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lowing year he traveled tocambridge and boldly called upon the university鈥檚 lucasian professor of mathematics； isaacnewton； in the hope that he could help。
newton was a decidedly odd figure鈥攂rilliant beyond measure； but solitary； joyless； pricklyto the point of paranoia； famously distracted （upon swinging his feet out of bed in the morninghe would reportedly sometimes sit for hours； immobilized by the sudden rush of thoughts tohis head）； and capable of the most riveting strangeness。 he built his own laboratory； the firstat cambridge； but then engaged in the most bizarre experiments。 once he inserted a bodkin鈥攁 long needle of the sort used for sewing leather鈥攊nto his eye socket and rubbed it around鈥渂etwixt my eye and the bone as near to ＇the＇ backside of my eye as i could鈥潯ust to see whatwould happen。 what happened； miraculously； was nothing鈥攁t least nothing lasting。 onanother occasion； he stared at the sun for as long as he could bear； to determine what effect itwould have upon his vision。 again he escaped lasting damage； though he had to spend somedays in a darkened room before his eyes forgave him。
set atop these odd beliefs and quirky traits； however； was the mind of a supreme genius鈥攖hough even when working in conventional channels he often showed a tendency topeculiarity。 as a student； frustrated by the limitations of conventional mathematics； heinvented an entirely new form； the calculus； but then told no one about it for twenty…sevenyears。 in like manner； he did work in optics that transformed our understanding of light andlaid the foundation for the science of spectroscopy； and again chose not to share the results forthree decades。
for all his brilliance； real science accounted for only a part of his interests。 at least half hisworking life was given over to alchemy and wayward religious pursuits。 these were not meredabblings but wholehearted devotions。 he was a secret adherent of a dangerously hereticalsect called arianism； whose principal tenet was the belief that there had been no holy trinity（slightly ironic since newton鈥檚 college at cambridge was trinity）。 he spent endless hoursstudying the floor plan of the lost temple of king solomon in jerusalem （teaching himselfhebrew in the process； the better to scan original texts） in the belief that it held mathematicalclues to the dates of the second ing of christ and the end of the world。 his attachment toalchemy was no less ardent。 in 1936； the economist john maynard keynes bought a trunk ofnewton鈥檚 papers at auction and discovered with astonishment that they were overwhelminglypreoccupied not with optics or planetary motions； but with a single…minded quest to turn basemetals into precious ones。 an analysis of a strand of newton鈥檚 hair in the 1970s found itcontained mercury鈥攁n element of interest to alchemists； hatters； and thermometer…makersbut almost no one else鈥攁t a concentration some forty times the natural level。 it is perhapslittle wonder that he had trouble remembering to rise in the morning。
quite what halley expected to get from him when he made his unannounced visit in august1684 we can only guess。 but thanks to the later account of a newton confidant； abrahamdemoivre； we do have a record of one of science鈥檚 most historic encounters：
in 1684 drhalley came to visit at cambridge ＇and＇ after they had some timetogether the drasked him what he thought the curve would be that would bedescribed by the planets supposing the force of attraction toward the sun to bereciprocal to the square of their distance from it。
this was a reference to a piece of mathematics known as the inverse square law； which halleywas convinced lay at the heart of the explanation； though he wasn鈥檛 sure exactly how。
srisaac replied immediately that it would be an ＇ellipse＇。 the doctor； struck withjoy & amazement； asked him how he knew it。 鈥榳hy；鈥櫋aith he； 鈥榠 have calculatedit；鈥櫋hereupon drhalley asked him for his calculation without farther delay；srisaac looked among his papers but could not find it。
this was astounding鈥攍ike someone saying he had found a cure for cancer but couldn鈥檛remember where he had put the formula。 pressed by halley； newton agreed to redo thecalculations and produce a paper。 he did as promised； but then did much more。 he retired fortwo years of intensive reflection and scribbling； and at length produced his masterwork： thephilosophiae naturalis principia mathematica or mathematical principles of naturalphilosophy； better known as the principia 。
