What Is Freedom? Nobody Else Can Write in Your Book

You have one slice of pizza left, which you can't cut, and two friends who are equally hungry. You've already eaten.

Give the slice to either friend and that's fine. Keep it while they watch and it isn't.

Now swap the slice for a pot of soup, which you can ladle out any way you like. More choices should mean more freedom. It means less. With soup there's exactly one right way to ladle it, and every other way is wrong.

Soup is the unfree option.

The pizza and the soup are a drawing of a real mechanism, and Step 5 works it out with exact numbers. Beside it sits a second fact, and it's stranger: whichever way you go, nobody else can write your side of it for you.

So what is freedom? Two exact things, and they pull in opposite directions.

The short answer

Freedom is owning your side of every relationship. Reality keeps a permanent record of every event, and freedom comes in two halves that both fall out of how that record is kept. (The reasons for the starting claims, the permanent record and the cost of a relationship included, come right after the route.)

Half one: the pen is yours. Every relationship between two people is recorded twice, once at each end, in that end's own book. (A book is a drawing of one person's side of the record. Step 1 says what's real.) Nobody writes in another's book, and every record has to stay true, so an act may change a relationship only when both of its ends write on it. An act that pushed a cost onto you would have to make your own record false. That is exactly what harm is, and the moral code forbids it. (The code is four clauses and a judgment, and Step 4 states all of it.) And nobody can hold you in a relationship, because either end can end it alone.

Half two: the room is small and exact. The code forbids every act that breaks one of its four clauses. Of the acts that don't, it permits only those that leave the least total cost on the record, and it forbids the rest. That includes being more generous than balance asks. So you are free exactly where the best acts tie. When an act can be divided as finely as you like, only one outcome is permitted. Real choice between different outcomes comes from what can't be divided: a slice, not a pot of soup.

Underneath both halves sits a fact from physics: from every balanced set of books, the laws that price every entry allow at least two different next entries at exactly the same price, and nothing in them picks one.

Morality here is physical structure, as objective as charge or temperature. It runs on the same record, the same relationships and the same cost as the rest of physics.¹

Here's the whole answer in six steps. The rest of this post takes them one at a time and shows how we know each one. What's still being worked out has its own section near the end.

1. Your side is written by you or by nobody. Each relationship is recorded twice, once in each end's own book. The authors of an act are the people whose own books it changes. Consent is the record of who wrote.
2. An act may change a relationship only when both ends write. So an act that pushes a cost onto someone who didn't write has to make that person's own record false. That's harm. It's forbidden, and nothing physical stops it.
3. Nobody can hold you in, and an ending deletes no one. Either end can end a relationship alone. The ended relationship stays on the record with all its cost.
4. Inside the clauses, only the least-cost acts are permitted. No act goes beyond the requirement. Freedom lives where the best acts tie.
5. Free choice comes from what can't be divided. The cost curves upward, so a choice you can divide finely has exactly one best outcome.
6. Underneath, the laws leave the next entry open. From every balanced set of books (every entry matched by its mirror, the way bookkeepers balance), they allow at least two different next entries at exactly the same price.

Why this matters: freedom isn't a feeling, and nobody grants it. It's the shape of the record: who can write what. That answers questions people keep asking. Can anyone sign for you? No. Does a favor you never asked for count as your yes? No. Can you leave? Nobody can hold you in, and what you leave behind stays on the record. How much room does the code leave you? Exactly the ties. And every forbidden act stays possible, so nothing in the record stops you from doing wrong. That's what makes a wrong a wrong and not an impossibility.

Here's the route. I'll end each step with a line on why the next one comes next, so you always know where we are.

Where the argument starts

This post stands on its own. It uses three ideas from this series on Recognition Science, the physics our institute develops. Each comes with its reason.

The smallest event is one thing told apart from another. You're doing it right now: reading these words tells one shape from another. Telling two things apart takes information about both of them, and the least information there can be is one yes or no. So the smallest event takes two things and one yes or no, and the unit of the record is a relationship between two things, with one end for each.

Nothing that happens is ever erased. Every event leaves a complete trace, and the full record of what happened is part of reality now. The past still exists. Physics gives the reason: its basic laws never destroy information. In quantum mechanics this is unitarity. The present fixes the past exactly, and running the laws backward recovers every earlier state. This work gives the record a reason of its own: it only grows. Each new entry is added with every earlier entry kept, and writing a new entry never alters an earlier one.² (Other posts in this series call the record the Ledger.)

