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The theory of impetus was an auxiliary or secondary theory of Aristotelian dynamics, put forth initially to explain
projectile motion Projectile motion is a form of motion experienced by an object or particle (a projectile) that is projected in a gravitational field, such as from Earth's surface, and moves along a curved path under the action of gravity only. In the particul ...
against
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
. It was introduced by
John Philoponus John Philoponus (Greek: ; ; c. 490 – c. 570), also known as John the Grammarian or John of Alexandria, was a Byzantine Greek philologist, Aristotelian commentator, Christian theologian and an author of a considerable number of philosophical tr ...
in the 6th century, and elaborated by Nur ad-Din al-Bitruji at the end of the 12th century. The theory was modified by
Avicenna Ibn Sina ( fa, ابن سینا; 980 – June 1037 CE), commonly known in the West as Avicenna (), was a Persian polymath who is regarded as one of the most significant physicians, astronomers, philosophers, and writers of the Islamic ...
in the 11th century and
Abu'l-Barakāt al-Baghdādī Abu'l-Barakāt Hibat Allah ibn Malkā al-Baghdādī ( ar, أبو البركات هبة الله بن ملكا البغدادي; c. 1080 – 1164 or 1165 CE) was an Islamic philosopher, physician and physicist of Jewish descent from Baghdad, Iraq. ...
in the 12th century, before it was later established in Western scientific thought by
Jean Buridan Jean Buridan (; Latin: ''Johannes Buridanus''; – ) was an influential 14th-century French philosopher. Buridan was a teacher in the faculty of arts at the University of Paris for his entire career who focused in particular on logic and the wor ...
in the 14th century. It is the intellectual precursor to the concepts of
inertia Inertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his first law ...
,
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass ...
and
acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by ...
in
classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classi ...
.


Aristotelian theory

Aristotelian physics is the form of
natural science Natural science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer review and repeatab ...
described in the works of the
Greek philosopher Ancient Greek philosophy arose in the 6th century BC, marking the end of the Greek Dark Ages. Greek philosophy continued throughout the Hellenistic period and the period in which Greece and most Greek-inhabited lands were part of the Roman Empire ...
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
(384–322 BC). In his work ''
Physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
'', Aristotle intended to establish general principles of change that govern all natural bodies, both living and inanimate, celestial and terrestrial – including all motion, quantitative change, qualitative change, and substantial change. Aristotle describes two kinds of motion: "violent" or "unnatural motion", such as that of a thrown stone, in the ''Physics'' (254b10), and "natural motion", such as of a falling object, in ''On the Heavens'' (300a20). In violent motion, as soon as the agent stops causing it, the motion stops also: in other words, the natural state of an object is to be at rest, since Aristotle does not address
friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of ...
.


Philoponan theory

In the 6th century,
John Philoponus John Philoponus (Greek: ; ; c. 490 – c. 570), also known as John the Grammarian or John of Alexandria, was a Byzantine Greek philologist, Aristotelian commentator, Christian theologian and an author of a considerable number of philosophical tr ...
partly accepted Aristotle's theory that "continuation of motion depends on continued action of a force," but modified it to include his idea that the hurled body acquires a motive power or inclination for forced movement from the agent producing the initial motion and that this power secures the continuation of such motion. However, he argued that this impressed virtue was temporary: that it was a self-expending inclination, and thus the violent motion produced comes to an end, changing back into natural motion.


