A lesson from Sir Isaac Newton on the value of persistence

Most people know something about Sir Isaac Newton’s so-called “miracle years,” when he invented calculus (both differential and integral - and he proved the relationship between the two), discovered the spectral content of light, and made inroads into the theory of gravity, all in about two years. But far less widely known is the story of what set Newton down the intellectual path that ultimately led him to those discoveries. The latter, however, can provide important insights into the nature of innovation and what it requires.

Newton’s revolutionary breakthroughs in physics and mathematics began with two purchases that he made in 1663 at an outdoor market in Cambridge called the Stourbridge Fair: a glass prism and a book on astrology. Yes, astrology. In his book, The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World, Edward Dolnick observes that “The astrology book had no significance in itself, but it helped change history.”

It changed history because Newton “read it ‘til he came to a figure of the heavens which he could not understand for want of being acquainted with trigonometry,” as he himself recalled. He wanted to understand trigonometry so he bought a book on that. But he didn’t understand trigonometry either because he was not acquainted with geometry. So he obtained a book on Euclidean geometry and, as he recounts, easily understood the classical geometry.

Newton’s journey did not end there. After Euclid and trigonometry, he turned to Descartes’ analytic geometry, which he grappled with and eventually mastered, after a struggle familiar to many a scientist or engineer: he would read a page or two, get a bit lost, go back over the previous material, move forward again, etc. Until it congealed into a solid understanding.

After two years of studying thus, upon mastering these foundational subjects by studying the works of others, Newton began to embark on creative efforts of his own. This began with a proof of the binomial theorem in early 1665, then:

“The same year in May I found the method of Tangents … and in November had the direct method of fluxions [differentiation] and the next year in January had the Theory of Colours and in May following I had entrance into ye inverse method of fluxions [integration]. And the same year I began to think of gravity extending to ye orb of the Moon…”

People continue to be appropriately in awe of the fact that after only two years of study, and in such a short amount of time, Newton was able to accomplish all that he did. The flip side of that strikes me as important also, and often overlooked: in reading a book about an invalid pseudo-science, Newton happened upon a diagram that he didn't fully understand. Instead of shrugging his shoulders and moving on, he pursued his curiosity, not knowing at the time where it would lead, and he stayed with the problem for two years, exploring one subject after another until he had achieved a deep understanding of the entire related subject matter.

In the course of his investigations, Newton acquired the mathematical “parts” that could then be integrated into a new, previously unknown whole: calculus, which then made possible his work in physics, celestial mechanics. And so on. His persistent studies had, in the language of complexity theory, unlocked his door to the adjacent possible.

Note the following, which is the essential point of this discussion: when he began his exploration, Newton could not have possibly known that it would lead him to (among other things) the invention of calculus – because calculus did not yet exist. It did not exist because he himself (and Leibnitz, independently) had not yet invented it! This is the nature of a genuinely new idea. One cannot anticipate coming upon that which is not yet known to anyone.

I have had the same type of experience over and over again in my career, though certainly not on a scale as grand as Newton’s: simply staying with a problem and refusing to accept anything less than full understanding leads to unforeseeable and unanticipated insights of great value; elegant solutions, new inventions, eureka moments. But only after relentless work: staying with the problem, looking up scholarly papers that seem relevant, reading one until I come upon a term I don't understand, then looking that term up, then going back to the paper, then looking up another term, then ordering a book on Amazon and reading the relevant sections… You get the idea.

The “miracle years” were anything but. Newton was not struck with a revelation like a bolt out of the blue – nor even quite like an apple falling from a tree, at least not onto his head. He was a great genius of the ages, but his brain was constructed in the same fashion as all humans. Better than most perhaps, but essentially the same. He still had to work to acquire knowledge with effort and set off down paths leading to unknown destinations – some of them dead ends – then turn around and start again, and so on. He was a tinkerer. He was curious and determined. He worked for it. Eureka moments come only to those who earn them.

Keep that in mind next time you are struck with a spark of curiosity, a question, or a vague sense that there is something more to what you are looking at, but you're not sure what. Maybe just a better way to do something you've done many times before. It doesn't have to be a set of fundamental breakthroughs in math and physics. Stay with it. Even in the face of outside pressures or inclinations to doubt yourself. Don’t give up. You never know where your path of discovery might lead.