7. On the Curious Difficulty of Being Definite

The Senior Common Room at St Anselm's

Evening. Rain presses softly against the windows. Professor Quillibrace sits reading. Miss Elowen Stray writes notes beside the fire. Mr Blottisham enters carrying an enormous rolled sheet of paper.

Quillibrace: Good Lord.

Blottisham: Ah! Excellent.

Quillibrace: I distrust that tone immediately.

Blottisham: I have solved everything.

Quillibrace: Of course you have.

Blottisham: I have drawn reality.

He triumphantly unrolls the paper across the table.

It is covered in boxes connected by arrows.

Quillibrace: Ah.

Blottisham: There.

Everything accounted for.

Objects.

Properties.

Causes.

Outcomes.

Everything leading neatly to everything else.

Quillibrace: Mm.

Blottisham: What?

Quillibrace: You've built a flow chart.

Blottisham: Exactly.

Reality must ultimately reduce to a complete description.

There must be a final account of what everything is.

Quillibrace: Ah.

He removes his spectacles slowly.

Quillibrace: Mr Blottisham—

over these past weeks reality has taken away:

intrinsic properties,

separable systems,

passive measurement,

probability as ignorance,

and independent parts.

And after all this—

you have attempted to save matters with stationery.

Blottisham: You make that sound unreasonable.

Quillibrace: I make it sound administrative.

Blottisham: But surely some final determinacy remains.

Things must ultimately possess definite states.

Otherwise reality dissolves into fog.

Quillibrace: Why?

Blottisham: Because—

because things must be something.

Silence.

Quillibrace: Ah.

There it is.

Blottisham: There what is?

Quillibrace: The final classical assumption.

That determinacy is a possession.

That a thing possesses a state in the same way one possesses an umbrella.

Blottisham: Things have properties.

Quillibrace: Once we thought so.

But where precisely have our discussions led?

Superposition became non-closure.

Measurement became construal.

Probability became constraint.

Entanglement became non-separable structure.

Parts became derived projections.

The pattern is rather difficult to miss.

Blottisham: I have been missing it heroically.

Quillibrace: Yes.

With uncommon determination.

Quillibrace folds his hands.

Quillibrace: Determinacy has not disappeared.

It has merely moved.

Blottisham: Moved where?

Quillibrace: Into relational closure.

Blottisham: That sounds suspiciously abstract.

Quillibrace: Reality has become increasingly suspicious of your preference for furniture.

Blottisham: I dislike that reality and I are drifting apart.

Quillibrace: A determinate outcome is no longer something a system simply has.

It is something that emerges when relational potential stabilises under constraint.

Blottisham: So determinacy happens?

Quillibrace: Precisely.

It occurs.

It is not an attribute sitting permanently inside things.

It is an event of closure.

Blottisham: Good heavens.

He stares uneasily at his chart.

Blottisham: Then different contexts may generate different determinate outcomes.

Quillibrace: Continue.

Blottisham: And those outcomes may not combine into one globally complete description.

Quillibrace: Continue.

Blottisham: Which means—

His face slowly changes.

Blottisham: There may be no final list of what reality is.

A silence falls.

Quillibrace studies him carefully.

Quillibrace: Mr Blottisham—

have you been reading ahead?

Blottisham: No.

I assure you this is entirely accidental.

Elowen: Then facts themselves become local stabilisations.

Blottisham: Local?

Elowen: Not unreal.

Not arbitrary.

Simply contextually closed.

They remain perfectly real, but they do not assemble into a single universal catalogue.

Quillibrace: Exactly.

Blottisham: So reality does not possess a finished description.

Quillibrace: Mm.

Blottisham: Then what is real?

Quillibrace: Ah.

The final question.

He gestures toward the papers scattered across the room.

Quillibrace: Not objects carrying intrinsic properties.

Not hidden states beneath appearances.

Not some completed inventory of the universe.

What persists are relational constraints:

stable transformations,

coherent actualisations,

reproducible closure structures.

