Is Reality Physical or Mental? Yes. It's One Event With Two Sides.

You stub your toe on the leg of the coffee table.

A doctor can trace what happens next. The table leg presses on the skin. Nerve endings in the toe fire. The signal runs up the leg, along the spinal cord and into the brain, where cells fire in one region after another. Every link in that chain is an event an instrument can read.

Now look for the "ow."

It isn't in the pressure. It isn't in the signal in your leg, or the one in your spine, or in any one cell in your brain. Follow the chain to its last link and the ow never turns up as one more link. And the ow is the loudest thing that has happened to you all morning.

Philosophers call the question of why any of that comes with an ow the hard problem.¹ People have argued about it for more than two thousand years, and three answers have lasted.²

• Materialism says there is only matter. The ow is what the signals are, or what they make.
• Idealism says reality is made of mind. The table, the toe and the nerves are ideas in a mind.
• Dualism says mind and matter are two different kinds of thing, joined somehow.

Each one gets stuck in its own place. Materialism can't find the ow in the chain. Idealism has to explain why the table is so stubbornly there, the same for everybody. Dualism has to explain how two different kinds of thing push on each other.

Each one also keeps one true thing. This post shows which, and why the three fit into one picture.

Two words first. Physical means what any instrument can read: the pressure, the signal, the firing. Mental means what it's like: the ow, the taste of coffee, the redness of red. The question is whether reality is made of the first, the second, or two different things.

The short answer

Both, and they aren't two kinds of stuff. Reality is one kind of event, repeated everywhere, and every event has two sides. The outside is what any measurement reads. The inside is experience. Matter is the outside of events. Experience is the inside of the same events.

Neither side is more basic: the price of an event (how far out of balance its two sides are) comes out the same with the two sides swapped. Neither side reduces to the other: the outside alone doesn't fix the inside, and the inside alone doesn't fix the outside. And the inside isn't beyond physics. It shows up in how the event responds when you push on it.

So experience isn't a ghost in a machine, and matter isn't a dream in a mind. Experience is the inside of physics itself.

Part 1 of The Universe Writes in Pen, What You Are, says this in one paragraph: every event has two sides, one event seen from without and from within. This post gives the reasons, with numbers. One link in the answer isn't derived yet, and Step 3 says which.

Why this matters. The old argument asked which kind of stuff reality is made of, and every answer paid for its choice. Materialism paid with the ow, idealism with the table, dualism with the link between two worlds. One kind of event with two sides changes the bill. There's no second world to connect to the first, and no level where experience switches on, because every event has an inside. And because it's a claim about how events are built, it comes with numbers: a price, a push and a recovery, all worked out below.

Here's the answer in seven steps. The rest of the post takes them one at a time and shows how we know each one.

1. Every event has two sides. The smallest event is one thing told apart from another. A lone number means nothing, so an event holds one size against a second size, both above zero. Call them the outside and the inside.
2. The price gives neither side priority. An event whose sides don't match has an exact price, and the price is the same with the sides swapped.
3. The inside is experience. Experience exists, and the inside of every event is where it sits.
4. Neither side fixes the other. Two events can read the same outside and differ inside.
5. The inside shows up in physics. Push on the outside, and events that read the same outside but differ inside respond differently. The response gives the inside back exactly.
6. One number per event can't hold experience. Give each event a single number and there's no room for how intense an experience is, for what the outside leaves open, or for what an event is directed at. A pair of numbers has room for all three.
7. Each old answer keeps one true thing. Materialism keeps the one physical reality, idealism keeps experience all the way down, and dualism keeps the gap between inside and outside. None of them needs a second world.

Step 1: Every event has two sides

The smallest thing that can happen is one thing being told apart from another, a single yes or no. You're doing it right now: your eyes are telling the dark marks on this page from the light around them. Every measurement is the same act. A thermometer tells hot from cold. A detector tells a click from silence. Telling two things apart takes information about both of them, and the least information there can be is one yes or no. Every larger event is built from that one, and What You Are shows the small process that does the building. So every event comes down to a comparison.

