Why Do We Suffer? Because You're Connected

It's 2 a.m. and you're crossing the bedroom in the dark. The bedpost is exactly where it was yesterday. Your toe finds it anyway.

OW.

For ten seconds you know one thing in the universe, and it's your foot. Every other fact about your life has left the room.

A week later it's 2 a.m. again, and you're awake again. This time nothing has touched you. Nothing is broken. But there's a friend you've driven to the airport four times, and she's driven you once. Neither of you has ever mentioned it, and tonight it's sitting on your chest.

Two hurts. One is in your foot, and it has a cause you can point to and a bedpost you can blame. The other is in your life. It has no wound, and it hurts anyway.

So here's the question. Why does anything hurt? Is there one reason behind the toe and the friendship, or are they two different things that happen to share a word?

There's one reason. It comes with an exact formula, and the rest of this post works it through with numbers.

The short answer

You suffer because you're connected.

A connection between two people compares two amounts. In the airport friendship, drawn as rides given against rides received, the amounts are 4 and 1. I'll call a connection like that a bond. When the two amounts match, the bond is level, and nothing in it is strained. When they don't match, the mismatch has an exact cost. Every event is felt from the inside (Step 2 gives the reason), and an event is felt as hard as its mismatch costs. A bond that's off level is strained, and suffering is a strain, felt.

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

1. A mismatch has an exact cost. Compare two amounts. If they match, the cost is zero. If they don't, the cost has one exact formula, and it has no top.
2. Every event is felt at the size of its cost. Every event has an outside and an inside, and the inside is experience. How hard an event is felt is the cost of the mismatch between its two sides.
3. You're joined by bonds, and you carry their cost. What you carry is the sum of the costs of every bond you're on. Strain any one of them and what you carry goes up.
4. Only a bond can be strained. With no bonds, nothing anyone does can raise your cost. With even one, something can. Being able to be hurt is being connected.
5. Relief is exact too. Relief is a fall in cost. Between two people the cheapest repair from inside the pair is to meet in the middle, and giving relieves more than it costs.

Why this matters: suffering has a source, a size and a way down. The source is a strained bond. The size is its cost. The way down is a move back toward level. Suffering isn't a punishment, because a strain says nothing about whose fault it was. And it isn't a malfunction, because it comes with having bonds at all. The bonds that can be strained are the same bonds that love repairs.

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

The steps use one idea from other posts on this site: the Ledger, the permanent record of everything that happens. Start with what physics already says: its basic equations never destroy information about the past. In quantum mechanics that's unitarity: the present fixes the past exactly, and running the equations backward recovers every earlier state. The Ledger goes further: nothing in it is ever erased. Every event leaves a complete trace, and the past still exists. The record is reality's own, and it keeps every entry, because writing a new entry never alters an earlier one.¹ Among its entries is a number for every bond between people. What You Are goes through it in full, but you don't need it to follow this post.

Step 1: A mismatch has an exact cost

Compare two amounts and you get a ratio: how many times bigger one is than the other. Eight apples against two apples is a ratio of 4. Two apples against two apples is a ratio of 1, and a ratio of 1 means the amounts match. I'll call that level.

Any other ratio is a mismatch, and a mismatch has a cost. The cost isn't a payment to anyone. It measures imbalance: it's zero when the two amounts match, and it grows as they pull apart. It has one exact formula, and I'll call it J. For a ratio x:

J(x) = (x + 1/x) / 2 - 1

In words: add x to its flip (1 divided by x), halve the sum, and take away 1. For a ratio of 4, that's 4 + 1/4 = 17/4. Half of that is 17/8. Take away 1 and you get 9/8.

Here's the price list: what a few ratios cost.

The 10 is ten rides given for every one received.

Four things to notice.

Only level is free. The cost can also be written (x - 1)² ÷ 2x. A square is never negative, and 2x is always above zero, so the cost is never negative. It reaches zero only when x - 1 is zero, which happens at 1 and nowhere else. Nothing costs less than level.

The same either way round. A ratio of 2 and a ratio of 1/2 both cost 1/4. Having twice as much as the other side costs exactly what having half as much costs.

It climbs fast. A ratio of 4 costs 9/8, which is four and a half times what a ratio of 2 costs.

It has no top. Make one side a thousandth of the other, so the ratio is 1,000, and the cost is about 499. Make it a millionth and the cost is about half a million. No mismatch is too big to have a cost.

