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 the one that knows everything. 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, because from every balanced set of books they allow at least two different next entries at exactly the same 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, 1/4. 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 mind finishes a record of itself. A mind that keeps a record of itself can never finish it. At every tick (one step of the process that writes the record), some fact about its own record is still missing from it.
5. Every entry has an author. The record keeps a line for who wrote each entry, 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.

Here's the route. I'll stop after each step to zoom out, so you always know where we are, what we've got, and why the next step comes next. The Ledger will keep the map.

What you need from the earlier posts

This post stands on its own. It uses three ideas from this series on Recognition Science.

First, reality keeps a permanent record of every event, and nothing in it is ever erased. We call it the Ledger, and I draw it as a thick book with reading glasses and exactly one response to anything that happens: Noted. (Part 1 introduces it.)

Second, 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.

Third, "now" is the front edge of the 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, down to the dinosaurs' dullest Tuesday. 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 the third plain fact from Part 1 again: 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, by two writers, at two moments. A weather forecast isn't the weather.

Zoom out. Step 1 is done. A record holds what has happened, so it holds predictions of your next move and never the move itself. Next, and why: the record isn't the only thing that bears on the next entry. The laws do too. If the laws fixed the next entry, it would be as good as written, even with no record holding it yet. 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. Start with a picture. Think of a choose-your-own-adventure book whose pages are printed only after you turn to them. The book has rules about which pages are allowed next, and the list always has more than one page on it. That book is a drawing of the real mechanism: the pages are entries in the Ledger, and the rules are the Ledger's laws. Now the real thing.

The laws this step uses come to four lines.

• An entry compares two accounts at a ratio. 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. 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 rules for comparing things, plus one calibration to set the scale, leave exactly this recipe.²
• Every entry adds one line to the record.

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.³

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.

Yeah-But has the obvious fix. "Easy. Nature takes the cheapest step."

That's a tie here, 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 very thrifty blank book. Ours has written every line you've ever lived. Writing nothing is the cheapest step, and the Ledger writes anyway, so "always take the cheapest step" isn't the rule that runs the world.

Zoom out. Step 2 is done. The laws price every entry and keep the books balanced, and from every balanced set of books they leave at least two next entries open at the same price. "Always take the cheapest step" isn't the rule. Next, and why: a keyboard that reads the whole record, laws included, still has to pick an entry. 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, one for each tick (Part 1's name for one step of the process that writes the record). 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.⁴

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.

And Step 2 is what gives this teeth. Whenever the books are balanced, whatever a rule predicts for the next entry, the laws leave open at least one entry it didn't predict. That entry is a lawful future that fits the record, and the rule loses to 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.

Zoom out. Step 3 is done. For any rule that reads the record up to now, some future fits the record and defeats every prediction the rule makes. Predictions can come out right, and none comes with a guarantee. A match picked after the fact is an echo. Next, and why: so far the guesser has stood outside you. One reader knows you better than any keyboard does: you. Step 4 asks whether a mind can finish a record of itself.

Step 4: No mind finishes a record of itself

A mind that keeps a record of itself can never finish it. At every tick, some fact about its own record 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. 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.⁵

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.

Yeah-But has an answer for that too. "Then register it!"

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. To predict your own next move for certain from a record of yourself, you'd need that record finished: what you did, what you noticed, and that you noticed it. Write it the way registering works, each fact on a page of its own, and the diagonal applies. There's always a fact about the record that isn't on any page, so a finished record of yourself, written that way, doesn't exist.

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.

Zoom out. Step 4 is done. A mind that keeps a record of itself never finishes it, because there are always more facts about the record than pages to write them on. Next, and why: the next entry is open, no prediction certifies it, and no mind finishes a record of itself. So who writes the entry? Step 5 asks what the record says about that.

Step 5: Every entry has an author

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

Here's how we know. In A Favor Isn't a Yes, every event between people has three separate facts: who wrote 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. When it gets written, the line says you. Nobody else can write on your side for you. (The Ledger has no opinion on what you'll do. It has opinions about whose entry it is.)

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 the starting facts.⁶

Here's what's settled around it. The pick isn't a cheapest-step rule: Step 2 closed that. Part 2 said the present holds exact odds for what comes next. Odds say how likely each entry is. They don't say what writes one, and nothing derived so far says the writing is a dice roll. Whether the one doing the picking is you, your consciousness, belongs to the same open step.

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.

Zoom out. Step 5 is done. Every entry goes into the record under its author's name, and your next move will too. Next, and why: that's the last of the five steps. 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.

Right now, nothing anywhere 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.

The whole trip, in one breath

Your next move isn't written anywhere. A record holds what has happened, so it holds predictions of your next move and never the move itself. From every balanced set of books the laws allow at least two different next entries at the same price, and "always take the cheapest step" isn't the law, because the cheapest step is a blank. For any rule that reads the record up to now, some future fits the record and beats every prediction. A mind that keeps a record of itself can't finish it, because there are always more facts than pages. Every entry goes in under its author's name.

(The Ledger would like you to know that line 101 is still blank. It has noted that you read this far, and it has nothing on file for what you do next.)