4. Maps, Mirrors, and Models

A large map of the county lay spread across the central table of the Senior Common Room.

Professor Quillibrace stood examining it with unusual concentration.

Mr Blottisham entered, paused, and smiled triumphantly.

"Professor!"

Quillibrace looked up.

"Good afternoon."

"I believe I have finally discovered something that really is a representation."

"Oh?"

"A map."

"A promising beginning."

"And scientific models are simply more sophisticated versions of the same thing."

Miss Stray looked up from the fireplace.

"So today's subject is representation?"

"So it would appear," said Quillibrace.

Blottisham pulled out a chair.

"I don't see how you can possibly object this time."

"I rarely object."

"You usually dismantle."

"I prefer to think of it as careful dusting."

Miss Stray laughed.

Blottisham pointed decisively at the map.

"This represents the county."

Quillibrace nodded.

"What is omitted?"

"Omitted?"

"Yes."

"The trees."

"Good."

"What else?"

"The buildings."

"The people."

"The weather."

"The smells."

"The history."

Blottisham shrugged.

"Naturally."

"So..."

Quillibrace looked gently at him.

"...does the map represent the county?"

"Of course."

"Or does it represent certain distinctions useful for travelling through it?"

Blottisham frowned.

"I should say both."

"Would a geologist use this map?"

"Probably not."

"A sailor?"

"No."

"A migrating goose?"

Blottisham smiled despite himself.

"I imagine not."

"So..."

Quillibrace waited.

"...the usefulness of the map depends upon what one is trying to do."

"Precisely."

Miss Stray had wandered over to the table.

She studied the map for several moments.

"It isn't pretending to be the county."

"No."

"It couldn't."

"No."

"So perhaps..."

She traced one of the roads with her finger.

"...its success lies in not representing everything."

Quillibrace inclined his head.

"A useful observation."

Blottisham protested.

"But it still corresponds to reality."

"In what sense?"

"The roads are really there."

"Excellent."

"And the villages."

"Indeed."

"And the rivers."

"Quite."

Quillibrace smiled.

"So if we produce another map..."

"Yes?"

"...showing rainfall instead of roads..."

"It would also correspond."

"And another showing geological strata?"

"Certainly."

"And another showing electoral boundaries?"

"Of course."

The Professor folded his arms.

"Which one represents the county?"

Blottisham opened his mouth.

Then closed it again.

"All of them."

"Splendid."

"Well..."

"Do they all represent the same reality?"

"I suppose..."

He hesitated.

"...they represent different aspects."

Miss Stray looked thoughtful.

"Or perhaps they make different distinctions."

Quillibrace looked at her approvingly.

"A subtle difference."

Blottisham shook his head.

"I don't see it."

"The aspects are already there."

"Perhaps."

"And the maps simply copy them."

Quillibrace walked slowly towards the window.

"When did contour lines first exist?"

Blottisham looked puzzled.

"In the hills."

"No."

"They're on the map."

"The hills existed long before contour lines."

"Indeed."

"So contour lines..."

"...are a way of organising elevation."

"Very good."

"They aren't found in nature."

"No."

"They're invented."

"As distinctions."

Miss Stray smiled.

"Yet once invented..."

She looked at the map again.

"...they allow us to see something we couldn't previously see."

Quillibrace nodded.

"Exactly."

Blottisham looked unconvinced.

"But surely science is trying to discover what reality is actually like."

"I sincerely hope so."

"And models help us do that."

"They certainly do."

"So models represent reality."

Quillibrace poured himself another cup of tea.

"Suppose Newton and Einstein are discussing gravity."

"Very well."

"Which model represents reality?"

Blottisham smiled.

"Einstein's."

"So Newton's represented reality until Einstein arrived?"

"Well..."

"And Einstein's will represent reality until someone else arrives?"

Blottisham sighed.

"You've made it sound rather temporary."

"I merely repeated your account."

A comfortable silence settled over the room.

Miss Stray spoke quietly.

"I wonder whether we've confused two different questions."

Quillibrace looked interested.

"What questions?"

"Whether a model is successful..."

"Yes."

"...and whether success consists in copying reality."

Blottisham looked towards her.

"They're the same thing."

"Are they?"

She gestured towards the map.

"This one is successful because I can find my way home."

"Yes."

"But I don't think it's successful because it's secretly a tiny county."

Quillibrace laughed.

"I wish I'd said that."

Blottisham laughed too.

"Very well."

"I concede the point."

"Do you?"

"Maps don't have to copy everything."

"Good."

"They organise what matters."

"Excellent."

"But scientific theories..."

He hesitated.

"...surely they're different."

Quillibrace raised an eyebrow.

"Are they?"

Another silence.

Outside, the college clock struck four.

Blottisham stared thoughtfully at the map.

"You know..."

"Yes?"

"I've always imagined theories as mirrors."

"And now?"

"I'm beginning to wonder whether they're more like..."

He searched for the word.

"...instruments."

Miss Stray looked up immediately.

"Not mirrors..."

She smiled.

"...but ways of seeing."

The room became still.

Quillibrace carefully folded the map.

"My dear Miss Stray."

"Yes?"

"I think you have just saved us several centuries of unnecessary philosophy."

Blottisham laughed.

"I don't suppose that's quite true."

"No."

Quillibrace placed the folded map back on the shelf.

"But it is an excellent direction in which to begin walking."

Outside, the rain had finally stopped.

For a brief moment, sunlight fell across the old stone quadrangle.

No one seemed inclined to leave.