Where do you do your best work? Possibly not here looking at the screen, nor in the ergonomic workplace so thoughtfully provided by your employer. I know a lawyer who solves cases while asleep; Mozart composed most fluently at the billiard table; Thomas Wolfe wrote his novels atop a refrigerator. The Irish mathematician William Rowan Hamilton, finding himself on a walk without a pencil when his life's great discovery occurred to him, scratched the formula for quaternions on a stone bridge with a nail. Many research institutes, mindful that the most fruitful exchanges come from chance meetings on the stairs, put in extra staircases, with whiteboards on every landing.
What makes these semi-irregular environments so productive? Their semi-irregularity. Thought is a distillation of experience, with the constant risk that the essence will be boiled away, leaving only an insipid wash. Semi-irregularity, by combining the familiar and the changeable, gives the mind its best tools for effective thought: patterns and exceptions. Patterns to suggest abstraction; exceptions to prevent abstraction going too far.
In this, we are like ancient hunter-gatherers, creeping through the forest, guessing the habits of an unseen prey or location of a buried tuber. For some, the forest is the thicket of numbers in a table; the prey, the giants that range across the Universe.
On this day in 1846, an astronomer at the Berlin Observatory put eye to telescope and saw exactly what he expected to see - yet saw it for the very first time. His gaze had been directed by an expert hunter, Urbain Le Verrier, who had identified the hidden beast through odd exceptions in the tables of planetary motions. The beast was called Neptune.
Neptune had been observed before, but in ways that had critically blurred the distinction between pattern and exception. Galileo himself may have seen it but, by mischance, on the very dates that the planet appears to halt in its orbit as the Earth overtakes it - so he took it for a fixed star. Astronomers in Paris in 1795, on the other hand, saw this assumed star move between observations - and therefore decided their observations were in error. It was only after John Herschel had discovered Uranus that minds opened again to the possibility of planets beyond the traditional six - and only after astronomers built up a detailed body of rigorously exact observations that any discrepancy became a matter for curiosity rather than embarrassment.
Uranus was behaving oddly, speeding beyond the predictions of Alexis Bouvard's tables at one point, slowing behind at another. Either the normally impeccable Bouvard had made an error in his calculations, or Newton's laws did not apply beyond Saturn - or something was out there, perturbing the field. Le Verrier and an English undergraduate, John Couch Adams, independently took up the task of identifying and locating this something based only on its influence on Uranus. Their differing success depended as much on mundane matters as on their own genius: Adams had little effective help from British observatories, while the Berlin astronomers redirected their telescopes the very day they received Le Verrier's prediction. The point, though, was that the never-before-recognized object was there - within one degree of its theoretical position.
After the announcement, there was an unseemly dispute about precedence; Adams' come-lately supporters (though not Adams himself) claimed his earlier calculations deserved the credit of discovery. Le Verrier's arrogant dismissal of all work but his own lost him friends even in Paris. After the the celestial glow of discovery faded, humans showed again that, despite our vaunted powers, we live on a very small planet.
If you enjoy such tales of human fallibility, you will find a new one every day on my sister site, Bozo Sapiens. See you there.