Reality is not a finished collection of facts.

It is what consistently constrains the production of facts.

Blottisham sits silently.

After some time he looks down at his enormous diagram.

Then very slowly he begins rolling it back up.

Quillibrace: Not keeping it?

Blottisham: Oh, I shall keep it.

Quillibrace: Really?

Blottisham: Certainly.

He tucks it under his arm.

Blottisham: It may not describe reality—

but it appears to provide a very satisfactory description of my previous mistakes.

Silence.

Miss Stray smiles into her teacup.

Quillibrace puts his spectacles back on.

Quillibrace: Well.

That is at least a determinate outcome.

6. On the Curious Difficulty of Taking Things Apart

The Senior Common Room at St Anselm's

Late afternoon. Mr Blottisham sits triumphantly in the middle of the room surrounded by springs, screws, gears, and several pieces whose original purpose has become doubtful. Professor Quillibrace enters and stops abruptly. Miss Elowen Stray lowers her book slowly.

Quillibrace: Good heavens.

Blottisham: Ah! Excellent timing.

Quillibrace: Why is there a clock in fragments on my table?

Blottisham: Science.

Quillibrace: I feared as much.

Blottisham: I am demonstrating a profound metaphysical truth.

Quillibrace: One approaches this statement with understandable caution.

Blottisham: The world is made of parts.

You understand a thing by taking it apart.

Observe.

He holds up a gear triumphantly.

This does gear-like things.

Quillibrace: A devastating argument.

Blottisham: Larger systems are simply collections of smaller systems.

Parts possess properties.

Interactions produce wholes.

Simple.

Quillibrace: Ah.

Blottisham: What?

Quillibrace: We have located today's classical assumption.

Blottisham: Surely not.

Quillibrace: Entirely.

You have smuggled decomposition in before the discussion began.

Blottisham: But decomposition is how understanding works.

We break things apart to explain them.

Quillibrace: Frequently yes.

Blottisham: There we are then.

Quillibrace: Mr Blottisham—

using a method successfully does not establish that reality itself is organised according to that method.

Blottisham: Doesn't it?

Quillibrace: No more than successfully using maps proves the Earth is constructed from paper.

Blottisham pauses.

Blottisham: Hm.

Quillibrace: Classical thinking assumes something rather strong.

That wholes are built from parts.

That parts possess independently specifiable properties.

That the whole may be reconstructed from those parts and their interactions.

Blottisham: Entirely sensible.

Quillibrace: Sensible perhaps.

Guaranteed no.

Blottisham: But surely entanglement merely complicates decomposition.

Quillibrace: Ah.

No.

It removes its foundation.

Blottisham: Removes—

He stares suspiciously.

Blottisham: You keep removing things.

Quillibrace: Reality began this unpleasant habit.

I merely report developments.

Blottisham: But entangled systems still possess parts.

Quillibrace: Do they?

Blottisham: Well—

they appear to.

Quillibrace: Better.

Because what fails is not merely separability.

It is independent state assignment itself.

If subsystems possess no independent actualisation, then what exactly are the parts?

Blottisham: Smaller things.

Quillibrace: Smaller versions of the original mistake.

Miss Stray smiles faintly.

Elowen: Then perhaps decomposition itself becomes secondary.

Blottisham: Secondary?

Elowen: We usually imagine:

parts → whole

But perhaps the relational structure comes first—

and what we call parts are stabilised extractions from it.

Quillibrace: Exactly.

Blottisham: No no no.

That seems entirely backwards.

Wholes come from parts.

Quillibrace: Why?

Blottisham: Because—

because—

He gestures helplessly at the disassembled clock.

Quillibrace: Ah yes.

Mechanical theology.

Blottisham: Mechanical what?

Quillibrace: The belief that because clocks are assembled from gears, reality itself must be assembled from pieces.

Blottisham: You're making me sound unreasonable.

Quillibrace: I am making you sound mechanical.

