Is Your Next Move Already Written?

Your phone's keyboard guesses your next word, and it's right a lot.

Type "see you" and it offers three words, say "tomorrow", "soon" and "there". Plenty of the time, one of them is the word you were about to type.

Now give the keyboard more. Your group chats. Your search history. Then everything: every fact about you and your past, the state of your brain this second, the room around you, the position of every atom in it.

Is it right every time?

If the world is a film that's already been shot, it is. Your next move is on the reel, and the keyboard only has to read it. In 1814 the mathematician Pierre-Simon Laplace described exactly this keyboard: an intellect that knows every force in nature and where every piece of matter sits at one instant, and can do all the arithmetic. Nothing would be uncertain for it, he wrote. The future would be as plain as the past.¹

That's the free will question in one picture. If your next move can be read off the present, how can it be yours to make?

The answer is exact: no keyboard can be certain of your next move, not even one that knows every fact about you, every line of the past and every law that prices and balances the books. This post shows why, one step at a time.

The short answer

No. Your next move isn't written anywhere before you make it. Not in the past, because the record of the past holds only what has happened. Not in the laws that price and balance the books, because from every balanced set of books they allow at least two different next entries at exactly the same price (Step 2 explains the books, the entries and the price). And not in any prediction, because for every prediction built from the record there's a future that fits the record and makes it wrong. The future isn't a film that's already been shot.

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. Your next move isn't in the record. The record holds what has happened. It can hold a prediction of your next move, and the prediction is a different entry from the move.
2. The laws leave it open. Every entry has a price, and the books have to balance. From every balanced set of books, at least two different entries are allowed next at exactly the same price. And "always take the cheapest step" isn't the law, because the cheapest step is to write nothing.
3. No prediction is certain. Take any rule that reads the record up to now and predicts later entries. Some future fits the record exactly and makes every one of its predictions wrong.
4. No record of yourself is ever finished. A record of yourself, each fact written on a page of its own, can never be finished. At every tick (one step in the writing of the record), some fact about that record is still missing from it.
5. Every act has an author. The record keeps a line for who wrote each act, and your move goes in under your name.

Why this matters: the free will question asks two things. Is your next move already settled? And are you the one who settles it? Steps 1 to 4 answer the first question, exactly. If your next move were already written, deciding would be watching. It isn't, and Step 5 takes up the second question.

Where the argument starts

This post stands on its own. It uses four ideas from this series on Recognition Science. Recognition Science is the physics our institute develops. It starts with distinction (one thing told apart from another) and consistency, derives what they require, and connects those results to the world we observe. Each idea comes with its reason.

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. We call this record the Ledger (Part 1 introduces it). 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. That's why physicists treat the black hole information problem as a real problem: losing information would break the laws. This series gives the same fact a reason of its own: the record only grows. Each new entry is added with every earlier entry kept, and writing a new entry never alters an earlier one.² What an entry is rests on a separate fact: a comparison needs information about both of its sides, so every entry is written against what came before. Keeping every past state doesn't fix the next one. Unitarity preserves information about the past; it doesn't settle which outcome gets recorded next. In quantum physics the state evolves exactly, but the answer a measurement records isn't fixed in advance, and Bell tests rule out answers set beforehand and carried along by the particles.³

The smallest event is one thing told apart from another, a single yes or no. You're doing it right now: every perception and every measurement tells one thing from another. Telling two things apart takes information about both, and the least information there can be is one yes or no.

Nobody holds the pen. The writing isn't done to events. The writing is the events. So when you act, your act is the entry. No scribe stands outside events, recording them. The record is written one step at a time, and we call a step a tick.

"Now" is the front edge of your record, your own part of reality's record. Everything behind it is written. Part 2 puts the other side in one line: the future isn't written yet, anywhere. This post is the why.

Step 1: Your next move isn't in the record

The record holds what has happened. It can hold a prediction of your next move, but never the move.

A prediction is a statement, made from the record, about a later entry. Here's how we know no record can hold the entry itself, starting with the keyboard.

