.

The short answer

We need each other because nothing happens alone and nothing heals alone.

The smallest thing that can happen is one thing told apart from another, and telling two things apart takes both of them. You're doing it right now: reading this tells one letter from the next. So reality's record of everything that happens is made of pairs, and I'll call one pair a bond. The record is permanent, because the basic laws of physics never destroy information, so nothing in it is erased. A bond that's off balance, which I'll call strained, has an exact cost, one formula that the requirements on a cost leave as the only choice, and each of the bond's two ends carries all of it. You count in the record because you're an end of bonds: an act can change what you carry only through them. A bond is repaired only when both of its ends write the repair, because each end keeps its own record of the bond and nobody writes in anyone else's. So what's strained between you and another person is fixed with them or not at all. And some of what you need reaches you only through another person's act.

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

1. The smallest event takes two. One thing told apart from another needs both, so the record's unit is a bond between two.
2. You count because you're an end of bonds. What you carry is the cost of the bonds you're on, and being able to be wronged is a different ability from being able to act.
3. Nobody heals a bond alone. An act may change a bond only when both of its ends write on it. A lone write moves nothing. A change without the other end's write is harm: possible, and forbidden.
4. Some of what you need goes through someone else's act. In a small constructed economy, Bob can't get a meal while Alice only waits, and he can when she acts.
5. Needing runs one way. The cost runs both ways. Bob can need Alice without Alice needing Bob. A strained bond costs each of its ends all of it.
6. Starting is free, and a bond stays where acts leave it. A new bond enters the record level. Nothing moves a bond between acts.
7. Walking away frees nobody. Either end can end a bond, nobody outside can, and an ended bond stays on the record with all its cost.
8. Loneliness is where the derived part stops. A hurt is a strain felt at the size of its cost. Step 8 says what that gives us and names the step there that isn't derived.

Why this matters: need stops being a feeling or a failing and becomes structure you can point at. It says what makes you someone an act can reach, why the fix for a strained relationship has to be written twice, why some help can only come from one person in particular, and why leaving a strained bond leaves the strain.

Here's the route. I'll stop after each step to say where we are and why the next step comes next.

Step 1: The smallest event takes two

The smallest thing that can happen is one thing told apart from another, a single yes or no. It takes two things, so the unit of the record is a relation between two. The record's entry for a relationship between two people is a bond.

How we know. You're doing it right now. Reading this tells one letter from another, a "b" from a "d", and every measurement and every perception works the same way. Telling two things apart takes information about both of them, and the least information there can be is one yes or no: different, or the same. That's the smallest event.

Now take one of the two away. Picture a single "b" with nothing else at all, not even a blank page around it. There's nothing to tell it from, so there's no yes or no, and no event. A comparison needs both of its terms and reads nothing else.¹ Reality's smallest event isn't a thing. It's a difference between two things. (Part 1 draws that event as two little clocks passing one yes or no back and forth. The clocks are a drawing, and the event is two things and one yes or no.)

So the record's entries are relations between two terms. Each is carried as one number: one term's amount divided by the other's. When the two amounts match, the number is 1, and I'll call the relation level. Any other number means the relation is strained. Read from the other end, the number x becomes 1/x, and nothing changes. A relation at 2 from one end is at 1/2 from the other, and it's the same relation.

A relationship between two people is one of these relations. I'll draw bonds with numbers you can count: dishes washed, homework help given. The counts are my drawing. The bond is the real thing.

The record keeps everything. Every event leaves a complete trace, and none is ever erased. The full record of what happened is part of reality now: the past still exists. The reason starts in known physics: its 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.² The record has a rule of its own as well. It only grows. Each new entry is added with every earlier entry kept, and writing a new entry never alters an earlier one.³ I'll call this permanent record the record. Earlier posts in this series call it the Ledger.

Every bond has a cost, and the formula is forced. A level bond costs nothing. Any other number costs something. The cost isn't a payment to anyone. It measures imbalance: zero only at level, growing as the two sides pull apart, with no top. For a bond at x it's J(x) = (x + 1/x)/2 - 1. Add the number to its flip (1 divided by the number), halve the sum, and take away 1.

Check the last row: 4 + 1/4 is 17/4, half of that is 17/8, and 17/8 minus 1 is 9/8.

The formula isn't a choice. A cost has to be zero when the two sides match, grow as they differ, and come out the same whichever side you put first. Add the rule for how the costs of combined comparisons add up, and one calibration for how sharply the cost rises near level, and exactly one formula is left.⁴ Why Do We Suffer? has the full price list, and Meet in the Middle builds the formula from scratch.

Next, and why: the record is made of bonds, and bonds cost. So what counts, in a record like that?