Where does the formula come from? We didn't pick it. We asked for a cost that meets five requirements, and exactly one function meets them:

1. No jumps: a small change in the ratio makes a small change in the cost.
2. A ratio and its flip cost the same, so it doesn't matter which side is put first.
3. A match costs zero.
4. Costs combine by one fixed rule: J(xy) + J(x/y) = 2J(x) + 2J(y) + 2J(x)J(y). The 2 in the rule fixes the cost's unit.
5. One calibration: it sets how sharply the cost rises near level (its second derivative at 1 equals 1).

That function is the J above, and the result is published: Washburn and Zlatanović, in the journal Mathematics, 2026.² Two of the five, numbers 4 and 5, already settle it: the combining rule and the calibration leave exactly one function. The function (ln x)² has requirements 1 to 3 but fails the rule, so it's out. The love post works through the combining rule with numbers.

What the cost does: it doesn't pick the next step. It weights the odds, so that in the long run a state with more imbalance is less likely and balance is the single most likely state, the way a warm physical system favors its lowest-energy states without sitting in them.

Zoom out. Step 1 is done. Two amounts give a ratio, and 1 is level. Every other ratio costs, by one exact formula: 2 costs 1/4, 4 costs 9/8, and there's no top. Next, and why: the question this post is named for. What does a cost have to do with hurting? Step 2 joins them.

Step 2: Every event is felt at the size of its cost

Every event has an outside and an inside, and the inside is experience. How hard an event is felt is the cost of the mismatch between its two sides.

An event is one thing happening: a bump, a signal, a flash. The Ledger writes down every one. Every event is a comparison. The smallest thing that can happen is one thing told apart from another, and telling two things apart takes information about both of them. You're doing it right now: reading this tells one letter from another. So every event compares two amounts, and I'll give them names. The first is what a measurement reads: the outside. The second is what that reading is held against: the inside. Neither is ever zero. An empty side would cost more than any number can name, which is Step 1's "no top".

The inside is experience. It's what the event is like. The outside and the inside aren't two things stuck together. They're one event, seen from without and from within. Here's the reason. Experience happens in this world: you're having one now. So it has a place in the same structure as everything else that happens, and that structure is events, each a comparison with two sides. Experience is the inside of those events, the very events that do the physical work, not a second thing added on top of them. Every event has an inside, so every event is felt: the bumps in a coffee mug, the signals in a brain, all of it. The coffee mug post takes the argument through step by step.

Now the new part. The two sides don't have to match. When they don't, the mismatch costs J of the outside divided by the inside, the same J as in Step 1. I'll call how hard an event is felt its intensity, and here's the claim:

An event's intensity is its cost.

The thermometers are my drawing of intensity. The costs are exact: 0, 1/4, 1/4 and 9/8.

How we know. An event has two sides and nothing else, so how hard it's felt depends on how the two compare. Step 1 gives every comparison exactly one cost. That cost is the event's own, and it's the event's intensity. It's zero exactly when the sides match, so a level event is felt and nothing in it is strained. It's above zero at every mismatch. And it's the same for a swapped pair: an outside of 2 over an inside of 1 is felt as hard as an outside of 1 over an inside of 2. The paper "The Self Is Never Free" works this out.³

Notice what the intensity belongs to: the ratio of both sides, not the inside alone. Take an inside of 1. Against an outside of 1 it costs 0. Against an outside of 4 it costs 9/8. Same inside, very different intensity. What's felt hard is how far the inside sits from the outside.

A fair question: if every event is felt, does a mug suffer when you squeeze it?

Every event in the mug is felt, at its own size. The mug isn't someone. A self is a pattern, not material: the material of your body is replaced continually, much of it within months to years, and you stay you. That pattern is one stable rhythm in the Ledger's record of events, and What You Are counts which rhythms can last. A mug is a great many felt events that aren't one rhythm. So there's felt strain in it, and nobody there. Experience is everywhere, and selves are rare. The coffee mug post draws that line. Who can be wronged is a separate question, and this post doesn't settle it.

Zoom out. Step 2 is done. Every event has an outside and an inside, and the inside is experience. How hard an event is felt is its cost: zero at a match, above zero at every mismatch, the same for a swapped pair. Next, and why: that's one event at a time. You aren't one event. You're joined to other people and things by bonds, and Step 3 is how those add up.

Step 3: You're joined by bonds, and you carry their cost

A bond is a comparison that joins two people. Its number is one amount divided by the other, and 1 is level. What you carry is the sum of the costs of every bond you're on.

Back to the friendship. I'll draw it as two bonds, one running each way, each with its own number. You've driven her four times for her once, so the bond from you to her reads 4. The bond from her to you reads 1.

A bond that reads 4 costs 9/8. A bond that reads 1 costs 0. Together the friendship costs 9/8 + 0 = 9/8.

