An analysis ofmotion ought to begin with the Ancient Greeks3 . Since the influence of theGreeks lasted two millennia, it is inconceivable to describe the growth ofdynamics without mentioning them. The dominant figure in the ancientdevelopment of dynamics was Aristotle (384 BC– 322 BC).
His writings(Aristotle, 330 B.C.) on this and on many other subjects held sway over much ofscience for the next two thousand years. Much of his reasoning on motionstemmed from the faulty concept of the classical elements (fire, air, water andearth). Each of these is given its own natural place in the world: fire at thetop; air underneath fire; water below air; and finally earth resting beneaththem all.
Whenever an element was taken from its natural place it wouldendeavour to return. This reasoning explained why an air bubble breathedunderwater floats to the surface, and why a rock thrown upwards falls back tothe Earth. Each object was then a combination of all of these. A feather,lighter than a rock, must have more air than the rock, but less than the airitself. From this line of thinking arose “natural motion”: motion that occursdue to the nature of the object. All other motion was violent; it had aseparate cause. A brick falling to the ground would be natural, but a brickthrown through the air would be violent. Aristotle concluded that heavierobjects fall faster than light objects, and that this fall–rate is proportionalto their weights: an object twice as heavy falls twice as fast.
He alsoreasoned that the speed of progression through a medium was inversely proportionalto the density of that medium. This reasoning implied that the speed ofprogression in the void would be infinite; thus he concluded that the veryexistence of a void was impossible (Aristotle (330 B.C.), Book IV:8). arefinite), but there is no ratio of void to full. In the same section, he wrotethat if a void were to exist, heavy objects would fall at the same rate aslight ones (“Therefore all will possess equal velocities.
But this isimpossible.”). He used this supposed equality of fall rates to then say bymodus tollens that a void cannot exist. He further wrote that, in a void, therewould be no reason for a body to stay in one place or move to another, and somotion would continue forever. It is often said, based on this statement, thathe enunciated or foresaw a principle of inertia, but this is only possible by aselective reading of his works. Among the various physical questions ponderedby ancient philosophers, the question of why an arrow continues to fly after ithas left its bowstring was particularly perplexing. Aristotle reasoned that thearrow displaced the air in front of it, which rushed behind and then pushed thearrow forwards. The idea of a thing moving violently without some other thingpushing it along the way; moving without a mover, was entirely alien toAristotelians.
This fallacious separation of natural and violent motion wouldhaunt physics for two thousand more years. The progress towards a truerrepresentation was slow and halting. Aristotle’s worldview became ingrained uponboth Western and Arabic science and theology. His prevalence in the latter ofthese fields impacted the progression of the former.
Much of it became Churchdogma. By raising his theology above and beyond criticism, it raised aprotective wall, by proxy, around his physics. The lengthy dominance ofAristotle is now difficult to imagine. Even into the early Renaissance entirecontributions on physics from philosophers would consist solely of commentarieson Aristotle’s works: two millennia after they were composed. The 6th centuryAlexandrian philosopher, John Philoponus (ca. 490–ca.
570), wrote extensivecritiques of Aristotelian physics (Philoponus, 2006), and it is here that theinklings of a modern approach to dynamics can be seen. Philoponus found littlesatisfaction in Aristotle’s approach to motion, indeed he also found littlesatisfaction in his other approaches. In his commentaries he demolishedAristotle’s work on both natural and violent motion. For natural motion,Philoponus posited that an object has a natural rate of fall. Falling through amedium would hinder this natural rate: But a certain additional time isrequired because of the interference of the medium.
He introduced a naturalfall rate in the void, and subtracted from this the effect of the resistance ofthe medium. This concept allowed him to reject the Aristotelian concept thatthe speeds at which objects fall at are in proportion to their weights. He didthis with appeal to the same kind of experiment carried out in Renaissance Italyaround a millennium later4 . Philoponus did not believe in the equality offall–rates in the void.