Now the ruler. Measure a door. It's 2 meters tall, or 200 centimeters, or about 6.6 feet. One door, three numbers, and the number changed every time the ruler did. A lone number means nothing until you say what it's held against. What the measurement told you is that the door is twice as tall as a 1-meter stick: 2 against 1, or 200 against 100, or 6.56 against 3.28. The numbers follow the ruler. The ratio, 2, doesn't.

When you measure a door, a person picks the ruler. When two molecules bump, nobody holds a ruler. The event holds both sizes itself: a reading, and the size that reading is held against. Both are above zero, because a comparison with an empty side isn't a comparison. You can't say how many times bigger than nothing something is.³

I'll name the two sides. The side a measurement reads is the outside. The side it's held against is the inside. They aren't two things stuck together. They're one event. Is Your Coffee Mug Conscious? works through this step and the next at length, with a mug.

Next, and why: the two sides don't have to match. When they don't, the event is out of balance, and the imbalance has an exact price.

Step 2: The price gives neither side priority

Divide the outside by the inside and call the result x. The price of the event is a rule that gives one number for each x. I'll call it J:

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

Add x and 1/x, halve the sum, take away 1. Try an outside of 2 and an inside of 1. Then x is 2, and the price is (2 + 1/2) / 2 - 1 = 1/4. A perfect match, x = 1, has price 0. Every mismatch has a price above 0. The price is a pure number with no units: it measures the imbalance between the two sides of one event, zero when they match and growing as they drift apart.

Swap the sides, an outside of 1 and an inside of 2, and x is 1/2. The price is (1/2 + 2) / 2 - 1 = 1/4 again. Swap any pair and the price is the same. And the ruler doesn't matter: 200 against 100 has the same ratio as 2 against 1, so its price is 1/4 too.

The price isn't chosen because it looks tidy. It has to be zero when the sides match, grow as they differ, and come out the same whichever side you put first. Those requirements, a rule for how the prices of combined comparisons add, and one calibration (how sharply the price rises near a match) leave exactly one formula.⁴ And it's one price list for everything: a bump in your coffee and a bump in your brain are priced by the same function of the same two numbers. There isn't a second list for minds.

The swap is the point of this step. The price can't tell which side you call the outside. Put the sides the other way round and the event has exactly the price it had. So the price gives neither side priority, and neither one is the real event with the other tacked on.

Next, and why: the question this post is named for. The outside is the side a measurement reads. What is the inside?

Step 3: The inside is experience

The inside of every event is experience: what the event is like.

Here is the reason. Experience exists. You're having some right now, and it's an occurrence in reality like any other, in the same world as the table leg and the nerves. Any explanation that keeps the table and the nerves real as well has to say where experience sits, and there are three places to put it.

• Beside physics, as a second kind of thing. Then something has to connect the two kinds.
• Switched on partway up, at some level of organization. Then there's a line, and the events just on either side of it are nearly identical, yet one is felt and the other isn't.
• In every event, as its inside. Then there's one kind of event, no line, and nothing added beside physics.

Only the third has no seam. Philosophers call views of this shape dual-aspect views: one reality, two aspects. Here the two aspects are two numbers with an exact price between them.

That is the reason for the identification. The identification itself isn't derived yet: that the inside of every event is experience, in a bump between two molecules as much as in a brain. What is derived beside it: the price, and every result in Steps 4 to 6 about the inside.

Experience isn't the same as being someone: having an inside doesn't make an event a mind. What makes a someone is a separate question, and What You Are and Is Your Coffee Mug Conscious? take it up.

Next, and why: if the inside is experience, the outside should leave it open, the way a list of nerve readings leaves open what the toe feels like. It does, exactly.

Step 4: Neither side fixes the other

The outside alone never tells you the inside. Take two events. One has outside 1 and inside 2. The other has outside 1 and inside 3. A meter that reads the outside gets 1 both times, and nothing in the structure of an event turns the outside number into the inside number. So no rule computes the inside from the outside.

