a brief history of science: part 6: the newtonian synthesis

A Brief History of Science:Part 6: The Newtonian Synthesis

Soumitro Banerjee∗

AS WE HAVE SEEN in the last install-ment of this article, the second half of

the seventeenth century saw a rapid devel-opment in science. After centuries of slum-ber during the middle ages, people startedtaking a fresh look at nature with eyes un-hindered by religious dogma. The mood ofthe time was probably best expressed byHooke who insisted on the use of “a sincerehand, and a faithful eye, to examine and torecord, the things themselves as they ap-pear.” “The truth is,” wrote Hooke, “the sci-ence of nature has already been too longmade only a work of brain and fancy: Itis now high time that it should return tothe plainness and soundness of observa-tions on material and obvious things.” TheRoyal Societies were formed in England andFrance, which acted as rallying points forthe new breed of scientists. Excitement wasin the air, and Boyle, Hooke, Wren, Halley,and many others made seminal discoverieswhich were presented and discussed in theRoyal Society.

The contribution of Isaac Newton tow-ers over everybody else of that period. Hisbook “Philosophiae Naturalis Principia Math-ematica” (Mathematical Principles of Natu-ral Philosophy) had enormous influence onhuman thinking; it shaped the face of sci-ence for centuries to come. That is why it isnecessary to understand the source of his

∗Dr. Banerjee is a Professor of Physics, Indian In-stitute of Science Education & Research, Kolkata, anda member of the Editorial Board of Breakthrough.

inspiration — what determined the contentand the direction of his scientific work. Butthe problem is confounded by the mythsthat have been built up around the person-ality of Newton: that he was an unsocialisolated eccentric genius; that the fall of anapple on his head caused the discovery ofthe theory of gravitation, etc. We need tounearth the reality by removing the veils ofsuch common misconceptions.

The history of science is a part of worldhistory. And there are two points of viewin looking at world history. One point ofview sees history as a chronological accountof the kings’ ascent to power, conflicts be-tween kings and kingdoms, the rise and fallof empires, and the gallantry and heroics ofkings and their generals. This is how his-tory is taught in our schools and colleges.This is not a scientific viewpoint of history,because, while the focus is on the eventsof the past, the underlying social processesthat determine the course of events are ob-scured from view. A scientific view of his-tory, on the other hand, focuses on thepeoples’ life and livelihood, and the devel-opment of the productive forces in the dif-ferent epochs, as reflected in the peoples’livelihood. The social factors underlying themajor developments in history are then un-derstood in terms of the conflict betweenthe productive forces and the productionrelation prevailing in each phase in history.This is how we understand the transitionfrom a hunting-gathering society to slavery,

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from slavery to feudalism, and from feudal-ism to capitalism. The kings and emperorswho ruled in these periods are important,but are not central to the understanding ofthe course of history.

That is why, in order to understand themotivation behind Newton’s scientific work,we have to look at the development of theproductive forces in that period of time, andthe scientific problems posed by it.

The development of theproductive forces

What was the social condition in the periodpreceding Newton’s time? In the earlier in-stallments of this article we have seen thatit was a time marked by the transition fromthe feudal middle ages to a new capitalistform of production. The merchant classthat developed within the womb of the feu-dal society was becoming financially pow-erful, and was starting mass-production ofgoods in “manufactories”. Initially thesewere simply sheds where a number of ar-tisans together produced goods using theraw material and implements supplied bythe merchant. But slowly, through the 16thand 17th centuries these manufactories be-came bigger, produced larger quantities ofgoods, and consequently the financial andpolitical power of the producers increased.

The increase in production posed a fewscientific problems. The goods had to besent to distant lands for trade and com-merce. But in those times, land transportwas very rudimentary. The ox-drawn cartscould not carry much load, and were veryslow. In comparison, waterborne transportin barges, ferries and ships could carry farmore goods, and was much faster. That iswhy the focus of that time was in improv-ing waterborne transport. This demandedimproved design of the ships, and for thatone had to know the laws governing themotion of floating bodies. The tonnage ca-

pacity of the ships could be calculated onlyif one knew the quantity of water it dis-places at different depths of submergence.While maritime transport was the preferredmode for reaching one country from an-other, river-based transport was the pre-ferred mode for goods transport within acountry. In addition, to increase the reachof inland transport, an elaborate systemof canals was developed. The design ofefficient canals and lock-gates demandedknowledge of the rules governing the flowof liquids through channels and cavities ofdifferent cross sections. Thus, waterbornetransport posed various problems in hydro-statics and hydrodynamics.

