Professor Quillibrace was standing at the blackboard.
This was not unusual.
What was unusual was that the blackboard contained only one word.
INFORMATION
Mr Blottisham entered, glanced at it, and stopped.
“I see.”
Quillibrace turned.
“What do you see?”
“The subject.”
“Do you?”
“Yes.”
“What is it?”
“Information.”
Quillibrace waited.
Blottisham looked at the board.
“Information.”
“Yes.”
“So…”
“Yes?”
“That is information.”
Quillibrace looked at the word.
“No.”
Blottisham stared at him.
“You wrote it.”
“I did.”
“It's a word.”
“Yes.”
“And the word refers to information.”
“Perhaps.”
“Then what exactly is the problem?”
Quillibrace put down the chalk.
“The problem is that we have been using this word for years without ever deciding what sort of thing it is.”
Miss Elowen Stray looked up from her tea.
“That may be rather more important than it sounds.”
Blottisham sat down.
“I have a feeling we're going to spend the afternoon discovering that nouns aren't nouns.”
“An excellent preliminary hypothesis,” said Quillibrace.
I. Information everywhere
Elowen looked at the blackboard.
“We use the word constantly.”
“We store information,” said Quillibrace.
“Transmit it.”
“Process it.”
“Encode it.”
“Retrieve it.”
“Lose it.”
Blottisham nodded.
“Yes.”
“And now,” said Elowen, “people increasingly speak as though information belongs on the same list as matter and energy.”
Quillibrace wrote:
MATTER
ENERGY
SPACE
TIME
INFORMATION
Blottisham nodded approvingly.
“Looks perfectly respectable.”
“Does it?”
“Yes.”
“Why?”
“Because they're all basic features of reality.”
Quillibrace looked at him.
“Are they?”
Blottisham paused.
“Well…”
Elowen smiled.
“The list feels natural.”
“Exactly,” said Quillibrace. “Which is why we should be cautious.”
Blottisham sighed.
“You really don't like natural-looking lists.”
“Not when they contain concepts from different categories.”
II. The message
“Let's start with the ordinary meaning,” said Elowen.
“Information is something communicated.”
Blottisham nodded.
“I tell you it is raining.”
“You receive the information.”
“A newspaper contains information.”
“A book contains information.”
“A photograph contains information.”
“Exactly.”
“So information is content.”
Quillibrace nodded.
“Useful.”
“Good.”
“Incomplete.”
“Of course.”
He turned to Elowen.
“Take a photograph.”
She held up an imaginary camera.
“A photograph of a tree.”
“Yes.”
“What is the information?”
Blottisham answered immediately.
“The picture of the tree.”
“Which part?”
“The pixels.”
“Only the pixels?”
“The colours.”
“The shapes?”
“Yes.”
“The arrangement?”
“Yes.”
“The fact that I can infer something about the tree?”
Blottisham paused.
“Yes.”
“The meaning I give it?”
“Perhaps.”
“The physical correlations between the photograph and the tree?”
Blottisham frowned.
“Those too.”
Quillibrace nodded.
“And where exactly is the information?”
Blottisham pointed at the photograph.
“In the photograph.”
“Which part?”
“The whole thing.”
“Then is the information the photograph?”
“No.”
“Is it the ink?”
“No.”
“The pixels?”
“No.”
“The meaning?”
“No.”
“The correlations?”
“Yes.”
Blottisham stopped.
“So…”
“Yes?”
“It isn't any one of those things.”
“Not straightforwardly.”
Elowen leaned forward.
“The physical things are physical.”
“Yes.”
“But the information about the tree arises from the relationships among them.”
Blottisham nodded slowly.
“So information is not another substance.”
“Now we're making progress.”
III. The invisible fourth substance
Blottisham looked again at the list.
“Suppose I have a book.”
“Yes.”
“The book is physical.”
“Yes.”
“The information in the book is…”
He hesitated.
“Also physical?”
“Not in the sense of being a second material substance.”
“So if I weigh the book—”
“You weigh the paper and ink.”
“Not the information.”
“Correct.”
“But if I destroy the book—”
“You may destroy the physical pattern that encoded the information.”
“So information depends upon physical things.”
“Yes.”
“But isn't itself another physical thing.”
“Not in the ordinary substance sense.”