Step 2: You count because you're an end of bonds

A participant is anything that is an end of a bond. What a participant carries is the cost of the bonds it's an end of. Some act changes what you carry exactly when you're an end of a bond, so being an end of a bond is what makes you count.

How we know. Start with what you carry. Each end of a bond carries the bond's whole cost, and what you carry, your burden, is the sum of the costs of every bond you're an end of. A bond at 2 costs 1/4, so each of its two ends carries 1/4. The record's own total counts that bond once.

Now ask what an act can do to you. An act changes what you carry only by changing a bond you're an end of. Something that's an end of no bond carries an empty sum, which is zero, and no act anywhere changes that. Something that's an end of even one bond can be reached by some act. So the ability to be reached by what others do, to be hurt or helped or wronged, is a single fact: being an end of a bond. That's what counts you.⁵ Why Do We Suffer? works it through with numbers in its Step 4.

Being able to act and being able to be wronged are separate abilities, and each occurs without the other. To act, you write. To be wronged, you only have to be an end of a bond. A newborn can't act at all: she can't agree to a change or refuse one. She counts in full: what's owed her is owed in full. A Favor Isn't a Yes works through who can be wronged and who says yes.

Counting isn't the same as being. What you are is the question of Part 1. Counting is about one thing: what an act can change in what you carry. And the need in this post comes from bonds and repair, not from everyone being one whole. If We're All One, Why Can't I Feel Your Headache? takes up that question.

Next, and why: counting is the setup. The first place need shows up as something you can't do for yourself is repair: what happens when a bond is strained?

Step 3: Nobody heals a bond alone

A bond is repaired only when both of its ends write the repair. A lone write moves nothing. A change to a bond without the other end's write is harm: possible, and forbidden. Others can help. They can't write it.

A handshake is a drawing of the real rule. You can't shake your own hand, and you can't shake someone else's without them. Here's the real rule, with numbers.

You and your roommate share a kitchen. This month you've washed the dishes 8 times and she's washed them 4. That's a bond at 2. It costs 1/4, and each of you carries all of it.

The record of that bond is kept twice. Each end holds its own record of it, in its own books, and nobody writes in anyone else's books. (A book is a drawing of one end's side of the record. The two records are real.) To write on a bond is to enter a change in your own books. A record is true when it gives the bond's actual number. Right now both books say "8 to 4", and both are true.

One more idea, then the cases. The moral code is the rule that judges acts on the record. It has four clauses, listed under "How we know" below, and a judgment: of the acts that meet the clauses, the code permits exactly those that leave the least total cost on the complete record, which counts every moment still to come, and it forbids every other act. "Forbidden" in this post means the code forbids it. The code judges acts and makes no one do anything, so a forbidden act is as possible as a permitted one.

Both write. She washes four more, and you both write it. The bond reads 8 to 8, level, and its cost falls from 1/4 to 0. That's a repair, and it took two writes.

One writes. You write "even" in your book, and she writes nothing. A write enters a change in your own books. It doesn't make the change: no dish got washed. So the bond is still at 2, still costing 1/4, and your book now says something the bond isn't. Your book is false. A lone write moves nothing.

A change without her write. Suppose an act does change the bond without her write, and it now reads level. Her book still says "8 to 4", so her book is false, and she never wrote the change that made it false. A book goes false when the bond changes and its owner didn't write the change. That's harm made physical: a false entry in someone else's own record. The act is possible, because nothing physical stands in its way. It's forbidden, even though the bond's cost went down, because a better outcome never makes a one-sided act allowed. A Favor Isn't a Yes works through a favor nobody asked for.

How we know. An act is admissible when it meets four clauses:⁶

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

So an act may change a bond only when both of its ends write on it. That clause is about acts, and acts are what move bonds: a bond changes only through what someone sends, and sending is an act. (In the kitchen drawing, washing a dish is sending.) The clauses aren't chosen. They're what a record kept twice admits. If a bond moved when only one end wrote, the other end's kept record would be false, and nobody else can write in that end's books to fix it. Right and Wrong Aren't Opinions works the whole code through on one case.

Consent is a hard condition, not a price. Put a fine on false records instead, and no finite fine works: a bond's cost has no top, so the relief a one-sided act can buy has no top either. What Do We Owe Each Other? has the arithmetic in its Step 3.

One step under all this isn't derived yet: that each end's record holds one exact state of the bond. The both-ends rule holds exactly when it does.

Others can help. They can't write it. Your friend Carol can say what she saw, bring dinner, lend you a dish rack, or talk you both into a better mood. Whatever she writes goes on her own bonds, because she isn't an end of the bond between you and your roommate, so "someone else will sort it out" repairs nothing. And what others do on bonds your act doesn't touch changes nothing in the code's judgment of your act: it adds the same cost whichever act you take. Help that reaches someone through a bond your act also moves is different, and it does count in that judgment. What Is Justice, and What Is Fair? works through who can help and who can write.