An important problem in maritime trans-port was the problem of determining aship’s position in open sea. The positionis specified by the latitude and longitude.Determining latitude was relatively easy:it could be found from the altitude of thesun at noon (i.e., at its highest point), ifone has a pre-calculated table giving thesun’s declinationfor the day at different lat-itudes. But the determination of longitudeposed a tough scientific challenge. Untilthe solution of the problem was found, theships had to move close to the shore, andthus had to travel much longer distances toreach the destination. People realized thatthe problem of determination of longitudeis essentially the same as that of determi-nation of the time at a given location, rel-ative to the time at a “standard” location.A way of finding the time was through theobservation of the bodies in the sky — themoon, planets, and stars. Thus, prepara-tion of the catalog of the positions of theseheavenly bodies became a matter of practi-cal importance, and in most of the seafar-ing nations observatories were establishedwith the express objective of preparing thecharts of the positions of these heavenlybodies. Some of these bodies, like the moonand the planets move, and hence it became

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Isaac Newton (1642-1727) at a young age.

necessary to know the laws governing theirmotion. Scientific attention was thus di-rected to the objects in the sky, and theirmotion.

In this period the struggle between theold kings, nobles and aristocrats, and theemerging bourgeois class took the form ofarmed fight for supremacy. As a result,warfare increased in number as well as inintensity. The demands of warfare alsoposed important problems before science.Firearms and cannons were already in usesince the thirteenth century. For effectiveuse of the firearms it became necessary toknow the process that takes place whengunpowder is ignited. Why does a gun re-coil, and by how much? At what angleshould the cannon be inclined so that thecannonball can hit the target at a given dis-tance? What is the trajectory of a bulletafter it is fired? What is the effect of airresistance on the trajectory? Solution ofthese problems demanded the development

of mechanics.

The necessities of larger volume of pro-duction needed ever larger quantities ofmetals — especially iron and copper. In-creased warfare only increased the demandof metals. Thus mining came out of the old“craftsmen” character and became a majorindustry. Deeper and deeper mines had tobe explored in order to reach the right kindof ores. This again posed important scien-tific problems. Water had to be continu-ously pumped out of the mine chambers.The mines had to be ventilated by pumpingin air. The ore had to be transported outof the mine. The metallic iron and copperhad to be extracted from the ore. These areproblems of mechanics and chemistry. Theexcavation of the mine chambers and theconnecting tunnels also needed a good ideaof solid geometry.

In those days the main medium of ex-change in trade was gold. The increasein the volume of trade needed ever largerquantities of gold. The gold mines of Europewere soon exhausted, resulting in a “goldfamine”. This was one of the reasons be-hind the royal patronage of the expeditionsto distant lands. The gold famine also re-sulted in a great interest in alchemy — theforerunner of chemistry — because at thattime it was believed that it was possible toturn other metals into gold using chemicalprocesses.

Thus we see that the rapid developmentof productive forces in the period follow-ing the renaissance posed important sci-entific problems — in mechanics, hydro-statics, hydrodynamics, mathematics, andchemistry. But, out of all these, the mostprofound questions concerned mechanics,which absorbed the attention of scientistsof that time. The further development of theproductive forces crucially depended on thesolution to these scientific problems.


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Age of reason — personified: thelife of Isaac Newton

It is a common belief that the making ofa genius requires a complacent childhood,favourable hereditary tracts, and guidanceand financial resource of parents. In thisyardstick nobody would expect Newton tobe what he was. His life confirms that everyman is a product of his own struggle, andthe people whom we call genius are moreso.

Isaac Newton was born on December 25,1642 (the year Galileo died) in the village ofWoolsthorpe, England. His father, who diedbefore Newton’s birth, was a farmer of mod-erate means. Newton descended from com-mon men on both sides; there is no recordof any notable ancestor.

Newton’s mother remarried and left herthree year old son with his grandmother.At the age of twelve Newton was sent toschool at Grantham. Here, during hisleisure hours, he constructed a numberof innovative mechanical toys including awater clock, a mill (powered by a mouse),and many sun-dials (one of which still sur-vives). In 1656 Newton’s mother was wid-owed again and Newton was called home tohelp with the farm at Woolsthorpe becauseof the family’s financial crisis. He proved tobe useless in taking care of sheep, and wassent back to school, and in 1661, at the rec-ommendation from his uncle, he proceededto the University of Cambridge for furtherstudies.