Arabic theories

In the 11th century,
Avicenna Ibn Sina ( fa, ابن سینا; 980 – June 1037 CE), commonly known in the West as Avicenna (), was a Persian polymath who is regarded as one of the most significant physicians, astronomers, philosophers, and writers of the Islamic ...
(Ibn Sīnā) discussed Philoponus' theory in '' The Book of Healing'', in Physics IV.14 he says: Ibn Sīnā agreed that an impetus is imparted to a projectile by the thrower, but unlike Philoponus, who believed that it was a temporary virtue that would decline even in a vacuum, he viewed it as persistent, requiring external forces such as
air resistance In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding flu ...
to dissipate it. Ibn Sina made distinction between 'force' and 'inclination' (called "mayl"), and argued that an object gained mayl when the object is in opposition to its natural motion. Therefore, he concluded that continuation of motion is attributed to the inclination that is transferred to the object, and that object will be in motion until the mayl is spent. He also claimed that a projectile in a vacuum would not stop unless it is acted upon, which is consistent with Newton's concept of inertia. This idea (which dissented from the Aristotelian view) was later described as "impetus" by
Jean Buridan Jean Buridan (; Latin: ''Johannes Buridanus''; – ) was an influential 14th-century French philosopher. Buridan was a teacher in the faculty of arts at the University of Paris for his entire career who focused in particular on logic and the wor ...
, who may have been influenced by Ibn Sina.Sayili, Aydin. "Ibn Sina and Buridan on the Motion the Projectile". Annals of the New York Academy of Sciences vol. 500(1). p.477-482. In the 12th century, Hibat Allah Abu'l-Barakat al-Baghdaadi adopted Philoponus' theory of impetus. In his ''Kitab al-Mu'tabar'', Abu'l-Barakat stated that the mover imparts a violent inclination (''mayl qasri'') on the moved and that this diminishes as the moving object distances itself from the mover. Like Philoponus, and unlike Ibn Sina, al-Baghdaadi believed that the ''mayl'' self-extinguishes itself. He also proposed an explanation of the acceleration of falling bodies where "one mayl after another" is successively applied, because it is the falling body itself which provides the mayl, as opposed to shooting a bow, where only one violent mayl is applied. According to
Shlomo Pines Shlomo Pines (; ; August 5, 1908 in Charenton-le-Pont – January 9, 1990 in Jerusalem) was an Israeli scholar of Jewish and Islamic philosophy, best known for his English translation of Maimonides' ''Guide of the Perplexed''. Biography Pines ...
, al-Baghdaadi's theory was
the oldest negation of Aristotle's fundamental dynamic law amely, that a constant force produces a uniform motion nd is thus ananticipation in a vague fashion of the fundamental law of
classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classi ...
amely, that a force applied continuously produces acceleration
Jean Buridan Jean Buridan (; Latin: ''Johannes Buridanus''; – ) was an influential 14th-century French philosopher. Buridan was a teacher in the faculty of arts at the University of Paris for his entire career who focused in particular on logic and the wor ...
and
Albert of Saxony en, Frederick Augustus Albert Anthony Ferdinand Joseph Charles Maria Baptist Nepomuk William Xavier George Fidelis , image = Albert of Saxony by Nicola Perscheid c1900.jpg , image_size = , caption = Photograph by Nicola Persch ...
later refer to Abu'l-Barakat in explaining that the acceleration of a falling body is a result of its increasing impetus.


