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?

(Yes, that Gary: the drummer from Part 1 of The Universe Writes in Pen. The band stopped calling, and he has a day job now.)

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.

On Monday, Gary's grab went into reality's permanent record, under his name, and nothing erases it. It also made the bonds between you and him lopsided. (A bond compares two amounts, and lopsided means they don't match. I draw each relationship as two bonds, one running each way.) A lopsided bond costs, and both ends of it carry the cost: Gary's end carries exactly what yours does. And that cost is charged again every cycle he keeps the bonds lopsided.

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. Harm lands on people who did nothing, and nothing in physics makes anyone good.

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. Repair and forgiveness are new lines after it. They never edit it.
2. Taking is never free. Push a level pair of bonds apart, one up and one down, and nothing is made or lost. The pair still costs something: 1/2 for a push by a factor of 2.
3. Both ends carry it, equally. A bond has two ends, and each end carries the whole of it. Gary can't put a cost on your end without putting the same cost on his.
4. Holding it is a standing charge, and it runs out. Each cycle (the eight-tick beat from Part 1) the pair stays pushed apart, its cost comes out of a reserve, the amount you have left to keep going on. When that bill is bigger than what comes back each cycle, the reserve falls until it's gone.
5. What karma isn't. No referee sends a matching event back. Harm lands on people who did nothing. Nothing forces anyone to be good.

Why this matters: it tells you what to expect. Not a payback from outside, and not nothing: a bill. It's written under the name of whoever did it, it sits on both ends of the bond, and it comes due every cycle the imbalance is held. The same rule runs the other way, too: lighten a bond and you lighten your own end by exactly as much as you lighten theirs. And it shows where the way out is: the same price list that makes a push 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. The Ledger, who you'll meet in a minute, will keep the map.

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.

Here's the one idea you need from Part 1: the past still exists. Reality keeps a permanent record of every event, and nothing in it is ever erased. We call it the ledger. In the drawings it's a character called the Ledger: a thick book in reading glasses with one response to everything that has ever happened. Noted. The face is a drawing. The record is real.

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

Here's how we know the line can't come out. Step 1 of Part 1 starts with a cup of coffee. You can only know your second sip is colder if something kept a note about the first, because "colder" compares two moments and needs information about both. And looking at a note is itself an event, one that comes after the thing it looks at. It doesn't reach back. Follow that through and you get one record of every event, where each new event adds to the record and none of them rewrites an earlier entry.

Gary can do plenty after Monday. On Friday he can confess and give you the credit at the next company meeting. That's a repair, and it's real: from then on, what each of you holds is different. It's also a new line, and Monday is still above it. You can say "forget it" and release what he owes you. That's real too. It changes what's owed. It's a new line as well, and Monday is still above it. Sorry Doesn't Rewind the Tape works through both 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 Ledger. Now put a price on it. A lopsided relationship costs something, and the cost has an exact size.

Step 2: Taking is never free

Push a level pair apart, one side up and one side down, and nothing is made and nothing is lost. The pair still costs something, and the cost climbs faster than the push.

Start with what a bond is. A bond joins two people and 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 level. When one side has twice as much, the number is 2, and read from the other end, the same bond is 1/2. I'll draw each relationship between two people as two bonds, one running each way, each with its own number.

I'll draw Gary's grab with the credit as the bond's number. Level means each of you holds the credit for what you did. The bond is real: it's what the Ledger keeps for a relationship between two people. The credit is the drawing. What a real working relationship's bond compares is still being worked out. Everything below uses only the number on the bond, so it holds whatever the bond compares.

Every number except 1 costs something. The price list is one formula: add the number to its flip (1 divided by the number), halve it, and subtract 1.¹

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 bond read from the other end.

Now the move. In the Ledger, a move that tips a level pair apart, one number up a doubling and the other down a halving, is what I'll call taking. The name is ours. The arithmetic isn't.

