Can We Ever Know Everything? The Laws, Yes. The Record, Never.

Your aunt texts you on Friday at lunch: They lose by 3.

Saturday night, they lose by 3.

On Sunday your friend watches the replay and says, "I knew it."

Both of them are right. Only one of them knew anything.

Look at what each of them risked. Your aunt put her claim out in the open on Friday, where the score was free to break it. If the team had won, her text would have been wrong, and the whole family chat would have seen it. Your friend spoke after the score was in. Whatever the score had been, he'd have said "I knew it." No score makes him wrong.

Her claim stuck its neck out and survived. His never left the couch. That's the difference between a forecast and a victory lap.

Hold on to it, because it answers a much bigger question than who called the game. Can we ever know everything? I don't mean "is the universe too big?" or "are we clever enough?" I mean: will there ever be a day when the list of what's known is complete, with nothing left to find out?

The answer has two halves, and people keep gluing them together.

The short answer

You can know the laws. You can't finish the record. Reality keeps one permanent record of everything that happens. Nothing in it is ever erased: every event leaves a complete trace, and the past still exists. Part 1 of our series The Universe Writes in Pen calls it the ledger. The laws are the rules for how the ledger gets written.

Physics already agrees on the part it covers. Its basic equations never destroy information about the past. In quantum mechanics that's unitarity: the present fixes the past exactly, and running the equations backward recovers every earlier state. 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, and most physicists now expect the information to come back out in the radiation. The open question is how.¹ The ledger is reality's own record, and our institute's work proves that it keeps every entry: writing a new entry never alters an earlier one.²

The ledger includes every look anyone takes at it, and each look adds one more entry. So no list of everything is ever finished, and the reason has nothing to do with how big the universe is or how clever we are.

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. A test is a forecast that can fail. A claim made before the result can turn out wrong, so checking it against the result tests something. A claim made after the result, or worked out from it, can't turn out wrong, so checking it tests nothing.
2. Every check writes something new. Looking at a record is an event, and the record can't hold the look that comes after it.
3. Passing never locks in the next test. However many forecasts have come true, some future fits everything written so far and breaks the next one.
4. You are in the ledger. A knower is anything that keeps a record of what it has looked at. If its own looks go into the record it studies, it never finishes: either it keeps finding something new, or it stops with something still unlooked at.
5. The laws can finish. The ledger can't. The laws are a finite target, and a finite target can be reached. Reaching it is the work we're doing, and it isn't done. The ledger has you in it, so every look you take makes it longer.

Why this matters: "know everything" is two questions that look like one. Can we learn how reality is built? Yes. That has an end, and we're working toward it. Can we finish the story of what happens, every look included? No, and the reason isn't effort or brains. The one doing the looking is part of the story. The two answers fit together: the rules can be learned in full, and there's always something left to look at.

It also changes what knowing is. Knowing isn't a view from outside, and it isn't a finish line. Each check is something reality does. It stays done, and the next one is new.

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: A test is a forecast that can fail

A check counts only when the reading comes after the record the forecast was worked out from. Here's how we know, with two Saturdays.

Two Saturdays start out identical. Everything through Friday lunch is the same in both. Then they split. In Saturday A, the team loses by 3. In Saturday B, they win. Call each way things can go a history. A and B are two histories.

Now score the two claims.

Your aunt's Friday text is right in A and wrong in B. It tells the two histories apart: check it against the score on Saturday night and you know which one you're in. A forecast that can come out wrong is a test, and comparing it with the reading is the check.

Your friend's "I knew it" is right in A, because he knew they'd lose. It's right in B, because he knew they'd win. It's right in every history, so it tells no two histories apart. Checking it tells you nothing about the game.

Here's the exact version. Take a forecast worked out from the record through some point, about a reading at a later point. As long as the reading can come out at least two ways (win or lose is two), that forecast can fail on some history. Now take a reading the record already holds. The forecast that copies it is right on every history, and it can't fail. So a check can catch every forecast out exactly when its reading lies after the record. Your friend's claim is the copy.