Blottisham looked irritated.
“That's terribly inconvenient.”
Quillibrace smiled.
“Many useful concepts are.”
Elowen added:
“The distinction matters because otherwise we start imagining information as though it were a fluid.”
“A fluid?”
“Something that can be poured from one container into another.”
Blottisham brightened.
“Like wine.”
Quillibrace looked at him.
“An analogy I fear you have selected with ulterior motives.”
“Not at all.”
Elowen laughed.
“But the analogy is revealing.”
“Because information isn't wine.”
“Correct.”
“Though it can be transmitted.”
“Yes.”
“Stored.”
“Yes.”
“Processed.”
“Yes.”
“And still not be a substance.”
“Precisely.”
Blottisham frowned.
“That is deeply unsatisfactory.”
IV. Shannon enters the Common Room
Quillibrace wrote another name on the board.
SHANNON
“Claude Shannon.”
“Information theory,” said Blottisham.
“Yes.”
“What did he actually do?”
“One of the most important things he did was separate information from meaning.”
Blottisham looked surprised.
“Separate them?”
“Yes.”
“Surely information means something.”
“Not in information theory.”
Quillibrace wrote:
THE MEETING IS TOMORROW
Then:
XQJ7KPL9
“Which contains more information?”
“The first.”
“Why?”
“Because it means something.”
“Ah.”
Elowen smiled.
“You have just supplied the intuition Shannon's framework asks us to resist.”
Blottisham looked at the second string.
“It doesn't mean anything.”
“Perhaps not to you.”
“So it has information?”
“In the information-theoretic sense, certainly.”
“How?”
“Because it can distinguish among possibilities.”
Blottisham looked at Quillibrace.
“Even if nobody understands it?”
“Yes.”
“Even if it is nonsense?”
“Yes.”
“Even if it means absolutely nothing?”
“Yes.”
“That seems wrong.”
“It seems wrong because you are using information in the semantic sense.”
“And Shannon wasn't.”
“Correct.”
Quillibrace wrote:
MEANING ≠ INFORMATION
“Or, more carefully, semantic information and information-theoretic information are not identical.”
Elowen nodded.
“This is one of the crucial distinctions for the black-hole problem.”
V. Two kinds of information
Blottisham considered the two messages.
“So in ordinary life, information means meaningful content.”
“Usually.”
“And in information theory?”
“Something more austere.”
“What?”
“Uncertainty, probability, distinguishability, encoding.”
“That sounds terribly dry.”
“It is mathematically productive.”
“I knew there had to be a catch.”
Elowen smiled.
“Imagine a system that can be in one of two states.”
She wrote:
A / B
“If A and B are physically distinguishable, then the distinction between them matters.”
“Yes.”
“If the system is in A rather than B, something is physically different.”
“Yes.”
“That difference can carry information.”
Blottisham nodded.
“Because I can tell them apart.”
“Exactly.”
“So information is the distinction.”
“Or associated with the distinction.”
“Between possible states.”
“Yes.”
Blottisham looked at the board.
“That is very different from a message.”
“Exactly.”
“No sentence.”
“No.”
“No meaning.”
“Not necessarily.”
“No one has to understand anything.”
“Correct.”
“Then the universe can contain information without anyone reading it.”
“Yes.”
Blottisham paused.
“That sounds rather important.”
“It is.”
VI. Information without an observer
Quillibrace took over.
“Suppose there are four possible states.”
He wrote:
A B C D
“Before we know which state the system occupies, there is uncertainty.”
“Yes.”
“Once we determine the state, the uncertainty is reduced.”
“Yes.”
“We can quantify that.”
“Information theory.”
“Correct.”
“And does someone have to experience the uncertainty?”
“No.”
Blottisham frowned.
“But uncertainty belongs to someone.”
“Psychological uncertainty does.”
“But this isn't psychological.”
“Not necessarily.”
“Then whose uncertainty is it?”
Quillibrace looked at him.
“The probability distribution describes the possibilities available in the physical model.”
“So information isn't simply what someone knows.”
“Correct.”
“Then it isn't subjective.”
“Not so quickly.”
Elowen intervened.
“The distinction still depends on a space of possible states and on what counts as physically distinguishable.”