In fact he concluded that this concept was wrong. Hisbelief was that heavier objects do fall faster than light ones in a void. Forviolent motion, he asserted that when an object is moved, it is given a finitesupply of forcing impetus5 : a supply of force that, while it lasted, wouldexplain the object’s continuing motion: Rather it is necessary to assume thatsome incorporeal motive en`ergeia is imparted by the projector to theprojectile… This incorporeal motive en`ergeia is exhausted over the course ofan object’s motion, which rests once this exhaustion is complete. This propertywas internal to the body.
He struck fairly close to some kind of rudimentaryconcept of kinetic energy. At the very least, he struck close to some conceptwhich we can now relate to kinetic energy. The conclusion of the sentencequoted above is: …and that the air set in motion contributes either nothingat all or else very little to this motion of the projectile. The strongest andmost groundbreaking insight that Philoponus made was that a medium does notplay a role in maintaining motion. It acts as a retarding force.
This notionwas in direct opposition to Aristotle, who required that the medium shouldcause the continuing motion. This paradigm shift that John Philoponusintroduced allowed him to explain that motion in a void was possible. Hislasting contribution is with these qualitative analyses. His quantitativeexplanations are without merit, although these analyses resonate throughGalileo’s dynamics. In the centuries that followed Philoponus, otherphilosophers followed in a staggering and haphazard progression towards Newton.It would be another millennium before Aristotelian motion would be disregarded.The reasons are various, but much of them are theological in nature.
Philoponus’ writings on Tritheism were declared anathema by the Church, whichled to the neglect, condemnation, and ridicule of his writings. Zimmerman had the following to say(Zimmerman, 1987): His writings, then and later, enjoyed notoriety rather thanauthority. The inferior works on mechanics from his contemporaries, such asSimplicius, were treated in a more favourable light. The middle agesIn the following centuries, the development of dynamics was very slight. Thereis a pernicious popular belief that science stood still from the fall of theWestern Roman Empire (476 A.D.) until the Renaissance: the so called Dark Ages.
While the remark may hold water for certain periods of the Early Middle Ages,it has no standing whatsoever with the High and Late Middle Ages. The idea thatthe world of understanding stood still for a millennium is a hopelesslyincorrect one. Aristotle’s views, or variations on these, were analysed furtherby the likes of the Andalusian–Arabs Avempace and Averr¨oes6 in the mid–13thcentury.
The gratitude owed to these philosophers should not be understated. Itis through their works that Philoponus’thoughts were preserved: his books were not published in Western Europe untilthe early 16th century. Averr¨oes wrote such extensive treatises onAristotelian physics and theology that he was nicknamed The Commentator byThomas Aquinas. The intellectual stupor existed in the West because anAristotelian theological worldview was dogma. Those studying mechanics werereticent to go further than simple reinterpretation of Aristotle, even when somuch of it was clearly wrong. The stimulus that reinvigorated the field can betraced to the Condemnations of 1277. In this year, Tempier, the Bishop ofParis, condemned various doctrines enveloping much of radical Aristoelianismand Averr¨oeism, among others. This event is important because the condemnationof Aristotle’s theology led philosophers to question the truth of the rest ofhis worldview.
Deviating from dogma was then, and remained for centuries more,very dangerous for philosophers, but now Aristotle’s physics were no longerprotected. The importance of the Condemnations led to what Duhem (1917) called: …a large movement that liberated Christianthought from the shackles of Peripatetic and Neoplatonic philosophy andproduced what the Renaissance archaically called the science of the ‘Moderns.’Soon after, in the early 14th century, the Oxford Calculators7 explained, in akinematic sense, the motion of objects under uniform acceleration. Importantly,these men did not concentrate solely on the qualitative description of motion.What was previously a murky description of motion became a quantitativederivation.