There's a sneakier version: the pick made after the result. Three people each make a guess before the game: one says win, one says lose, one says tie. After the final whistle you announce whichever guess matched. "Dana called it!" Every guess was a real forecast. But "whichever one matched" is right whichever way the game goes, so it's no forecast at all.

The number of guesses matters too. Give two guessers three results to cover and some result breaks them both: a tie sinks the win-and-lose pair. A hit is worth what it risked, so count the shots before you count the hit.

Zoom out. Step 1 is done. A forecast can be caught out only if its reading comes after the record it was worked out from. A claim made after the result, or from it, tests nothing. Next, and why: the check itself. When the aunt's text meets the score, something happens in the world. What does it do to the record?

Step 2: Every check writes something new

Checking a forecast adds an entry the record didn't hold.

Part 1 starts from three plain facts, each one something you meet in the act of asking whether it holds: things can be told apart, comparing two things needs information about both, and examining a record is a new event. This post uses the third. A photo of your kitchen doesn't contain you looking at the photo. It can contain a description of that look ("someone will look at this"), but the description and the look are different events, and the look comes later.³

Back to your aunt. Friday's record holds her text. It can't hold Saturday night's event, "the text is checked against the score," because that event happens after Friday's record ends.

So what does the new entry do? It tells the two Saturdays apart. Friday's record fits both of them, because everything through Friday lunch is the same in A and in B. The aunt's text passes in one and fails in the other, and the check says which one is real. Here's the exact version: among the histories a record can't tell apart, a forecast of a later reading passes on some and fails on others, so checking it adds a distinction the record didn't hold.

A check isn't a peek at the record from outside. It's an event, and it makes the ledger one line longer.

Zoom out. Step 2 is done. A check is an event. It happens after the record its forecast came from, and it adds an entry that record didn't hold. Next, and why: if every check adds something new, can a long run of passed checks lock in the next one?

Step 3: Passing never locks in the next test

However many forecasts have come true, some future fits everything written so far and breaks the next one.

Say your aunt has called the last ten games, and the ledger holds the results. W is a win and L is a loss: W W L W L L W W L W. Today she makes forecasts for games 11 to 16: L W W L L W.

Build a future like this. Copy games 1 to 10 exactly. Then, for each later game, write the opposite of her forecast. You get W L L W W L.

That future agrees with everything written so far, and it breaks all six of her forecasts. Nothing in the record rules it out. The record so far doesn't say which future gets written. Only the next entries show it.

It doesn't depend on her being bad at this. Hand me any forecasts for any later games, as many as you like, worked out any way you like from the record so far, and I can build the opposite future. That's the exact result: at every point, for any forecasts of all the later readings, some history agrees with the record so far and makes every one of them fail.

It's the diagonal trick: take any list, and build an entry that differs from item n at place n, so it can't be on the list. Is Math Invented or Discovered? uses it on a list of every endless pattern. Here the list is the forecasts, and the opposite future is the one none of them gets right.

So the record can't pin down what comes next. This is where the word "science" fits. A science is forecasts kept before the reading and compared after it. The Actuals calls that actual science. No record of forecasts and results is ever a finished science, because the next reading is always one it hasn't secured. That's a fact about records and readings. It says nothing about the laws, and Step 5 comes back to them.

A side trip: a reading is silent past its reach. One more limit. Ana is 1.80 m tall and Ben is 1.60 m. Both step on a bathroom scale, and it reads 70 kg for both.

Take two pictures of the world. In one, Ana and Ben are the same height. In the other, Ana is 20 cm taller. Both pictures are right as far as the scale can tell. The scale doesn't say "same height." It's silent about height, and silent isn't no.

Here's the exact version. Take two instruments. Every picture that's right on the first is also right on the second exactly when the second one's reading can be worked out from the first one's. Height can't be worked out from weight, so some pictures that pass the scale fail the tape measure. An instrument that can't tell two worlds apart gives every picture the same verdict on both.