A bond has two ends, one at each person, and each end carries the bond's full cost. The Ledger keeps every bond on both people's own books, and read from either end it costs the same, because a ratio and its flip cost the same. So you carry 9/8, and she carries 9/8. That's why it weighs on both of you when nobody has said a word.

Now add your other bonds. Your sister's bond with you is level, so it costs 0. And you have a bond with yourself: the Ledger writes the load you carry alone as a bond from you to you, and its number reads how heavy that load is. Say yours reads 2. That costs 1/4.

You carry the sum: 9/8 + 0 + 0 + 1/4 = 11/8.

Every number in that sum is exact. Push any bond you're on further off level and the total rises by exactly what that bond's cost rises by.

A bond is a comparison, so it has an outside and an inside like any event. A strained bond is felt at the size of its cost, which is Step 2. That's what the friendship is doing at 2 a.m. The toe is strain too, arriving all at once.

Is a friendship really two numbers?

No. The ride counts are my drawing. The bond is real: it's what the Ledger keeps for a relationship between two people. Not yet derived: which physical quantities are the two amounts, the outside and the inside, for one particular hurt, the toe or the friendship. Derived: the cost of every comparison, and from it the results in Steps 4 and 5.

How it's counted. The sum is the Ledger's own count. Every bond has a direction and a positive number, 1 is level, and a person's cost is the sum of J over the bonds that touch them.⁴ A shared bond is one entry: the Ledger's total for everyone counts it once, and each of its two ends carries all of it.

Zoom out. Step 3 is done. A bond is a comparison joining two people, and you carry the sum of the costs of every bond you're on. A bond at 4 costs 9/8, and both ends carry it. Next, and why: you can see where strain lives. It lives on bonds. So what happens to something that has none?

Step 4: Only a bond can be strained

Your cost can go up exactly when you have a bond. With no bonds, nothing anyone does can raise it. With even one bond, something can.

Here's why. What you carry is a sum over your bonds. With no bonds it's an empty sum, and an empty sum is zero, the way an empty shelf holds zero books. Whatever anyone does anywhere in the Ledger, you're still carrying zero. What an act does to someone is the change in what they carry: their cost after it minus their cost before. For something with no bonds, every act changes it by exactly zero. It's beyond reach.⁵ The word harm names something narrower: a false entry in someone else's own record. Harm is a physical fact and a moral one at once, because the moral law is the physical law: there's one Ledger, and its bonds are physical relations between people. Each person keeps their own record of each bond they're on, and nobody else can write in it. An act that would make another person's record false is a wrong act. An allowed act, one that leaves every record true, never does it.

One bond puts you within reach. Take a level bond, so you carry 0. An act may move a bond only when both of its ends write on it. Writing on a bond means taking part in the change with your own entry: your own yes. That's why a physical bond needs consent: the bond sits on both people's own records, nobody else can write in yours, and a move you didn't write would leave your record false. So say you and the person at its other end both write a move to 2. Now you carry 1/4, and so do they. Push it to 1/2 and you carry 1/4. Push it to 4 and you carry 9/8. Every push off level costs something, because J is above zero everywhere except at 1. Push a level bond by any factor and the cost it adds is exactly J of that factor. The rule that both ends write rests on one step still being derived: that each person's record holds one exact state of the bond.

So the ability to be strained and the ability to be joined are one fact. A bond is a thing that can be strained, and a strain is a thing that's felt. The ability to be hurt and the ability to be reached are the same ability.

And a strain doesn't point at a culprit. A change in what you carry doesn't say whose fault it was, or whether any person chose it. Strain from a deal you both wrote, strain from what feels like bad luck and strain from a bedpost all read the same on the cost, which reads how far a bond sits from level and nothing else. Nothing in the record is authorless: every change to a bond comes from something sent, and who sent it sits on its own line of the record.

Then why not have no bonds, and so no cost?

Something that has never had a bond does carry 0, and nothing anyone does can raise it or lower it. But you can't get there by cutting, and a cut isn't a repair. Cut the friendship and its two bonds stay on the Ledger, because nothing in it is ever erased. They stay at the numbers they had when they ended, 4 and 1, with all of their 9/8. The cut takes away the only route to repairing them, so their cost stays above what meeting in the middle would have left, for good. Counting only the bonds still open gets this wrong. That count drops the whole 9/8, so the cut looks like relief, and it has no way to register what was lost. You can tell the difference. One is a friend. The other is gone.⁶

Zoom out. Step 4 is done. Strain needs a bond: with none, nothing can raise your cost, and with one, something can. A strain says nothing about fault. Next, and why: the same list that prices the hurt prices the repair. Step 5 asks what brings a strained bond back.

Step 5: Relief is exact too

Relief is a fall in what you carry. Between two people, the cheapest way to bring a strained pair down from inside the pair is to meet in the middle, and giving relieves more than it costs.

