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4 THE MEASURE OF THINGS
if you had to select the least convivial scientific field trip of all time； you could certainlydo worse than the french royal academy of sciences鈥櫋eruvian expedition of 1735。 led by ahydrologist named pierre bouguer and a soldier…mathematician named charles marie de lacondamine； it was a party of scientists and adventurers who traveled to peru with the purposeof triangulating distances through the andes。
at the time people had lately bee infected with a powerful desire to understand theearth鈥攖o determine how old it was； and how massive； where it hung in space； and how it hade to be。 the french party鈥檚 goal was to help settle the question of the circumference ofthe planet by measuring the length of one degree of meridian （or 1/360 of the distance aroundthe planet） along a line reaching from yarouqui； near quito； to just beyond cuenca in what isnow ecuador； a distance of about two hundred miles。
1almost at once things began to go wrong； sometimes spectacularly so。 in quito； the visitorssomehow provoked the locals and were chased out of town by a mob armed with stones。 soonafter； the expedition鈥檚 doctor was murdered in a misunderstanding over a woman。 thebotanist became deranged。 others died of fevers and falls。 the third most senior member ofthe party； a man named pierre godin； ran off with a thirteen…year…old girl and could not beinduced to return。
at one point the group had to suspend work for eight months while la condamine rode off tolima to sort out a problem with their permits。 eventually he and bouguer stopped speakingand refused to work together。 everywhere the dwindling party went it was met with thedeepest suspicions from officials who found it difficult to believe that a group of frenchscientists would travel halfway around the world to measure the world。 that made no sense atall。 two and a half centuries later it still seems a reasonable question。 why didn鈥檛 the frenchmake their measurements in france and save themselves all the bother and disfort of theirandean adventure？
the answer lies partly with the fact that eighteenth…century scientists； the french in particular；seldom did things simply if an absurdly demanding alternative was available； and partly witha practical problem that had first arisen with the english astronomer edmond halley manyyears before鈥攍ong before bouguer and la condamine dreamed of going to south america；much less had a reason for doing so。
* triangulation； their chosen method； was a popular technique based on the geometric fact that if you know thelength of one side of a triangle and the angles of two corners； you can work out all its other dimensions withoutleaving your chair。 suppose； by way of example； that you and i decided we wished to know how far it is to themoon。 using triangulation； the first thing we must do is put some distance between us； so lets say for argumentthat you stay in paris and i go to moscow and we both look at the moon at the same time。 now if you imagine aline connecting the three principals of this exercise…that is； you and i and the moon…it forms a triangle。 measurethe length of the baseline between you and me and the angles of our two corners and the rest can be simplycalculated。 （because the interior angles of a triangle always add up to 180 degrees； if you know the sum of twoof the angles you can instantly calculate the third； and knowing the precise shape of a triangle and the length ofone side tells you the lengths of the other sides。） this was in fact the method use by a greek astronomer；hipparchus of nicaea； in 150 b。c。 to work out the moons distance from earth。 at ground level； the principles oftriangulation are the same； except that the triangles dont reach into space but rather are laid side to side on amap。 in measuring a degree of meridian； the surveyors would create a sort of chain of triangles marching acrossthe landscape。
halley was an exceptional figure。 in the course of a long and productive career； he was asea captain； a cartographer； a professor of geometry at the university of oxford； deputycontroller of the royal mint； astronomer royal； and inventor of the deep…sea diving bell。 hewrote authoritatively on magnetism； tides； and the motions of the planets； and fondly on theeffects of opium。 he invented the weather map and actuarial table； proposed methods forworking out the age of the earth and its distance from the sun； even devised a practicalmethod for keeping fish fresh out of season。 the one thing he didn鈥檛 do； interestingly enough；was discover the et that bears his name。 he merely recognized that the et he saw in1682 was the same one that had been seen by others in 1456； 1531； and 1607。 it didn鈥檛bee halley鈥檚 et until 1758； some sixteen years after his death。
for all his achievements； however； halley鈥檚 greatest contribution to human knowledge maysimply have been to take part in a modest scientific wager with two other worthies of his day：
robert hooke； who is perhaps best remembered now as the first person to describe a cell； andthe great and stately sir christopher wren； who was actually an astronomer first and architectsecond； though that is not often generally remembered now。 in 1683； halley； hooke； andwren were dining in london when the conversation turned to the motions of celestial objects。
it was known that planets were inclined to orbit in a particular kind of oval known as anellipse鈥斺�渁 very specific and precise curve；鈥潯o quote richard feynman鈥攂ut it wasn鈥檛understood why。 wren generously offered a prize worth forty shillings （equivalent to a coupleof weeks鈥櫋ay） to whichever of the men could provide a solution。
hooke； who was well known for taking credit for ideas that weren鈥檛 necessarily his own；claimed that he had solved the problem already but declined now to share it on the interestingand inventive grounds that it would rob others of the satisfaction of discovering the answer forthemselves。 he would instead 鈥渃onceal it for some time； that others might know how to valueit。鈥潯f he thought any more on the matter； he left no evidence of it。 halley； however； becameconsumed with finding the answer； to the point that the following 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 reactio