Blottisham: Hmph.

But surely decomposition always exists in principle.

Even if we cannot perform it.

Quillibrace: Quantum mechanics becomes awkward here.

Because non-factorisability is not merely difficult decomposition.

It is decomposition becoming undefined.

Blottisham: Undefined.

Quillibrace: There exists no assignment of independently actualised local states preserving the coherence of the whole.

The issue is not that the parts are hidden.

The issue is that the system was not built from independently actualised parts to begin with.

Blottisham: Good Lord.

He looks uneasily at the clock fragments.

Blottisham: Then reductionism fails.

Quillibrace: Quietly.

Not dramatically.

Nothing explodes.

No contradiction appears.

One simply discovers that the conditions reductionism assumes are not universally available.

Blottisham: That's rather sneaky.

Quillibrace: Reality occasionally is.

Elowen: Then even causation changes.

Quillibrace: Mm?

Elowen: If parts are not fundamental, then causal chains between parts cannot be fundamental either.

What appears as local interaction becomes a projection of deeper relational organisation.

A pause.

Quillibrace lowers his teacup.

Quillibrace: Miss Stray—

you continue displaying a troubling tendency to arrive at the centre of discussions before everyone else notices there is a centre.

Blottisham: I dislike this immensely.

Quillibrace: Why?

Blottisham: Because I preferred reality assembled neatly from little pieces.

Quillibrace: Ah.

Quillibrace looks thoughtfully at the scattered gears.

Quillibrace: The difficulty, Mr Blottisham, is that you assumed reality resembled a clock.

Blottisham: Yes.

Quillibrace: Whereas it increasingly appears that clocks resemble reality only under rather special circumstances.

Silence.

Blottisham stares down at the dismantled mechanism.

Blottisham: I suddenly feel I owe the clock an apology.

5. On the Curious Difficulty of Choosing

The Senior Common Room at St Anselm's

Early evening. Rain has returned. The fire crackles quietly. Professor Quillibrace is arranging papers into unnervingly exact piles. Miss Elowen Stray is reading by the window. Mr Blottisham enters carrying a small leather bag emitting the atmosphere of dangerous enthusiasm.

Blottisham: Ha!

Quillibrace: Oh dear.

Blottisham: I have it at last.

Quillibrace: Have what?

Blottisham: Probability.

Quillibrace: Ah.

Blottisham: I've solved quantum mechanics.

Quillibrace: Naturally.

Blottisham: Ah—blast.

Quillibrace: You walked directly into that one.

Blottisham: Probability means uncertainty.

We lack information.

Reality itself remains perfectly determinate.

Quantum mechanics simply quantifies our ignorance.

Silence.

Quillibrace: Mr Blottisham—

there are moments when one admires persistence.

This is not one of them.

Blottisham: But surely probability has always meant uncertainty.

Quillibrace: Classical probability frequently does.

One tosses a coin.

One lacks information regarding exact forces, air resistance, and initial conditions.

The uncertainty belongs to us.

Reality itself remains complete beneath our ignorance.

Blottisham: Exactly.

Quillibrace: Quantum mechanics continues displaying its regrettable habit of refusing invitations to classical parties.

Blottisham: Then probability doesn't mean ignorance?

Quillibrace: Not in the ordinary sense.

Blottisham: Then what on earth does it mean?

Quillibrace: Ah.

An excellent question.

And therefore one I distrust immediately.

Quillibrace folds his hands.

Quillibrace: Recall where we have arrived thus far.

Properties no longer belong intrinsically to things.

Superposition is non-closure.

Measurement is construal.

Blottisham: Yes.

Quillibrace: Then the question becomes unavoidable.

What governs which actualisations stabilise?

Blottisham: Chance.

Quillibrace: No.

Blottisham: Randomness.

Quillibrace: No.

Blottisham: Statistical indecision.

Quillibrace: Also no.

Blottisham: You are becoming rather difficult.

Quillibrace: Constraint.

Blottisham: Constraint?

