A walk through the garden · Step 4 of 19 · What is there

What is the world made of?

What exists is what has been written.

Branch of philosophy: Ontology and the philosophy of mathematics. What exists, and what numbers, shapes and truths are.

Where the question lives

Hold your hand in front of your face.

What is it made of?

Flesh. Skin, bone, blood, nerve. Press, and flesh becomes cells. Press again: molecules, atoms, protons, electrons, quarks, fields, equations. Then the pressing has nowhere left to go.

You started with your hand. You ended with mathematics. Every answer on the way down was true at its own level. And every one pointed below itself, to something that was supposed to be more real.

Now picture three apples on a table. Three stars in the sky. Three beats in a bar of music. The apples, the stars and the beats share nothing material. Yet they share something. What is it? Where is it?

This is the question of ontology, the part of philosophy that asks what exists. It has been asked since philosophy began. What is at the bottom? The thing not made of anything else. The stuff your hand finally is. Philosophy has been pressing for two and a half thousand years.

Three more questions hang from it. What is information? Where does mathematics come from, and why does it work? What do three apples share? Four chapters carry these questions, one after the other. Each stands on the one before.

What philosophy said

What exists?

Six answers have been given. Each has had its century. Each survives today in some serious tradition.

Matter. Everything is matter, arranged. Mind is matter doing certain things. This is materialism.

Mind. Everything is appearance to a mind. Take the minds away and the world has nothing to stand on. This is idealism. Berkeley held a strong form of it in the eighteenth century.

Structure. Numbers, sets and shapes are the real things, in a realm of their own. The physical world is a copy. This is mathematical Platonism.

Process. There are no things, only stable patterns in change. The world is a doing, not a thing done. This is process metaphysics.

One neutral ground. Neither mind nor matter, but something under both, with mind and matter as its two faces. This is neutral monism. Spinoza held a version of it in the seventeenth century.

Experience all the way down. Every scrap of matter carries a flicker of experience. Minds are what happens when the flickers combine. This is panpsychism.

Six candidates for the bottom. They all fail at the same place. Every one of them takes for granted that there is a substance to find: a stuff the world is made of. They disagree only about which stuff. That picture is older than any of the six. It came down from Aristotle, who made substance the basic category of being. It is built into grammar. “The cup is blue.” There is a cup, a thing, and blueness belongs to it.

What is information?

A fingerprint on a glass. A name spoken across a crowded room. A photograph you have not looked at in years. Each is a record. What does each one carry? The classical word for what is carried is information.

In 1948 Claude Shannon made the question precise. Information is the reduction of uncertainty. Settle which of two equal options happened, and you have one bit. In 1961 Rolf Landauer showed that erasing a bit costs a minimum amount of heat. Small, but never zero. Physicists write that minimum as kT ln 2, where k is a fixed constant and T is the temperature. Information is physical. Later John Wheeler said “it from bit”: information comes first, and particles, fields and spacetime come after.

Four answers recur. Each reaches part of the thing.

Count it. Shannon’s measure is not wrong. It leaves out meaning on purpose, and that discipline made telephones possible. But a book and a pile of random letters with the same statistics score the same. You know they are not the same. The measure counts one shadow.

Make it meaning. The book is about something. The letters are not. But meaning needs a reader, and fingerprints were on glasses before anyone could read them. The world manages information without an interpreter. Meaning is real, and meaning is later.

Make it fundamental. Wheeler saw that information is structural, not added. Then he stopped at making it the basic stuff. If information is more basic than physics, what does it live in? A question answered with a deeper question.

Eliminate it. Information is just a word for physical state. The fingerprint is molecules on glass. But then why do some arrangements work as records of others, and some do not? “They just do” is a refusal.

Measured. Made into meaning. Made fundamental. Eliminated. Not dissolved.

Where does mathematics come from?

A child counts three apples on a table. The count comes out three. An astronomer, using equations written three hundred years ago, says where a comet will be in eleven years. The comet is there. Why does mathematics describe the world at all?

The Pythagoreans of ancient Greece found that strings sounding in harmony stand in small whole-number ratios. A relation in the world matched a relation in the mind. They concluded that number was the substance of things. The discovery was real. The conclusion was a frame, and it stuck for two thousand years. In 1960 the physicist Eugene Wigner asked why mathematics was so unreasonably effective. The effectiveness was a fact. The unreasonableness was a confession.

Five answers recur.

Platonism. Numbers are real, in a realm of their own. It captures that theorems hold everywhere and feel found, not made. It brings in a second realm with no account of where it is.

Formalism. Mathematics is symbols moved by rules, about nothing. It captures the discipline of proof. It cannot say why a game never asked to track anything tracks the comet.