Say line 98 of the record reads: you type "see you". Line 99: the keyboard offers "tomorrow" as its first guess. Line 100: you look at the offer. All three are written, in pen. "Now" is the front edge, the newest line.

Line 101 is your move: you tap a word, or you don't. It isn't written, and it isn't hidden somewhere. It doesn't exist yet.

Everything behind line 100 is in the Ledger, however far back. Nothing ahead of it is.

Why can't line 101 already be in the record? A record through line 100 holds the events up to line 100, and your tap comes after all of them. It's a plain fact about any note, set out in Part 1: a note holds what happened before the note was made, and whatever happens after, even checking the note, is a new event that isn't in it. The record can hold a description of your tap. Line 99 is exactly that, the keyboard's prediction. But a description of an event is a different occurrence from the event. Line 99 is the keyboard talking. Line 101 is you doing.

Even if you tap "tomorrow", lines 99 and 101 are two entries, one the keyboard's and one yours, at two moments. A weather forecast isn't the weather.

Next, and why: if the laws fixed the next entry, it would be as good as written even with no record holding it yet, so Step 2 asks what the laws say.

Step 2: The laws leave it 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.

Here's how we know. The laws this step uses, the laws that price and balance the books, come to four lines.

• An entry compares two accounts at a ratio. An account is one of the two quantities being compared. Entry A, below, compares account 0 with account 1 at ratio 2: one holds twice what the other does.
• Every entry has a mirror: the same comparison read from the other end, account 1 with account 0 at ratio 1/2. Like any double-entry books, the Ledger's are balanced when every entry has been matched by its mirror.
• Every entry has a price, a measure of imbalance. Take the ratio, add 1 divided by the ratio, cut that in half, subtract 1. Ratio 2: 2 + 1/2 = 2.5, half of that is 1.25, minus 1 is 1/4. The mirror, at ratio 1/2, comes to 1/4 too. It's the recipe for strain in A Favor Isn't a Yes, and it isn't a choice: the rule for combining prices, plus the calibration, leaves exactly one price, and this is it.⁴
• Every entry adds one line to the record.

Here's what makes it the only price. It has to meet three requirements: it is zero when the two accounts match (ratio 1), it grows as they differ (that's what "out of step" means), and it is the same whichever account is put first, so an entry and its mirror cost the same. Add the rule for combining prices, P(xy) + P(x/y) = 2P(x) + 2P(y) + 2P(x)P(y), where P(x) is the price at ratio x, and the calibration, which sets how sharply the price rises near a match, and no other recipe is left. You can check that the rule does real work: (ln x)² meets all three requirements and fails it. The price isn't paid to anyone.

Now start from balanced books and ask what the next entry can be. Here are two.

• Entry A: account 0 with account 1, at ratio 2.
• Entry B: account 2 with account 3, at ratio 2.

Put each one to the laws. Is it allowed? Both are. Can the books be balanced again? Both can: add the mirror and they're square. Does it add one line? Both do. What does it cost? Both cost 1/4.

Every one of those four laws gives the same answer for A and B. And A and B are different entries: they set different accounts out of step, so the record reads differently depending on which one gets written. Nothing in them picks one. The laws can price both entries to the fraction and still say nothing about which one gets written. It isn't a quirk of the first move, either: it holds from every balanced set of books, however much has been written.⁵

These four laws say what any next entry has to satisfy, not which one comes next, so the real question is whether something further picks. Earlier entries can't. The tie holds from every balanced set of books, whatever they hold, so no disturbance breaks it the way a tiny push tips a pencil balanced on its point: a disturbance is something that happened, and it's already in the books. Nor are A and B one entry with the accounts renamed. Say the books already hold a settled comparison between accounts 0 and 1. Entry A adds a second one between those same two accounts; entry B starts the first between accounts 2 and 3. No renaming of accounts turns one result into the other without rewriting what's already written.

It's the same pattern as in Did Time Have a Beginning? There, the laws allowed a first page and a past with no bottom, and the record decided. Here the laws allow two next entries, and the record will show which one got written.