Quillibrace: The Born rule does not distribute ignorance.

It distributes admissibility.

Blottisham: Admissibility sounds alarmingly bureaucratic.

Quillibrace: Reality occasionally resembles a committee meeting.

Certain pathways are structurally permitted.

Others possess stronger support within the relational organisation itself.

Blottisham: So nature prefers some outcomes?

Quillibrace: "Prefers" is unfortunate.

Reality does not possess hobbies.

Blottisham: Then what does it possess?

Quillibrace: Constraint structures.

Some actualisation pathways possess greater coherence within the relational configuration.

Blottisham: Hm.

Quillibrace: Probability therefore ceases to be a statement about hidden facts.

It becomes a statement about the geometry of actualisation itself.

Blottisham: Geometry.

Quillibrace: Yes.

Blottisham: Reality has become very architectural recently.

Quillibrace: One notices these things.

Blottisham: But surely outcomes still exist in advance somewhere?

Like dishes on a menu waiting to be selected?

Quillibrace: Ah yes.

The restaurant interpretation of quantum mechanics.

Blottisham: Perfectly sensible.

Quillibrace: Entirely disastrous.

No menu exists.

No completed list waits in advance.

Measurement does not select an already existing item.

It stabilises an actualisation under constraint.

Blottisham: So nothing chooses?

Quillibrace: Correct.

Blottisham: Nothing selects?

Quillibrace: Correct.

Blottisham: Good heavens.

Blottisham sits heavily into an armchair.

Blottisham: Reality is becoming increasingly difficult to picture.

Quillibrace: That may be because you insist on turning it into furniture.

Blottisham: But randomness must remain.

Surely outcomes are still random.

Quillibrace: Ah.

Another dangerous word.

Randomness suggests absence of structure.

But nothing here lacks structure.

The outcomes are not predetermined—

yet nor are they arbitrary.

Blottisham: Then what are they?

Quillibrace: Constraint-governed non-determinacy.

Blottisham: That sounds suspiciously like randomness wearing academic robes.

Elowen: Perhaps the difference is that randomness usually suggests disorder.

But here the structure already exists.

Only the closure remains undetermined.

Quillibrace slowly turns.

Quillibrace: Yes.

Quite so.

Elowen: So probability is not ignorance over hidden actualities.

It is a visible trace of how relational constraints organise possible actualisations.

Quillibrace: Exactly.

Blottisham stares at the fire for some time.

Blottisham: Then frequencies themselves are secondary.

Quillibrace: Continue.

Blottisham: We do not observe repeated outcomes and invent probabilities.

The probabilities already belong to the relational structure that generates stable frequencies.

A long silence.

Quillibrace removes his spectacles.

Quillibrace: Mr Blottisham—

this is becoming genuinely unsettling.

Blottisham: Again?

Quillibrace: You continue wandering accidentally into understanding.

Blottisham: I assure you it was entirely unintentional.

Elowen: Then perhaps probability was never a confession of ignorance at all.

Perhaps it was always a description of structure.

Quillibrace: Miss Stray—

once again you have quietly arrived at the centre of the matter.

Blottisham: I still preferred coins.

Quillibrace: Why?

Blottisham: One always felt the answer was already there.

Quillibrace: Ah.

And reality, Mr Blottisham, continues displaying a rather unfortunate reluctance to arrange itself for your convenience.

4. On the Curious Difficulty of Merely Looking

The Senior Common Room at St Anselm's

Late afternoon. The fire burns low. Professor Quillibrace is making notes with the air of a man attempting to prevent reality from becoming untidy. Mr Blottisham is standing beside a cabinet holding scientific instruments of uncertain age and doubtful accuracy. Miss Elowen Stray is seated nearby with a cup of tea.

Blottisham: Ah! Here we are.

He lifts an antique thermometer triumphantly.

Quillibrace: Good heavens.

Blottisham: Measurement.

Quillibrace: Put it down.

Blottisham: I have finally located something sensible in physics.