In those days the custom was that thestudents from poor families had to workas servant (called a subsizer) to studentsfrom richer families. Newton had to workas a subsizer at the university to makeboth ends meet. His academic record inhis undergraduate years seems to be out-wardly undistinguished. However, thesewere the years of formation of his scientificbeing and he waged a serious struggle to in-

herit the contemporary philosophical cross-currents and scientific ideas. From thecritical notes in his notebooks, researchershave concluded that in these years he thor-oughly studied Aristotle’s “Organon” and“Ethics”, Euclid’s “Elements”, Galileo’s “Di-alogo”, Descartes’ “Geometrie” and “Prin-cipia Philosophiae”, and other importantbooks on philosophy and science. Fromthese studies he developed his own per-sonal viewpoint in the matter of scientificinvestigation, and it seems the mathemati-cal approach of Descartes has profound ef-fect on his thought process.

In 1665, an outbreak of plague causedthe universities to close and Newton re-turned to his home in the country, wherehe remained till 1667. There, in the twoyears of rustic solitude — age 22 to 24 —his creative genius burst forth in a floodof discoveries unsurpassed in the history ofhuman thought: the binomial series of neg-ative and fractional exponents, the differ-ential and integral calculus, universal grav-ity as a key to the mechanism of the so-lar system, the splitting of sunlight into thevisual spectrum by means of a prism —with its implication of understanding thenature of light, etc. He was a very cautiousman in the matter of scientific work, anddid not want to make his discoveries pub-lic until he obtained definitive experimen-tal evidence confirming his analytical work.Yet, his mathematical abilities were so evi-dent that his teacher Prof. Isaac Barrow re-signed his Lucasian Professorship in 1669and Newton was offered the post at the ageof 27.

He initially conveyed his discoveries onthe nature of light and colours to the RoyalSociety. But soon he retreated into his shellbecause some criticisms were raised whenhis communications were read at the RoyalSociety meetings. He kept working, per-forming experiments, checking his conclu-sions. Then in 1684 a meeting with Hal-


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A surviving copy of the Principia Mathematica.

ley changed all that. By then Halley hadcome to the conclusion that there must bea central force acting on the planets, but atthat time nobody had been able to work outthe orbit of the planets starting from thatpremise. He asked Newton what would thetrajectory of a planet be, if it is acted on bya central force of the inverse square type.Newton answered, simply, that it would bean ellipse. “How do you know?” “I have cal-culated it.”

Halley was flabbergasted. This manknows the answer to a question everybodyis looking for, and yet he has not publishedit? He urged Newton to let the world knowabout his calculations. This prompted New-ton to embark on a grand plan to writedown everything that he has obtained in thearea of mechanics into a single book. Thistook an almost inhuman effort, working dayand night for two years. Finally when it waspublished in 1687, the Principia Mathemat-ica went on to become one of the books thatchanged human history.

The Principia Mathematica

The Principia Mathematica was written inan abstract mathematical language. Thiscould not be otherwise, because Newton’sintention was to tell the world how the prob-lems of the day could be solved by assum-ing a few “laws” of nature, using the tech-niques of mathematics. Still he took care tobe intelligible to the learned people. Eventhough he had arrived at most of the re-sults using the technique of calculus whichhe invented, he never used calculus in hisexpositions. Instead, he took pains to de-rive the same results using the methods ofgeometry which the learned people of thattime were familiar with.

The Principia Mathematica is written inthree volumes. In the first volume New-ton clearly defines the terms to be used inthe exposition1, and then states the lawsof motion. Thus, he lays the groundwork

1Here he adheres strictly to the demands of formallogic.


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on the basis of which the theoretical frame-work will be built.

The second volume is devoted to the ap-plication of these laws to achieve the solu-tion of mechanical problems related to themovement of bodies. He treats motion ofbodies in resistive medium (this solves theproblem of ballistics, and has direct im-plication in warfare), the motion of float-ing bodies and hydrostatics (this formed thetheoretical basis for the design of ships),the compression of gases and liquids un-der pressure (recall the problems posed bymining), movement of liquids in channelsand tubes (theoretical foundation for thedesign of canals, locks, and water pumpingequipment), and the movement of pendu-lums against frictional resistance (this hadimplication for the construction of pendu-lum clocks), etc.

