Are We Living in a Simulation?

Is our universe a computer simulation? No. There's no machine outside the universe reading its state and writing its next moment, because there's no outside for a machine to stand in. The reason is short. A machine that runs a world has to read it, and a reading is an event that has both the machine and the world in it. That event, like every event, is an entry in the one record of everything that happens. So the machine is in that record, with the world it runs. This post takes the argument one step at a time, with the reasons behind each step.

The question is a serious one. In 2003 the philosopher Nick Bostrom published a paper that asked whether our universe is a simulation, a world run by a computer the way a video game's world is.¹ He argued that at least one of three things is true. Almost every civilization like ours dies out before it can build computers that run whole worlds. Or almost none that get that far choose to run many. Or, in his words, "we are almost certainly living in a computer simulation." The third option has a console in it: a computer in some other world, reading ours and writing our next moment.

Here's a drawing of that third option. Pip is a character in a video game, and Pip has noticed some things.

The sky is a very flat blue. The world ends at an invisible wall, exactly where the map ends. Every tree has the same three branches.

"Somebody," says Pip, "is running this."

So Pip goes looking for the console. He digs under the village. He climbs the tallest mountain and knocks on the sky. He walks into the invisible wall.

He never finds it, and he never will. The console isn't in the game.

Now look from the other side of the screen. The console sits on a table in a living room, with a power cable. Pip's sword, his sky and his village are patterns of electricity in a chip. Every frame of his life is something that really happens in that living room: transistors flipping, sixty times a second or so.

Notice what that means. Pip can't find the console, but the console, the cable, the electricity and every pixel of Pip all sit in one world. Everything Pip does is an event in it.

So here's the question for our universe. Where's the console? And what's the living room?

What the record is, and why

Everything below rests on what happens at the smallest scale of reality and what becomes of it. Here it is, with the reasons.

Start with three facts you meet in the act of asking about them. Distinguishable occurrences exist: this letter is not that one, and you can tell the difference. Comparing two of them takes information about both. And looking back at an earlier occurrence is itself a new occurrence. None of the three assumes an observer outside the world.²

The smallest event is telling two things apart. It's a single yes or no, and you're doing it right now: reading this tells one letter from another. Every measurement and every perception tells one thing from another. Telling two things apart needs information about both of them, and the least there can be is one yes or no.

Nothing that happens is ever erased. Every event leaves a complete trace, and the traces together are the record of what happened. The record is part of reality now: the past still exists. Physics already agrees on the part it covers. Its basic laws never destroy information. In quantum mechanics this is called 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. Hawking's 1976 calculation said a black hole destroys the information that falls into it.³ That clashed with unitarity, which is why it became a famous problem. Most physicists now expect the information to come back out in the radiation, and the open question is how.

In our work there are two separate reasons the record keeps everything. Each new entry is a comparison, and a comparison needs information about both sides, so every entry is written against what came before. And the record only grows: each new entry is added with every earlier entry kept. The record this post describes is reality's own, and our institute's work proves that it keeps every entry.⁴

The short answer

No. Nothing is running us. 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.

1. Whatever reads you is in your record. Running a world means reading its state and writing the next one. Reading is comparing, and comparing puts both sides in one record. A machine that runs us is written in the same record as us. There's no second record.
2. Every world has your shape. Any world that meets the conditions in Step 2 (it tells things apart, compares them at a price, builds its levels by joins and keeps what it records) has the same price of a mismatch, the same three directions of space, the same eight-step cycle and the same ladder of levels. Its units can differ. Its shape can't. There's no "base reality" with different rules.
3. No part of reality holds a complete copy of reality. For any collection of things there are more yes-or-no markings than places to write them. A machine inside reality that tries to copy all of it, itself included, always has something it doesn't hold.
4. Nothing writes the record one place at a time. The simplest host is one clock with one slot per tick (a tick is one step in the writing of the record): one write, then the next. Two small pieces of the record already write more often than one slot per tick holds, so the one-at-a-time machine is out.
5. The record's rules are steps a computer can follow. That's what the simulation idea gets right. Rules a computer can follow don't need a computer to follow them.
6. Your moments are real, and nothing is under the record. Every moment you live is an entry in the one record. The record is the bottom layer of physics, not a picture drawn by something deeper.

