Karma Is Real, and It Isn't a Referee

Your coworker Gary took credit for your project.

You spent three months on it. Gary presented it to the whole company, with the word "my" in every other sentence. Last week he got promoted.

So where's the karma?

Everyone knows how this story is supposed to end: "It'll come back to him." But come back how? Through what? Who's doing the sending?

The short answer

Yes. What you do comes back to you, and it comes back the moment you do it. Nobody sends it.

On Monday, Gary's grab went into reality's permanent record, under his name, and nothing erases it. Physics already agrees on the part it covers: its basic laws never destroy information about the past. The grab is a line in Gary's own book, the record he keeps of his relationship with you, and the line is false: it says the credit stands 2 to 1 his way, and the relationship didn't move. An act may change a relationship only when both of its ends write on it, and Gary alone can't move it, so your own book is still true. His false line is his, under his name, for good, and the code set out in our paper The Moral Code, which judges acts between people, forbids writing it. A relationship between two people that does sit out of balance has a cost. Each end carries all of it, and the record charges it again at every step the relationship is held out of balance.

What doesn't exist is a referee: nothing that watches for the foul, blows a whistle and hands Gary a matching penalty later. He can keep the promotion. Nothing in physics makes anyone good. And nothing Gary writes alone reaches into a relationship you're in, then or later. Nothing moves a relationship between acts: a relationship changes only through what someone sends, and sending is an act. The code leaves one gap open, at a relationship's own repair reserve, and Step 5 says what it is.

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

1. Nothing you do is erased. Every act is a permanent entry under your name. The basic laws of physics never destroy information, and in the record a new entry never alters an earlier one. Repair and forgiveness are new lines after an entry. They never edit it.
2. Taking is never free. A relationship is a comparison of two amounts, with one number and one cost: zero when the amounts match, growing as they differ. Move it out of balance and nothing is made or lost. The relationship still costs something: 1/4 for a move by a factor of 2. But an act may move a relationship only when both of its ends write on it. Gary, writing alone in his own book, moves nothing: his own record is false, and the false line stays under his name for good. Acting to change the relationship without your write would be harm, and the code forbids it.
3. Both ends carry it, equally. A comparison needs both of its terms, so each person is an end of the whole relationship and carries all of its cost: 1/4 each at 2, counted once in the record. No allowed act moves a relationship you're in without your write. One that does is harm: possible, and forbidden. And writing alone moves no relationship, so Gary can't raise your end at all by writing alone.
4. Holding it is a standing charge, and it runs out. The record charges the relationship at every step it stays out of balance. When each step's charge comes out of a reserve, the amount a person has left to keep going on, and the charge is bigger than what comes back each step, the reserve falls until it's gone.
5. What karma isn't. No referee sends a matching event back. Nothing moves a relationship between acts, so nothing reaches someone who wrote nothing later, on its own. Nothing forces anyone to be good.

Why this matters: it tells you what to expect. Not a payback from outside, and not nothing: a record and a charge. The record is yours: what you write is under your name for good, and a false record stays false until you correct it with a new line. The charge sits on a relationship held out of balance, on both of its ends, and the record charges it again at every step the imbalance is held. The same rule runs the other way, too: lower the relationship's cost and your own end falls by exactly as much as theirs does. And it shows where the way out is: repair takes both of you, and the same cost formula that makes a move off balance cost something shows the cheapest way back, and Meet in the Middle works it out.

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.

Step 1: Nothing you do is erased

Every act is a permanent entry under your name. A later act adds a line after it. It never rewrites it.

Reality keeps a permanent record of every event, and nothing in it is ever erased. No outside keeper writes it: every event leaves a complete trace, and the traces together are the record. The past still exists.

Known physics already says this for the part it covers. Its basic laws never destroy information. In quantum mechanics that is 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. Hawking's 1976 calculation said a black hole destroys the information that falls into it. That clashed with unitarity, which is why it became a famous problem. Most physicists now expect the information to come back out in the radiation, and the open question is how.¹

Our claim goes further. The record this post describes is reality's own, and our work proves that it keeps every entry: writing a new entry never alters an earlier one.² What You Are develops the record and the process that writes it.