A relationship has a cost. A relationship compares two amounts, and its number is their ratio. Alice has cooked Bob two dinners, and Bob has cooked her one: ratio 2. (Dinners keep the numbers small. Which physical amounts a real relationship compares is part of the first open step at the end.) Read from Bob's end it's 1/2, and that changes nothing. A ratio of 1 is balanced. Any other ratio is a relationship that's off balance, and I'll call it strained. A strained relationship has a cost, and the cost measures how far off it is. It has to meet three requirements: it's zero only at balance, it grows with the mismatch, and it's the same from either end. The recipe is to take the ratio, add its flip (1 divided by it), halve that, and subtract 1.

• Balanced, 1 to 1: (1 + 1) / 2 − 1 = 0. No cost.
• 2 to 1: (2 + 1/2) / 2 − 1 = 1/4.
• 1 to 2: (1/2 + 2) / 2 − 1 = 1/4 again.

The recipe isn't a choice. Those three requirements, one rule for how the costs of combined comparisons add up, and one calibration (how sharply the cost rises near balance) leave exactly one formula, and this is it. I'll write J for it.³

Step 1: Your side is written by you or by nobody

Every relationship is recorded twice, once at each end, in that end's own book. Nobody writes in another's book. The authors of an act are exactly the people whose own books it changes, and consent is the record of who wrote.

Here's how it works, with small numbers. Take the dinners: Alice has cooked two for Bob, and Bob has cooked one for her. Ratio 2, cost 1/4. Each of them keeps a record of it, and I call a person's records their book. (The book is a drawing. The two records are real: each end of a relationship holds its own.) Alice's book says "2 to 1". So does Bob's.

A record is true when it gives the relationship's actual ratio, so both of these are true, and two true records agree. That gives a plain test. When two records of one relationship disagree, at least one of them is false.

Each end carries the whole cost. A person's burden is the total cost of the relationships they're an end of, so this one relationship puts 1/4 on Alice's burden and 1/4 on Bob's. The record's own total counts the relationship once, so it adds 1/4, not 1/2.

Now, what writes? An act is a change written in books. When Alice cooks Bob a dinner and both of them write it, both books change, so both are authors. When Alice writes in her own book alone, only her book changes, so only she is the author. An author is exactly a person whose own book the act changed, and consent is the record of that. A Favor Isn't a Yes shows what a yes covers and what it doesn't. Is Your Next Move Already Written? shows the same line from the physics side: every act has an author. What matters here is the layout. Your side of every relationship is written by you or by nobody.

That's ownership, and it isn't license. After every act, every record has to be true, and yours is no exception. Writing in your own book a ratio the dinners don't have is forbidden, as Step 2 shows.

One step under all of this isn't derived yet: that the physical record holds each relationship as two exact records, one at each end, each written only by its own end. It's the first item in "What's still open." Steps 2 and 3 stand on it.

Next, and why: each end holds its own book, so what happens when an act changes a relationship and only one end writes? That's Step 2.

Step 2: An act may change a relationship only when both ends write

An act may change a relationship only when both of its ends write on it. So an act that pushes a cost onto someone who didn't write has to make that person's own record false. That is what harm is. It's forbidden, and nothing physical stops it.

Here's how we know, with the dinners at 2 to 1. Alice wants Bob to owe her more, so she writes "3 to 1" in her own book. Bob writes nothing. There are two cases.

• The relationship doesn't move. Bob didn't write, so it's still 2 to 1, and Alice's book now says something untrue.
• The relationship moves anyway. Now it's 3 to 1, and Bob's book still says "2 to 1", because nobody but Bob writes in Bob's book. The relationship moved out from under what his book says, so his record is false. His burden would jump from 1/4 to 2/3, since J(3) = (3 + 1/3) / 2 − 1 = 2/3, and he wouldn't have written a word. (Alice's burden would jump too, since each end carries the whole cost. The difference is that she wrote and he didn't.)

Either way, a record is false after the act. The code's second clause, truth, says that after an act every record of every relationship is true, so this act breaks it. The one way "3 to 1" can sit in both books and be true is for both ends to write it.