It works the other way too. The events (1, 2) and (2, 2) share the inside, 2, and differ in the outside. Neither side reduces to the other.

That's the doctor's chain again. Every link is an event with an outside and an inside, and the doctor's instruments read the outsides: pressure, voltage, firing. Tracing the chain more finely only adds more outsides. The inside was never going to turn up in a list of outside readings.

This is a statement about the outside reading by itself. It isn't a claim about every possible measurement, and Step 5 is about what else reaches the inside.

Next, and why: if the inside is hidden from the outside reading, is it hidden from physics too? Is it a ghost beside the event, with no effect on it?

Step 5: The inside shows up in physics

The inside changes how an event responds. It's a magnitude of the event, not a ghost beside it.

The idea first, on a bathroom scale. Two people stand on a scale, and it reads 70 kg for both. The reading can't tell you which of them is braced and which is relaxed. Give each a gentle shove. The braced one barely moves. The relaxed one sways. Same reading, different response.

The scale is a drawing of the real mechanism. The reading stands for the outside, how braced the person is stands for the inside, and the shove stands for a push on the outside. The sway is the price changing. The numbers below are the mechanism itself, and in it the push is doubling the outside and leaving the inside alone.

Take the event (1, 2): outside 1, inside 2. Its price is 1/4. Double its outside and you get (2, 2), a perfect match, price 0.

Now take (1, 1/2). It has the same outside, and its price is 1/4 as well: x is 1/2 for one event and 2 for the other, and J gives 1/4 for both, the swap rule again. Double its outside and you get (2, 1/2), where x = 4 and the price is (4 + 1/4) / 2 - 1 = 9/8.

A third event, (1, 3), starts at 2/3 and ends at 1/12.

The first two rows are the point. Same outside, same price, and nothing in the price tells them apart. Push, and one falls to 0 while the other climbs to 9/8.

The push also gives the inside back, and it does so exactly. Call the price before the push b and the price after it d. Then

x = (4 × d - 2 × b + 2) / 3

where x is the outside divided by the inside. Try it on (1, 1/2): b = 1/4 and d = 9/8, so x = (9/2 - 1/2 + 2) / 3 = 6/3 = 2. The outside is 1, so the inside is 1 ÷ 2 = 1/2. Try it on (1, 2): b = 1/4 and d = 0, so x = (0 - 1/2 + 2) / 3 = 1/2, and the inside is 1 ÷ 1/2 = 2. And on (1, 3): b = 2/3 and d = 1/12, so x = (1/3 - 4/3 + 2) / 3 = 1/3, and the inside is 3.

Here's why it works. Before the push, b = J(x) = x/2 + 1/(2x) - 1. After doubling the outside the ratio is 2x, so d = J(2x) = x + 1/(4x) - 1. Four times d minus twice b leaves 3x - 2, because the 1/x parts cancel: 4 × 1/(4x) is 1/x, and so is 2 × 1/(2x). Add 2 and divide by 3 and you have x.

Read that again. Two events that no reading of the outside can tell apart, and one push tells them apart and hands the hidden number back exactly.

So the inside isn't hidden from physics. It's hidden from the outside reading by itself. Push on the outside and the inside answers.⁵

The recovery is exact for the two-sided event. Giving a real event this push, and calibrating it, hasn't been done, so no inside has been measured. What the recovery shows is how an event is built: the inside changes the event's response, so it belongs to the physics and isn't a second world beside it.

Next, and why: the last result. Why does an event need a second number at all? One number would be simpler.

Step 6: One number per event can't hold experience

A description that gives each event a single number has no room for experience. A pair of numbers has room.

