2. On the Dangerous Multiplication of Worlds

The Senior Common Room at St Anselm's had entered the subdued phase of the morning in which tea had been replenished and intellectual disasters could proceed at a measured pace.

Mr Blottisham sat in evident satisfaction.

"Well," he said, "I believe matters have recovered nicely."

Professor Quillibrace looked up slowly.

"Recovered?"

"Indeed. Last time you informed me that universal time had been abolished and that reality was no longer one gigantic committee meeting. Disturbing, naturally. But I have since reflected and found the solution."

Miss Elowen Stray glanced up from her notes.

"You've found one?"

"Certainly." He waved a hand confidently. "Different people simply have different perspectives on the same world."

Quillibrace stared into the middle distance.

"Oh dear."

Blottisham frowned.

"What now?"

"My dear fellow, you have merely rebuilt the demolished house and painted it a different colour."

"I have?"

"Entirely."

Elowen tilted her head.

"Because 'perspective' still assumes a world already sitting there waiting to be viewed?"

Quillibrace pointed at her with his teacup.

"Exactly."

Blottisham looked suspicious.

"I dislike agreement occurring before I've understood anything."

Quillibrace settled back into his chair.

"Consider what a frame is usually said to be. Popular accounts describe it as a kind of viewpoint—as though reality were a landscape and each observer merely stood on a different hill."

"Perfectly sensible."

"It is also disastrously misleading."

Blottisham sighed.

"I had feared that."

Quillibrace folded his hands.

"A viewpoint presupposes a completed object being viewed. One imagines a fixed world and different positions from which to inspect it."

"Yes."

"But special relativity does not merely rearrange viewpoints."

He paused.

"It rearranges what counts as a coherent world in the first place."

Blottisham blinked several times.

Elowen had become very still.

"So a frame isn't describing an already organised set of events."

"No."

"It's generating one."

Quillibrace smiled faintly.

"Precisely."

Blottisham stared.

"I beg your pardon?"

"A frame," Quillibrace continued, "is not a coordinate grid laid gently over reality like graph paper over a map."

"Good."

"It is a rule-governed system specifying how events become related at all."

Blottisham's brow furrowed dangerously.

Elowen looked thoughtful.

"So from a relational perspective, a frame behaves less like a picture and more like a system of construal."

Quillibrace nodded.

"Construal before representation."

Blottisham groaned softly.

"I remember this word."

"Representation assumes an object awaiting description," said Quillibrace. "Construal does not. Construal is constitutive. It actualises a determinate field from a wider relational potential."

"So the frame isn't observing the world."

"No."

"It is cutting a world from relational possibility."

"Yes."

Blottisham looked around uneasily.

"How many worlds are there now?"

Quillibrace rubbed his temples.

"One must be careful."

"There it is," said Blottisham. "The sentence professors utter immediately before catastrophe."

Quillibrace ignored him.

"We should not imagine countless universes multiplying like rabbits in a field. The issue is not multiple realities in that sense."

He lifted a finger.

"It is multiple coherent regimes of relational ordering."

Blottisham looked injured.

"You've somehow made it worse."

Elowen had resumed writing.

"Within a frame, everything appears stable. Events occur in order. Distances remain measurable. Simultaneity is coherent."

"Exactly."

"But from outside—though outside already means another construal—we see that this stability depends upon the constraints generating it."

Quillibrace nodded approvingly.

"So within a frame, events appear given and relations measured."

"And outside?"

"Relations are generating the events themselves."

Blottisham looked alarmed.

"You appear to be telling me that the furniture has become secondary to the arrangement of the room."

Quillibrace blinked.

Then blinked again.

Elowen looked surprised.

"That's...rather good."

Blottisham looked pleased.

"I've been improving."

Quillibrace looked reluctant.

"There may be traces of understanding emerging."

Blottisham sat up.

"Excellent."

Then his expression darkened.

"Though something troubles me."

"Predictably."

"If each frame constructs its own coherent ordering, how does anyone ever agree about anything?"

Quillibrace leaned forward.

"Ah."

He smiled.

"This is where people imagine everything collapsing into relativism."

Elowen looked up.

"But it doesn't."

"No."

"Because the frames aren't arbitrary."

"Exactly."

Quillibrace stood and wandered toward the window.

"The Lorentz transformations ensure something extraordinary."

Blottisham narrowed his eyes suspiciously.

"I distrust anything described as extraordinary."

"They ensure that different systems of construal remain mutually coherent."

He turned.

"So the frames do not share a single world-slice."

Silence.

"They share rules governing conversion between world-slices."

Blottisham stared.

Elowen's face slowly brightened.

"So the unity isn't in the content."

"No."

"It's in the transformations."

Quillibrace nodded.

"Very good."

Blottisham sat very still.

Then he said:

"So reality isn't one giant atlas seen from different angles."

"No."

"It's a collection of internally complete maps with strict translation rules."

Silence.

Quillibrace looked at him.

Elowen looked at him.

Blottisham looked at himself.

"My God," he whispered, "I've done it again."

Quillibrace sat down slowly.

"Mr Blottisham, I fear you may be becoming dangerous."

Blottisham frowned.

"Though I still have one concern."

"Yes?"

"If reality is generated through systems of construal..."

He glanced anxiously toward the door.

"...how exactly does Cook generate the pudding menu?"

Quillibrace stared at him for several seconds.

"My dear fellow," he said quietly, "there are domains in which even invariant transformations offer no assistance."