An in the null would be infinite;

An analysis of motion need to begin with the Ancient Greeks . Since the effect  of the Greeks lasted two millennia, it is unthinkable to describe the growth of dynamics without noting on  them. The dominant figure in the ancient evolution of dynamics was Aristotle (384 BC– 322 BC). His writings (Aristotle, 330 B.C.) on this and on many other subjects  held affect  over much of science for the next two thousand years. Much of his reasoning on motion emanated from the wrong concept of the classical elements (fire, air, water and earth). Each of these is given its own natural place in the world: fire at the top; air infra fire; water below air; and finally earth resting beneath them all. Whenever an element was taken from its natural place it would attempt to return. This reasoning explained why an air bubble breathed underwater floats to the surface, and why a rock thrown upwards falls back to the 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 air itself. From this line of thinking arose “natural motion”: motion that occurs due to the nature of the object. All other motion was violent; it had a separate cause. A brick falling to the ground would be natural, but a sett thrown through the air would be violent. Aristotle concluded that heavier objects fall faster than light objects, and that this fall–rate is proportional to their weights: an object twice as heavy falls twice as fast. He also reasoned that the speed of progression through a medium was inversely proportional to the density of that medium. This intellection implied that the speed of progression in the null would be infinite; thus he concluded that the very existence of a null was impossible (Aristotle (330 B.C.), Book IV:8). are finite), but there is no ratio of void to full. In the same section, he wrote that if a void were to exist, heavy objects would fall at the same rate as light ones (“Therefore all will possess equal velocities. But this is impossible.”). He used this supposed equality of fall rates to then say by modus tollens that a void cannot exist. He further wrote that, in a void, there would be no reason for a body to stay in one place or move to another, and so motion would continue forever. It is often said, based on this statement, that he enunciated or foresaw a principle of inertia, but this is only possible by a selective reading of his works. Among the various physical questions pondered by ancient philosophers, the question of why an arrow continues to fly after it has left its bowstring was particularly perplexing. Aristotle reasoned that the arrow displaced the air in front of it, which rushed behind and then pushed the arrow forwards. The idea of a thing moving violently without some other thing pushing it along the way; moving without a mover, was entirely alien to Aristotelians. This deceptive division of natural and violent motion would haunt physics for two thousand more years. The progress towards a real proxy was slow and halting. Aristotle’s worldview became rooted into both Western and Arabic science and divinity. His dominance in the last of these fields impacted the progression of the late. A lot  of it became Church belief. By raising his theology above and over roast, it raised a protective wall, by proxy, around his physics. The lengthy dominance of Aristotle is now difficult to think up. Nay into the early Renaissance totsl contributions on physics from philosophers would hold solely of commentaries on Aristotle’s works: two millennia after they were composed. The 6th century Alexandrian philosopher, John Philoponus (ca. 490–ca. 570), wrote large censures of Aristotelian physics (Philoponus, 2006), and it is here that the intimation of a modern coming to dynamics can be seen. Philoponus found little satisfaction in Aristotle’s coming to motion,actually  he also found little satisfaction in his other approaches. In his commentaries he demolished Aristotle’s work on both natural and violent motion.For natural motion, Philoponus posited that an object has a natural rate of fall. Falling through a medium would hinder this natural rate: But a certain additional time is required because of the interference of the medium. He introduced a natural fall rate in the void, and subtracted from this the effect of the resistance of the medium. This concept allowed him to reject the Aristotelian concept that the speeds at which objects fall at are in proportion to their weights. He did this with appeal to the same kind of experiment carried out in Renaissance Italy around a millennium later4 . Philoponus did not believe in the equality of fall–rates in the void. In fact he concluded that this concept was wrong. His belief was that heavier objects do fall faster than light ones in a void. For violent motion, he asserted that when an object is moved, it is given a finite supply of forcing impetus5 : a supply of force that, while it lasted, would explain the object’s continuing motion: Rather it is necessary to assume that some incorporeal motive en`ergeia is imparted by the projector to the projectile… This incorporeal motive en`ergeia is exhausted over the course of an object’s motion, which rests once this exhaustion is complete. This property was internal to the body. He struck fairly close to some kind of rudimentary concept of kinetic energy. At the very least, he struck close to some concept which we can now relate to kinetic energy. The conclusion of the sentence quoted above is: …and that the air set in motion contributes either nothing at all or else very little to this motion of the projectile. The strongest and most groundbreaking insight that Philoponus made was that a medium does not play a role in maintaining motion. It acts as a retarding force. This notion was in direct opposition to Aristotle, who required that the medium should cause the continuing motion. This paradigm shift that John Philoponus introduced allowed him to explain that motion in a void was possible. His lasting contribution is with these qualitative analyses. His quantitative explanations are without merit, although these analyses resonate through Galileo’s dynamics. In the centuries that followed Philoponus, other philosophers 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, which led 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 than authority. The inferior works on mechanics from his contemporaries, such as Simplicius, were treated in a more favourable light. The middle agesIn the following centuries, the development of dynamics was very slight. There is a pernicious popular belief that science stood still from the fall of the Western 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 that