# An upwards falls back to the Earth. Each object

An analysis of
motion ought to begin with the Ancient Greeks3 . Since the influence of the
Greeks lasted two millennia, it is inconceivable to describe the growth of
dynamics without mentioning them. The dominant figure in the ancient
development 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 of
science for the next two thousand years. Much of his reasoning on motion
stemmed from the faulty 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 underneath fire; water below air; and finally earth resting beneath
them all. Whenever an element was taken from its natural place it would
endeavour 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 brick
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 reasoning implied that the speed of
progression in the void would be infinite; thus he concluded that the very
existence of a void 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 fallacious separation of natural and violent motion would
haunt physics for two thousand more years. The progress towards a truer
representation was slow and halting. Aristotle’s worldview became ingrained upon
both Western and Arabic science and theology. His prevalence in the latter of
these fields impacted the progression of the former. Much of it became Church
dogma. By raising his theology above and beyond criticism, it raised a
protective wall, by proxy, around his physics. The lengthy dominance of
Aristotle is now difficult to imagine. Even into the early Renaissance entire
contributions on physics from philosophers would consist 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 extensive
critiques of Aristotelian physics (Philoponus, 2006), and it is here that the
inklings of a modern approach to dynamics can be seen. Philoponus found little
satisfaction in Aristotle’s approach to motion, indeed 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 ages
In 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