Gary's Monday is a line in the record. It's still there.

Two separate facts say where later events go. The first says what an entry is. Each entry is a comparison, and a comparison needs information about both of its sides: "colder" compares your second sip of coffee with the first. So every entry is written against what came before. The second: looking at an entry is itself an event, one that comes after the thing it looks at. It doesn't reach back. So whatever Gary does after Monday is a new event, written after Monday's line. What keeps Monday there is one thing, the record's own rule: writing a new entry never alters an earlier one.

Gary can do plenty after Monday. On Friday he can confess at the next company meeting, give you the credit there, and correct his own book with a new line. That's real: from then on his book is true again. It's also a new line, and Monday is still above it. Forgiveness is real too. Where one person owes another, a release of what's owed changes it once both of them write it: one says "forget it," and the other takes it. That's a new line as well, and what it releases is still above it. Sorry Doesn't Rewind the Tape works through repair and release with numbers.

So the first thing that comes back is the plainest one: the thing you did. It never left.

Zoom out. Step 1 is done. Every act is a permanent entry under your name, and repair and forgiveness are new lines after it. Next, and why: Gary's line is in the record. Now ask what it does to the relationship between you and him. A relationship out of balance has a cost with an exact size, and an act may move a relationship only when both of its ends write.

Step 2: Taking is never free

Move a relationship out of balance and nothing is made and nothing is lost. The relationship still costs something, and the cost climbs faster than the move. But an act may move a relationship only when both of its ends write on it. Gary, writing alone in his own book, moves nothing: his own record is false, and the false line stays under his name for good. Acting to change the relationship without your write would be harm, and the code forbids it.

Start with what a relationship is. A comparison needs both of its terms and reads nothing else, so the basic unit of the record is a relationship: a comparison between two things. Between two people, it compares two amounts of the same kind. Its number is one amount divided by the other. When the two match, the number is 1, and I'll call that balance. When one side has twice as much, the number is 2, and read from the other end, the same relationship is at 1/2. It's one relationship with one number, read from its two ends. The two ends are the two people it joins.

I'll draw Gary's grab with the credit as the relationship's number. Balance means each of you holds the credit for what you did. The relationship is real: it's what the record keeps for two people. The credit is my choice for this example. Not yet derived: which comparisons in a working relationship the record carries, and what each one compares. Derived: everything below uses only the number, so it holds whatever the relationship compares.

Every number except 1 costs something. The cost measures how far the two sides are from matching. It has to be zero when they match, grow as they differ, and be the same whichever side you read from. Add the rule for how costs combine when comparisons chain (A is twice B and B is three times C, so A is six times C) and one calibration, how sharply the cost rises near balance, and exactly one formula is left: add the number to its flip (1 divided by the number), halve it, and subtract 1.³

Check the middle row. 2 plus its flip, 1/2, is 5/2. Half of that is 5/4, and 5/4 minus 1 is 1/4. For 1/2 the flip is 2, so the sum is the same, and so is the cost. Having twice as much as the other side costs exactly what having half as much costs. It's the same relationship read from the other end.

Now the records. In our paper The Moral Code, which sets out the code for acts between people, each relationship is recorded twice, once by each of its ends, in that end's own book.⁴ Nobody writes in another's book. A record is true when it gives the relationship's actual number. Two true records of one relationship agree, so a gap between the two records is not a claim on anyone. It means at least one of them is false.

Now Monday. Gary presents your project as his, and he writes in his own book that the credit now stands 2 to 1 his way. You write nothing, so your book still says 1. An act may change a relationship only when both of its ends write on it, and no written entry moves a relationship of someone who wrote nothing. So the relationship doesn't move. It's still at 1, and it still costs 0. Your book says 1, and it's true. Gary's book says 2, and it's false, because the relationship's actual number is 1.