Zoom out. Step 3 is done. No record locks in its own future: for any forecasts, some continuation fits the record and breaks them all. And a reading says nothing past its reach. Next, and why: so far the checker has stood outside the record, like a referee. That isn't where the checker stands.

Step 4: You are in the ledger

A knower whose own looks go into the record it studies never finishes. Either it keeps finding something new, or it stops with something still unlooked at.

By a knower I mean anything that keeps a record of what it has looked at and adds to it. Everything so far had the knower outside the record, like a referee. The knower isn't outside. Step 2 said a check is an event, and every event is an entry in the ledger, which is the record of everything that happens. A look is an event too. When you look at the ledger, you're writing in it.

Here's the everyday version. Photograph your desk, and set the print on the desk. Photograph the desk again: the new photo shows the desk and the first print. Set that print down too and photograph again. Every photo shows the desk and every print before it. None shows itself. The desk, right now, holds one more photo than the newest photo does.

That's one photo short. The real gap is much bigger, and a mathematician named Georg Cantor counted it. Mark each of three things yes or no and you have 2 × 2 × 2 = 8 ways to do it. Ten things have 1,024 ways. A record of n entries has 2ⁿ ways of marking its entries yes or no, and 2ⁿ always beats n. Each marking is a fact about the record, and a fact the record has registered has to be readable back from it: if two facts shared one entry, reading that entry wouldn't tell you which of them was registered. So a record can't hold an entry of its own for every yes-or-no marking of its entries, and that stays true even if the record never ends.

The post on the infinite regress works this out in full, along with the old question of who watches the watcher. Here's the result in plain words. A knower whose own looks are entries in the record it studies never finishes its list. At every moment there's something about its own record it hasn't looked at. If it keeps looking, a later look always finds something new. If it stops, it stops with something unlooked at.

Compare a list outside the knower, like the times tables up to 12. A learner can finish that list and go quiet, because the learner isn't on it.

A self is a knower like that. It keeps a record, its own looks go into the record, and it keeps looking. That's why noticing that you noticed is hard work, and why there's always another step up. Each step up costs something, and The Drive Home You Don't Remember puts a price on each one.

Not yet derived from the starting rules, and the one open link in this argument: that the physics itself builds knowers with exactly this structure, ones that keep a record of what they've looked at, put their own looks into that record, and keep looking. Derived: a knower with this structure never finishes its list, even if its record never ends.

No amount of cleverness changes any of this. The wall isn't about how much a knower can hold. It's about where the knower stands: inside. The knower is part of what there is to know.

Zoom out. Step 4 is done. A knower that's part of its own record never finishes: it keeps finding something new, or it stops with something unlooked at. Next, and why: that's the wall around one thing, the record of looks. The last step sorts what can be finished from what can't.

Step 5: The laws can finish. The ledger can't.

The laws are a finite target, and a finite target can be reached. The ledger is never a finished thing, because looking is part of it.

Put the two side by side.

The laws are the rules for how the ledger gets written. Think of an odometer: the laws are its gears, which fix how the numbers roll over. (The odometer is a drawing of the real relation between laws and record, and Did Time Have a Beginning? uses the same drawing.) The laws are few and they're fixed, and your reading them doesn't add one. That makes them the times table from Step 4: a closed list, and the learner isn't on it.

The ledger is the miles actually driven, and every look is an entry: you opened this post, you read Step 4, you noticed that you looked. Each look is a new event, so there's no point where you're done with the ledger.

How finite are the laws? Start at the bottom, where we've finished a piece. The smallest thing that can happen is one thing told apart from another. It takes two things and one yes or no, and you're doing it right now: reading this tells one letter from another. Below atoms, that is the whole process, repeated everywhere: two units joined by a link pass a bit, one yes or no, back and forth, and each pass is one step in the writing of the ledger. A unit is full or empty, and a pass goes through only when one is full and the other empty. When the two match, the pass is silent. Each unit has a setting: what it does with the bit it receives (flip it or keep it), and which kind of pass it's tuned for (one that goes through, or a silent one). When a pass of the other kind catches it, a coin toss decides whether it flips or keeps.