Gary presents your project as his. His number goes from 1 to 2. Yours goes from 1 to 1/2. Check what that did: his went up one doubling and yours went down one halving, and 2 × 1/2 is 1, the same as 1 × 1. Counted in doublings, nothing was made and nothing was lost. One doubling moved from your side to his.

Now price the pair. The bond at 2 costs 1/4. The bond at 1/2 costs 1/4. Together: 1/2. A moment ago the pair cost 0.

Counted in doublings, taking is zero-sum: the doubling Gary gains is the one you lose. On the Ledger's price list it isn't. The pair got 1/2 more expensive.

That isn't the luck of pushing by 2. For a push by any factor x, one bond sits at x and the other at 1/x. They cost the same, so the pair costs twice one of them: x + 1/x − 2. That equals (x − 1)² divided by x, a square over a positive number. It's never negative, and it's zero only when x is 1. So every push costs. A push by 3/2 costs the pair 1/6. A push by 2 costs 1/2. A push by 4 costs 9/4. Double the push from 2 to 4 and the pair costs four and a half times as much.

Zoom out. Step 2 is done. A pair pushed apart by a factor of x costs x + 1/x − 2: more than zero for every push, and climbing faster than the push. Next, and why: who carries that cost? A bond has two ends, and that decides it.

Step 3: Both ends carry it, equally

A bond has two ends, one at each person, and each end carries the whole of it. So Gary can't put a cost on your end without putting the same cost on his.

Here's how the Ledger counts it, and why. Where does the pair's 1/2 sit? On each person, in full. When a bond is out of balance, Gary stands in an unbalanced relationship, and so do you. Neither of you stands in half of one.²

Count it. Before the push, Gary's end carried 0 and so did yours. After it, Gary's end carries both bonds: 1/4 + 1/4 = 1/2. Your end carries both bonds: 1/4 + 1/4 = 1/2. Gary's cost rose by 1/2, and so did yours.

The general fact is exact, and it holds for any price list, 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 Ledger, a bond between two people can't cost one of them without costing the other the same.

So Gary can't make your end heavier without making his own heavier by exactly as much, and he can't lighten his own without lightening yours by the same. Meet in the Middle shows the move that lowers it the most.

Yeah-But, the small voice in the back of your head that has never once said wow, clears his throat. "But Gary started it. Why does it cost you?"

The Ledger looks up. "Noted. The bond has two ends."

The cost doesn't ask who started it. The Ledger does keep that, on a different line. Each end keeps its own book and writes only its own. Gary's pen wrote Monday's line in Gary's book. You wrote nothing, and your book has no line. The gap between the two books belongs to the relationship, and only one of the two people at its ends, writing alone, can close it. Nobody else can. Carol, three towns over, who has never met either of you, can't write in either book, and a change inside your bond leaves what she carries exactly as it was. A Favor Isn't a Yes works this out.

A gap shows its size. It doesn't show who opened it. That's on the Ledger's other line: who wrote this.

Zoom out. Step 3 is done. Each end of a bond carries the whole of it, so what Gary does to your end he does to his own, by exactly the same amount. Each end is written only by its own author, and the books show the size of a gap, not who opened it. Next, and why: a cost that sits there is one thing. A cost that's charged again every cycle is another. How long can Gary keep paying?

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

Every cycle the pair stays pushed apart, its cost comes out of each end's reserve again. If the bill is bigger than what comes back each cycle, that reserve falls by the difference every cycle until it's gone.

Step 2's push was a move: one moment, one cost. But the pair doesn't snap back. It stays pushed apart for as long as the books stay that way, and the Ledger charges for every cycle it's held. That recurring charge is the standing charge. A cycle is eight ticks, the beat Part 1 counts time in.³

Three more words. A person's reserve is what they have left to keep going on. Their budget is what comes back into the reserve each cycle. Call the pair's cost per cycle the bill. This example runs on one rule:⁴ every cycle, the budget goes in and the bill comes out. After n cycles:

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

I chose the numbers to fit on a napkin: a reserve that starts at 1, and a budget of 1/4 a cycle. Now run Gary's three options.