Logicism. Mathematics is logic in disguise. It could not reduce all of mathematics to logic, and it left logic itself unexplained. The problem moved one step.

Intuitionism. Mathematics is built by the mind. Brouwer saw rightly that mathematics is something done. He put the doing in the mind alone. The doing is what records do. The mind is one place where it reads itself.

Fictionalism. Numbers are useful fictions. It cannot say why “force equals mass times acceleration” is a fiction physics cannot do without, and Sherlock Holmes is one it does not need.

Five partial captures. None reaches the level where the structure lives.

What do three apples share?

A child sees that two cats are alike in a way a cat and a dog are not. A potter sees that two bowls have the same shape, though thrown from different clay. The shared something is called a universal. The question has been asked since Plato. It has not been closed.

Plato said the many red things share Redness, a Form in a realm of its own, and they take part in it. He saw that a universal does not depend on any one instance: destroy three apples and threeness survives. He put it in the wrong place.

Aristotle asked how an apple in space could take part in a Form that is in no place. His answer: universals are real, but only in their instances. Redness is in the red things. He saw that universals are not somewhere else. He erred in putting them inside the instances, like seeds in the apple.

The nominalists of the Middle Ages, Ockham among the loudest, said only particular things exist. The universal is just the name we give to things that resemble each other. They saw that nothing extra needs adding to the world. They erred in making the likeness a matter of words.

The conceptualists put universals in the mind, as ideas formed by meeting things. They saw that universals become visible when someone recognises them. They erred in putting them in the mind alone.

The positions did not reduce to each other. The question did not close. Location is still where the disagreement lives.

What the 420 Code sees

All four chapters dissolve their question. As in step three, a dissolution shows that a question assumed something that is not there. The three Resolutions chapters also supply what each question was reaching for, once the wrong frame drops. Read together, the four give one answer: what exists is records, and the relations between records.

What exists? Records, not stuff

The axiom does not produce a substance. It produces records.

That is where the dissolution begins. The axiom does not answer the question the six are asking. It does not say what stuff is at the bottom. It says what a record needs in order to exist. Under those four conditions, records pile up in the now. And there is no further question about what they are made of.

Records are not made of anything. Ask what a record is made of, and you have asked what the number seven is made of. In the substance picture, everything is made of something smaller, until you hit the bottom. In the axiom, records are not built of parts. They are events: a distinction, made and held. They have structure: relations to other records, sequence, accumulation. They do not have substance.

The materialist presses. If a record is not made of anything, in what sense does it exist? To exist is to be made of something.

But that is the substance picture defining existence in its own favour. In the axiom, to exist is to be recorded. The reading you are doing now exists. It is not made of anything. It is real because it is being written.

Two frames. Two different questions. What is X made of? Under what conditions can X be a distinction? The axiom answers the second.

Four words do the work from here on. A record is a distinction made and held. A coupling is two records meeting so that each is now a distinction for the other. Light on a retina. A molecule at a receptor. This word, and you reading it. A record-architecture is records coupling in a stable pattern across time. A hand. A brain. A star. Not a new kind of thing: records, holding together. And the Actualization State, which you met in step two, is the now. Not a place. Not a container. The condition under which any record can be written or read at all. None of these is added to the axiom. They are names for what it produces.

Now read the six from inside the axiom. Each saw a real feature, and called it the substance.

Matter is right that what exists is physical. Matter is what records of a certain kind look like from the outside. A proton is a stable coupling. Your hand is a very large coupling of atoms. But matter is not the substrate, the stuff everything else is made from. There is nothing under the records.

Mind is right that every coupling has an inside. Mind is what certain records look like from inside. Matter is what the same records look like from outside. Neither is the ground. The ground is that records are being written.

Structure is right that mathematical truth holds everywhere. But it is not in a separate heaven. It is the shape of the relations records actually have.

Process is right that the unit is an event, not a thing. What it lacked was an axiom. Process is what records do under the third condition: they pile up, one way, without undoing.

The neutral ground is right that mind and matter are two faces of one thing. The thing is records, coupling. The two faces are the inside reading and the outside reading of the same coupling.

Experience all the way down is right that every coupling has an inside reading. But that is not an extra property bolted onto matter. It is what a record is from its own position.

Six partial readings. The question was never wrong. It was answered unevenly, because the axiom that unifies the answers was not in hand.

What is information? The record’s own history

Take the two jars from step two. One grain of sand falls into one jar. All four conditions are in that one event: a symmetry to break, the smallest break, a trace that does not undo itself, in this jar and not everywhere.

And the grain is the bit. The bit, the unit Shannon counted with, is one grain. One break. One ε. A bit is what one smallest break amounts to, named at the level of information.

Below ε there is no record. No half-grain. No quarter-bit. A distinction either holds or it does not. Shannon’s measures can come out in fractions, but those are averages over many possible records. They are not half-records.

