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's exact, and it comes 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, 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 Ledger will keep the map.

If you haven't met the Ledger, it's the permanent record of everything that has ever happened. It keeps a number for every bond between people, and it never erases a line. We draw it as a book in reading glasses with one response to everything: "Noted." The face is a drawing. The record is real. It comes from What You Are, but you don't need that post to follow this one.

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 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 Gary and his long-suffering driver from the love post: ten rides to his one.

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 choose it. Ask for a cost with five properties: it has no jumps, it treats a ratio and its flip alike, it's zero at a match, it combines the costs of comparisons by one fixed law, and one calibration sets how sharply it curves up from level. Exactly one function has all five. That's proved, and published.¹ The love post works through the combining law with numbers, if you want to check it by hand.

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 of 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. So every event is felt: the bumps in a coffee mug, the signals in a brain, all of it. The coffee mug post gives the reasons, 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.²

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.

Yeah-But, the voice in the back of your head that questions every big claim, has a question. "Yeah, but if every event is felt, my mug suffers when I squeeze it."

Every event in the mug is felt, at its own size. The mug isn't someone. A self is one stable rhythm in the Ledger, which is what What You Are is about, and 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 both ends carry all of it. Neither end carries half. 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 of your own, which reads how heavy your own 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.

Yeah-But clears his throat. "Yeah, but a friendship isn't 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. Which physical comparisons make up a particular hurt, the toe or the friendship, is still being mapped. The cost on each one is exact.

How we know. 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.³ The world counts a shared bond 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. The Ledger calls a change in what someone carries harm: their cost after an action minus their cost before. For something with no bonds, the harm of every action is exactly zero. It's beyond reach.⁴

One bond changes that. Take a level bond, so you carry 0. Push it to 2 and you carry 1/4. 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.

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. Harm is a change in what you carry. It doesn't say whose fault it was, or that anyone's was. Strain from a wrong, strain from 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. The bedpost has never been convicted of anything. A strain isn't a sentence.

Yeah-But is back. "Fine. Then I'll have no bonds. Zero cost."

With no bonds, the Ledger does write 0 for you, and it's right. Nothing anyone does can raise it, and nothing anyone does can lower it either. But a cut isn't a repair. Cut the friendship and your cost drops by the whole 9/8, which is more than meeting in the middle would save, because the cost only counts the bonds that still exist. It reads a cut as relief, and it can't register what was lost. You can tell the difference. One is a friend. The other is gone.⁵

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, harm 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's a different act with its own question: who pays for it.) 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.⁶ 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 touches only those two bonds. Your sister's bond with you stays level. Nobody outside the pair carries any of it.

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.

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. Whatever her load, her relief is always 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. If the middle costs a helper more than the helper's reserve can keep paying for, the helper runs down. Then 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. It isn't built with suffering added on. It's built out of bonds, and a bond is something that can be strained and something that can be repaired, and the arithmetic for both is exact.

(The Ledger would like you to know that it noted the toe, the airport and this post. It notes everything. It's keeping the airport at four to one, and it isn't taking sides. Don't take it personally.)