once in a great while； a few times in history； a human mind produces an observation soacute and unexpected that people can鈥檛 quite decide which is the more amazing鈥攖he fact orthe thinking of it。 principia was one of those moments。 it made newton instantly famous。 for the rest of his life he would be draped with plaudits and honors； being； among much else；the first person in britain knighted for scientific achievement。 even the great germanmathematician gottfried von leibniz； with whom newton had a long； bitter fight over priorityfor the invention of the calculus； thought his contributions to mathematics equal to all theaccumulated work that had preceded him。 鈥渘earer the gods no mortal may approach；鈥潯rotehalley in a sentiment that was endlessly echoed by his contemporaries and by many otherssince。
although the principia has been called 鈥渙ne of the most inaccessible books ever written鈥�
（newton intentionally made it difficult so that he wouldn鈥檛 be pestered by mathematical鈥渟matterers；鈥潯s he called them）； it was a beacon to those who could follow it。 it not onlyexplained mathematically the orbits of heavenly bodies； but also identified the attractive forcethat got them moving in the first place鈥攇ravity。 suddenly every motion in the universe madesense。
at principia 鈥檚 heart were newton鈥檚 three laws of motion （which state； very baldly； that athing moves in the direction in which it is pushed； that it will keep moving in a straight lineuntil some other force acts to slow or deflect it； and that every action has an opposite andequal reaction） and his universal law of gravitation。 this states that every object in theuniverse exerts a tug on every other。 it may not seem like it； but as you sit here now you arepulling everything around you鈥攚alls； ceiling； lamp； pet cat鈥攖oward you with your own little（indeed； very little） gravitational field。 and these things are also pulling on you。 it wasnewton who realized that the pull of any two objects is； to quote feynman again；鈥減roportional to the mass of each and varies inversely as the square of the distance betweenthem。鈥潯ut another way； if you double the distance between two objects； the attractionbetween them bees four times weaker。 this can be expressed with the formulaf = gmmr2which is of course way beyond anything that most of us could make practical use of； but atleast we can appreciate that it is elegantly pact。 a couple of brief multiplications； a simpledivision； and； bingo； you know your gravitational position wherever you go。 it was the firstreally universal law of nature ever propounded by a human mind； which is why newton isregarded with such universal esteem。
principia鈥檚 production was not without drama。 to halley鈥檚 horror； just as work wasnearing pletion newton and hooke fell into dispute over the priority for the inversesquare law and newton refused to release the crucial third volume； without which the firsttwo made little sense。 only with some frantic shuttle diplomacy and the most liberalapplications of flattery did halley manage finally to extract the concluding volume from theerratic professor。
halley鈥檚 traumas were not yet quite over。 the royal society had promised to publish thework； but now pulled out； citing financial embarrassment。 the year before the society hadbacked a costly flop called the history of fishes ； and they now suspected that the market fora book on mathematical principles would be less than clamorous。 halley； whose means werenot great； paid for the book鈥檚 publication out of his own pocket。 newton； as was his custom；contributed nothing。 to make matters worse； halley at this time had just accepted a positionas the society鈥檚 clerk； and he was informed that the society could no longer afford to provide him with a promised salary of 锟�50 per annum。 he was to be paid instead in copies of thehistory of fishes 。
newton鈥檚 laws explained so many things鈥攖he slosh and roll of ocean tides； the motions ofplanets； why cannonballs trace a particular trajectory before thudding back to earth； why wearen鈥檛 flung into space as the planet spins beneath us at hundreds of miles an hour2鈥攖hat ittook a while for all their implications to seep in。 but one revelation became almostimmediately controversial。
this was the suggestion that the earth is not quite round。 according to newton鈥檚 theory；the centrifugal force of the earth鈥檚 spin should result in a slight flattening at the poles and abulging at the equator； which would make the planet slightly oblate。 that meant that thelength of a degree wouldn鈥檛 be the same in italy as it was in scotland。 specifically； the lengthwould shorten as you moved away from the poles。 this was not good news for those pe