A Golden Opportunity

Mr Blottisham entered the Senior Common Room carrying a sunflower.

He held it aloft with the satisfaction of a man who had brought decisive evidence to a long-running dispute.

“I believe,” he announced, “that I can now settle our recent discussion of geometry.”

Professor Quillibrace lowered his newspaper.

“Which discussion?”

“The one about whether geometry governs the natural world.”

Miss Stray looked at the sunflower. “And you believe this will settle it?”

“Look at it!” said Blottisham. “The spirals. The proportions. The mathematical regularity. The Fibonacci sequence itself, growing quite happily in a garden without the assistance of a mathematician.”

“An admirable achievement,” said Quillibrace.

Blottisham frowned. “You are making fun of me.”

“Not at all. I was congratulating the sunflower.”

Miss Stray accepted the flower and turned it gently in her hands.

“The remarkable thing,” she said, “is that the pattern need not have been imposed on the plant. It may emerge from the way the plant grows.”

“Precisely!” cried Blottisham. “Nature follows mathematics.”

“Does it?” asked Quillibrace. “Or do mathematical relationships help us describe what happens when nature grows?”

Blottisham considered this distinction.

“I fail to see that it matters.”

“Then let us suppose,” said Quillibrace, “that the plant is not consulting a mathematical textbook.”

“Obviously not. Plants don't read.”

“Yet its developing structures interact in ways that can produce recognisable patterns. In many sunflower heads, the spirals running in opposite directions have counts corresponding to neighbouring numbers in the Fibonacci sequence.”

“Exactly!”

“But that does not mean every plant follows the sequence, nor that the plant is attempting to reproduce a mathematical ideal.”

Blottisham looked at the sunflower with renewed suspicion.

“Are you suggesting that it has done this accidentally?”

“I am suggesting,” said Miss Stray, “that accidentally may not be the right word. A pattern can arise from the relations between things as they develop, without having been designed in advance.”

Blottisham sat down.

“I had hoped for a simpler conclusion.”

“You have a sunflower,” said Quillibrace. “Surely that is sufficient for one afternoon.”

“It is not merely a sunflower. It is an example of the golden ratio.”

“Ah,” said Quillibrace. “Now we approach the second difficulty.”

Blottisham brightened. “The golden spiral!”

“Not quite the same thing.”

“Surely a golden spiral is a spiral governed by the golden ratio?”

“In a particular mathematical sense, yes. Its dimensions increase according to a precise relationship. But not every spiral found in nature is a golden spiral.”

“Then what of the nautilus?”

Miss Stray smiled. “I wondered how long it would take you to reach the nautilus.”

“I have read extensively on the subject.”

“Have you measured any shells?”

“Certainly not. I am not a zoologist.”

“Nor, I think,” said Quillibrace, “are you yet a mathematician.”

Blottisham ignored this.

“But the shell grows in a spiral!”

“Many shells grow in logarithmic spirals,” said Miss Stray. “That does not establish that their spirals have precisely the proportions of a golden spiral. The resemblance is often more persuasive in diagrams than in measurements.”

Blottisham looked from one to the other.

“Are you telling me that the golden ratio is not responsible for the beauty of nature?”

“I am telling you,” said Quillibrace, “that beauty does not constitute a measurement.”

For a moment, nobody spoke.

Outside, a gardener was pruning a rosebush.

Miss Stray placed the sunflower on the table.

“Perhaps we have been asking the wrong question. We keep asking whether nature follows geometry, as though geometry were a set of instructions delivered from elsewhere. But what if certain geometrical relationships arise from the ways things grow, occupy space, and affect one another?”

“Then geometry would be descriptive rather than governing,” said Blottisham.

“Not necessarily,” said Quillibrace. “A description can reveal constraints. A relationship can help explain why certain arrangements are possible and others difficult to sustain. But we must distinguish the pattern we identify from the processes that produce it.”

“And the processes,” Miss Stray added, “may be more interesting than the pattern alone.”

Blottisham regarded the sunflower again.

“I begin to regret bringing this.”

“You have brought us something quite valuable,” said Quillibrace.

Blottisham looked pleased.

“What, precisely?”

“A reason to be cautious.”

The pleasure disappeared.

Miss Stray laughed. “I think the flower has done enough for one day.”

She took it home with her.

After she had gone, Blottisham turned to Quillibrace.

“Still, you must admit that the Fibonacci sequence is not imaginary.”

“Certainly not.”

“And the golden ratio is a genuine mathematical relationship.”

“Entirely genuine.”

“And geometry is present in the natural world.”

“Mathematical relationships are certainly found in the patterns we observe.”

Blottisham stood up.

“Then I shall write an essay demonstrating that the golden ratio is the key to understanding the universe.”

“Which universe?” asked Quillibrace.

Blottisham paused at the door.

“I shall have to think about that.”

It was, Professor Quillibrace reflected, the most promising thing Mr Blottisham had said all afternoon.