Buridanist impetus

In the 14th century, Jean Buridan postulated the notion of motive force, which he named impetus. Buridan gives his theory a mathematical value: impetus = weight x velocity Buridan's pupil Dominicus de Clavasio in his 1357 ''De Caelo'', as follows: :"When something moves a stone by violence, in addition to imposing on it an actual force, it impresses in it a certain impetus. In the same way gravity not only gives motion itself to a moving body, but also gives it a motive power and an impetus, ...". Buridan's position was that a moving object would ''only'' be arrested by the resistance of the air and the weight of the body which would oppose its impetus. Buridan also maintained that impetus was proportional to speed; thus, his initial idea of impetus was similar in many ways to the modern concept of
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass ...
. Buridan saw his theory as only a modification to Aristotle's basic philosophy, maintaining many other
peripatetic Peripatetic may refer to: *Peripatetic school The Peripatetic school was a school of philosophy in Ancient Greece. Its teachings derived from its founder, Aristotle (384–322 BC), and ''peripatetic'' is an adjective ascribed to his followers. ...
views, including the belief that there was still a fundamental difference between an object in motion and an object at rest. Buridan also maintained that impetus could be not only linear, but also circular in nature, causing objects (such as celestial bodies) to move in a circle. Buridan pointed out that neither Aristotle's
unmoved movers The unmoved mover ( grc, ὃ οὐ κινούμενον κινεῖ, ho ou kinoúmenon kineî, that which moves without being moved) or prime mover ( la, primum movens) is a concept advanced by Aristotle as a primary cause (or first uncaused cau ...
nor Plato's souls are in the Bible, so he applied impetus theory to the eternal rotation of the celestial spheres by extension of a terrestrial example of its application to rotary motion in the form of a rotating millwheel that continues rotating for a long time after the originally propelling hand is withdrawn, driven by the impetus impressed within it. He wrote on the celestial impetus of the spheres as follows: :"God, when He created the world, moved each of the celestial orbs as He pleased, and in moving them he impressed in them impetuses which moved them without his having to move them any more...And those impetuses which he impressed in the celestial bodies were not decreased or corrupted afterwards, because there was no inclination of the celestial bodies for other movements. Nor was there resistance which would be corruptive or repressive of that impetus." However, by discounting the possibility of any resistance either due to a contrary inclination to move in any opposite direction or due to any external resistance, he concluded their impetus was therefore not corrupted by any resistance. Buridan also discounted any inherent resistance to motion in the form of an inclination to rest within the spheres themselves, such as the inertia posited by Averroes and Aquinas. For otherwise that resistance would destroy their impetus, as the anti-Duhemian historian of science Annaliese Maier maintained the Parisian impetus dynamicists were forced to conclude because of their belief in an inherent ''inclinatio ad quietem'' or inertia in all bodies. This raised the question of why the motive force of impetus does not therefore move the spheres with infinite speed. One impetus dynamics answer seemed to be that it was a secondary kind of motive force that produced uniform motion rather than infinite speed, rather than producing uniformly accelerated motion like the primary force did by producing constantly increasing amounts of impetus. However, in his ''Treatise on the heavens and the world'' in which the heavens are moved by inanimate inherent mechanical forces, Buridan's pupil Oresme offered an alternative Thomist inertial response to this problem. His response was to posit a resistance to motion inherent in the heavens (i.e. in the spheres), but which is only a resistance to acceleration beyond their natural speed, rather than to motion itself, and was thus a tendency to preserve their natural speed. Buridan's thought was followed up by his pupil Albert of Saxony (1316–1390), by writers in Poland such as
John Cantius John Cantius ( la, Joannes Cantius; pl, Jan z Kęt or ; 23 June 1390 – 24 December 1473) was a Polish priest, scholastic philosopher, physicist and theologian. Biography John Cantius was born in Kęty, a small town near Oświęcim, Pola ...
, and the
Oxford Calculators The Oxford Calculators were a group of 14th-century thinkers, almost all associated with Merton College, Oxford; for this reason they were dubbed "The Merton School". These men took a strikingly logical and mathematical approach to philosoph ...
. Their work in turn was elaborated by
Nicole Oresme Nicole Oresme (; c. 1320–1325 – 11 July 1382), also known as Nicolas Oresme, Nicholas Oresme, or Nicolas d'Oresme, was a French philosopher of the later Middle Ages. He wrote influential works on economics, mathematics, physics, astrology an ...
who pioneered the practice of demonstrating laws of motion in the form of graphs.