That false line is Gary's, under his name, for good (Step 1). Writing it isn't allowed. The code has four clauses, the conditions an act must meet before its cost is even weighed, and Step 5 lists them. Its second clause says that after the act, every record of every relationship is true. Gary's line leaves his own record false, so the code forbids it. Gary can make his own book true again by correcting it with a new line. The false line stays above the correction, and nobody else can write in his book.

Now the move. Take a relationship at balance and move it to 2. Read from Gary's end, its number goes from 1 to 2, one doubling up. Read from yours, it goes from 1 to 1/2, one halving down. I'll call a move like that taking. The word is mine. The numbers come from the cost formula.

A doubling multiplies by 2 and a halving multiplies by 1/2, so one cancels the other: 2 × 1/2 is 1, the same as 1 × 1. Counted in doublings, Gary's end gained one and yours lost one, so nothing was made and nothing was lost. One doubling moved from your side to his.

Now price it. The relationship at 2 costs 1/4. A moment ago it cost 0. And a move like this takes both of you: Gary can't write it alone.

Counted in doublings, taking is zero-sum: the doubling Gary's end gains is the one yours loses. On the cost formula it isn't: the relationship got 1/4 more expensive.

That isn't the luck of moving by 2. For a move by any factor x, the relationship sits at x from one end and 1/x from the other, and it costs one number: (x + 1/x)/2 − 1. That equals (x − 1)² divided by 2x, a square over a positive number. It's never negative, and it's zero only when x is 1. So every move costs. A move by 3/2 costs 1/12. A move by 2 costs 1/4. A move by 4 costs 9/8. Double the move from 2 to 4 and the cost is four and a half times as much.

Zoom out. Step 2 is done. A relationship is one comparison with one number and one cost, kept in two records, one in each end's own book. A move by a factor of x costs (x + 1/x)/2 − 1: more than zero for every move, and climbing faster than the move. Gary, writing alone in his own book, moves nothing: his own record is false, and the false line stays under his name for good. Yours is still true. Next, and why: who carries that cost? A relationship has two ends, and that decides it.

Step 3: Both ends carry it, equally

A relationship has two ends, one at each person, and each end carries the whole of its cost. At 2, Gary's end carries 1/4 and yours carries 1/4, and the record counts the cost once. And no entry written without you can move a relationship you're in, so Gary can't raise your end at all by writing alone.

Where does the relationship's 1/4 sit? On each person, in full. The reason is what a comparison is: it needs both of its terms, so each of you is an end of the whole relationship, and each stands in the whole unbalanced relationship. This is the count in The Moral Code. It defines a participant, anything that is an end of a relationship, and says what a participant carries: the cost of the relationships it is an end of.

Count it. Suppose you and Gary both write a move to 2. Before it, Gary's end carried 0 and so did yours. After it, Gary's end carries the relationship's cost, 1/4, and so does yours. Gary's cost rose by 1/4, and so did yours. The record doesn't add the two ends: its real cost counts the relationship once, at 1/4, and the code's verdicts use that real cost. Not yet derived: why those verdicts count by relationships and not by persons. The code still forbids this move, because doing nothing leaves less cost. An act both ends write can still be forbidden.

The general fact is exact, and it holds for any cost formula, not only ours: the two ends do the work, not the formula. If a change sits entirely inside the relationship between two people, it changes the cost at one end by exactly the amount it changes the cost at the other. Raise the cost and both ends rise by the same amount. Lower it and both fall by the same amount. In the record, a relationship between two people can't cost one of them without costing the other the same.

So no change inside the relationship can make your end heavier without making Gary's heavier by exactly as much, and none can lighten his without lightening yours by the same. Meet in the Middle shows the move that lowers it the most.

And no act can change a relationship you're in unless you write on it. That holds at the step the act is done, when every record is true. The reason is in the clauses: to push cost onto you, an act would have to make your own record false, and nobody writes in another's book. A false entry in someone else's own record is what the code calls harm, and its second clause excludes it. Nothing moves it later, on its own, either: nothing moves a relationship between acts, and Step 5 says why.

A fair question: Gary started it. Why does it cost you?