Quillibrace: Then it is almost certainly not what you think it is.

Blottisham: Measurement is perfectly straightforward.

You observe reality and discover what was already there.

Temperature exists.

Length exists.

Position exists.

One simply reads them off.

Quillibrace: Ah.

Blottisham: What?

Quillibrace: You have once again arrived carrying classical metaphysics disguised as common sense.

Blottisham: I merely described measurement.

Quillibrace: No, you described an assumption about measurement.

Blottisham: Which assumption?

Quillibrace: Several, in fact.

That properties belong intrinsically to systems.

That observation is passive.

That the observer somehow remains outside what is observed.

Blottisham: Entirely reasonable assumptions.

Quillibrace: Yes. Which unfortunately does not make them true.

Blottisham: Then what exactly is wrong with reading reality?

Quillibrace: Reading suggests a pre-written text.

Blottisham: Doesn't reality possess one?

Quillibrace: That is precisely the issue.

Blottisham: Oh dear.

Quillibrace: Quite.

Blottisham returns the thermometer to the cabinet with reduced enthusiasm.

Quillibrace: Classical thinking imagines the world already completed.

Measurement merely lifts a curtain.

Reality sits politely behind it waiting to be observed.

Blottisham: Yes.

Quillibrace: Quantum mechanics grows increasingly reluctant to cooperate with this arrangement.

Blottisham: Because properties are not fully determinate beforehand.

Quillibrace: Good.

Blottisham: Ah! I understood something.

Quillibrace: Do not interrupt it.

Blottisham: Sorry.

Quillibrace: If properties are not determinate prior to measurement, then one must ask a rather uncomfortable question.

What exactly is measurement doing?

Blottisham: Revealing—

Quillibrace: No.

Blottisham: Discovering—

Quillibrace: No.

Blottisham: Extracting—

Quillibrace: You are merely rotating the same mistake through different verbs.

Blottisham: Then what remains?

A pause.

Quillibrace: Construal.

Silence.

Blottisham: I dislike that immediately.

Quillibrace: Naturally.

Blottisham: Ah—sorry.

Quillibrace: A construal is not an interpretation of a completed thing.

It is a structured organisation through which something becomes determinate in a particular way.

Blottisham: That sounds suspiciously active.

Quillibrace: Because it is.

Measurement does not reveal a finished reality.

It enacts a regime within which determinate outcomes become possible.

Blottisham: Good Lord.

Elowen: So measurement is not asking reality a question?

Quillibrace: Mm.

Elowen: It is establishing the conditions under which something can become answerable.

Quillibrace turns slowly.

Quillibrace: Yes.

Precisely.

Blottisham: This is becoming a disturbing trend.

Quillibrace: Miss Stray does insist on understanding things.

Blottisham: But surely observers remain external.

Someone must be doing the observing.

Quillibrace: Ah yes. The old observer standing outside the universe with a clipboard.

Blottisham: A perfectly respectable fellow.

Quillibrace: Entirely fictional, unfortunately.

Measurement does not require consciousness.

Nor does it require an ontologically privileged observer.

Blottisham: Then who measures?

Quillibrace: Wrong question.

Blottisham: What question should I ask?

Quillibrace: What relational structure has become established such that determinate actualisation occurs?

Blottisham: That's an awful question.

Quillibrace: Reality occasionally prefers difficult company.

Elowen: Then observer and observed cease being fundamentally different categories.

Quillibrace: Exactly.

Elowen: They become participants in a shared constraint structure.

Quillibrace: Quite so.

Blottisham: Shared structure.

He stares into the fire.

Blottisham: Then facts themselves become rather strange.

Quillibrace: Continue.

Blottisham: If outcomes emerge through construal rather than revelation...

then facts are not tiny objects waiting to be collected.

A pause.

Quillibrace: Continue.

Blottisham: They are... stabilised outcomes?

Long silence.

Quillibrace slowly lowers his spectacles.