“So…”
“Information is neither simply a private mental state nor a mysterious substance floating independently of physical description.”
“What is it, then?”
She paused.
“Something like a relation among state, possibility and distinction.”
Blottisham looked at Quillibrace.
“She is going to make you work for the noun.”
“Quite rightly.”
VII. The two coins
Elowen picked up two coins from the table.
“Suppose these are correlated.”
“How?”
“If the first is heads, the second is heads.”
She turned them over.
“If the first is tails, the second is tails.”
Blottisham nodded.
“So if I know the first, I know something about the second.”
“Exactly.”
“Information.”
“Yes.”
“Where is it?”
Blottisham looked at the first coin.
“In the first.”
“No.”
“The second?”
“No.”
“Both?”
“Closer.”
“In the relationship?”
“Yes.”
Quillibrace nodded.
“The information lies in the correlation.”
Blottisham looked uncomfortable.
“But a correlation isn't a thing.”
“Precisely.”
“Where is a correlation?”
“That's the point.”
“It doesn't have a location.”
“Not in the same sense as a coin.”
Elowen smiled.
“So we have moved from information as a thing to information as a relation.”
Blottisham stared at the coins.
“This is becoming increasingly inconvenient.”
VIII. Quantum mechanics makes it worse
Quillibrace wrote:
ENTANGLEMENT
“Quantum mechanics takes this relational character further.”
Blottisham looked at the word.
“Entanglement.”
“Yes.”
“Two systems can have correlations such that the state of the whole cannot always be reduced to independently specified states of the parts.”
“So the whole contains something the parts don't.”
“Careful.”
“Sorry.”
“The point is that the information associated with the joint state need not be assignable to either subsystem independently.”
“So again…”
“The relation.”
“Yes.”
Elowen nodded.
“Information may be distributed across correlations.”
Blottisham looked alarmed.
“Distributed?”
“Yes.”
“Where?”
“Across the relationship.”
“That isn't an answer.”
“It is the answer.”
“It's not a location.”
“Exactly.”
Blottisham leaned back.
“I begin to see the attraction of saying information is a substance.”
Quillibrace smiled.
“Because substances are easier to locate.”
IX. Scrambling
Elowen took a sheet of paper.
“Suppose this is a book.”
Blottisham nodded.
“We shred it.”
She tore the imaginary sheet.
“The information is gone.”
“Not necessarily,” said Quillibrace.
“If every fragment survives, and we know where every fragment is…”
“We can reconstruct it.”
“So the information is scrambled.”
“Exactly.”
“Not destroyed.”
“Correct.”
“Now mix the fragments with millions of other fragments.”
“Reconstruction becomes practically impossible.”
“But the physical distinctions may remain.”
“Yes.”
“And only if those distinctions genuinely disappear do we have something stronger than scrambling.”
“Precisely.”
Quillibrace wrote:
ACCESSIBLE
INACCESSIBLE
SCRAMBLED
ENCODED
DESTROYED
“Not the same.”
Blottisham nodded.
“Important distinction.”
“Very.”
“Especially for black holes.”
“Especially.”
X. The quantum state
Quillibrace sat down.
“Now we can return to the real problem.”
“The quantum state.”
“Yes.”
“A quantum state isn't simply a list of classical properties.”
“No.”
“It encodes possible measurement outcomes and the relations among them.”
“Yes.”
“And for a closed system, unitary evolution preserves the structure of the quantum state.”
“Yes.”
“So if a pure state evolves unitarily…”
“It remains pure.”
“But Hawking's semiclassical argument seems to produce…”
“A thermal mixed state.”
Blottisham looked at the board.
“So…”
Quillibrace wrote:
PURE → MIXED
“That is the problem.”
“Not merely that the radiation looks messy.”
“Correct.”
“A scrambled pure state can look thermal if we ignore some of its correlations.”
“Exactly.”
“So the real question is whether the complete final state contains the distinctions necessary to distinguish the possible initial states.”
“Yes.”
Blottisham nodded.
“That is much more precise than saying the message disappeared.”
“And much less likely to generate a cartoon of a little letter being swallowed by a black hole.”
XI. The black hole as hard drive
Blottisham suddenly brightened.
“I have it.”
Quillibrace looked worried.
“The black hole is a hard drive.”
“No.”