It doesn't, not by anything he writes alone. Look at what he wrote. Gary wrote Monday's line in Gary's book. You wrote nothing, and your book has no line. No allowed act moves a relationship of someone who wrote nothing. An act that does is harm, and the code forbids it. Gary only wrote, so the relationship didn't move, your book is still true, and your end carries what it did before. The cost doesn't ask who started it. It sits on both ends of a relationship that is out of balance, and an act may move a relationship only when both ends write. The record does keep who wrote, on a different line: the authors of an act are exactly the participants whose own records it changes, and consent is the record of who wrote. Monday has one author, Gary.

Carol, three towns over, who has never met either of you, can't write in either book. She isn't an end of your relationship, so a change inside it leaves what she carries exactly as it was. A Favor Isn't a Yes works this out.

A gap between two records means at least one of them is false. It doesn't say who wrote the false one. That's on the record's other line: who wrote this.

The code builds a clause on this: an act may change a relationship only when both of its ends write on it, so that both records stay true. That clause rests on one step still being derived: that each record holds the relationship's one exact state. And that an act physically moves a relationship only when both ends write, with every write on it landing at both ends at once, is the step our current work is deriving. Gary wrote alone, so the relationship didn't change, and your record of it is still true. His own record is the false one, and the code forbids writing it. Step 5 says what forbidden means.

Zoom out. Step 3 is done. Each end of a relationship carries the whole of its cost, and the record counts it once. No allowed act moves a relationship you're in without your write. One that does is harm: possible, and forbidden. And writing alone moves no relationship, so Gary can't raise your end at all by writing alone. Each end is written only by its own author, and the record keeps who wrote. Next, and why: a cost that sits there is one thing. A cost that's charged again at every step is another. How long can an end keep paying?

Step 4: Holding it is a standing charge, and it runs out

The record charges a relationship again at every step it stays out of balance. Take a person's reserve, what they have left to keep going on. If each step's charge comes out of it, and the charge is bigger than what comes back each step, the reserve falls by the difference every step until it's gone.

Step 2's move was one moment, one cost. But a relationship stays where it was moved until it's moved again, and the record charges for every step it's held. Here's why: the code reads time through the complete record, which holds every relationship at the number it actually has and adds up a history's cost at every step. So a relationship held out of balance is charged again at every step it's held. The Moral Code proves the general fact for a record that decides each relationship's charge from that relationship's own entry alone, the way a comparison reads only its own two terms: when two histories agree everywhere except at one step, where one costs more, the record charges that excess at every later step, undiminished.⁵ Not yet derived: that the record reads each relationship that way.

That recurring charge is the standing charge. Call each step of the standing charge a cycle.⁶ The numbers below count cycles, so they hold however long a cycle lasts.

What the standing charge does to a person depends on where it's paid from. This example runs on one adopted rule:⁷ every cycle, the person's budget goes into their reserve and the bill comes out. The budget is what comes back into the reserve each cycle, and the bill is the relationship's cost per cycle. Each end gets the same bill, because each end carries the whole cost. After n cycles:

reserve = starting reserve + n × (budget − bill)

I chose the numbers to keep the arithmetic small: a reserve that starts at 1, and a budget of 1/4 a cycle. Say you and Gary both wrote the relationship out of balance and hold it there. It stays where the two of you put it, because nothing moves a relationship between acts. Now run three places it can sit.

Read the rows. At 3/2 the relationship costs 1/12 a cycle, less than the 1/4 that comes back, so the reserve grows and either of you can hold it forever. At 2 it costs 1/4 a cycle, exactly what comes back, so the reserve holds at 1. At 4 it costs 9/8 a cycle, 7/8 more than comes back, so the reserve reads 1/8 after one cycle and −3/4 after two: it's gone at cycle 2.

The rule behind the table is exact, and it doesn't depend on my numbers. If the bill is at most the budget, the reserve never falls. If the bill beats the budget by some amount d every cycle, the reserve falls by d each cycle, so it's at zero or below from cycle R ÷ d on, rounded up to a whole cycle, where R is the starting reserve. Here R is 1. At 4, d = 9/8 − 1/4 = 7/8, so 1 ÷ (7/8) = 8/7, which rounds up to 2. The dividing line is the relationship whose bill equals the budget: (x + 1/x)/2 − 1 = 1/4, so x + 1/x = 5/2, which gives x = 2 exactly. With this budget, a relationship at 2, or closer to balance, never runs a reserve down.

