Why Is There Something Rather Than Nothing?

Picture nothing.

Go on. Close your eyes if it helps. I'll wait.

What did you see? Black. Dark, empty space, with a few stars if you're showing off.

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 try harder. 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. 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."¹ 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 shows how we know each one.

1. "Nothing" means four different things. A world with nothing to tell apart. One side of a comparison shrinking toward zero. A record 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. You never arrive.
4. The one free state is balance. 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, from the cost of comparing to you, would be a surprise riding on a coincidence. It isn't. "Why does something win out over nothing?" pictures a contest with two entrants. Nothing isn't one of them.

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 from Part 1 keeps the map. If you haven't read Part 1, here's all you need: reality keeps a permanent record of every event, entries go in one after another, and nothing is ever erased. I draw that record as the Ledger, a thick book with a deadpan face and one response to anything that happens: Noted.²

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.

Yeah-But, the voice in the back of your head that never lets anything big go by, has been waiting for this. "Yeah, but what do you mean by nothing?"

Four things.

1. The void. A world with nothing to tell apart. Not a dark room, and not an empty one: a dark room has a dark and a light, a wall and a window. The void is a world where everything is exactly the same as everything else. I can't even draw it, and that isn't laziness. A drawing is ink against paper, and ink against paper is a difference.

2. The shrinking side. Every comparison has two sides, two amounts 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.

Those 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.

Zoom out. Step 1 is done. "Nothing" does four jobs: the void, the shrinking side, the empty Ledger and the empty box. Next, and why: the void first. It's what most people mean by "nothing at all," so it's the one to settle before the others.

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 do. 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. Everything else in this series needs it. The cost of comparing, the golden ratio, three dimensions and the eight-tick cycle from Part 1 can't exist in a world without two things that differ. A void holds none of them.

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 pass another over. If you picked out x and passed over 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.³

"Recognition," the word in Recognition Science, is one thing registering a difference in another. That's what an event is. So check the void for the three things that matter here:

• An event? An event is a difference registered. The void has no difference to register. No event.
• A law? Laws say 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 it, if you like. Count the pairs of different things in a world. Two things make 1 pair. Three make 3. Four make 6. Ten make 45. Every pair is a place where a comparison can happen. In the void everything is the same thing, so there's no pair to compare. The void 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. It has no adjectives. 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.

Yeah-But, naturally, has a follow-up. "Yeah, but why isn't reality just the void?"

Because the void isn't a rival version of reality. Reality has things in it that can be told apart, and you're doing it right now: this word from that one, this page from the room. The void has nothing like that.

Zoom out. Step 2 is done. The void holds no event, no law and no question, because all three need two things that differ. Reality isn't a void: things can be told apart. Two things that differ are the floor. Next, and why: the void was the nothing of "no differences." The second nothing is different. It's a comparison that's still being made, with one side shrinking toward zero, and that one has a cost.

Step 3: Nothing on one side costs more than any 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 has two sides, and a cost: the more lopsided it is, the more it costs. Write the two sides as a ratio, x: how many times bigger one side is than the other. The cost is

J(x) = (x + 1/x) / 2 - 1

The cost isn't chosen. Two requirements fix it: how the costs of comparisons have to combine, and a unit to set the scale. They leave exactly one cost, and it's this one.⁴ 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.

Now name a ceiling. A thousand. A billion. A number with a thousand zeros. Whatever you name, 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.

Yeah-But: "Yeah, but nobody's comparing anything to nothing. Nothing means no comparisons 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?

Zoom out. Step 3 is done. Shrink one side of a comparison toward nothing and the cost passes every number you can name. You never get there. Next, and why: 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. A comparison and its reverse cost the same, so that 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:

• Nothing owed. Every comparison that gets made goes in with its reverse: "A to B at ratio 2" always goes in with "B to A at ratio 1/2." The two cancel, so 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 to the total, 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, so the total goes from 0 to 1/4 + 1/4 = 1/2, and the books still balance. Make a comparison at ratio 1, where the sides are equal, and the total stays 0.

Yeah-But: "Yeah, but an empty Ledger sounds a lot like nothing."

It does. Now check the difference. 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.

Your bank balance works the same way. Suppose yours reads zero. (Sorry.) Is that the same as having no balance? No. You have a balance, and it says zero.

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 it stands on the floor like everything else. 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.

Zoom out. Step 4 is done. The only cost-free state is balance, and the empty Ledger sits in it: balanced, nothing owed, nothing spent. That's a state, one Ledger among many. It's something. Three of the four nothings are sorted: the void holds nothing, the shrinking side has no top and the empty Ledger is balance. Next, and why: one is left, the empty box. It's the nothing the question itself uses, and it's 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.

So you never reach the floor by an argument. You're already standing on it, and every argument stands there too.

Yeah-But has brought a shovel. He wants to dig under the floor and see what's down there. Good luck to him. A hole is a difference too.

That's the honest edge of this answer, and it's worth saying plainly. 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. 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.

Yeah-But, one last time: "Yeah, but isn't there something only because we're here to ask?"

No. That would make nothing a real alternative that happened to lose. Nothing isn't an alternative. The void isn't a world where nobody asks. It's a world with no event and no law. The cost of heading toward nothing has no top. And the free state is balance, which is something. There's no contest.

Zoom out. Step 5 is done. The empty box differs from a box with a marble, and the question can't be asked without that difference. Two things that differ are the floor, and no rung lies below it. All four nothings are sorted. Next, and why: all five steps are done, so here's the whole trip in one breath.

The whole trip, in one breath

"Nothing" means four things, and none of them is a real alternative to something. A world with nothing to tell apart holds no event, no law and no question, and reality isn't one: things can be told apart. Shrink one side of a comparison toward nothing and the cost passes every number you can name, and you never arrive. The only comparison that costs nothing is two equal sides, and the Ledger with nothing written in it is balanced: zero is a state, and it's something. You can't ask the question without telling something from nothing, and that telling is the floor under everything else. So there's something because nothing isn't an option. You can't dig under the floor, and you can't even ask what's under it without standing on it. That's how reality is built.

A Ledger with nothing written in it isn't nothing. It's zero.

(The Ledger would like you to know that it has an entry for "Tuesday, nothing happened." It's in the same ink as every other line. Even the Ledger's nothing is something.)