Now look at what the question needs. For “what is information?” to have force, information must be separate from the record, at least in thought. Otherwise it is just the question “what is a record?”.

That separation cannot hold.

A record is not a thing to which information has been added. A record is a thing whose existence is the having-been-distinguished. The fingerprint is the pattern that tells this glass apart from the same glass without it. The pattern does not undo itself. The difference and its lasting are not something the record has. They are what the record is.

Information is what that amounts to, read as a history. Three pieces, each doing work.

History, because R gives the record a direction. The moment the grain dropped is kept in the structure. R is the past kept readable from the present.

The record, because there is nothing further the record carries. The fingerprint is not molecules plus a ghost about who left it. Strip the pattern away and there is no information left to find.

Read, because history is what becomes legible when the structure is examined. Without reading, the history is there but hidden. With reading, it becomes plain in the reader.

The chapter puts it in two sentences: “Information is the record history, literally. The carrier is the carrying.”

The same sentence can be ink on paper, sound in air, pixels on a screen, magnetic marks on a disk, voltage in a wire, dots in Braille or marks in clay. Does that not show information floats free of any record? No. Those are seven records, alike at the level that matters for the sentence. The pattern lives in each one. Strip the records away and nothing is left. It is repeatability, not freedom from records.

Is this only a new name? Landauer says no. Erasing a bit costs heat. On Shannon’s account that is a strange coincidence. On the meaning account it is a mystery. On the dissolution it is expected. To erase a bit is to force something that could be in either of two states into one. That is trying to undo R in one place: pushing the grain back out of the jar. R does not allow it for free. The cost is paid elsewhere, as heat. The ln 2 in the cost comes from the break being two-sided. The kT comes from the temperature of the surroundings. If information were a carried thing, throwing it away would not disturb the carrier. The cost shows the separation is not there.

And you, reading, are a place where record history is being written. A distinction was just made in you, and held. The grain has long stood for smallness: one life against deep time. At the level of the axiom it means more. “You are not in the desert. You are the grain making the desert distinguishable from itself.”

Where does mathematics come from? The language of the wake

Notice what you are doing now. You read these words in order. First, second, third. You cannot stop tracking the order without ceasing to read. That tracking is mathematics in its earliest form. To count three apples is to tell one apart, then another, then another, and to stop. Try to deny it. The denial is a sequence of words. You are already inside.

The puzzle has two faces, and mixing them up kept it open. What is mathematics: what kind of thing is a number? And why does it work: why does the squiggle predict the comet? Each of the five answers handles one face. The dissolution answers both at once.

“Mathematics is the relational reading of records.” It is the language records produce when their relations are read at the level where those relations show. That is what it is. And it works because records have the structure they have, and reading that structure is what the language does.

A relation between records is a fact about how they sit together. Which came first. Which is made of which. Which limits which. Relations are not added to records. They are what records, taken together, are.

The marks on a mathematician’s page are records too. What makes them mathematics and not scribbles is that the relations between them mirror the relations between other records. The mirroring is not luck. It is what reading relations does.

The floor of mathematics shows in the jars.

Logic comes from the break. The grain is in the jar or it is not. True and false are that either-or, read in statements.

Algebra comes from records combining. The grain lands. Water is pushed aside. The jar’s centre of gravity shifts. Any two of these records make a combined record.

Geometry comes from the limit on spread. A ripple spreads from where the grain fell, at the rate the water allows. A circle is what spreading from a point at a bounded rate is.

Counting comes from telling things apart. Put more jars on the table. Counting pairs each one with a number, until the laying-out stops.

None of the four works alone. The steps are in the full chapter, and in the work’s formal papers.

Now the book’s second picture. A ship moves on an ocean.

The ship is the now: the Actualization State, the edge where the next distinction is being made. There is one ship, everywhere coupling is happening. It moves forward. That is all it does.

Behind it, a wake. The wake is the record history. Read it and you recover where the ship has been, how fast, which way it turned. The wake is not the ship. Measurement receives the wake: what has already been written. The wake is yesterday. Now is not in the wake.

Beneath both, the ocean. It receives the wake as the wake fades. Fading is not unwriting: the fact that the ship passed stays in the total record. The ocean is Ø: the pre-state, perfect symmetry before the break, which every ship moves through and every wake returns to.

“Mathematics is the language of the wake.” The wake is the record history, and mathematics reads the relations in it.

Platonism adds a fourth thing: above the ocean, an ideal ship the real ship is trying to copy. There is no ideal ship. The relations records have are real, universal, and independent of any one instance. And they are in the records, read where relations show. Three. Not four.