A reserve at zero or below isn't viable: there's nothing left to keep going on. So no one whose relationship costs more each cycle than the budget brings back keeps going. The rule doesn't say every relationship out of balance is ruinous. One whose cost is inside the budget never is, and someone whose relationships all sit at balance pays nothing, so their reserve only grows.

Not yet derived: what a person's reserve and budget are in physical terms and how large they are, and why each cycle's bill comes out of the reserve. The rule bills each end what Step 3 says it carries: the relationship's whole cost. Derived: given a reserve, a budget and a bill, a bill above the budget runs the reserve out.

So here's Gary, holding a relationship out of balance that you both wrote there. Every cycle its cost comes out of his reserve. If his budget covers it, he can hold it and pay for it forever. If it doesn't, the standing charge is what uses him up. Step 3 says your end carries the same cost, so the same bill comes out of your reserve too. Gary's lone line on Monday starts no bill of this kind: it moved no relationship, so it put no cost on either end.

The two of you can end the standing charge by repairing the relationship. Bringing it back to balance changes it, so both of its ends write the repair, and one end alone can't. The code puts it in three words: love takes two.

Walking away doesn't end it. Either of you can end the relationship alone: the fourth clause, in Step 5, lets one end end it. But an ended relationship stays on the record with all of its cost, and the record still charges it at every step. It keeps that cost: no allowed act touches an ended relationship, and nothing moves a relationship between acts. So ending a strained relationship removes the only route to repairing it.

Zoom out. Step 4 is done. A relationship held out of balance is charged every cycle, on each end. A bill within the budget can be paid forever, and a bill above it runs the reserve to zero. A repair takes both ends' writes, and ending the relationship leaves its cost on the record. Next, and why: the limits. Three things people expect from karma aren't in any of this. Each has an exact reason.

Step 5: What karma isn't

Three limits.

No referee. Nothing in the record schedules a matching event. It writes down what happened under the name of whoever wrote it, puts a relationship's whole cost on both of its ends, and charges each end every cycle. It has no step where it looks up Gary and arranges something bad for him: no lost project, no stubbed toe, no worse boss. What the record holds against Gary is his own false line, under his name, and the standing charge on any relationship of his that sits out of balance. Nothing weighs the promotion against either one. Gary can keep the promotion for good.

Does Gary get away with it? He keeps the promotion, and the record doesn't take it back. He also keeps the line he wrote: it's false, the code forbids it, and it stays under his name for good. His book stays false until he corrects it with a new line. And any relationship of his that sits out of balance is charged every cycle, out of his reserve.

Nothing reaches you later, on its own. Gary's line moved nothing of yours: no written entry moves a relationship of someone who wrote nothing. So harm, a false entry in someone else's own record, is excluded by the code's clauses.⁸ And nothing moves a relationship between acts.

Here's why. Between acts, the record holds where the last act left it. Strain enters a relationship only through what someone sends, and every sending belongs to an act. So nothing reaches you except through an act, and an act that moves a relationship you're in without your write is harm: possible, and forbidden.

The one gap is a relationship's own repair reserve: the clauses don't yet read changes to it, so a taking from it passes them with no write. Not yet derived: whether reading consent through the amounts an act moves closes that gap. Gary's Monday is a line in his own book. It takes from no one's reserve.

Now a network, where it matters that the clauses come first. Here's the smallest example: a way of settling a debt that lowers the total cost and would still put cost on someone who had nothing to do with it.

Three people, Ann, Ben and Cy, are each joined to the other two. To keep the arithmetic small, I'll give each relationship an amount. Ben owes Ann 1. Cy owes nothing and is owed nothing. In this example a relationship carrying an amount t costs t²/2, half the square. That is almost exactly the cost formula from Step 2 for small amounts, where t is the log of the relationship's number (a relationship at e^t costs cosh t − 1), and the square keeps the arithmetic exact. The one debt sits on the Ben and Ann relationship and costs 1/2.