The tunnel experiment and oscillatory motion

The Buridan impetus theory developed one of the most important
thought experiments A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences. History The ancient Greek ''deiknymi'' (), or thought experiment, "was the most anci ...
in the history of science, the 'tunnel-experiment'. This experiment incorporated oscillatory and pendulum motion into dynamical analysis and the science of motion for the first time. It also established one of the important principles of classical mechanics. The pendulum was crucially important to the development of mechanics in the 17th century. The tunnel experiment also gave rise to the more generally important axiomatic principle of Galilean, Huygenian and Leibnizian dynamics, namely that a body rises to the same height from which it has fallen, a principle of
gravitational potential energy Gravitational energy or gravitational potential energy is the potential energy a massive object has in relation to another massive object due to gravity. It is the potential energy associated with the gravitational field, which is released (conver ...
. As
Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He ...
expressed this fundamental principle of his dynamics in his 1632 '' Dialogo'': This imaginary experiment predicted that a cannonball dropped down a tunnel going straight through the Earth's centre and out the other side would pass the centre and rise on the opposite surface to the same height from which it had first fallen, driven upwards by the gravitationally created impetus it had continually accumulated in falling to the centre. This impetus would require a violent motion correspondingly rising to the same height past the centre for the now opposing force of gravity to destroy it all in the same distance which it had previously required to create it. At this turning point the ball would then descend again and oscillate back and forth between the two opposing surfaces about the centre infinitely in principle. The tunnel experiment provided the first dynamical model of oscillatory motion, specifically in terms of A-B impetus dynamics. This thought-experiment was then applied to the dynamical explanation of a real world oscillatory motion, namely that of the pendulum. The oscillating motion of the cannonball was compared to the motion of a pendulum bob by imagining it to be attached to the end of an immensely long cord suspended from the vault of the fixed stars centred on the Earth. The relatively short arc of its path through the distant Earth was practically a straight line along the tunnel. Real world pendula were then conceived of as just micro versions of this 'tunnel pendulum', but with far shorter cords and bobs oscillating above the Earth's surface in arcs corresponding to the tunnel as their oscillatory midpoint was dynamically assimilated to the tunnel's centre. Through such '
lateral thinking Lateral thinking is a manner of solving problems using an indirect and creative approach via reasoning that is not immediately obvious. It involves ideas that may not be obtainable using only traditional step-by-step logic. The term was first u ...
', its lateral horizontal motion that was conceived of as a case of gravitational free-fall followed by violent motion in a recurring cycle, with the bob repeatedly travelling through and beyond the motion's vertically lowest but horizontally middle point that substituted for the Earth's centre in the tunnel pendulum. The lateral motions of the bob first towards and then away from the normal in the downswing and upswing become lateral downward and upward motions in relation to the horizontal rather than to the vertical. The orthodox Aristotelians saw pendulum motion as a dynamical anomaly, as 'falling to rest with difficulty.'
Thomas Kuhn Thomas Samuel Kuhn (; July 18, 1922 – June 17, 1996) was an American philosopher of science whose 1962 book '' The Structure of Scientific Revolutions'' was influential in both academic and popular circles, introducing the term ''paradig ...
wrote in his 1962 ''The Structure of Scientific Revolutions'' on the impetus theory's novel analysis it was not falling with any dynamical difficulty at all in principle, but was rather falling in repeated and potentially endless cycles of alternating downward gravitationally natural motion and upward gravitationally violent motion. Galileo eventually appealed to pendulum motion to demonstrate that the speed of gravitational free-fall is the same for all unequal weights by virtue of dynamically modelling pendulum motion in this manner as a case of cyclically repeated gravitational free-fall along the horizontal in principle. The tunnel experiment was a crucial experiment in favour of impetus dynamics against both orthodox Aristotelian dynamics without any auxiliary impetus theory and Aristotelian dynamics with its H-P variant. According to the latter two theories, the bob cannot possibly pass beyond the normal. In orthodox Aristotelian dynamics there is no force to carry the bob upwards beyond the centre in violent motion