Why does Bob's old record go false when the relationship moves? Because a record gives one state. "2 to 1" is true of the dinners at 2 to 1 and of nothing else. A record that said "at most 2 to 1" would be true of many states, and a move from 2 to 1 down to 3 to 2 would leave it true. The code reads each record as one exact state. So even a move toward balance, written by one end alone, leaves the other end's record false. A better outcome never makes a one-sided act allowed.

So an act may change a relationship only when both ends write. That's the third clause, both write. It works in the good direction too. Bringing a relationship to balance changes it, so both ends write the repair: Bob cooks the dinner he owes, both of them write it, and the dinners read 2 to 2, ratio 1, cost 0. Repair takes both ends. That's the code's statement that love takes two, and Meet in the Middle works out what love does.

Now what this means for freedom. To push a cost onto Bob without his write, an act has to make Bob's own record false, and the second clause forbids exactly that. So when the books start true, no act that meets the clauses moves the burden of anyone who didn't write it. A push is a false entry in another's own book, and that is what harm is.

"Forbidden" is the right word, and "impossible" is the wrong one. The act that moves the relationship without Bob's write is on the menu, the list of acts someone can actually do, like any other act, and the code forbids it. The record alone excludes nothing.

The no-push rule holds at the moment an act is done, and nothing moves a relationship between acts: a relationship changes only through what someone sends, and sending is an act. One gap stays open at reserves: the clauses take an act's writes and books as handed over, so a taking from a reserve passes them with no write.

What the books don't hold is why you wrote. A pressured joint write and a free one are the same entry. Two things about how a yes was given are exact: a later yes doesn't reach back to an earlier one-sided demand, and under deception your yes covers only what you were shown. A Favor Isn't a Yes works both out. On true books every consent is informed, because how an act changes your burden on your books and how it changes in reality agree. And consent is per relationship: writing on one never consents to a change on another, and one person's relief of you never offsets another's harm to you.

Next, and why: an act may change a relationship only when both ends write, so what about ending one? That's Step 3.

Step 3: Nobody can hold you in, and an ending deletes no one

A relationship is ended only by one of its own two ends, and either end can end it alone. Nobody outside can end it, and nobody can hold you in it. An ending deletes no one: the ended relationship stays on the record with all its cost.

Here's how we know. Ending a relationship changes no ratio, so it makes no record false, and nothing the clauses protect is touched. An ending is recorded, and only a relationship's ends hold its records, so only they can write it. One end is enough. A relationship is a comparison, and a comparison needs both of its terms present, and both present are enough. So when one end withdraws, the comparison is gone, and nobody else has to write anything. That cuts both ways: your friend can end it without asking you, and you can end it without asking your friend. That's the fourth clause, own endings.

Two things here aren't derived yet: that a comparison with both terms present needs nothing else, and that each end's presence is an entry of its own, changed only by that end's write. Both belong to the open step in Step 1.

Now what an ending does and doesn't do. It deletes no one. The ended relationship stays on the record with all its cost, because nothing recorded is ever erased. An act can touch only a live relationship (the first clause, live only), so no act can ever repair it. An ended relationship keeps its cost: no allowed act touches it, and nothing moves a relationship between acts. Say Bob ends the dinners at 2 to 1. They stay on the record at 2 to 1, cost 1/4, in every future. Had the two of them balanced it first, at 2 to 2, it would stay at cost 0.

So cutting someone off is never relief on the complete record. The cost doesn't leave. It stays.

An ending by one of the relationship's own ends breaks no clause. Whether the code permits it depends on what else is on the menu, because the judgment prices every act against the others. Step 4 reads that price.

Next, and why: the clauses rule some acts out and leave many in. Which of the rest does the code permit? That's Step 4.

Step 4: Inside the clauses, only the least-cost acts are permitted

Of the acts the four clauses admit, the code permits exactly those that leave the least total cost on the complete record. Every other act is forbidden. No act goes beyond the requirement, and freedom lives only where the best acts tie.

There is one moral code, and it fits in four clauses and a judgment.¹ You've met each clause. An act is admissible when all four hold:

1. It touches only relationships that are live.
2. Every record of every relationship is true after it.
3. It changes a relationship only when both of its ends write on it.
4. It ends a relationship only when one of that relationship's own ends ends it.