Doesn't nature just take the cheapest step? No. Here that's a tie, 1/4 each. And it fails in a bigger way. What's the cheapest thing the books can do? Write nothing. A blank costs 0, and any entry that sets two accounts out of step costs more than 0. So a world that always took the cheapest step would be a blank book. Ours has written every line you've ever lived. Writing nothing is the cheapest step, and entries get written anyway, so "always take the cheapest step" isn't the rule that runs the world. Physics' principle of least action isn't that rule either. It isn't a step-by-step cheapest choice; it's a way of writing laws that fix a whole path at once. No law of that kind runs the books: Part 2 shows that everything the present holds about what comes next is a set of exact odds, and a law that fixed the path would turn those odds into certainties.

Next, and why: a keyboard that reads the whole record, laws included, still has to pick an entry, so Step 3 asks whether any pick built from the record can be certain.

Step 3: No prediction is certain

Take any rule that reads the record up to now and predicts later entries. Some future fits the record exactly and makes every one of its predictions wrong.

Here's how we know. Let the record be a row of yes-or-no entries, the smallest events there are. Ticks 1 to 4 are written: yes, no, yes, yes. "Now" is tick 4.

Someone hands you a rule that reads those four entries and predicts the next four. Any rule at all: a clever statistician, a perfect keyboard, Laplace's intellect. Say it predicts yes, yes, no, yes for ticks 5 to 8.

Build a future by flipping every prediction: no, no, yes, no. Attach it to the record and you get yes, no, yes, yes, no, no, yes, no.

Two checks. Does this future fit the record? Yes, its first four entries are the record. Does it beat the rule? Yes: the rule said yes and the future says no, and so on down the row. Every prediction is wrong.

That works against any rule. A rule reads only ticks 1 to 4, and every future that starts with those four hands it the same four entries, so it gives the same predictions for all of them. Flip that one set of predictions and you have a future the rule loses to. The same move works at every "now", for any number of predictions, and for entries with any number of values, as long as there are at least two.⁶

On its own, that's a fact about records and rules: "fits the record" means only that the future agrees with every entry written so far. Step 2 makes it a fact about the laws too. The flip needs only two possible next entries, and Step 2 supplies two lawful ones. Whenever the books are balanced, the laws allow both entry A and entry B next. A rule that predicts the next entry names one entry, so at least one of A and B isn't it. That entry is allowed by the laws, it fits the record, and the rule loses to it.

A prediction can still come out right. Your keyboard is right a lot. If the future that happens is one that matches the prediction, the prediction was right. What no prediction has is a guarantee: nothing in the record up to now certifies it.

There's one way to be right every time: wait. Let the entry get written, then pick the prediction that matched. Ten forecasters each name a different digit, 0 to 9, for the next number a machine prints. One of them has to be right. Pick the winner after the number shows up and you have a forecaster who's never wrong. That's an echo, not a prediction: the ten covered every digit, and the pick copied the reading. With nine forecasters and ten digits, a digit is always left out, and a future that prints it beats all nine at once.

Hindsight is the same forecaster. "It was always going to happen" is easy to say afterward, because said after the fact it passes whatever happened. It tells you nothing about the next entry.

Next, and why: so far the guesser has stood outside you, but the reader who knows you better than any keyboard does is you, so Step 4 asks whether a mind can finish a record of itself.

Step 4: No record of yourself is ever finished

A record of yourself, each fact on a page of its own, can never be finished. At every tick, some fact about it is still missing from it.

Here's how we know, starting with the smallest record that shows it.

Take a record with 3 pages. A fact about it is a yes or a no for each page. For instance: page 1 yes, page 2 no, page 3 yes. Three pages, two answers each: 2 × 2 × 2 = 8 possible facts.

Now let a mind keep a record of itself. It registers facts about its own record, and to register a fact is to write it into the record, on a page of its own. A page of its own, because a registered fact has to be readable back from the record: if two different facts shared a page, reading that page couldn't tell you which one was registered. So with 3 pages, the mind can register at most 3 of the 8 facts, and 5 are left out.

