Some of us are old enough to remember the much-ballyhooed appearance of Halleys comet in 1986 -- it swoops past Earth only once every 76 years, after all, and isnt due back until 2061. (So mark your calendars!) It also provides a handy framework on which to hang the scientific concepts featured in this weeks episode of "Cosmos: A Spacetime Odyssey."

It starts with a nod to the human gift for pattern recognition -- both a blessing and a curse, since sometimes we see patterns that arent really there, like the face of Jesus in a piece of toast. (The technical term is pareidolia.)

We also see patterns and messages in the stars. We were born into a mystery, Neil deGrasse Tyson intones over an image of a baby in a basket, gazing up at the night sky as the stars are reflected in the infants eyes. We see shapes in the form of constellations, for instance, and past civilizations read dire portents of doom in the periodic appearance of comets streaking across the sky. Chinese astronomers began keeping records of comets around 1400 BC, including one in 240 BC that we now know as Halleys comet, after the 17thcentury astronomer Edmund Halley.

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Halley first observed a comet in 1664. It happened to coincide with the outbreak of the plague in England, as well as the Great Fire of London, but it inspired the young Halleys love of the night sky. He gained notoriety for his voyage to map the stars of the Southern Hemisphere and soon became part of the vibrant intellectual community that frequented the local coffeehouses, vividly brought to life in another of the series clever animated sequences.

During one conversation, Halley offered to pay 40 shillings to the first person to demonstrate a simple mathematical law explaining why the planets move in elliptical orbits rather than perfect circles. But nobody could do the math -- except for Isaac Newton, who was a bit of a recluse by this point thanks to his squabbles with Hooke and many other scientists of that era. Newton was a difficult man. But he was also brilliant. Halley learned that Newton had solved this calculation five years earlier, part of the manuscript hed been writing: thePrincipia. Spoiler alert: This is one of the greatest scientific treatises ever written, outlining the laws of motion and the universal law of gravitation, as well as the invention of calculus.

It was just the sort of thing that the Royal Society would publish -- except the society was strapped for cash that year, having blown its budget on a lavishly illustrated tome called "History of Fish" that proved to be a colossal failure in terms of sales. Apparently the society was paying Halleys salary in copies of books it couldnt sell, which does make for an amusing domestic scene in which Halleys wife is dismayed when he comes home with yet another copy of "History of Fish."

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Long story short: Halley decided to pony up the cash to publish thePrincipiahimself, and a scientific revolution ensued. Newtons laws explain how nature works, and it does so in the language of mathematics. When mankind sent the first rockets to the moon, it was Newton in the drivers seat.

Newton was such a towering figure that we tend not to remember his gifted contemporaries -- like Halley, who did not actually discover the comet that bears his name. But he was the first to notice an interesting pattern in comet sightings, after poring over first-hand accounts from several centuries. He realized that the comet recorded in 1682 was the same as the one that had been recorded in 1531 and 1607. It was orbiting the sun in a long elliptical path. Halley predicted the same comet would reappear at the end of 1758 -- and it did.

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'Cosmos' recap: The meaning and math of comets