“Information goes in.”
“No.”
“It gets stored.”
“No.”
“It gets encrypted.”
“No.”
“Then the radiation retrieves it.”
“No.”
Blottisham looked disappointed.
“That was quite a good model.”
“It was an excellent collection of metaphors.”
“Thank you.”
“And an inadequate account of the physics.”
“Why?”
“Because storage suggests a container.”
“The black hole isn't one.”
“Correct.”
“And information becomes a thing inside it.”
“It need not be.”
“And retrieval makes it sound like a parcel coming back out.”
“Again.”
Elowen added:
“The deeper physical issue is whether the correlations and distinctions encoded in the initial state remain present in the later state.”
“So the radiation doesn't need to contain little files.”
“No.”
“It needs to contain the relevant correlations.”
“Precisely.”
Blottisham nodded.
“That is annoyingly less visual.”
“Fundamental physics is frequently disappointing in this respect.”
XII. Information as something carried
“But we say information is transmitted,” Blottisham objected.
“Yes.”
“And that's useful.”
“Very.”
“Then information can travel.”
Quillibrace considered this.
“Something can travel that carries information.”
“Isn't that the same thing?”
“No.”
“Explain.”
“The physical carrier travels. The information concerns the distinctions encoded in its state.”
“So a radio wave travels.”
“Yes.”
“And it carries information.”
“Yes.”
“But the information isn't a little object sitting inside the wave.”
“Correct.”
“It is a pattern in the physical state.”
“Better.”
“And the pattern is defined through possible alternatives.”
“Yes.”
Blottisham looked pleased.
“So information travels by being instantiated in changing physical relationships.”
Quillibrace paused.
“That will do.”
Elowen smiled.
“You see how the verb travel has changed?”
Blottisham nodded.
“It no longer requires information itself to be a traveller.”
“Exactly.”
XIII. Information about what?
Elowen returned to the photograph.
“We have another problem.”
“What now?” asked Blottisham.
“We often say that information is information about something.”
“The photograph is information about the tree.”
“Yes.”
“The thermometer gives information about temperature.”
“Yes.”
“DNA contains information about an organism.”
“Yes.”
“But does information in the black-hole problem have to be about something?”
Blottisham frowned.
“The initial quantum state.”
“About what?”
“The thing that formed the black hole.”
“Not necessarily.”
Quillibrace nodded.
“The quantum state is not a little description of some other physical object. It is the physical state itself.”
“So information doesn't always mean representation.”
“Correct.”
“That is another ordinary-language assumption.”
“Yes.”
Elowen smiled.
“We keep finding the same pattern.”
“What pattern?”
“A word that works perfectly well in ordinary contexts carries several relationships with it. Then we move it into fundamental physics, and the relationships begin to separate.”
Quillibrace nodded.
“Information is content.”
“Sometimes.”
“A message.”
“Sometimes.”
“Knowledge.”
“Sometimes.”
“A pattern.”
“Sometimes.”
“A correlation.”
“Sometimes.”
“A distinction among possible states.”
“Yes.”
“And those are related but not interchangeable.”
“Precisely.”
XIV. The ontology of information
Blottisham looked again at the original list.
MATTER
ENERGY
SPACE
TIME
INFORMATION
“I have a question.”
Quillibrace looked wary.
“Go on.”
“Is information real?”
“Yes.”
Blottisham looked surprised.
“That was quick.”
“Relations can be real.”
“Such as?”
“Gravitational relations.”
“Yes.”
“Causal relations.”
“Yes.”
“Entanglement correlations.”
“Yes.”
“So the fact that information is relational doesn't make it imaginary.”
“Correct.”
“But is it fundamental?”
Quillibrace paused.
“That is a more difficult question.”
Elowen nodded.
“Perhaps we should resist turning information into a substance simply because it is physically significant.”
“So it might be fundamental without being stuff.”
“Possibly.”
“Like a relation.”
“Perhaps.”
“Or a constraint.”
“Yes.”
“A structure.”
“Yes.”
“An organisation of possibilities.”
“Yes.”
Blottisham looked at the board.
“That sounds more plausible than another cosmic fluid.”
Quillibrace nodded.
“Marginally.”
XV. “It from bit”
Blottisham pointed at Quillibrace.
