The sun rose, heralding the beginning of a new spring morning, as well as the end of another all-night study session. Everyone was familiar with the occasional cram session into the early hours of the morning on a school-night, but this young girl had been burning the midnight oil on what was now Saturday morning.
She had always been extremely studious, but this situation had come about as a bit of vengeful procrastination. She was pouring over her English work, which was far-and-away her strongest subject, while neglecting her mathematics studies. She had never really struggled with the subject; it just never managed to capture her interest as so many other subjects had. Stirred by the morning sun, her orange-striped cat made his way over to her desk, conspicuously planting himself right on her study materials. The cat looked at her quizzically, and she was now realizing how long of a night it had been. She was weary of course, but it felt like the kind of weariness sleeping wouldn’t fix. Looking out the window at the glowing landscape, she seemed to know just what she needed.
She turned and made eye contact with the cat; “Want to go for a walk, Thoreau?” she asked.
Wordlessly, he seemed to agree to the idea.
She rounded up what she needed in her bag, making sure to leave enough room for Thoreau to pile in as well. Arriving at the bus stop, she was able to catch the first morning arrival. It was a bit of a trip, and Thoreau seemed to be getting restless inside her bag.
The bus pulled to a stop where she needed to get off, the metropolitan landscape had melted away into a countryside wilderness. As soon as the bus pulled away, she unzipped her bag and Thoreau eagerly plopped out.
At the beginning of the wilderness trail, she found herself much more relaxed. The lush greenery was a much needed reprieve. The air carried the scent of spring on it, as well as the distant sounds of birds singing in the trees..
They both continued on the trail, eventually coming upon a stream. On the bank was a knee-high, flat rock, perfect for taking a load off. Thoreau, excited by his surroundings, seemed intent on wandering off.
“Don’t go too far, buddy” she whispered, not wanting to disturb the peacefulness of the environment.
She closed her eyes and focused on the babbling of the stream. Like the music she liked so much, it was perfect for keeping your mind from wandering to places she didn’t want it.
Her pensive moment was broken by a nudge against her leg. She looked down to see Thoreau, who had a pinecone in his mouth, and seemed quite happy.
“Get that out of your mouth, silly” she chided, pulling it out of his maw. Thoreau seemed a little disappointed, as he jumped up and curled himself next to her on the rock.
She held the pinecone in her hand, examining it intently. Looking from the bottom, she gazed directly into the center spiral. She counted the spirals, the ones going to the right… eight of them. She did the same for the left… thirteen. It almost seemed like she had done it out of compulsion.
Something sprang from the recesses of her mind, then she too sprang to her feet. Jogging over to one of the bases of the trees, she found more cones. She picked up as many as she could, brought them back over to the rock, and counted them the same.
The numbers weren’t always the same, but the left and right counts always made familiar pairs… five and eight, eight and thirteen, and the largest one even had thirteen and twenty-one.
“Fibonacci numbers…” she muttered to herself. She recalled reading about them begrudgingly during one of her rare math study sessions. A recursive sequence of numbers where the next number was the sum of the previous two, and it had a curious knack for occurring within nature.
She sighed and shook her head. While it was a neat fact, this was explicitly what she was out here trying to avoid thinking about. She roused herself and Thoreau again, continuing on the trail.
She stopped again at a dense collection of what she recognized as lady ferns. Crouching down, she again seemed compelled to closely examine the specimens. She found herself entranced in the level of detail in its leaves, how each one was made up of a tinier version of itself.
“Just like… fractals!” she thought. She couldn’t believe her mind had been drawn to math again, this time with the concept of infinitely detailed, self-similar geometric structures.
She got herself moving again, but her mind was now stuck on the intersection of math and nature. The regular hexagons of a beehive, the concentric circles of a tree’s trunk, the logarithmic spirals of a nautilus shell.
The trail eventually looped back around to where it started. For the second half of it or so, her mind was racing, making connection after connection between math and nature, tying it to all sorts of topics, beyond biology and into culture, architecture, and art. There was an undeniable beauty it was responsible for.
Back at the bus stop, Thoreau respectfully clambered back into her bag as the bus pulled up. A few minutes into the ride, she unzipped the bag to check on him. While peering in, she noticed a book he was nestled against. She pulled it out and surveyed the cover: Principles of Abstract Mathematics. She had forgotten it was in there, but it made sense since she had been so resistant to open it at home. After a short pause, she found herself splitting it open.
Before she knew it, the bus came to a rest at her stop. She couldn’t help but feel like she was eager to keep at it - but definitely after some much-needed rest.
(Voiceover by Maggie Ross)