The third volume of Principia is fullydevoted to what he calls “System of theWorld”. Based on the laws of motion andthe theory of universal gravitation, he ex-plained the observed motion of the planets,proved Kepler’s laws, explained why tidesoccur, and showed how one can predict theposition of the moon and the planets atany time in the future. This not only hadimmense importance in navigation, as weshall soon see, it completely changed theway scientists perceived nature.

Thus we see that the problems posed bythe contemporary society and the develop-ment of the productive forces supplied thesubject matter of Newton’s line of thinking.The picture of Newton’s character as an iso-lated genius, unconcerned about the soci-ety, discoveries sparked by falling apples— these are simply myths propagated bypeople who have failed to understand thecontent of Newton’s work because of theabstractness of his exposition and the ab-sence of direct reference to the above prac-tical problems.

It is always found in the history of science

that, whenever the society is ready for cer-tain development of ideas, usually a num-ber of people would be working on eachidea at the same time. We have seen thatat that time the society posed certain sci-entific questions, and the further develop-ment of the productive forces crucially de-pended on the solution of these problems.In that situation it is natural to expect thatmany people would be contemplating thesolution of each problem at the same time.That is exactly what had happened. TheRoyal Society records show that many peo-ple at that time were working on the prob-lems of hydrostatics, hydrodynamics, andmechanics. In fact, both Hooke and Halleyhad realized that the motion of the plan-ets must be under the action of a centralforce, and guessed that the force would fol-low an inverse square law. But, they couldnot prove that a force that goes as the in-verse square of the distance between twoobjects would mathematically imply the Ke-pler’s laws of planetary motion. Hooke andNewton were working on optics, the the-ory of colours, and the nature of light atthe same time, and had reached differentconclusions. While Hooke saw light as awave, Newton favoured a corpuscular the-ory of light. Newton and Leibniz developedthe methods of calculus at the same time.

In such a situation it is not unnatural tosee debates between scientists on the con-tent of the discoveries, and controversiesconcerning who discovered something first.Today, the primacy of a discovery is decidedon the basis of who communicated a discov-ery to a scientific journal first. At that timethere were no scientific journals or systemof recording the date when a paper is com-municated, and so it was difficult to settlethe claims. Mostly the scientists made thediscoveries while working away from eachother, and so it was impossible to ascertainwho made a discovery first. The disputesbetween Newton and Hooke on the nature


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Robert Hooke (1635-1703). Artist’simpression, drawn at a later time.

of light, and that between Newton and Leib-niz on the primacy of the discovery of calcu-lus should be seen from this angle. It maybe true that each piece of idea may havebeen worked out by different people at al-most the same time, but there is no denyingthat it was Newton who achieved the grandsynthesis — to create a system of knowl-edge which was to form the basis of scien-tific thinking for centuries to come.

There is another aspect worth keepingin mind when evaluating the contributionof Newton. We have seen that Newton’stime immediately followed the renaissancein Europe. We have seen in the last in-stallment that, through the period of the re-naissance, people like Galileo, Bacon, andDescartes charted out a new path of do-ing science. The change happened with in-credible swiftness: Copernicus’ book waspublished in 1543, Galileo died in 1642,and Newton was born in the same year.Thus, after a millennium of unquestioningsubmission to religious dogma, the “age ofreason” took root in a section of the peo-ple within a short span of only a hundredyears. But the majority of the populationwas still under the spell of the Church —

Catholic as well as Protestant. Religious ob-scurantism, bigotry, and blind beliefs werestill ruling the minds of the common people.Only among a section of the learned peo-ple the seed of doubt had been sown aboutthe correctness of beliefs propagated by theChurch. The central belief that everythingin the world is created and controlled byGod was till intact. The universities werestill centres of dry scholasticism.

Thus, in those tumultuous times, old reli-gious values were still very strong; the newoutlook based on reason had taken birth,and was in struggle with the old. Everyman’s thought process is built by absorb-ing the cross-currents of thought existingin the contemporary society. So was New-ton’s. Many commentators have not eventried to understand this aspect, and havemade Newton’s religious belief a focal pointin their evaluation. We have to understandthat this contradiction in Newton’s person-ality was only normal. The philosophicalground for the emergence of a secular mindcompletely devoid of religious influence hadnot yet been created in Europe’s intellectualatmosphere. The evaluation of any greatman has to be done on the basis of whichphilosophy — the old backward-looking lineof thought or the newly emerging line ofthought — is reflected in a greater measurein his work. Seen from this angle we findthat the newly emerging age of reason hadits best personified expression in Newton.