Quillibrace: Mr Blottisham—

this is becoming genuinely alarming.

Blottisham: What have I done?

Quillibrace: You have wandered dangerously close to understanding.

Elowen: Then objectivity survives, but in a different place.

Quillibrace: Mm?

Elowen: Not outside construal, but within stable patterns of relational actualisation.

Not discovered facts—

reproducible ones.

Quillibrace smiles faintly.

Quillibrace: Miss Stray, once again you have arrived quietly at the centre of the discussion.

Blottisham: I still preferred thermometers.

Quillibrace: Why?

Blottisham: They simply told one things.

Quillibrace: Ah.

And there lies the difficulty.

You assumed reality was already speaking before anyone had established a language.

3. On the Curious Difficulty of Being Separate

The Senior Common Room at St Anselm's

Several days later. Afternoon sunlight enters in thin pale bands through tall windows. Professor Quillibrace is inspecting a teacup with an expression suggesting philosophical suspicion. Mr Blottisham has acquired a newspaper and appears energised by imminent misunderstanding. Miss Elowen Stray is reading quietly nearby.

Blottisham: Ah! Excellent.

Quillibrace: I dislike that tone immediately.

Blottisham: Quantum entanglement.

Quillibrace: Worse and worse.

Blottisham: I have been reading about it.

Quillibrace: My condolences.

Blottisham: Two particles become mysteriously linked across vast distances and communicate instantaneously.

Quillibrace: Ah.

Blottisham: Faster than light.

Quillibrace: Ah.

Blottisham: Secret messages darting invisibly across the universe.

Quillibrace: Ah yes. The telepathic-particle interpretation.

Blottisham: Mock all you wish; that appears to be what everyone says.

Quillibrace: Everyone says many things. A distressing proportion of them with confidence.

Blottisham: Then explain where I have erred.

Quillibrace: Gladly.

Tell me, before these particles become "mysteriously linked"—

what are they?

Blottisham: Particles.

Quillibrace: Yes.

What kind of things?

Blottisham: Independent things.

Quillibrace: Ah.

There we are.

Blottisham: There we are where?

Quillibrace: At the scene of the crime.

Blottisham: I merely assumed there were two objects.

Quillibrace: Exactly.

You began with separability already installed.

Blottisham: Well naturally—

Quillibrace: Careful.

You have abused naturally several times this week.

Blottisham: Very well. I merely assumed there were distinct systems.

Quillibrace: Classical physics does precisely that.

Each system possesses its own state.

Joint descriptions are constructed from independent components.

Correlations arise because independently existing things interact.

Blottisham: Entirely reasonable.

Quillibrace: Quantum mechanics occasionally regards reasonableness with active hostility.

Blottisham: So entanglement adds a mysterious connection between independent things?

Quillibrace: No.

Blottisham: Hidden communication?

Quillibrace: No.

Blottisham: Invisible influence?

Quillibrace: Also no.

Blottisham: You are removing possibilities at a rate that feels personally directed.

Quillibrace: Entanglement does not introduce a strange connection between independent entities.

It removes the independence.

Blottisham blinks.

Blottisham: Removes it?

Quillibrace: Entirely.

Blottisham: But there are obviously two particles.

Quillibrace: Ah yes—the obvious.

A dangerous category.

Elowen: The issue seems similar to the previous discussion.

Blottisham: How so?

Elowen: We assumed superposition meant several completed states existing simultaneously.

Perhaps now we assume entanglement means several completed entities existing independently.

Quillibrace: Very good.

Blottisham: But surely there are still two things involved.

Quillibrace: There may be two outcomes.

Two measurement locations.

Two descriptive perspectives.

But the assumption of two independently actualised systems is precisely what fails.

Blottisham: Good heavens.

Quillibrace: Quite.

Blottisham: Then what exactly exists?

Quillibrace: A non-separable relational structure.

Blottisham: Which sounds suspiciously like saying "one thing" while charging extra syllables for it.