Why this matters: the question is really asking whether your life is the real thing or a show on somebody else's screen, and whether somebody can pause it, edit it or switch it off. With no outside, there's nobody to do any of that from.

Here's the route. I'll stop after each step to zoom out, so you always know where we are, what we have, and why the next step comes next. Part 1 of this series, What You Are, tells the story of the record in full.

Step 1: Whatever reads you is in your record

A machine that runs a world has to read it, and reading puts both sides in one record. So whatever runs a world is written in the same record as the world. There's no second record.

Here's how we know. Start with what a simulation does. Strip it down and it's a loop: read the world's state (where Pip is, what he's holding), work out the next state from the rules, write it, and go around again. Read, work out, write.

Everything hangs on the first word. What is it to read?

When the console reads Pip's position, it takes a stored number and tells it apart from the other numbers that were possible. A thermostat reads a room by comparing its temperature with a setting. A hard drive reads a bit by telling a 1 from a 0. Reading is comparing, and comparing is the most basic act there is. This series calls it recognition: one thing registering a difference in another.

Of the three facts above, the second is the one that matters here: comparing two things needs information about both. Colder than what? To say the second sip of coffee is colder, you need the first sip and the second, both available to the comparison.

So when the console reads Pip, the reading has Pip's side in it and the console's side in it. A reading is an event, and every event is an entry in the record. Somewhere there's an entry that says the console read Pip's position, with the console and Pip together in it, in the same ink.

That's what "in the same world" means. Not the same room: the same entry. A machine that reads you is in an entry with you.

Try it from the other end. Suppose there's another world, outside ours and different from ours. Being different from ours means being told apart from ours, and telling apart is comparing. A comparison takes information about both sides, so the comparison that tells the two worlds apart is an event with both worlds in it. That puts both worlds in one record.

So where would "outside" be? Outside would be a place no entry reaches. The entry for the console reading Pip reaches both of them. A machine that reads our world isn't outside it. There's one record, and there's no second page for anything to stand on.

Here's the obvious objection. "Pip can't read the console. The console reads Pip through a channel that runs one way, and that's all."

One-way reading is still reading, and a one-way channel still connects the two ends. The entry for the reading has both ends in it, whether or not Pip can ever read the console back. Pip not finding the console tells you how far Pip's reach goes. It tells you nothing about how far the record's goes.

Here's exactly where this step stands. Derived: in the writing of the record, a comparison that registers an outcome has both of the things it compared already in the record. Not yet derived: that every comparison between two systems that keep records, including a machine and the world it would run, is an event in one record. Steps 2 to 5 each rest on a proof, with the conditions named in the step.

Zoom out. Step 1 is done. A machine that runs a world has to read it, and reading puts both sides in one record, so whatever runs a world is in that world's record. There's no second one. Next, and why: a machine in the same record still has to live in some world. Is it a stranger one, a "base reality" with rules of its own? Step 2 answers.

Step 2: Every world has your shape

Any world that meets the conditions below (it tells things apart, compares them at a price, builds its levels by joins and keeps what it records) has the same price of a mismatch, the same ladder of levels, the same three directions of space and the same eight-step cycle. Its units can differ. Its shape can't. There's no "base reality" with different rules.

Here's how we know. Earlier posts in this series found four things that reality's structure forces. Each one has the same form: given these conditions, exactly one option works.⁵ Here are the four, each with its reason.

The price of a mismatch. Compare two quantities, one x times the other. The price of that mismatch is J(x) = (x + 1/x) / 2 - 1. The price has to meet three requirements: it's zero when the two match (x = 1), it never falls as they differ more, and it's the same whichever one you put first (x or 1/x). Those requirements, the rule for how the prices of combined comparisons add, and a choice of unit (it sets how sharply the price rises near a match) leave exactly one formula. What the price measures is imbalance: it's zero only when the two sides match, and it grows with the mismatch. See Did Time Have a Beginning?.