“You mentioned Wheeler.”
“Not yet.”
“You were going to.”
“I was.”
“Then mention him.”
Quillibrace wrote:
IT FROM BIT
“The slogan associated with John Wheeler.”
Blottisham nodded.
“Meaning?”
“Roughly, that physical reality might ultimately be understood in informational terms.”
“Excellent.”
“Yes.”
“Then information is fundamental.”
“Not so fast.”
“Why not?”
“Because a slogan isn't a theory.”
“What is a bit, then?”
Blottisham paused.
“Information.”
“No.”
“A piece of information.”
“No.”
“Zero or one.”
“Better.”
“What is the physical significance?”
“The distinction between two alternatives.”
Blottisham looked at the board.
“So even the bit isn't a little piece of information-stuff.”
“Correct.”
“It is a distinction.”
“Yes.”
Elowen smiled.
“Once again, relation appears before substance.”
Blottisham looked slightly defeated.
“I feel as though I am being systematically deprived of things.”
Quillibrace nodded.
“That is one of the educational benefits of philosophy.”
XVI. The possibility of difference
Elowen stood.
“Perhaps we can put the matter another way.”
She wrote:
COULD HAVE BEEN OTHERWISE
“This may be the hidden structure.”
Blottisham looked at it.
“What does?”
“Information.”
“How?”
“If there is only one possible state, there is nothing to distinguish.”
“Yes.”
“If there are alternatives, then there are distinctions.”
“Yes.”
“If a physical system occupies one alternative rather than another, that difference can carry information.”
“Yes.”
“So information requires possibility.”
Quillibrace nodded.
“Or, at least, a structured space of alternatives.”
Elowen continued.
“To preserve information is therefore to preserve distinctions among possibilities.”
“And to destroy information?”
“To erase distinctions that could otherwise have remained distinct.”
Blottisham looked at the phrase.
“So the black-hole paradox can be rewritten.”
“How?”
He thought.
“Not ‘Where did the information go?’”
Quillibrace nodded.
“Good.”
“But…”
He paused.
“‘What happened to the differences between the possible initial states?’”
Elowen smiled.
“Yes.”
Blottisham sat down.
“That is much nastier.”
“Indeed.”
XVII. The observer disappears
Blottisham looked thoughtful.
“There is something else.”
“Yes?”
“If information isn't about what someone knows…”
“Yes.”
“And doesn't require meaning…”
“Yes.”
“And can exist in correlations…”
“Yes.”
“Then the observer can disappear.”
“From the fundamental description, yes.”
“So the universe doesn't need somebody to read the information.”
“Correct.”
“Then what does it mean for information to be available?”
“It means, roughly, that the relevant physical distinctions are accessible through some physical relation.”
“Accessible to whom?”
“An observer, perhaps.”
“Or an apparatus.”
“Or another physical subsystem.”
“Or…”
Elowen smiled.
“Or simply preserved in the structure of the state, whether or not anyone ever reconstructs it.”
Blottisham nodded.
“So there is a distinction between information existing in the physical state and information being available to an observer.”
“Precisely.”
“And that matters for black holes.”
“Enormously.”
XVIII. The final return to the black hole
Quillibrace stood and returned to the board.
He drew the outline of a black hole.
Then radiation emerging from it.
“Suppose the radiation looks thermal.”
“Yes.”
“Does that automatically mean it contains no information?”
“No.”
“Why?”
“Because the information might be encoded in correlations among the radiation quanta.”
“So particle by particle…”
“It may look thermal.”
“But collectively…”
“The full state may contain the distinctions.”
Blottisham nodded.
“Like a scrambled book.”
“Precisely.”
“Except vastly more complicated.”
“Vastly.”
“So the appearance of randomness doesn't prove information has disappeared.”
“No.”
“Because randomness at one level can coexist with structure at another.”
“Exactly.”
Elowen looked at the diagram.
“That is one of the most important conceptual distinctions in the whole problem.”
“Thermal appearance versus complete quantum state.”
“Yes.”
“Local appearance versus global structure.”
“Yes.”
“Accessible information versus information encoded in correlations.”
“Yes.”
Blottisham looked at the black hole.
“And now the question becomes…”
He paused.
Quillibrace waited.
“Whether the correlations really survive.”