Start with the floor. From level, the change in what you carry can only be zero or positive, because nothing is lower than zero. Off level, an action can bring what you carry down. That's relief.

Back to the airport. The pair's bonds read 4 and 1. The pair costs 9/8, and both of you carry it.

Now move them to 2 and 2. There's one rule: keep the product. 4 × 1 = 4 and 2 × 2 = 4. Keeping the product is what makes it a repair inside the pair: nothing is added from outside, and nothing is carried off. (Setting both bonds to 1 would cost less still, but it changes the product, so it isn't a repair inside the pair.) The move to 2 and 2 is what the love post calls love.

Each bond now costs 1/4, and the pair costs 1/4 + 1/4 = 1/2. Each of you carries 1/2 instead of 9/8. Each of you is 5/8 lighter.

How we know it's the cheapest. Walk along the pairs that multiply to 4. At 1 and 4 the pair costs 9/8. At 4/3 and 3 it costs 17/24. At 2 and 2 it costs 1/2. The cost is lowest where the two bonds are equal, and that holds for any starting pair: of all the ways to ease two bonds while keeping their product, exactly one is cheapest, and it's the one where they're equal.⁷ The number they meet at, the square root of their product, is called the geometric mean.

The middle isn't 2.5, the ordinary average of 4 and 1. Put both bonds at 2.5 and their product is 6.25, not 4. That's no longer a repair inside the pair, and it costs 0.9, more than 1/2.

And the move rewrites only those two bonds. Your sister's bond with you stays level, and anyone who isn't on those two bonds carries exactly what they carried before.

Now a second case: one of you is carrying a load alone. Another week, your friend is moving apartments by herself. Her own load reads 4. Yours is level, at 1, so you carry nothing. You show up with a van.

She says yes, and you take on part of her load until you meet at 2 and 2. Her load falls from 4 to 2, so it goes from costing 9/8 to costing 1/4. Yours rises from 1 to 2, so it goes from costing 0 to costing 1/4.

She's 7/8 lighter. You carry 1/4 more. The pair's total falls by 7/8 - 1/4 = 5/8, the same saving as before. And 7/8 divided by 1/4 is 3 and a half, so her relief is three and a half times what it cost you.

That isn't the luck of the number 4. Say her load reads r × r, here 2 × 2, so you meet at r. Her relief divided by your cost works out to exactly r + 1/r + 1. For r = 2 that's 2 + 1/2 + 1, which is 3 and a half. And r + 1/r is more than 2 for every r except 1, where her load is level and there's nothing to share, so whatever her load, her relief is more than three times what it costs the helper. The helper pays, and the one who's relieved gains more than the helper pays. Giving relieves more than it costs.

Love has a limit, and the limit is exact too. Say the helper pays each day's cost of the middle out of a reserve, a store of what they have to give. A fixed budget adds the same amount to that reserve every day. If the middle costs more each day than the budget adds, the reserve shrinks day after day until it's empty, and the helper runs down. So love goes as far as both of you can carry and still keep going. The love post works out the numbers for the pair, the load and the limit.

One more thing about relief. It changes what you carry from now on. It doesn't edit the Ledger. The strain you carried is still written down, because nothing in the Ledger is ever erased. The sorry post is about exactly that.

Level is where nothing is strained. The cost stops there, because there's nothing lower. What gladness is, the cost doesn't say.

Zoom out. Step 5 is done. Relief is a fall in cost. Between two people the cheapest repair from inside the pair is to meet in the middle: 4 and 1 become 2 and 2, and 9/8 falls to 1/2. Giving relieves more than three times what it costs. That's every step.

The whole trip, in one breath

You suffer because you're connected. A bond compares two amounts, and a mismatch has an exact cost: 2 costs 1/4, 4 costs 9/8, and there's no top. Every event has an outside and an inside, the inside is experience, and how hard an event is felt is its cost. You're joined to others by bonds, and you carry the sum of their costs. Only a bond can be strained: with none, nothing reaches you, and with one, something can. A strain says nothing about fault. And the same list that prices the hurt prices the repair: 4 and 1 meet at 2 and 2, and giving relieves more than three times what it costs.

The toe at 2 a.m. and the friendship at 2 a.m. are both strain. Something you're joined to went off level, and you feel it at the size of its cost. None of that makes a hurt smaller. It says what a hurt is, and it says what brings it down.

That's how reality is built. Its record is made of comparisons, each one thing told apart from another and written against what came before, and a bond between two people is one of them. Reality isn't built with suffering added on. A bond is a comparison that can be strained and a comparison that can be repaired, and the arithmetic for both is exact.