So here's where need comes in. Your side of a repair is yours to write, and the other side is hers. However strong or clever you are, you can't complete a repair alone, and neither can she. "Love takes two" is the code's own sentence for it, and Meet in the Middle works out what love does.

Next, and why: repair isn't the only thing that goes through another person. Some of what you need can only reach you through someone else's act.

Step 4: Some of what you need goes through someone else's act

An outcome needs an actor when it can be reached, and can't be reached once that person's actions are ruled out. Outcomes like that exist. A small constructed economy shows one exactly: while Alice only waits, Bob can't get a meal, and when Alice acts, he can.

I'll build the world in the open, so nothing is hidden in it. There are two people, Alice and Bob, and one meal, ready to eat. Alice holds it. Bob holds nothing at all. Each person can wait, eat a meal they hold, or hand a meal they hold to the other. The world has one rule about custody: only the holder hands a meal over. Bob's aim is to eat a meal.

Alice waits. Say Alice does nothing but wait, forever, while Bob does anything he's allowed to, in any order, for as long as he likes. Bob never ends up with a meal. His holdings stay at nothing in every run, of any length.

Alice acts. She hands him the meal. That's one step, and now he holds it and can eat it.

Bob can't just take it. The step exists: physically, a meal can move from Alice's hands to Bob's with Bob doing the moving. But the world's custody rule says only the holder hands a meal over, so Bob's taking it isn't authorized. There's enough in this world for Bob to eat, and enough isn't control. Being able to reach a thing isn't being in charge of it.

Alice doesn't need Bob. She can eat the meal herself. And if Bob had a meal of his own, he wouldn't need Alice either: the dependence disappears.

How we know. These are exact statements about this world, proved for every possible run, whatever its length.⁷ The custody rule is the world's own. It's an input, and not a derived law of property. This is one small world, built so every run can be followed. It shows that needing someone's act is a precise property you can check: reachable overall, unreachable once that person's actions are struck out. It doesn't say that every need in every economy runs through one person.

This is the second way we need each other. Step 3 was about repair, which takes both ends. This is about getting things: some of what you need sits in someone else's hands, and only their act brings it to yours.

Next, and why: Step 4 gave need a direction. Does the cost of an unmet need have one too?

Step 5: Needing runs one way. The cost runs both ways.

Need has a direction: Bob can need Alice's act while Alice needs nothing from Bob. The cost of a strained bond has no direction: each end carries all of it, and the record counts it once.

How we know. Look back at Step 4. Bob needs Alice, and Alice doesn't need Bob. Being able to affect each other is a different relation, and it's symmetric. In the record, two people can affect each other exactly when they share a bond, so if Bob can affect Alice, Alice can affect Bob. Need doesn't work that way. In the small economy, no arrangement of bonds turns "can affect" into "needs".⁷

The cost works the other way. Say a classmate has helped you with homework four times for every once you've helped her. Draw that as a bond at 4. It costs 9/8, and each of you carries all of the 9/8, not half each. Read from her end the bond is at 1/4, which costs 9/8 too. The record's own total counts the bond once: 9/8, not 9/4.⁵

Put the two together. If a need is strain on a bond the two of you share, it weighs on the one who can meet it exactly as much as on the one who has it. She carries what you carry, though you did most of the needing.

The stranger is owed. The code requires you to help wherever an act both of you write lowers the cost; then doing nothing is forbidden. No promise is needed anywhere. What Do We Owe Each Other? works through a neighbor you've never spoken to. And in the shared-load case, helping costs the helper little against what it relieves: giving relieves more than three times what it costs the giver (Meet in the Middle, Step 3).

Next, and why: all of that is about bonds that exist. What about starting one, and what happens to a bond nobody acts on?

Step 6: Starting is free, and a bond stays where acts leave it

A new bond enters the record level, so reaching out costs nothing. Nothing moves a bond between acts, so a bond stays where the last act left it: a level bond stays level, and a strained bond stays strained until an act moves it.

How we know. What does it cost to make a new bond? Nothing. A new bond enters the record level, at 1, and level costs zero at any size. The record has no entry fee: creating a level bond, or ending one, changes no cost.⁸ (A strain an act puts on the new bond counts as a strain, like any other.) So a stranger who becomes a friend, with nothing owed either way yet, adds nothing to what anyone carries.

Then what happens to a bond nobody acts on? Nothing. Nothing moves a bond between acts: a bond changes only through what someone sends, and sending is an act. So a level bond needs no upkeep to stay level. And a strained bond doesn't ease with time. Leave the kitchen bond alone for a month and it's still at 2, still costing 1/4, until an act moves it, and a repair takes both of you. Time doesn't heal a bond. Two people do.