The clauses aren't chosen. They're what a record kept twice admits. The judgment comes after them: of the admissible acts, the code permits exactly those that leave the least total cost on the complete record. Every other act is forbidden. An act is forbidden when it breaks a clause or when some admissible act leaves less cost. Doing nothing is always admissible, so among any finite set of acts, some act is permitted.

The measure is the record's total, which counts each relationship once. It isn't anyone's own burden. And "complete record" means it reads every later checkpoint, every later moment the record is totaled, not just one moment. Right and Wrong Aren't Opinions works the judgment through on a promise to bring a neighbor groceries, including why it reads the whole record.

Here's the judgment at work on the dinners at 2 to 1. To keep it small, say six acts are the only ones on the menu, each with its writes. Nothing moves unless somebody writes, so each cost stays where its act leaves it.

The arithmetic: two more dinners make the ratio 2/3, and J(2/3) = (2/3 + 3/2) / 2 − 1 = 13/12 − 1 = 1/12. The last two acts leave a balanced relationship, and a balanced relationship costs 0 whether it's live or ended.

Alice's lone entry breaks a clause, so it never gets as far as a cost. The other three break no clause, but each leaves more cost than one more dinner does: 1/4, 1/4 and 1/12 against 0.

Doesn't giving more than balance count for something? Past balance, the relationship just tips the other way. Bob is ahead by one dinner instead of behind, it's strained again, and the cost is back, at 1/12. There is no act beyond the requirement. A more generous act leaves strictly more cost, so it's forbidden. And isn't doing nothing the safe choice? It's always possible, and where an admissible act lowers the cost, it's forbidden.

Now freedom. Once something is permitted, every property of the outcome falls into exactly one of three classes:

• Required: every permitted act has it. Here, the dinners end at balance.
• Excluded: no permitted act has it. Here, a false record, a strained relationship left strained, a tipped one.
• Free: some permitted acts have it and some don't. Here, whether the relationship stays live.

That's the whole room. Freedom exists only between acts that tie at the least cost. The two permitted acts tie at 0, and they differ in one thing: stay or go. Once the dinners are even, you can keep the relationship or end it, and both cost nothing. While a repair is on the menu, ending it unrepaired is forbidden, because the repair leaves less.

One step under "forbidden" isn't derived yet. I've used "forbidden" the way the code does: an act that breaks a clause, or leaves more cost than another admissible act. The record charges the extra cost of a departure at every later checkpoint, undiminished, on a reading that decides each relationship from its own entry. But the record alone excludes nothing: omission, forever, is possible on every world while its charge grows without bound. The step from "the record charges this" to "this must not be done" is still being derived.

Next, and why: the ties are where freedom lives. Where do ties come from? That's Step 5.

Step 5: Free choice comes from what can't be divided

The cost curves upward everywhere. So when the possible acts can be divided, exactly one outcome is permitted. Free choice between different outcomes arises only from what can't be divided.

Here's how we know. Take two different states of one relationship, say ratio 1 and ratio 4. The state halfway between them is 2: each step multiplies by the same factor, 1 × 2 = 2 and 2 × 2 = 4. The halfway state costs less than the average of the two ends. The ends cost 0 and 9/8, which average 9/16. The halfway state costs 1/4. That holds for every pair of states. It's what "curves upward everywhere" means.

Now suppose two acts with different outcomes both left the least cost, and suppose the acts can be divided, so that between any two of them, every act in between is possible too. Then the act halfway between them is possible, and it leaves less. So the two weren't least after all. With divisible acts, exactly one outcome is permitted. A tie between different outcomes needs a gap in the menu, a place with no halfway.

Here's the pizza and the soup with numbers. Everyone also carries a load of their own. It's a relationship of their own, joining a person to themselves: how heavy their own life weighs right now, hunger included. Its number is a ratio like any other, balanced at 1, with the same cost. Only that person writes on it, so each friend has to take the food. Both friends are hungry, and both loads sit at 4: cost 9/8 each, 9/4 in all. (The 4 is the example's own number, and hunger is a drawing. What a person's own relationship physically compares is part of the open step in Step 1.) One unit of relief is exactly enough to take one load from 4 to 1. Relief multiplies like everything else here, so half a unit divides a load by 2, since two halves make 2 × 2 = 4. The slice is one unit of relief that can't be divided. The pot of soup is one unit that can.

