Reinventing the Axle
Patterns behind breakthrough innovation, human ingenuity, and parallel discovery.
Posted April 30, 2025 | Reviewed by Monica Vilhauer Ph.D.
Nobody had thought of a time machine until H.G. Wells first wrote about it in 1895. As soon as the novel The Time Machine was published, others quickly picked up on the concept of a machine that could travel through time and put their own spin on it—the DeLorean took its passengers through time, and so did the TARDIS and the Hot Tub Time Machine.
However “obvious” something seems today, every little thing had to be invented once, including the tiniest detail you can think of. Before someone came up with the idea of a corridor, people lived in houses where rooms opened from other rooms like you see in museums today. It’s easy to say duh now, but when the first Roman patrician built corridors in a villa, it was just as forward looking in their time as sustainable architecture is in ours.
You’d think that something as basic and ubiquitous as the equal sign, one of the world’s most recognized symbols and one of the most frequently used concepts in mathematics, is as old as time itself. But you’d be surprised to learn that it was introduced as late as 1557, by the Welsh mathematician Robert Recorde, who, as rumor has it, came up with the “emoji” because he got tired of writing “is equal to” all the time.
Everything in the world, however important or however humble, had to be invented by someone at least once. Maybe even more than once: We keep reinventing the wheel so often that we even made a proverb out of it. (Never mind that we got that one wrong; when we’re reinventing the wheel, what we’re really reinventing is the axle.)
Innovation as broccoli
During grocery shopping, I sometimes shout “Let’s buy a fractal,” and I don’t even mean it as a joke.
If you look at Romanesco broccoli (some may call it Romanesco cauliflower ), you can see that it really is a naturally occurring fractal, with its buds forming a logarithmic spiral that displays self-similarity at various scales.
Setting this aside aside, in his book Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies , theoretical physicist Geoffrey West draws an interesting parallel between the fractal nature of innovation and biological systems.
The idea is that innovations, like fractals, show self-similarity at different scales. Just as a small branch of a tree resembles the whole tree’s structure, small innovations often mirror the pattern of larger, breakthrough discoveries. Each innovation creates new possibilities for further ones, branching out in a fractal-like pattern of development.
Time machine spinoffs
H.G. Wells’ The Time Machine provided a new framework for time travel, which resonated with the technological and scientific mindset of the Industrial Age. Before this, time travel in fiction was often achieved through dreams or supernatural means; the key innovation wasn’t the concept of time travel itself, but rather the scientific context that made it feel “plausible.”
This specific fusion of Victorian-era industrialism with the desire to “go back in time” created what innovation theorists would call a “phase transition,” a moment when existing elements suddenly crystallize into a new pattern. Then, just as Romanesco broccoli exhibits self-similarity at different scales, the time machine concept spawned an ever-branching array of variations, each maintaining the core DNA of Wells’ original framework while evolving in new directions.
The fractal nature of innovation becomes evident in how subsequent authors built upon Wells’ framework. Each new iteration—from Asimov’s temporal mechanics to Zemeckis’ DeLorean—represents a similar pattern, preserving the core concept of mechanical time travel while adding new layers of complexity and interpretation. Just as each small bud in a head of Romanesco broccoli follows the same mathematical principles as the whole, each new time machine story carries the imprint of Wells’ original vision.
Though he doesn’t explicitly use the term “fractals,” media theorist Steven Johnson also touches on this concept in his book Where Good Ideas Come From: The Natural History of Innovation . He describes how innovations create “adjacent possibles”—new doors that open up only after other doors have been opened, creating a branching pattern of discovery that, as far as I’m concerned, resembles fractal geometry.
When ideas come from nowhere
While many inventions emerge from gradual refinement or simultaneous discovery, some breakthroughs still seem to materialize from thin air. In mathematics, logarithms are a good example of an invention that wasn’t directly inspired by previous research. E.T. Bell, when writing about the 16th-century mathematician John Napier, notes as such: “The invention of logarithms came to the world as a bolt from the blue… It stands isolated, breaking in upon human thought abruptly without borrowing from the work of other intellects.”
What makes logarithms even more intriguing is that they appeared as an already complete theorem. Most other innovations go through several iterations by various contributors, but logarithms appeared in essentially their final form. As mathematician Pierre-Simon Laplace later said, “By shortening the labors, logarithms doubled the life of astronomers.” In fact, the tool was so perfect for its purpose that its basic concept remained unchanged for centuries.
These “bolts from the blue” often reshape our understanding of what’s possible. As the science historian James Burke notes in the documentary The Day the Universe Changed , such moments reveal that what we believe to be absolute truth is shaped by the way we look at things. Napier’s logarithms didn’t just solve a mathematical problem; they fundamentally altered how we approach calculation itself, opening doors that weren’t previously known to exist—and so, another bud of math “broccoli” could start sprouting into a brand-new fractal.
Wells, H. G. (1895). The Time Machine. London, UK: William Heinemann.
West G., 2017, Scale. The universal laws of growth, innovation, sustainability, and the pace of life in organisms, cities, economies, and companies, New York, Penguin Press, 479 p. https://doi.org/10.4000/cybergeo.28543
Johnson, S. (2010). Where good ideas come from: The natural history of innovation. Riverhead Books.
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Richard Dancsi holds a master's degree in mathematics and computer science. He has built diverse software products across cultures and teams, including with Orange, IBM, and Vodafone.
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