Read the rows. A push by 3/2 costs 1/6 a cycle, less than the 1/4 that comes back, so the reserve grows and Gary can hold that push forever. A push by 2 costs 1/2 a cycle and only 1/4 comes back, so the reserve loses 1/4 each cycle: after four cycles it reads zero. A push by 4 costs 9/4 a cycle, and the reserve is gone in one.

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 is 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. The push by 2 has d = 1/4, so 1 ÷ (1/4) = 4 cycles. The push by 4 has d = 2, so 1 ÷ 2 = 1/2, which rounds up to 1. With a budget of 1/4, the dividing line is a push of about 1.64: hold a push up to that and the reserve never falls.

A reserve at zero or below isn't viable: there's nothing left to keep going on. So no one who holds a push above their budget, every cycle, keeps going. The rule doesn't say every push is ruinous. A push inside the budget never is, and someone who holds nothing pushed apart pays nothing, so their reserve only grows.

What a person's reserve and budget are in physical terms, how large they are, and why each cycle's bill comes out of the reserve are still being worked out. Given a reserve, a budget and a bill, the rule that a bill above the budget runs the reserve out is exact.

So here's Gary. His pair stays pushed apart for as long as he lets it, and 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.

Zoom out. Step 4 is done. A pair held pushed apart is charged every cycle. A bill within the budget can be paid forever, and a bill above it runs the reserve to zero. 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 Ledger schedules a matching event. It writes down what happened, puts the cost on both ends of the bond, and bills 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. The only thing the Ledger takes from Gary is the standing charge from Step 4, out of his own reserve. Nothing weighs the promotion against it. Gary can keep the promotion for good.

Yeah-But has been waiting for this one. "So Gary gets away with it?"

The Ledger looks up. "Noted. And billed."

Harm lands on people who did nothing. You are the first case. You did nothing on Monday, and the pair's cost sits on your end exactly as it sits on his. The same bill comes out of your reserve every cycle. If your budget is smaller than his, you can run out first.

Gary's push stayed inside your relationship, so Carol carries what she always did. But people sit in networks, and what runs through a network doesn't stay inside one bond. Here's the smallest example.

Three people, Ann, Ben and Cy, are each joined to the other two. To keep the arithmetic small, I'll draw each relationship as one bond that carries an amount. Ben owes Ann 1. Cy owes nothing and is owed nothing. In this example a bond carrying an amount t costs t²/2, half the square. The price list is almost exactly that for small amounts, and the square keeps the arithmetic exact. The one debt sits on the Ben and Ann bond 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. 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, now sits at the end of two bonds that cost 1/18 each. Before, they cost nothing.

Lowering the total isn't the same as burdening no one.

Nothing forces anyone to be good. Everyone lives under this price list, and people take anyway. Nothing in it stops a push: Gary pushed, and nothing prevented it. A push inside his budget is one he can afford to hold forever. The rule limits what anyone can afford to hold. It doesn't make anyone kind.

Zoom out. Step 5 is done. There's no referee: nothing sends a matching event back. Harm lands on the other end of the bond and, through a network, on bystanders. 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. Push a level pair apart and nothing is made or lost, yet the pair costs something: x + 1/x − 2 for a push by x, so 1/2 for a push by 2. Each end of a bond carries the whole of it, so what you do to the other end you do to your own, by exactly the same amount. Hold the pair pushed apart and its cost comes out of the reserve every cycle: past what the budget brings back, the reserve falls until it's gone. And there's no referee, harm lands on people who did nothing, and nothing makes anyone good.

That's how reality is built. It has no referee and sends nothing back, and it doesn't need one. It writes what you did in your name, charges both ends of the bond, and bills both ends again every cycle it stays lopsided. Karma is real, and it isn't a referee. It's a pen, a price list and a reserve.

(The Ledger would like you to know that it noted Gary's promotion too. Separate line. It has no comment.)