Suppose an event were a single number, a reading with no second side. Now ask for a rule that gives each event an intensity, a number for how intense it is. The rule shouldn't depend on the ruler, because nobody holds a ruler for a bump between molecules, and a lone reading changes with every unit (Step 1). Take one event that reads 3 on one ruler. On a ruler that makes every reading 5/3 as big, the same event reads 5. An intensity that ignores the ruler has to be the same for 3 and for 5. The same move turns any positive number into any other, so a ruler-free intensity is the same for every event. It can't tell a pinprick from a thunderclap.

A pair doesn't have that problem. Change the ruler and both numbers change together, so their ratio stays put, and the price of the ratio stays put with it. The event (1, 3) becomes (5/3, 5): the ratio is 1/3 both times, and the price is 2/3 both times. Meanwhile (1, 1) has price 0. The intensity is ruler-free and still differs from event to event.

Two more features have nowhere to live in a single number.

• Privacy. If an event is one number and a measurement reads that number, nothing is left over for the measurement to miss. The outside can't leave the inside open when there is only an outside.
• Direction. An event with one number has no second side to be held against, so there's nothing for it to be directed at.

Give each event a second number held against the first, and all three have a place. Intensity is the price. Privacy is the inside the outside leaves open (Step 4). Direction, in its barest form, is the pair itself: one side held against the other.

This is about descriptions that give each event one positive number and no reference. A description with more structure is a different object. And it doesn't show that the inside is experience, which is the identification in Step 3. It shows that two numbers held against each other is the smallest description with room for all three.

Next, and why: with six steps in hand, go back to the three camps from the top of the page.

Step 7: Each old answer keeps one true thing

Each camp keeps one true thing, and the two-sided event keeps all three.

• Materialism keeps the one reality. Reality is one thing, and it's physical all the way through: every event has an outside, and the outside is what physics reads. There's no second world. Where it stalls is the ow, and Steps 4 and 6 show why: readings of the outside alone can't hold the inside.
• Idealism keeps the experience. Experience is real, it isn't an accident of brains, and it goes all the way down: every event has an inside. What idealism doesn't need is a world made of mind, with the table as an idea in it. The outside is as real as the inside. Every event has both, and no inside fixes an outside (Step 4).
• Dualism keeps the gap. The inside can't be read off the outside (Step 4). What dualism doesn't need is a second world to sit in the gap. The inside is a magnitude of the same event, and it changes how the event responds (Step 5). There's nothing to connect, and nothing for two kinds of thing to push each other across.

So materialism held the outside, idealism held the inside, and dualism held both and pulled them apart into two worlds.

A few natural questions.

Where does the observer in quantum physics fit? A look at something is a contact that writes a record. It needs no eyes and no mind: a camera or a stray particle does it as well as a person. Does Looking at Something Change It? works through it.

Is it all one consciousness? That's a separate question, and If We're All One, Why Can't I Feel Your Headache? takes it up.

The World Underneath the Labels makes a similar point about a sandwich and five academic departments: the labels divide our attention, and the event stays connected. Physical and mental are labels for the two sides of one event, and the event stays connected too.

What's still open

• Open: that the inside of every event is experience, in a bump between two molecules as much as in a brain. Derived beside it: the price, and every result in Steps 4 to 6 about the inside.
• Open: reading an inside off a real event. Derived beside it: the push and the recovery are exact for the two-sided event. Not done: giving a real event the push and calibrating it, so no inside has been measured.

The whole trip, in one breath

The smallest event is one thing told apart from another, so every event holds two sizes against each other: an outside that a measurement reads and an inside it's held against, both always above zero. One price, J, covers every event, and it's the same with the sides swapped, so neither side comes first. The inside is experience. The outside never fixes it, and it never fixes the outside: two events can read the same and differ inside. The inside isn't hidden from physics, though. Push on the outside and two such events respond differently, and the response hands the inside back exactly. A single number per event has no room for intensity, privacy or direction, and a pair has room for all three. So reality isn't matter or mind, and it isn't two worlds. It's one kind of event with two sides, and each old camp held a piece of it.

The next time you stub your toe, the doctor's chain is the outside of what happened, and the ow is its inside. Both are real. It's one event.