Now settle the books. Re-route the debt so that everyone's net position (what they're owed minus what they owe) stays the same, and make the total cost as low as it can go. The cheapest way sends a third of the debt the long way round: send an amount x that way and the total cost is (1 − x)²/2 + x²/2 + x²/2, which is lowest at x = 1/3. Ben owes Ann 2/3 directly, Ben owes Cy 1/3, and Cy owes Ann 1/3. Ann is still owed 1 in all. Ben still owes 1 in all. Cy still nets zero.

Add it up. Ben and Ann: (2/3)² ÷ 2 = 2/9. Ben and Cy: (1/3)² ÷ 2 = 1/18. Cy and Ann: 1/18. The total is 2/9 + 1/18 + 1/18 = 1/3, down from 1/2. Ann and Ben each carry less than before. And Cy, who had nothing to do with the debt, would sit at the end of two relationships that cost 1/18 each. Before, they cost nothing.

The code doesn't allow this re-routing unless Cy writes on both of his relationships: an act may change a relationship only when both of its ends write on it. Without his writes it would leave his own records of them false, and the second clause rules that out. The clauses come first. No price can do the clauses' work: any finite charge on pushing cost onto others is outweighed by some push, because the relief a push can buy grows without bound. So the clauses decide which acts are allowed, and only then does cost compare them. Lowering the total isn't the same as burdening no one.

Nothing forces anyone to be good. Everyone lives under the same cost formula, and people take anyway. The code forbids a false line, and Gary wrote his anyway: nothing prevented it. A relationship that both ends hold out of balance, within what their budgets cover, can be held forever. The rule limits what anyone can afford to hold. It doesn't make anyone kind.

The code sorts acts into permitted and forbidden. An act is admissible, meaning it meets the code's four clauses, exactly when:

1. it acts only on live relationships, the ones that exist now;
2. every record of every relationship is true after it (a record is true when it gives the relationship's actual number);
3. it changes a relationship only when both of its ends write on it;
4. it ends a live relationship only when one of that relationship's own ends ends it.

Of the admissible acts, the code permits exactly those that leave the least total cost on the complete record. Every other act is forbidden.⁹ Gary's grab broke the second clause: after it, his own record of the credit is false. It didn't break the third, because it changed no relationship. So the code forbids it. Forbidden isn't prevented. He wrote it anyway, and it stays under his name. The record alone excludes nothing: doing nothing, even where a repair would lower the cost, stays possible forever, while the record's charge on it grows without bound.

Zoom out. Step 5 is done. There's no referee: nothing sends a matching event back. Nothing moves a relationship between acts, so nothing reaches someone who wrote nothing later, on its own, and a settlement that lowers the total still needs every end's write: the clauses come first. And nothing forces anyone to be good. Next: the whole trip, in one breath.

The whole trip, in one breath

What you do is written under your name, and nothing erases it: repair and forgiveness are new lines after it. A relationship is one comparison, and moving it out of balance costs something even when nothing is made or lost: (x + 1/x)/2 − 1 for a move by x, so 1/4 for a move by 2. But an act may move a relationship only when both of its ends write on it, and Gary, writing alone, moved nothing: his own record is false, and the false line is his for good. Each end of a relationship carries the whole of its cost, 1/4 each at 2 and counted once in the record, so a change inside it changes both ends by exactly the same amount. Hold it out of balance and the record charges it every cycle. When the charge comes out of a reserve, past what the budget brings back the reserve falls until it's gone. And there's no referee. Nothing moves a relationship between acts, so nothing Gary did reaches you later, on its own, and nothing makes anyone good.

That's how reality is built. It has no referee and schedules no matching event, and it doesn't need one. It records what you did under your name, puts a relationship's whole cost on both of its ends, and charges both ends again every cycle the relationship stays out of balance. Karma is real, and it isn't a referee.