They answered kinematic questions numerically. What is fantastic isthat the notion of instantaneous speed was within their grasp, even without thestrong grip afforded us by calculus. The mean–speed theorem dates from thisperiod, and is attributed to William Heytesbury8 . That theorem sprung from theinvestigations into how two bodies moving along a path at different speedsmight arrive at an endpoint at the same time (see the essay “Laws of Motion inMedieval Physics” in Moody (1975)). They were additionally responsible forseparating motion itself from its causes: the separation of kinematics andkinetics. Bradwardine9 also noted: All mixed bodies10 of similar compositionwill move at equal speeds in a vacuum. The statement above shows that theMertonians were well aware of the principle that objects of the samecomposition fall at the same rate, regardless of their mass. The fall rateswere still explained in terms of the nonsense classical elements of AncientGreece, but they were explained.
Within their work can be found thoroughanalyses of uniform and accelerated motion. Their analytical approaches tomotion were well received Europe–wide. French priest Jean Buridan (1300–1358)was by most accounts the giant of fourteenth century philosopy. He expounded atheory that can properly be described as an early and rudimentary concept ofwhat we now call inertia. He posited in a similar manner to Philoponus that themotion of an object was internal to it, and importantly recognised that thisimpetus does not dissipate through its own motion: that something else must actupon the object to slow its motion. His insights into the implications of thiswere more advanced than anything prior. In discussing a thrown projectile, hesaid that it would: .
..continue to be moved as long as the impetus remainedstronger than the resistance and would be of infinite duration were it notdiminished and corrupted by a contrary force resisting it or by somethinginclining it to a contrary motion. His statement is an early and rudimentarynotion that is qualitatively similar to Newton’s First Law. He entertained thisnotion of infinite motion, a full three centuries before. His talent indescriptions of the qualitative properties was not matched by his talent in thequantitative. Buridan’s student, NicoloOresm`e (ca.
1323–1382), developed geometrical descriptions of motion. Morethan that, he used geometry as a method of explaining the variations of anyphysical quantity. As great as this was, he had a poorer understanding ofdynamics than his tutor, and treated impetus as something which decays withmotion (Wallace, 1981). Oresm`e’swork is a prime example of the stumbling advancement of dynamics: it was rarethat any one person could advance in all areas at once.
Albert of Saxony (ca. 1316–1390), another student of Buridan, tookimpetus theory forwards in projectile motion. For an object propelledhorizontally, he reasoned that the motion had three distinct periods. The firstof these was purely horizontal, where the body moved by its own impetus. Thesecond was a curve towards the ground, as gravity began to take effect. Thethird was a vertical drop, as gravity took over and impetus died. Althoughmaintaining the distinction between natural and violent motion, Albert at leastcame closer to the true shape of projectile motion.
It is quite difficult toconceive the true effect that the philosophers from the Oxford and Parisianschools had on mechanics, and on science in general. Mechanics had moved fromindistinct qualities into defined quantities: if an object moves at this speed,how far does it go in this amount of time? If an object accelerates in thismanner, what will its speed be after a given period? These questions were askedand answered. Shortly after Giovannia diCasal`e (d. ca. 1375) returned to Genoa from studying at Oxbridge, hedeveloped a geometric approach in his book “On the velocity of the motion ofalteration” similar to that of Oresm`e. This work influenced the Venetian, Giambattista Benedetti, in his 1553demonstration of the equality of fall–rates.
The influence that Casali’sgeometric approach wielded is evident while reading Galileo’s works onkinematics. An important point is then evident: the field of kinematics hadleapt ahead of dynamics. Truesdell(1968) speaks of the impact of the Calculators in the following glowingterms: In principle, the qualities of Greek physics were replaced, at least formotions, by the numerical quantities that have ruled Western science eversince.
While kinematics was becoming more and more capable of describing bothuniform and accelerated motion, and was able to quantify these analytically,numerically and geometrically, philosophers remained unable to explain the whybehind them. The causes of motion, now separate and distinct from kinematics,were not very much closer to being discovered. This situation changed verylittle until the late 16th century.