Why Is There Something Rather Than Nothing?

Try to picture nothing.

What did you see? Black. Dark, empty space, with a few stars.

Now look at what you pictured. Black space has a here and a there. It has a near and a far. It has a you, looking at it from somewhere. That isn't nothing. That's a very large room with the lights off.

So take away the stars. Take away the space. Take away yourself. What's left? Whatever it is, you're picturing it, and a picture of nothing is still a picture.

You can't picture nothing.¹ That isn't a failure of imagination. A picture is made of differences, light against dark and here against there, and a world with nothing to tell apart has none. Hold on to that, because it's this whole post in miniature.

The question is old. Gottfried Leibniz put it this way in 1714: "Why is there something rather than nothing? For nothing is simpler and easier than something."² The second sentence is the sting. If nothing is the simple, easy default, then something is what needs a reason.

The plain answer takes that second sentence apart. There's something because "nothing" isn't one of the options reality has.

The short answer

Here's the whole answer in five steps. The rest of this post takes them one at a time and gives the reason for each.

1. "Nothing" means four different things. A world with nothing to tell apart. One side of a comparison (two amounts side by side) shrinking toward zero. A record of events with nothing written in it. A box with nothing in it. None of the four is a real alternative to something.
2. A world with nothing to tell apart holds no event, no law and no question. Nothing happens in it, and nothing can, because happening needs a difference.
3. Shrink one side of a comparison toward nothing and the cost climbs past every number you can name. The cost is zero when the two sides match and larger the more they differ. You never arrive.
4. The one free state is balance. "Free" means it costs zero. Two sides exactly equal cost nothing, and nothing else does. A record with nothing written in it is balanced. That's a state, and it's something.
5. The question answers itself. You can't ask it without telling "something" from "nothing," and telling things apart is already something.

Why this matters: the question treats nothing as the default and something as the surprise. If that were right, everything else in this series,³ from the cost of comparing (Step 3) to you, would be an exception to the default, there only by coincidence. It isn't. "Why does something win out over nothing?" pictures a contest with two entrants. Nothing isn't one of them.

Two facts from Part 1 of this series, with their reasons

The smallest event is one thing told apart from another. That's a single yes or no: this, not that. You're doing it right now, telling one word on this page from the next. Every measurement and every perception tells one thing from another, and telling two things apart takes information about both of them. The least information there can be is one yes or no. "Recognition," the word in Recognition Science, is one thing registering a difference in another. That's what an event is.

Reality keeps a record of every event, and nothing in it is ever erased. Entries go in one after another, and the full record of what happened is part of reality now. The reason in known physics is that the 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.⁴ Unitarity keeps the information about the past. It doesn't settle which outcome gets recorded next: the state evolves exactly, but the answer a measurement records isn't fixed in advance. So the record keeps every entry, and the next entry is still open. In this work the same thing is proved of the record itself: writing a new entry never alters an earlier one.⁵ One step is open: that physical evolution, the way the physical world changes over time, is this record running. The series calls the record the Ledger.

Step 1: "Nothing" means four different things

The word does four jobs, and people swap them without noticing. Pull them apart and the question gets simple. What does "nothing" mean here? Four things.

1. The void. A world with nothing to tell apart, which is what most people mean by "nothing at all." It isn't a dark room or an empty one: a dark room has a dark and a light, a wall and a window. The void is a world where no two things differ, so everything is exactly the same as everything else. It can't be drawn. A drawing is ink against paper, and ink against paper is a difference.

2. The shrinking side. Every comparison has two sides, two quantities side by side. Shrink one side until the other is a hundred times bigger. Then a thousand times. Then a million. Keep going. That's nothing as a direction: one side heading toward zero.

3. The empty Ledger. The Ledger with nothing written in it yet: no comparison made, no entry written.

4. The empty box. A box with nothing in it. In math, a collection with no members at all. This is the nothing the question itself sets beside "something": an empty box against a box with one thing inside.

These are four meanings of one word. They aren't four ages of the universe, and nothing on the list came before anything. Each one gets a step: the void in Step 2, the shrinking side in Step 3, the empty Ledger in Step 4 and the empty box in Step 5. The black space you pictured at the start isn't on the list. It's a something: a place, with a here and a there.

Step 2: In the void, nothing can happen

Nothing happens in the void, and nothing can: no event, no law, no question. Here's why.

Every world is one of two kinds. In the first kind, some two things differ. In the second kind, no two things differ. There's no third kind, and no world is both. It's pure logic: either two things differ or none do. The second kind is the void.