Add pages and it gets worse. Four pages make 16 facts, five pages make 32, and the facts always outnumber the pages. Endless pages don't fix it. In 1891 Georg Cantor showed that the endless rows of yes and no can't be matched one-to-one with the pages 1, 2, 3, and so on.⁷

His trick, the diagonal, is short, and it works at any size. Here it is on 3 pages. Take any three registered facts, one on each page. Each is a row of yes and no, one answer for each page. Now build one more fact, the flip. On page 1, say the opposite of what the fact on page 1 says about page 1. On page 2, the opposite of what the fact on page 2 says about page 2. Page 3, the same. The cyan squares are the answers it flips.

The flip differs from every registered fact, on that fact's own page, so it isn't any of them. It's a perfectly good fact about the record, and it's missing.

Why not register the flip too? Fine. Give it a page of its own, and the new list has a new flip. The facts about the record stay one step ahead of the record, every time.

It's the same move as Step 3. There we flipped every prediction. Here we flip the diagonal of a table. Either way, you build the one thing that disagrees with each item right where that item speaks.

So however long a mind has been registering itself, some fact about its own record is still missing. Now point this at yourself. Predicting yourself meets Step 3's flip from the inside, however few facts the prediction uses. Your predictions about yourself go into your own record too, and for every prediction read from your record so far, some continuation of that same record makes it wrong.

The keyboard that knows everything fails twice. Step 3 beats its predictions about you. And if it sits inside the world, "everything" includes the keyboard, so it has to register facts about its own record too, and anything that registers itself this way never finishes.

Another post in this series meets the same wall from the price side. In The Drive Home You Don't Remember, every extra look at yourself costs more than the one before, and there's always another step. That post counts the cost. This one needs only that the steps never run out.

Next, and why: the next entry is open, so Step 5 asks what the record says about who writes it.

Step 5: Every act has an author

The record keeps a line for who wrote each act, and your move goes in under your name.

Here's how we know. The record is kept as each party's own books, and each party writes only on its own. An act is a change written on the actor's books, or on both sides' books when two people act together. So the record needs no separate label for who did it: the author of an act is exactly the one whose books it changed. What reaches anyone else is a change on a relationship they share. That's why, as A Favor Isn't a Yes shows, every event between people has three separate facts: who wrote it (who did it), who it happened to, and whether they came out better. The record keeps the first on a line of its own, apart from every number that sums up how things came out. Your roommate painted your bedroom: she wrote it, and it happened to you.

Your next move is an entry on your own side of the record, your own books. When it gets written, the line says you. Nobody else can write on your side for you. That's also why nobody holds the pen: no one writes the record from outside, and your act is the change on your own books.

That line is bookkeeping about whose entry it is. It doesn't say what picks which of the open entries gets written. Step 1 showed the entry doesn't exist yet. Step 2 showed the laws price the options and pick none. Step 3 showed no prediction certifies it.

What picks which open entry gets written is the one step Recognition Science hasn't derived yet, meaning it isn't worked out from our starting facts.⁸ Whether the one doing the picking is you, your consciousness, belongs to that same open step.

Here's what's settled around it. The pick isn't a cheapest-step rule, and it isn't a law that fixes the entry in advance: Step 2 closed both. Part 2 derives exact odds for what comes next. Odds say how likely each entry is. They don't say what writes this one. The odds are derived, the writing isn't, and nothing derived so far says the writing is a dice roll.

So here's where things stand at the front edge of the record, as exactly as it can be drawn. Behind you, every line you've lived, in pen. In front of you, a blank line. The laws say which entries are allowed and what each costs. One gets written, and it goes in under your name.

Next, and why: that's the last of the five steps, so what's left is what they add up to.

What this changes

Deciding isn't watching. If your next move were on a reel, a decision would be the moment you found out what was on it. The record has no reel. A decision is the moment an entry gets written, and the record files it under your name.

Nothing in the record behind your now has what you'll do next on file. The most complete archive there is holds every line you've lived and not one line of the next.

And a record of yourself, each fact on a page of its own, is never finished. That isn't a flaw in you. It's how a record that includes itself is built: there are always more facts about it than pages.