Next, and why: a strained bond stays strained until both ends repair it. One way out is to leave. What does leaving do to a bond?

Step 7: Walking away frees nobody

Either end can end a bond alone, and nobody outside can. An ending deletes no one: the ended bond stays on the record with all its cost. Ending a strained bond removes the only route to repairing it, so its cost stays above what a repair would have left, in every future. Ending a level bond changes no cost.

How we know. Say the kitchen bond sits at 2, costing 1/4, and you end it. The fourth clause allows it: a bond is ended by one of its own ends, and either end is enough. Nobody else can end it for you, and nobody can hold you in it. One end is enough because a comparison needs both of its terms present, so when one end withdraws, the bond ends. That rests on a step not derived yet: that each end's presence is its own entry, changed only by its own write, and that a comparison with both terms present needs nothing else. But the bond doesn't leave the record. It stays at 2, with its 1/4, in every future. An ended bond keeps its cost: no allowed act touches it, and nothing moves a bond between acts. So no repair can reach it now. Had you brought it level first, it would stay on the record at cost 0, and leaving would have changed nothing.

So leaving isn't relief. A count of only the bonds still open gets this wrong, because it drops the whole 1/4 and has no way to register what was lost. The complete record keeps it.⁶ This is Step 3 seen from the other side. Repair takes two, so when one end leaves, the repair goes with them.

What Is Freedom? works through endings in its Step 3, and Why Do We Suffer? works the numbers in its Step 4.

Next, and why: that's every step the structure gives. The last one is where it stops.

Step 8: Loneliness, where the derived part stops

Loneliness is a strain on some bonds, felt at the size of its cost. What it's made of, exactly, is where the derived part stops.

Start with what's measured. In May 2023 the U.S. Surgeon General issued an advisory titled Our Epidemic of Loneliness and Isolation.⁹ In 2010 a pooled analysis of 148 studies, covering 308,849 people followed for 7.5 years on average, found an odds ratio of survival of 1.50 for people with stronger social relationships. The authors put that as a 50% increased likelihood of survival.¹⁰ Those are measurements of people, not derivations. They say the need is real and costs something.

What the record says is a separate line of reasoning. Why Do We Suffer? works out that a strained bond is felt at the size of its cost. An event has an outside and an inside, and the inside is experience. The reason: experience happens in this world, so it belongs to the same structure as everything else that happens, and that structure is events, each a comparison with two sides. How hard an event is felt is the cost of the mismatch between its two sides. That's the account of a stubbed toe, and it's the account of a friendship gone lopsided. Loneliness hurts, so it belongs in the same account, as strain on some bonds, felt at the size of its cost.

That last step isn't derived yet: which physical relations, and which two amounts on them, a lonely person's hurt is made of. It's the same step that post names for the toe and the friendship.

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

What's still open

The Moral Code preprint lists the derivations the code still needs.⁶ Three open steps touch this post.

• Which relations a lonely person's hurt is made of. That a strained bond is felt at the size of its cost is worked out in Why Do We Suffer? Which physical relations, and which two amounts on them, a particular hurt like loneliness is, isn't derived yet. It's the same step that post names for the toe and the friendship.
• What each end holds. That each end's record holds one exact state of a bond: the rule that an act may change a bond only when both of its ends write holds exactly when it does. And that each end's presence is its own entry, changed only by its own write, with a comparison needing nothing but its two terms present: the rule that either end can end a bond rests on that. A Favor Isn't a Yes and What Is Justice, and What Is Fair? name the first as an open step too, and What Is Freedom? names both.
• Who is allowed to hand over what. The small economy in Step 4 supplies its custody rule: only the holder hands a meal over. Deriving a holder's authority from the clauses is open, and so is the step from this small world to the needs of real people.

The whole trip, in one breath

The smallest thing that can happen is one thing told apart from another, which takes two, so reality's permanent record is made of bonds, each a relation between two. You count because you're an end of bonds, and each end of a strained bond carries all of its cost. An act may change a bond only when both of its ends write on it, so a lone write moves nothing, a change without the other end's write is harm that's possible and forbidden, and a strained bond is repaired only by both ends. Others can help and can't write it. Some of what you need goes through someone else's act: in the small economy, Bob can't get the meal while Alice only waits, and he can when she hands it over. Need runs one way, and the cost runs both ways. A new bond enters the record level and costs nothing to begin, nothing moves a bond between acts, and walking away deletes no one: the ended bond keeps its cost. And a lonely person's hurt is a strain, felt at the size of its cost.

That's how reality is built: a record whose smallest unit is a pair, so nothing in it happens alone and nothing in it heals alone. You can't shake your own hand.