The ladder of levels. Levels of structure scale by 1.618..., the golden ratio. Suppose every level relates to the next by the same factor, and each new level joins the two before it, with the first join of two different levels costing something. Then the factor, call it λ, has to satisfy λ² = λ + 1, and its positive solution is 1.618... See Why Does the Golden Ratio Keep Showing Up?.

Three directions of space. Lasting structure needs a connection that no smooth motion can undo, and linking is that connection: two rings of a chain can't be pulled apart without cutting one. Linked loops stay linked only in three dimensions. In two, loops can't wind around each other at all. In four or more, any two loops slip apart. That lasting pairs are joined by linking is the premise, and given it, space has three directions. See Why Space Has Three Dimensions.

Eight steps in a complete cycle. Three yes-or-no directions give 2 × 2 × 2 = 8 combinations, the eight corners of a cube. A complete cycle changes one yes-or-no per step and has to touch every corner, so the fastest complete cycle takes eight steps. See What You Are and Why Chemistry Runs on Eight.

None of those results is about our world in particular. Each one says what any world that meets its conditions has to have. The conditions are the ones every earlier post used: comparisons have prices that combine consistently and never fall as the mismatch grows, with a unit to set the scale; levels are built by joins; and a finished recognition is kept, meaning a completed pair stays linked. A world has a shape only if two of its things differ. The smallest event is one thing told apart from another, so a world with nothing to tell apart holds no event, and with no event there's nothing for a law to govern. Why Is There Something Rather Than Nothing? shows it in full.

Now take any two worlds that meet the conditions. If exactly one option works, the two worlds can't have picked different ones. Both have the same price of a mismatch, the same ladder, the same three directions and the same cycle of eight. What can differ is the size of the unit: the ruler, not the shape of what it measures. Is There Another Universe Out There? tries to build a world of a different kind, one part at a time, and every attempt either breaks a condition or changes only units and notation.

A host world that meets these conditions has this shape too: three directions of space, a cycle of eight and the same price for a mismatch. And by Step 1, a machine that reads our world is in our record, so the world it sits in is ours, conditions and all.

The result covers the shape and nothing else: the price, the ladder, the directions and the cycle.

Zoom out. Step 2 is done. Every world that meets those conditions has your shape, and only its units can differ, so no stranger "base reality" waits outside. Next, and why: Steps 1 and 2 put the machine in a world shaped like ours. Can a machine in that world hold a complete copy of the whole thing? Step 3 counts.

Step 3: No part of reality holds a complete copy of reality

For any collection of things there are more yes-or-no markings than places to write them down. So a machine inside reality that tries to keep a complete copy of reality, itself included, always has something it doesn't hold.

Here's how we know. A distinction is a yes-or-no mark on every one of the things in a collection: yes to this one, no to that one. Take a street with 4 houses, a collection small enough to count by hand. Each house gets a yes or a no, so there are 2 × 2 × 2 × 2 = 16 distinctions. (Yes, no, no, yes is one. No, no, no, no is another.)

Now suppose a machine on that street wants a complete copy of the street: every one of those distinctions written down, each at an address of its own. The only addresses on the street are the four houses. The machine needs 16 addresses. The street has 4.

Adding houses doesn't fix it. Add 12 houses to make room and you have 16 houses, and 16 houses have 65,536 distinctions. Every house you add doubles the distinctions and adds one address. The distinctions win at every size. For endless collections the same count holds by Cantor's diagonal:⁶ pair each thing with one marking, then build a new marking that answers the opposite of what each thing's own marking says about that thing. It differs from every marking in the pairing, so the pairing is missing one. Turtles All the Way Down? walks through the count and the diagonal in full.

Now put a machine in reality's place. A machine inside reality is one of reality's things, and its copy has to live at addresses inside reality. To hold a complete copy of reality, it has to give every yes-or-no marking of everything, itself included, an address of its own. There are never enough. Said another way: the copy has to include the machine that's making it, and the machine making it is always something the copy doesn't hold. No part of reality holds the whole of it.