the world of understanding stood still for a millennium is a hopelessly incorrect one. Aristotle’s views, or variations on these, were analysed further by the likes of the Andalusian–Arabs Avempace and Averr¨oes6 in the mid–13th century. The gratitude owed to these philosophers should not be understated. It is through their works that Philoponus’ thoughts were preserved: his books were not published in Western Europe until the early 16th century. Averr¨oes wrote such extensive treatises on Aristotelian physics and theology that he was nicknamed The Commentator by Thomas Aquinas. The intellectual stupor existed in the West because an Aristotelian theological worldview was dogma. Those studying mechanics were reticent to go further than simple reinterpretation of Aristotle, even when so much of it was clearly wrong. The stimulus that reinvigorated the field can be traced to the Condemnations of 1277. In this year, Tempier, the Bishop of Paris, condemned various doctrines enveloping much of radical Aristoelianism and Averr¨oeism, among others. This event is important because the condemnation of Aristotle’s theology led philosophers to question the truth of the rest of his worldview. Deviating from dogma was then, and remained for centuries more, very dangerous for philosophers, but now Aristotle’s physics were no longer protected. The importance of the Condemnations led to what Duhem (1917) called: …a large movement that liberated Christian thought from the shackles of Peripatetic and Neoplatonic philosophy and produced what the Renaissance archaically called the science of the ‘Moderns.’ Soon after, in the early 14th century, the Oxford Calculators7 explained, in a kinematic 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 quantitative derivation. They answered kinematic questions numerically. What is fantastic is that the notion of instantaneous speed was within their grasp, even without the strong grip afforded us by calculus. The mean–speed theorem dates from this period, and is attributed to William Heytesbury8 . That theorem sprung from the investigations into how two bodies moving along a path at different speeds might arrive at an endpoint at the same time (see the essay “Laws of Motion in Medieval Physics” in Moody (1975)). They were additionally responsible for separating motion itself from its causes: the separation of kinematics and kinetics. Bradwardine9 also noted: All mixed bodies10 of similar composition will move at equal speeds in a vacuum. The statement above shows that the Mertonians were well aware of the principle that objects of the same composition fall at the same rate, regardless of their mass. The fall rates were still explained in terms of the nonsense classical elements of Ancient Greece, but they were explained. Within their work can be found thorough analyses of uniform and accelerated motion. Their analytical approaches to motion were well received Europe–wide. French priest Jean Buridan (1300–1358) was by most accounts the giant of fourteenth century philosopy. He expounded a theory that can properly be described as an early and rudimentary concept of what we now call inertia. He posited in a similar manner to Philoponus that the motion of an object was internal to it, and importantly recognised that this impetus does not dissipate through its own motion: that something else must act upon the object to slow its motion. His insights into the implications of this were more advanced than anything prior. In discussing a thrown projectile, he said that it would: …continue to be moved as long as the impetus remained stronger than the resistance and would be of infinite duration were it not diminished and corrupted by a contrary force resisting it or by something inclining it to a contrary motion. His statement is an early and rudimentary notion that is qualitatively similar to Newton’s First Law. He entertained this notion of infinite motion, a full three centuries before. His talent in descriptions of the qualitative properties was not matched by his talent in the quantitative. Buridan’s student, Nicolo Oresm`e (ca. 1323–1382), developed geometrical descriptions of motion. More than that, he used geometry as a method of explaining the variations of any physical quantity. As great as this was, he had a poorer understanding of dynamics than his tutor, and treated impetus as something which decays with motion (Wallace, 1981). Oresm`e’s work is a prime example of the stumbling advancement of dynamics: it was rare that any one person could advance in all areas at once. Albert of Saxony (ca. 1316–1390), another student of Buridan, took impetus theory forwards in projectile motion. For an object propelled horizontally, he reasoned that the motion had three distinct periods. The first of these was purely horizontal, where the body moved by its own impetus. The second was a curve towards the ground, as gravity began to take effect. The third was a vertical drop, as gravity took over and impetus died. Although maintaining the distinction between natural and violent motion, Albert at least came closer to the true shape of projectile motion. It is quite difficult to conceive the true effect that the philosophers from the Oxford and Parisian schools had on mechanics, and on science in general. Mechanics had moved from indistinct 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 this manner, what will its speed be after a given period? These questions were asked and answered. Shortly after Giovannia di Casal`e (d. ca. 1375) returned to Genoa from studying at Oxbridge, he developed a geometric approach in his book “On the velocity of the motion of alteration” similar to that of Oresm`e. This work influenced the Venetian, Giambattista Benedetti, in his 1553 demonstration of the equality of fall–rates. The influence that Casali’s geometric approach wielded is evident while reading Galileo’s works on kinematics. An important point is then evident: the field of kinematics had leapt ahead of dynamics. Truesdell (1968) speaks of the impact of the Calculators in the following glowing terms: In principle, the qualities of Greek physics were replaced, at least for motions, by the numerical quantities that have ruled Western science ever since. While kinematics was becoming more and more capable of describing both uniform and accelerated motion, and was able to quantify these analytically, numerically and geometrically, philosophers remained unable to explain the why behind them. The causes of motion, now separate and distinct from kinematics, were not very much closer to being discovered. This situation changed very little until the late 16th century.


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