“Precisely.”
XIX. The thing that wasn't a thing
The room had grown darker.
Elowen returned to her chair.
“I think we can now see why the word information is so troublesome.”
Blottisham nodded.
“It sounded like a thing.”
“Yes.”
“Then it became a message.”
“Yes.”
“Then a quantity.”
“Yes.”
“Then a distinction.”
“Yes.”
“Then a correlation.”
“Yes.”
“And now…”
He looked at the board.
“A relation among possibilities.”
Quillibrace nodded.
“Not bad.”
“I'm getting better.”
“Don't ruin the moment.”
Elowen smiled.
“And notice what has happened to the black hole.”
Blottisham looked at the earlier diagram.
“In the previous discussion, it stopped being a container.”
“Yes.”
“And now information has stopped being a substance.”
“Yes.”
“So the two metaphors are beginning to come apart at the same time.”
“Exactly.”
“And perhaps that is why they fit together so badly.”
Quillibrace nodded.
“Now you are saying something interesting.”
XX. A better question
Blottisham stood.
“So let's ask the better question.”
Quillibrace looked at him.
“What happens to the distinctions and correlations encoded in the initial quantum state?”
“Yes.”
“If they survive…”
“The information has not been fundamentally destroyed.”
“If they become extraordinarily scrambled…”
“Then accessibility may be the problem.”
“If they are encoded in correlations among the radiation…”
“The apparent thermality need not imply information loss.”
“And if the distinctions disappear altogether…”
“Then we have a genuine challenge to unitary quantum evolution.”
Blottisham nodded.
“So the paradox is about what physical evolution can do to difference.”
Quillibrace looked at Elowen.
She nodded.
“Yes.”
“Can physical evolution erase a distinction between two genuinely different initial states?”
“Yes.”
“Can information survive without being locally accessible?”
“Yes.”
“Can it exist in correlations rather than objects?”
“Yes.”
“Can a black hole destroy it?”
“That,” said Quillibrace, “is precisely what we do not yet know how to reconcile with our best theories.”
Blottisham looked at the board.
“Then perhaps information isn't what disappears.”
“What?”
“Perhaps our picture of where information is supposed to be is what disappears.”
There was a silence.
Quillibrace looked at him.
Miss Stray smiled.
“That,” she said, “is worth keeping.”
XXI. The Common Room conclusion
Quillibrace erased the word INFORMATION.
Then he wrote:
DISTINCTION
Underneath it:
CORRELATION
Then:
POSSIBILITY
Then:
TRANSFORMATION
Blottisham read them.
“Is that information?”
“No.”
“Then what is it?”
“The structure in which information becomes meaningful as a physical concept.”
Elowen nodded.
“Perhaps information is the name we give to what becomes visible when we attend to differences among possibilities and to the relations that preserve those differences.”
Blottisham looked at the four words.
“So not another ingredient of reality.”
“Not necessarily.”
“Not a substance.”
“No.”
“Not a message.”
“Not necessarily.”
“Not meaning.”
“Not necessarily.”
“Not knowledge.”
“Not necessarily.”
“Not something sitting inside a black hole.”
Quillibrace smiled.
“Now you are learning.”
Blottisham looked satisfied.
“But if information is really a relation…”
“Yes?”
“…then asking where it is might be the wrong question.”
Quillibrace nodded.
“And what would be the right one?”
Blottisham thought.
“How is the relation realised?”
Elowen looked at him.
“Or perhaps…”
She glanced at the blackboard.
“…how is the distinction preserved?”
Quillibrace picked up his coat.
“Both will do.”
They walked toward the door.
Blottisham stopped.
“One final thing.”
Quillibrace sighed.
“Yes?”
“If information isn't a thing…”
“Yes?”
“…why does everyone keep talking about it as though it were?”
Quillibrace opened the door.
“Because,” he said, “language prefers nouns.”
Elowen smiled.
“And reality is under no obligation to provide them.”
Blottisham nodded thoughtfully.
“That's rather inconvenient.”
Quillibrace stepped into the corridor.
“Almost invariably.”
The door closed.
On the blackboard remained four words:
DISTINCTION
CORRELATION
POSSIBILITY
TRANSFORMATION
There was no word for information.
And somehow, for the moment, that seemed rather informative.