The pizza. Only the first two kinds of row exist. Giving it to A and giving it to B leave the same cost, 9/8, and keeping it leaves 9/4. So the code permits both gifts and forbids keeping it, and which friend gets the slice is free. The two gifts tie because the friends are equally hungry.

The soup. Every row exists, and so does every split in between. The least is half to each, at 1/2. The tie between "all to A" and "all to B" breaks the moment you can split, because the halfway act leaves less than either. Every other split leaves more than 1/2, so every other split is forbidden. Exactly one outcome is permitted, and nothing about the outcome is free. Soup is the unfree option, as promised.

The scope matters. This is proved for acts on a person's own relationships, like these loads. The code states it for every divisible set of acts. What can't be divided doesn't always give you a choice, either: the slice gives one because the two gifts tie.

Step 4's tie between staying and going comes straight from the cost: a balanced relationship costs 0 whether it's live or ended.

Next, and why: everything so far is about what the code permits. What do the laws of physics say about which entry gets written? That's Step 6.

Step 6: Underneath, the laws leave the next entry open

From every balanced set of books, the laws allow at least two different next entries at exactly the same price. Nothing in them picks one.

Is Your Next Move Already Written? works this out step by step. Here's the short version. Every entry compares two accounts, the two amounts a relationship compares, at a ratio, and every entry has the price J. Books are balanced, the way bookkeepers mean it, when every entry is matched by its mirror, the same comparison read from the other end. From balanced books, one allowed next entry puts accounts 0 and 1 at ratio 2. Another puts accounts 2 and 3 at ratio 2. Both add one line to the record, and both cost J(2) = 1/4. It holds from every balanced set of books, however much has been written.

It's the same shape as Step 5's tie: two options at exactly the same price, with nothing in the rules to choose between them. In Step 5 the tie is between acts the code permits. Here it's between entries the laws allow.

What's derived about the writing is the author line: the author of an act is exactly the one whose books it changes (Step 1). Whichever entry gets written on your side goes in under your name, and nobody else can write it. What picks which open entry gets written isn't derived yet. Whether the one doing the picking is you belongs to that same step, as that post says.

What's still open

The code is stated in full above. What's still being finished is the set of derivations that tie it to the foundations. These are the ones this post leans on.

• What each end holds. The code reads the record as two exact records of each relationship, one held and written at each end. That the physical record is built this way is the step being derived. So are three things that go with it: a record is one exact state, which is being derived from what a comparison of two records returns, "same" or "different" and never "bigger"; a comparison with both terms present needs nothing else; and each end's presence in a relationship is its own entry, changed only by its own write. "Both ends write" and "either end can end it" rest on these. The dinners and the hunger are drawings, with sizes chosen to keep the arithmetic small. Which physical amounts the ends of a real relationship hold belongs here too, including what one person owes another and what a person's own relationship compares.
• Reserves. The gap in Step 2: whether reading consent through the amounts an act moves closes it is being derived.
• From charge to must-not. The record charges the extra cost of a departure at every later checkpoint, undiminished, on a reading that decides each relationship from its own entry. Nothing in the record stops a departure. That this charge becomes "this must not be done", that reading, and that the record's price is the total of its relationships' costs, each counted once, are still being derived.
• What picks the next entry. The laws leave two next entries at the same price, and what writes one of them isn't derived. Is Your Next Move Already Written? states it.

The whole trip, in one breath

Every relationship is recorded twice, once at each end, in that end's own book, and nobody writes in another's, so your side is written by you or by nobody. An act may change a relationship only when both ends write, so an act that pushes a cost onto someone who didn't write has to make their own record false. That is harm: the code forbids it, and nothing physical stops it. Either end can end a relationship alone, and the ended relationship stays on the record with all its cost.

Of the admissible acts, the code permits only those that leave the least total cost, so everything else is forbidden, more generosity than balance included. You're free exactly where the best acts tie. The cost curves upward, so a choice you can divide has one best outcome, and ties come from what can't be divided: a slice, not a pot of soup. Once a relationship is balanced, staying and going tie, because balance costs nothing live or ended. And underneath, the laws leave the next entry open.

That's how reality is built. Each person writes only their own side. Every act the code admits leaves every record true. Among those acts, only the ones at the least cost are permitted. Freedom is owning your side: the pen is yours, and the room is exactly the ties.

Soup, as promised, is the unfree option.