I'll call two things that differ the floor, and I'll say a result stands on the floor when it depends on two things that differ. Every result this series builds stands on it, and a void holds none of them. Here are four, each with its own reason:

• The cost of comparing (Step 3) measures how far two sides are from matching. The void has no two sides to compare.
• The golden ratio. If every level of structure, from the bottom level up, relates to the next by the same factor, and each new level combines the two before it, the factor satisfies λ² = λ + 1. Its positive solution is the golden ratio, 1.618... The void has no levels that differ. The full reason is in the post on the golden ratio.
• 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. Persistent pairs of loops are joined this way. Loops can be linked only in three dimensions: in two, loops can't wind around each other at all, and in four or more any two loops slide apart. So space has three dimensions. The void has no two loops. The full reason is in the post on three dimensions.
• The eight-tick cycle. A tick is one step in the writing of the record. Each of the three dimensions gives one yes-or-no direction. Three yes-or-no directions give 2 × 2 × 2 = 8 combinations, the eight corners of a cube, and a complete cycle that visits every corner once takes eight steps, or ticks. The void has no yes or no. The cycle comes from Part 1.

Here's the proof that nothing can be recognized in a void, and it's two lines long. To recognize anything, you pick one thing out and leave another. If you picked out x and left y, then x and y differ. So in a world where no two things differ, nothing can be picked out, and nothing can be recognized.⁶

Check the void for the three things that matter here:

• An event? An event is a difference registered, and the void has no difference to register. No event.
• A law? A law says how one thing relates to another when they differ: how much bigger, how much later, how much farther. Nothing differs, so a law has nothing to relate. No law.
• A question? A question needs at least two answers that differ, even if they're only yes and no. No question.

Count the pairs of different things in a world. Two things make 1 pair, three make 3, four make 6. Every pair is a place where a comparison can happen. In the void no two things differ, so it has 0 pairs: zero comparisons, zero events.

The void isn't dark: dark differs from light. It isn't silent: silence differs from sound. It isn't even empty: empty differs from full. Every one of those words describes a difference, and the void has none. A world is in a state when it's one way and not another, and the void is no way in particular, so it isn't a state a world can be in.

Why isn't reality just the void? Because reality holds events, and the void holds none. You're having one right now: telling this word from that one, this page from the room. And the void isn't a rival version of reality that happened to lose. It isn't a state a world can be in, so there's no such world for reality to have been.

The second nothing is different: a comparison still being made, with one side shrinking toward zero. That one has a cost.

Step 3: Shrink one side toward nothing and the cost passes every number you can name

Back to Leibniz. He called nothing "easier." We have a way to check what a lopsided comparison costs, so let's check.

Shrink one side of a comparison toward nothing and the cost climbs past every number you can name. Here's how we know.

Every comparison puts two quantities side by side, and it has a cost: the more lopsided it is, the more it costs. The cost measures imbalance, how far the two sides are from matching. It weights the odds: in the long run, every added 1 of cost makes a state 1.618... (the golden ratio from Step 2) times less likely, so balance is the single most likely state, the way a warm physical system favors its lowest-energy states without sitting in them. Why the golden ratio: it scales the levels of structure (Step 2), and each level carries 1/1.618... the weight of the one below, so every added 1 of cost is one step down that ladder. The cost doesn't pick each step. Write the two sides as a ratio, x: how many times bigger one side is than the other. The cost is a plain number too, like the ratio it's computed from:

J(x) = (x + 1/x) / 2 − 1

The cost isn't chosen. It has to meet three requirements: it's zero when the two sides match (x = 1), it grows as they differ, and it's the same whichever side is put first (x or 1/x). Those requirements, the rule for combining costs and one calibration leave exactly one formula, and this cost is it.⁷ The combining rule says how the costs of combined comparisons add: J(xy) + J(x/y) = 2 J(x) + 2 J(y) + 2 J(x) J(y). The 2 in front of the last term, 2 J(x) J(y), fixes the unit of cost. The calibration sets how sharply the cost rises near balance. You can check the rule yourself. The cost (ln x)² meets the three requirements, but it fails the rule: for it, J(xy) + J(x/y) equals 2 J(x) + 2 J(y), with no 2 J(x) J(y) term.

Try it at ratio 2: (2 + 1/2) / 2 − 1 = 1/4. Here are more:

Watch the pattern. Each time the small side shrinks tenfold, the cost grows roughly tenfold: 4.05, then 49.005, then about 499 for a thousandth.

Name any ceiling, a thousand or a billion, and there's a size below which every comparison costs more. For a billion, one side at a three-billionth of the other already costs about a billion and a half.

You never arrive at nothing. The formula has a 1/x in it, so it can't even be worked out for a side of exactly zero. You can only get closer, and the cost keeps climbing. "Nothing on one side" isn't a place you can reach. It's a direction, and along it the cost has no top.