A bigger world can hold a copy of a smaller one, and this count has nothing against that: that's Pip's situation, a console in a living room. What the count rules out is a world holding a complete copy of itself. Step 1 is what makes it bite. It put any machine that runs our world in our record, so there's no bigger world around ours, and the world the machine would have to copy includes the machine.

Zoom out. Step 3 is done. There are always more yes-or-no markings than places to write them, so no part of reality holds a complete copy of reality, and Step 1 put any machine inside it. Next, and why: that closes the doors a machine would come through. The next question is how it would run us: tick by tick, on one clock. Does the record run that way?

Step 4: Nothing writes the record one place at a time

The simplest way to run a world is one clock with one slot per tick: one write, then the next. The record isn't written that way. Two small pieces of the record already write more often than one slot per tick can hold.

Here's how we know. Run a world on one machine and you loop over everything in it: take one thing, read it, work out its next state, write it, move on to the next. One write at a time. Picture the clock as a row of slots, one per tick, each with room for one write.

Does the record run like that? Take one piece of the record, the kind from Why Your Coffee Never Un-Stirs. A piece is a small stretch of the record with its own dials, the balances it keeps. On every tick it does one of two things: it holds, and its dials stay put, or it posts one new entry. The coffee post sets out four rules for how a piece's odds are set, and a piece that follows them has exactly one law, so nobody picks its numbers.⁷ Not yet derived: why a piece must follow those four rules. Derived: the one law they leave. At balance, that law has the piece post with chance 0.816: six possible entries at 0.136 each. In no arrangement of its dials does such a piece hold more than 49 times in 100, so it posts at least 51 times in 100.

Now take two pieces, anywhere. Each posts on a tick with a chance of at least 51 in 100. If one slot per tick ran the world, the two would never post on the same tick, so their chances wouldn't add up to more than 1. They add up to at least 51 + 51 = 102 in 100.

Here's a drawing of that count. Picture one drum with 100 slots, one per tick, where a beat is a tick on which a piece posts. Two pieces that each post on half the ticks can just fit on one drum if they take perfect turns: 50 + 50 = 100. A piece of the record posts at least 51 in 100. Two of them need at least 102 beats from a drum with 100 slots, so on average at least 2 beats in every 100 land on both at once. One drum can't take that.

The count doesn't care how the two pieces are coordinated, and it gets worse as pieces are added. Among a million pieces, at least 510,000 post on an average tick. A one-slot clock has room for one.

Slow every piece down so they can take turns, and a different problem shows up. A faster clock is the same move: by Step 1 its writes are entries in our record, so its ticks are steps in the writing of our record, and on them each piece gets a turn only now and then. A slowed piece no longer follows the four rules. And the more pieces there are, the slower each one has to go, so its pace depends on how many pieces there are in all, and no single piece's law contains that number. So the one-at-a-time machine is out.

That doesn't mean the record has no order. It has one: later entries come after earlier ones, and none reaches back to change them. Time is about that order. What the record lacks is one serial clock for everything: one slot per tick, one write at a time. You can number the entries, but the numbering is a chart. Renumber them with any numbers that keep later entries larger, and the order doesn't change, so the numbers carry nothing beyond the order. A map's lines of latitude are a drawing of the same fact: they help you find places, and the ground has no lines painted on it. The numbers on the record's entries are labels for finding entries. They aren't seconds, and they aren't slots on one serial clock.

Zoom out. Step 4 is done. The record isn't written one place at a time: two pieces already post more often than one slot per tick holds. The order is real, and the numbers on it are labels, not seconds. Next, and why: four doors are closed. The simulation idea still has something true in it, and it deserves a hearing.

Step 5: What the simulation idea gets right

The record's rules are steps a computer can follow. That's the true part of the simulation idea, and it's a fact about the record, not a sign that something is running it.

Here's how we know. The process that writes the record goes in steps, tick by tick, each by a rule. A computer is a machine for following rules one step at a time, so it can follow these. Here's the exact version. Say the record carries out a process when one fixed set of instructions, run one tick at a time, reading entries and writing new ones, gives the process's answer to every question it's asked. (Think of the digits of π: ask for digit number k, and the instructions hand it over.) Derived: the record carries out a process exactly when a program computes it. Not yet derived: that what happens physically is exactly what the record carries out. Is Math Invented or Discovered? arrives at the same place for numbers: the numbers the record holds are the ones a program computes.