That process is small enough to run every case. Two units can start in exactly 64 ways. Each unit is full or empty and has one of four settings (two moves times two tunings), which gives 2 × 4 = 8 ways for each unit and 8 × 8 = 64 for the pair. We ran all 64. Within three steps, 60 of them fall into coin-flip randomness, and exactly 4 keep a perfect, unbroken rhythm forever.⁴ That isn't "most of the cases." It's every one, and it's a piece of reality known completely. Part 1 walks through the count.

The rules around it have the same shape: each is the only answer left once its conditions are stated.

• One cost for comparing. Comparing two quantities has a cost, and the cost measures their imbalance. It has to be zero when the two match, grow as they differ, and come out the same whichever one you put first. Those three requirements, the rule for how the costs of combined comparisons add, and one calibration (how sharply the cost rises near balance) leave exactly one formula: (x + 1/x)/2 − 1, where x is the ratio of the two.⁵
• One ratio for the levels. Take levels of structure in which each level relates to the next by the same factor, and each new level combines the two before it. The factor then has to satisfy λ² = λ + 1, and its one positive solution is 1.618, the golden ratio. Why Does the Golden Ratio Keep Showing Up? works through it.
• Three dimensions. Lasting structure needs a connection that no smooth motion can undo, and linking is that connection: two linked rings can't be pulled apart without cutting one. Closed loops can link only in three dimensions. In two they can't wind around each other at all, and in four or more any two loops slide apart. So space has three dimensions. Why Space Has Three Dimensions works through it.
• Eight steps for the fastest complete moment. Three directions with two sides each give 2 × 2 × 2 = 8 corners of a cube. A complete moment is one trip that touches every corner and comes home, moving along one edge at a time. Eight corners need at least eight steps, and the fastest trip takes exactly eight.⁶

Deriving all of the laws this way is the work we're doing, and it isn't finished. But the target is finite, and a finite list can be completed.

A fair question: if you knew every law, wouldn't you know everything?

No. You'd know how every record gets written, and what any next entry has to satisfy. You wouldn't know which entry comes next, and you wouldn't have the record. Quantum physics already works this way: the state evolves exactly, and the answer a measurement records isn't fixed in advance. The laws also work the same whether the record has a first page or runs back forever, and the record decides which, as Did Time Have a Beginning? shows. Knowing every gear in an odometer doesn't tell you how far the car went.

One more consequence: knowing sticks. The ledger keeps every entry, so a passed test stays passed. Your aunt's text passed on Saturday night, and nothing later un-passes it, because writing a new entry never alters an earlier one. Every check you make is a permanent addition.

So, can we ever know everything? We can know the laws. We can know every check we've made, for good. We can't finish the ledger, because every look adds a line to it.

Zoom out. Step 5 is done. The laws are a finite target, the ledger is never finished, and a check, once made, stays made. Next, and why: all five steps are done, so here's what they add up to.

What this changes

Two things change. First, "I knew it" gets a test. Ask what was said on Friday. If nothing was said before the score, nothing was tested.

Second, you stop picturing knowing as a view from outside. You're not standing beside the ledger with a notebook. Your notes are entries in it.

The laws are a finite book you can finish. The ledger is a book you never finish, and every look you take is one more line in it. That's how reality is built: rules you can learn in full, and a story you never finish.

The whole trip, in one breath

A claim counts when the world can break it, so the forecast has to come before the reading. Checking it is an event, and it adds an entry the record didn't hold. No run of passed checks locks in the next one, because some future fits everything written so far and breaks the next forecast. The checker is part of the ledger, so a knower that looks at its own record keeps finding something new or stops with something unlooked at. The laws are a finite target, and a finite target can be finished. The ledger isn't a list anyone finishes. It has you in it, and it grows by one entry every time anyone looks.