Why Newtonian mechanics dealta blow to idealism

What is the essential content of Newtonianmechanics? Since time immemorial peoplehad seen motion of bodies — the motionsof the sun, moon and the planets, the mo-tion of an arrow released from a bow, etc.But in the ancient time people did not knowthe reason behind the motion of materialbodies. So they assumed a supernatural


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Gottfried Wilhelm von Leibniz (1646-1716).

hand behind every motion. They thoughtthat God makes the sun, the moon, and theplanets move. They even saw a divine handdeciding the path of an arrow released froma bow. This is because, following Aristotle’stheory, people thought force produces mo-tion. Thus, wherever they saw motion, theyassumed the existence of some entity con-tinuously applying force.

Galileo showed that force does not pro-duce motion; force in fact produces achange in motion — what we know today asacceleration. Newton made it his first law— “unless acted upon by an external force,a body will continue in uniform rectilinearmotion in a straight line.” This told peoplenot to look for something applying a forcewhenever they saw motion; and to look forit only if they saw change in motion. Thusthe role of God in causing all sorts of motionbecame truncated.

But we do see many instances of changeof motion in the bodies around us. Themotion of the moon around the Earth isan instance where change of motion is tak-ing place at every instant. Who is applyingthe force in this case? Newton showed that

gravitation — a universal property of matter— is responsible for it, and that it follows adefinite mathematical rule. Thus the appli-cation of this force does not depend on thewill of God. The role of God became furtherrestricted.

Then Newton showed that if a force is ap-plied, the change in motion of any body alsofollows a definite mathematical rule: force =mass × acceleration. Using this rule onecan obtain a differential equation for themotion of any body. Now, if we know theinitial condition of motion of the body (likethe initial position and velocity), then onecan solve the differential equation to ob-tain the condition of motion at any time inthe future. He showed that the motion ofthe planets, comets, arrows, and cannon-balls can be predicted by application of thismethod.

This implies that there is no role of theGod in the motions of the planets and other“heavenly” bodies. Man can calculate theirfuture positions using the method proposedby Newton. The motion of cannonballs andarrows would simply be parabolas — thesemay only deviate a bit from the parabolicpaths due to air friction. Newton alsoshowed by how much they would deviate.Thus there remained no role for God in anytype of motion.

After being eclipsed by idealism for mil-lennia, materialism made a forceful come-back in the sphere of philosophy. This iswhat set the agenda for science for cen-turies following Newton. And this is the his-torical importance of Newton and his Prin-cipia Mathematica.

The emergence of mechanicalmaterialism

Due to the influence of religious philosophy,many people could not digest the role ofGod becoming so insignificant in their pic-ture of the world. They agreed that if some-


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thing is in motion it will always remain inmotion unless acted upon by an externalforce. But they asked, who created motionfor the first time? Who gave the first im-pulse? They pictured this as the role ofGod: giving the first push and setting theuniverse in motion. Thus came the conceptof a “Prime Mover”. Due to his own religiousbelief, Newton himself sided with this posi-tion. This was the limitation of the time:the stage was not yet set for the emergenceof a truly secular world-view. That situa-tion emerged only in the nineteenth centurywhen the idea emerged that there can benothing in absolute rest, without any mo-tion. Matter exists means it exists in mo-tion. Therefore it is unscientific to thinkthat initially all matter was at rest, and atsome point of time somebody injected mo-tion into it. It is now understood that mo-

tion is a mode of existence of matter.Newtonian mechanics created a new pic-

ture of the universe, where everything is inmotion following the fixed laws. The starsand planets are moving in specific orbitsobeying the laws of motion, like the handsof a clock. In this mental picture the wholeuniverse looks like a gigantic machine. Themotion of each specific body is like that ofa part of the machine — each part mov-ing in its own course, following fixed rules.This line of thinking gave birth to a philoso-phy which is in nature materialistic, and inthat sense it worked towards freeing peoplefrom many obscurantist ideas and miscon-ceptions, but its form was mechanical. Thehistorical importance of this philosophicaltrend, known as mechanical materialism,was that it again brought materialism to thecentre of current thought. 2


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