Quillibrace: Not quite.

Because "one thing" still carries unfortunate metaphysical luggage.

Blottisham: Such as?

Quillibrace: Boundaries. Intrinsic properties. Independent existence.

No—the issue is relational organisation itself.

Elowen: So what appears as two systems may actually be derived partitions within a larger relational configuration?

Quillibrace: Precisely.

Subsystems become secondary.

The relational structure comes first.

Blottisham: Secondary.

He sits heavily into an armchair.

Blottisham: I am beginning to suspect reality has been assembled in the wrong order.

Quillibrace: On the contrary.

You are merely discovering that your preferred order of assembly was never guaranteed.

Blottisham: Then why do measurements appear coordinated across space?

Quillibrace: Because you continue imagining messages travelling between independent parts.

Blottisham: Naturally—

Quillibrace: Don't.

Blottisham: Habit.

Quillibrace: Correlations are not generated through transmission.

Nothing races between distant objects carrying instructions.

The outcomes arise through the resolution of a shared relational structure.

Blottisham: Shared.

Quillibrace: Yes.

Blottisham: So measurement does not uncover two separate values waiting in two separate places?

Quillibrace: Correct.

Blottisham: It resolves one non-factorisable structure into correlated outcomes?

Quillibrace: Good Lord.

Blottisham: What?

Quillibrace: There it was again.

A brief flicker of understanding.

Elowen: Then perhaps the discomfort comes from space itself.

Quillibrace: Mm?

Elowen: Space encourages us to imagine separation.

Separation suggests independence.

Independence suggests independently existing parts.

Quillibrace: Continue.

Elowen: But entanglement seems to suggest that spatial separation belongs to the description that emerges later, not to the deeper structure itself.

A pause.

Quillibrace lowers his teacup slowly.

Quillibrace: Miss Stray—

you continue displaying an unsettling tendency to arrive quietly at the centre of matters.

Blottisham: I still prefer my interpretation.

Quillibrace: Telepathic particles?

Blottisham: Yes.

It seemed simpler.

Quillibrace: Simpler perhaps.

Though one should remember that simplicity achieved by assuming the wrong ontology occasionally resembles solving a leaking roof by denying weather.

2. On the Curious Difficulty of Being Two Things at Once

The Senior Common Room at St Anselm's

The following evening. The rain has ceased. Professor Quillibrace is reading near the fire while Mr Blottisham paces beside a sideboard bearing an alarming quantity of biscuits. Miss Elowen Stray is writing notes in a small notebook.

Blottisham: I have corrected yesterday's misunderstanding.

Quillibrace: Which one?

Blottisham: The quantum one.

Quillibrace: Ah. All of it then.

Blottisham: I now understand superposition perfectly.

Quillibrace: How dreadful.

Blottisham: It means a thing occupies two states at once.

A pause.

Quillibrace: Remarkable.

Blottisham: Thank you.

Quillibrace: No, remarkable that one can misunderstand something with such efficiency.

Blottisham: Really, Quillibrace, I fail to see your objection. Everyone says this.

Quillibrace: Everyone also says one can "catch cold," as though influenza lurks in hedges waiting to leap upon passers-by.

Blottisham: That's entirely different.

Quillibrace: Not structurally.

Blottisham: Well then, explain.

Quillibrace: Very well. Tell me: when you say two states at once, what exactly are you imagining?

Blottisham: A particle here and there simultaneously.

Quillibrace: Mm.

Blottisham: Existing in multiple possibilities at once.

Quillibrace: Mm.

Blottisham: Like a sort of ghost spread across reality.

Quillibrace: Ah yes—the famous quantum ectoplasm interpretation.

Blottisham: You mock, but I detect no alternative explanation forthcoming.

Quillibrace: The difficulty is that your picture imports classical assumptions before the discussion has even begun.

Blottisham: Such as?

Quillibrace: Such as assuming there are already distinct states available for occupation.

Blottisham: Naturally there are.

Quillibrace: Naturally?