Even the program that runs acts built from the three plain facts (telling apart, comparing, looking again) is a plain one: it never needs a loop that runs until something turns up, because every loop in it has a length fixed before it starts.

Rules a computer can follow don't need a computer to follow them. Here's the same logic with a case nobody argues about. Every sum and every product is something a computer can compute, and nobody concludes that some machine is working them out behind the scenes to make 7 × 8 come out as 56. The rule holds whether or not anything follows it. The record's rules are the same.

We follow them ourselves. The page at recognitionphysics.org/simulation/ starts from the empty record and runs the rules forward in exact arithmetic, and your own browser does the arithmetic as you watch. That's a machine inside reality modelling a small piece of reality: one part of the world modelling another part. Every simulation is that, from Pip's game to a weather forecast. A simulation of the whole thing is something else: a machine outside all of reality, running all of it. Steps 1 to 4 rule that out.

Here's one more objection. "If reality's rules are computable, isn't reality a program?"

A program is rules plus a separate something that carries them out. Reality has the rules. The events themselves carry them out as they happen, and Steps 1 to 4 leave no place for anything separate.

Zoom out. Step 5 is done. The record's rules are steps a computer can follow, and rules a computer can follow don't need a computer. Our own simulations are one part of the world modelling another part. Next, and why: the last step is about you. If nothing runs the record, what is it, and where does that leave your life?

Step 6: Your moments are real, and nothing is under the record

Every moment you live is an entry in the one record, and the record isn't a picture drawn by something deeper. It's the bottom layer of physics.

Here's how we know. Take "real" in the record's own sense: it occurs in the record, and a later look tells it apart from everything else that occurred. In that sense, Pip's frames are real. Each one occurred, in the living room's part of the record, and a later look can tell it apart from every other frame. Every moment you've lived meets the same test. It occurred, and it still exists, written in pen, for the reasons above and in The Universe Has No Delete Key. Call it a simulation, call it a world, call it a dream: every moment you live is an entry in the one record.

Now the layer question. A picture sits on top of something. Pip's game sits on a console, and the console sits in a living room. The record doesn't sit on anything. The process that writes it, one thing told apart from another, over and over, isn't an analogy for physics. It's the bottom layer of physics: the step every larger event is built from. Everything in this series is built up from three plain facts and the conditions each result names, and no layer of abstraction sits between the record and the physics.

Nobody holds the pen, because the writing isn't done to events. The writing is the events: when two things bump into each other, the bump is the entry. Put that beside Step 1. A machine drawing the record would have to be written into the record to do it, so it would be in the record, not under it.

Pip's world sits inside a bigger one, and that's why it can be run: there's a living room. The record holds every event there is, so there's nothing bigger around it.

Zoom out. Step 6 is done. Every moment you live is an entry in the one record, and nothing sits under the record: it's the bottom layer. That's all six steps, so here's the whole trip in one breath.

The whole trip, in one breath

Running a world means reading its state and writing the next one, and reading is comparing, which puts both sides in one record. Whatever runs a world is written in that world's own record, and there's no second one. Any world that tells things apart, compares them at a price, builds its levels by joins and keeps what it records has your shape, so no stranger "base reality" waits outside. No part of reality holds a complete copy of reality, because there are always more yes-or-no markings than places to write them, and Step 1 put any machine inside. Nothing writes the record one place at a time: two small pieces of the record already write more often than one slot per tick holds. What the simulation idea gets right is that the record's rules are steps a computer can follow, and rules a computer can follow don't need a computer. And every moment you live is an entry in the one record, which is the bottom layer of physics, not a picture drawn by something deeper.

So, are we living in a simulation? No. That's how reality is built: one record, with everything that has ever happened on the same page, from the dinosaur's yawn to every console ever made to every frame Pip ever lived to this sentence, written by the bottom layer of physics. Pip has a console because his world sits inside a bigger one. Reality has no living room around it, so it has no console. Nobody holds the pen, and you're in the record.