Records are arrangements of Ø. A photon. A planet. A sentence. A moment of attention. “Mathematics is the language to describe the life of Ø in its many configurations.” That closes Wigner’s question. The effectiveness looked unreasonable only if mathematics was a human invention that happened to fit a world that was not mathematical. Mathematics is not an invention. It is a reading. There is nothing to line up. It is one structure, read at two levels.

The child who counts three apples is a record too: a nervous system, an eye scanning the table. Records, reading records, in the language records produce. “We did not invent mathematics. We read it off the structure we are made of.”

What do three apples share? Relations, not places

Look at what you did at the top of this page. You read “three apples, three stars, three beats”, and the threeness was there across all three without effort. The naming made it readable. It did not create it. Three apples nobody sees still share threeness.

What is threeness? A relation. It is the invariant any group of distinguishable records carries under counting: the feature that holds across them when the operation is applied. Count the apples: three. The stars: three. The beats: three. The invariant is what the operation produces. It is real because the operation is real. It is not in any one apple, because relations are not in things. They are between things.

So a universal is an invariant that any group of distinguishable records carries under a given operation. Threeness under counting. The shape of a sphere under rotation: the form kept through every turn about its centre. Primeness under division. Redness under a particular coupling of light, pigment and eye.

Physics has a proven case of the same form. In 1915 Emmy Noether proved that every continuous symmetry of a physical system goes with a quantity that is conserved. The laws are the same now as they were yesterday. That symmetry gives a quantity that is conserved: energy. The symmetry is the operation. The conserved quantity is the invariant. It is real, and used in every prediction about a closed system. And it is not somewhere. Energy is not at a place.

Not every word names one clean universal. “Game” covers chess, football and solitaire. Wittgenstein pointed out that they share no single feature, only overlapping likenesses. The network of overlaps is itself real. Invariants, networks of them: none has a place.

Ask where threeness lives and you have asked where “between” lives. Between is not anywhere. It is the relation between two things: everywhere they are, and nowhere else. It is not floating free of them. It is not inside either one. Located things are records. Universals are not. “They are relations between records, and relations do not sit at sites.” Not unreal. Just not at a place. Two and a half thousand years of debate turned on a question with no well-formed answer. The right question is not where, but what. Answer the what, and the where dissolves.

Properties work the same way. Redness is not something the apple has alone. In the dark it is not seen. But the surface is still ready to reflect some colours of light, whether anyone looks or not. But redness, the property, is the stable coupling between that surface, the light and an eye. Not dependent on minds. Not just the surface. The coupling pattern. Even an electron’s mass is not hiding inside the electron. It travels with it. Intrinsic means structure that travels, not structure at a place.

And propositions. A proposition is what a sentence says. “The apple is on the table.” Say it in English, German or Italian: three sentences, one proposition. The tradition put propositions in a realm of their own. The same answer applies. A proposition is a recordable constraint. Of all the ways the apple could be at that time, it records that only those with the apple on the table are open. It is true if the world matches. False if it does not. Many carriers. One proposition. No realm.

Every debate about abstract objects fused two questions. Is there something real beyond the single instance? Yes, as relation. Is it somewhere else? No. There was never a somewhere else.

One answer

Now the four answers stand together. What exists is records: distinctions made and held, coupling in the now. Information is the history of those records. Mathematics is the language of the relations between them. Universals, properties and propositions are stable relational structures: real, and not at any one place. The chapter on universals ends on one line: “The structure is what is real, and the structure is what is read.”

What it costs you

You came for the bottom: the stuff the world is finally made of. There is no stuff at the bottom. There are records, coupling in the now, under the four conditions.

You give up information as a thing carried. The word carry is retired. You give up mathematics as a human invention, and you give up the heaven of numbers. You give up the somewhere else. There never was one.

Sit here

Still growing

The chapter on what exists does not derive protons, fields or spacetime from the axiom. That is the work of the formal papers, and it goes as far as they take it. In Landauer’s cost, the kT part is not derived from the four conditions. It is open work. The full derivations of logic and counting are in the formal papers. Infinity, and the extra rules set theory adds for it, such as the axiom of choice and large cardinals, are treated elsewhere. Whether sentences about what ought to be are constraints of the same kind is the most open case, and the chapter does not commit either way.

Where it would die

Side paths

• This question in the canon — who asked it before, and what the 420 Code does with each answer.
• What Exists? — Ø Dissolutions, Chapter 2. Watch. The full book, pages 56 to 74.
• The Nature of Information — Ø Resolutions, Chapter 1. Watch. The full book, pages 36 to 64.
• The Source of Mathematics — Ø Resolutions, Chapter 2. Watch. The full book, pages 66 to 104.
• Abstract Objects and Universals — Ø Resolutions, Chapter 3. Watch. The full book, pages 106 to 139.