Does a cost with no top forbid anything? No. Step 3 doesn't claim that. It claims that a side of exactly zero is never reached, because zero isn't a ratio the formula can take, and that on the way the cost climbs past every number you can name.

Doesn't nothing mean no comparison at all? That's the void, and Step 2 settled it. This is the other nothing: a comparison still being made, with one side shrinking. Different meaning, same word.

The whole cost curve, drawn as a valley with a cliff on one side, is in Step 1 of Did Time Have a Beginning?

The cost is zero in exactly one place. That place is the third nothing, and it turns out not to be nothing at all.

Step 4: The one free state is balance

The only comparison that costs nothing is two equal sides, and balance is something. Here's how we know.

Why only one. The cost can be rewritten as (x − 1)² / (2x). The top is a square, and a square is never negative. The bottom, 2x, is positive, because x is a ratio of sizes. So the cost is never below 0, and it equals 0 only when x − 1 = 0, which means x = 1. Equal sides cost nothing, and every other ratio costs something. Check it at x = 10: 9² / 20 = 81/20 = 4.05. Ratio 10 and ratio 1/10 are a comparison and its reverse, and a comparison and its reverse cost the same, so this matches the 1/10 row.

Now the empty Ledger. The Ledger with nothing written in it reads zero twice, and the two zeros are different kinds. The books show two things. What's owed is what the comparisons and their reverses leave on balance. What's spent is the total cost of the comparisons made. Each entry is one comparison. "A to B at ratio 2" means side A is twice side B, and it always goes in with its reverse, "B to A at ratio 1/2": the same two sides in the other order.

• Nothing owed. The two ratios multiply to 1, the ratio of equal sides, so the pair cancels and nothing is owed on balance. That's true before any entry and after every one.
• Nothing spent. The total cost of the comparisons made is zero. It stays zero only until the first comparison whose two sides aren't equal. After that, every such comparison adds its cost, and no comparison takes anything away.

Work it through. Make a comparison at ratio 2, with its reverse at 1/2. Each costs 1/4, because a comparison and its reverse cost the same. The costs add instead of cancelling, so the amount spent, the total cost of the comparisons made, goes from 0 to 1/4 + 1/4 = 1/2, while the ratios still cancel and the books still balance. Make a comparison at ratio 1, where the sides are equal, and the amount spent stays 0. A comparison is balanced when its two sides are equal. A record is balanced when nothing is owed on balance.

Isn't an empty Ledger just nothing? No. A Ledger with nothing written in it isn't the same as no Ledger. The empty Ledger is a Ledger, with books you can read. They read zero: balanced, nothing owed, nothing spent. With no Ledger at all there are no books and nothing to read. One is a state. The other isn't.

The empty Ledger isn't alone, either. It's one Ledger out of all the Ledgers there are: the one with no entries. Picking it out takes a difference, the difference between "no entries" and "some entries." So it sits in a world where things differ, and, like everything else, it depends on two things that differ. Did Time Have a Beginning? starts from this same empty Ledger and asks what it has to do with the beginning of time.

So Leibniz was half right. The Ledger with nothing written in it costs nothing, and it's the state with the fewest entries. But that state isn't nothing. It's something, and it's balance.

One nothing is left, the empty box: the nothing the question itself uses, and where the question turns on itself.

Step 5: The question answers itself

You can't ask "why is there something rather than nothing?" without something. To ask it, you set "something" and "nothing" side by side and tell them apart. That takes two things that differ, and two things that differ are the floor. Here's how we know.

Go back to the empty box and a box with one marble in it. They're different boxes: one has a marble and one doesn't. Say "nothing differs from something" and you've used that difference. Say "there's no difference at all" and your sentence differs from its opposite. The statement and the thing it denies are both on the page.

The same goes for the first plain fact in Part 1: things can be told apart. Hot isn't cold. Here isn't there. Doubting it takes a difference between "it's true" and "it's false," and asking whether it's true is an event where you tell those two apart. You meet the fact in the act of asking whether it holds.

You never reach the floor by an argument. Every argument already uses it.

What lies under the floor? This is the honest edge of the answer. We don't claim that something came out of absolute nothing. No derivation can start below the floor: to write down "there is no difference" you need the sentence and the thing it denies, so the derivation already stands on a difference. No rung lies below the floor. What we do claim is different. There's no nothing for something to have come out of. The void holds no event. A side shrinking toward nothing never gets there. The one free state is balance. And the empty box and the question both stand on a difference.

Isn't there something only because we're here to ask? No. If that were so, nothing would be a real alternative that happened to lose, and nothing isn't an alternative. The void isn't a world where nobody asks. It's a world with no event and no law. There's no contest.

So why is there something?

So there's something because nothing isn't an option. That's how reality is built: on two things that differ, with everything else in this series standing on them.