Blottisham: Well... yes.

Quillibrace: Classical physics assumes reality always exists in a condition of closure.

Blottisham: Closure.

Quillibrace: At any moment a system possesses a complete state.

Properties are simultaneously determinate.

Evolution proceeds from one completed condition to another.

Blottisham: Quite sensible.

Quillibrace: Sensible perhaps. Necessary, no.

Elowen: The assumption is stronger than it first appears.

Blottisham: How so?

Elowen: It assumes reality is always already settled.

Quillibrace: Exactly.

Elowen: Even uncertainty becomes a temporary defect in us rather than a feature of structure.

We merely fail to know the already completed state.

Blottisham: Naturally.

Quillibrace: Stop saying naturally. Nature is receiving an undeserved reputation.

Blottisham: Then quantum mechanics says—

Quillibrace: Quantum mechanics says closure itself becomes questionable.

Blottisham: So we lose knowledge of the closed state?

Quillibrace: No.

Blottisham: Then we lose—

Quillibrace: The requirement that such a state exists prior to actualisation.

Blottisham frowns at the fire as if suspecting conspiracy.

Blottisham: I dislike this already.

Quillibrace: Superposition does not mean multiple actual states.

It means non-closure.

Blottisham: Non-closure.

Quillibrace: The system has not stabilised into a single coherent regime of determination.

Blottisham: That's infuriatingly abstract.

Quillibrace: Reality bears no obligation to assist pictorial thinking.

Blottisham: Then what exactly is present?

Quillibrace: Constraint.

Structured relational potential.

Multiple admissible ways the system might become determinate.

But no prior selection among them.

Blottisham: So it is both A and B—

Quillibrace: No.

Blottisham: Neither A nor B—

Quillibrace: Also no.

Blottisham: You appear determined to eliminate all available conjunctions.

Quillibrace: I am attempting to eliminate misplaced ones.

Elowen: It sounds less like both and more like not yet one.

Quillibrace turns slowly toward her.

Quillibrace: Yes.

Precisely.

Blottisham: That's it?

Quillibrace: That's the entire disaster, yes.

Elowen: Classical thinking wants alternatives to exist in advance as separate completed possibilities.

Quillibrace: Mm.

Elowen: But a superposed system hasn't yet entered a regime where one coherent determination exists.

Quillibrace: Quite so.

Blottisham: So reality itself remains... unresolved?

Quillibrace: Temporarily non-closed.

Blottisham: Which sounds suspiciously like unresolved with spectacles on.

Quillibrace: There is a difference.

Unresolved suggests deficiency.

Non-closure describes structure.

Blottisham: Hmph.

Then what of measurement?

We look, and reality finally tells us what was true.

Quillibrace: Ah yes. We have arrived once again at extraction.

Blottisham: Extraction?

Quillibrace: Your persistent fantasy that reality contains hidden objects in drawers waiting for inspection.

Blottisham: A perfectly respectable fantasy.

Quillibrace: Measurement does not reveal completed facts.

It imposes closure.

Blottisham: Imposes?

Quillibrace: A previously non-closed relational structure enters a determinate regime.

Nothing hidden emerges.

The system simply resolves into one admissible organisation.

Blottisham: Good Lord.

Quillibrace: Quite.

Silence settles for a moment.

Blottisham: Then all these years I have imagined quantum mechanics as reality being indecisive.

Quillibrace: Yes.

Blottisham: Whereas the difficulty is that I insisted on asking reality to finish a sentence it had not yet begun.

A faint smile appears on Quillibrace's face.

Quillibrace: Mr Blottisham—

that is dangerously close to understanding.

Elowen: Then perhaps superposition is only paradoxical because we keep demanding closure too early.

Quillibrace: Miss Stray, I believe you have once again committed the regrettable act of arriving quietly at the centre of the discussion.

Blottisham: I still preferred the ghost.

Quillibrace: Of course you did.

Ghosts at least have the decency to possess properties.