against its own gravity that carries it to the centre, where it stops. When conjoined with the Philoponus auxiliary theory, in the case where the cannonball is released from rest, there is no such force because either all the initial upward force of impetus originally impressed within it to hold it in static dynamical equilibrium has been exhausted, or if any remained it would act in the opposite direction and combine with gravity to prevent motion through and beyond the centre. The cannonball being positively hurled downwards could not possibly result in an oscillatory motion either. Although it could then possibly pass beyond the centre, it could never return to pass through it and rise back up again. It would be logically possible for it to pass beyond the centre if upon reaching the centre some of the constantly decaying downward impetus remained and still was sufficiently stronger than gravity to push it beyond the centre and upwards again, eventually becoming weaker than gravity. The ball would then be pulled back towards the centre by its gravity but could not then pass beyond the centre to rise up again, because it would have no force directed against gravity to overcome it. Any possibly remaining impetus would be directed 'downwards' towards the centre, in the same direction it was originally created. Thus pendulum motion was dynamically impossible for both orthodox Aristotelian dynamics and also for H-P impetus dynamics on this 'tunnel model' analogical reasoning. It was predicted by the impetus theory's tunnel prediction because that theory posited that a continually accumulating downwards force of impetus directed towards the centre is acquired in natural motion, sufficient to then carry it upwards beyond the centre against gravity, and rather than only having an initially upwards force of impetus away from the centre as in the theory of natural motion. So the tunnel experiment constituted a crucial experiment between three alternative theories of natural motion. Impetus dynamics was to be preferred if the Aristotelian science of motion was to incorporate a dynamical explanation of pendulum motion. It was also to be preferred more generally if it was to explain other oscillatory motions, such as the to and fro vibrations around the normal of musical strings in tension, such as those of a guitar. The analogy made with the gravitational tunnel experiment was that the tension in the string pulling it towards the normal played the role of gravity, and thus when plucked (i.e. pulled away from the normal) and then released, it was the equivalent of pulling the cannonball to the Earth's surface and then releasing it. Thus the musical string vibrated in a continual cycle of the alternating creation of impetus towards the normal and its destruction after passing through the normal until this process starts again with the creation of fresh 'downward' impetus once all the 'upward' impetus has been destroyed. This positing of a dynamical family resemblance of the motions of pendula and vibrating strings with the paradigmatic tunnel-experiment, the origin of all oscillations in the history of dynamics, was one of the greatest imaginative developments of medieval Aristotelian dynamics in its increasing repertoire of dynamical models of different kinds of motion. Shortly before Galileo's theory of impetus,
Giambattista Benedetti Giambattista (Gianbattista) Benedetti (August 14, 1530 – January 20, 1590 in) was an Italian mathematician from Venice who was also interested in physics, mechanics, the construction of sundials, and the science of music. Science of moti ...
modified the growing theory of impetus to involve linear motion alone:
... nyportion of corporeal matter which moves by itself when an impetus has been impressed on it by any external motive force has a natural tendency to move on a rectilinear, not a curved, path.Giovanni Benedetti, selection from ''Speculationum'', in Stillman Drake and I.E. Drabkin, ''Mechanics in Sixteenth Century Italy'' (The University of Wisconsin Press, 1969), p. 156.
Benedetti cites the motion of a rock in a sling as an example of the inherent linear motion of objects, forced into circular motion.


See also

*
Conatus In the philosophy of Baruch Spinoza, conatus (; :wikt:conatus; Latin for "effort; endeavor; impulse, inclination, tendency; undertaking; striving") is an innate inclination of a thing to continue to exist and enhance itself. This "thing" may b ...
*
Physics in the medieval Islamic world The natural sciences saw various advancements during the Golden Age of Islam (from roughly the mid 8th to the mid 13th centuries), adding a number of innovations to the Transmission of the Classics (such as Aristotle, Ptolemy, Euclid, Neoplatonism ...
*
History of science The history of science covers the development of science from ancient times to the present. It encompasses all three major branches of science: natural, social, and formal. Science's earliest roots can be traced to Ancient Egypt and Meso ...


References and footnotes


Bibliography

* * * Duhem, Pierre. 906–13 ''Etudes sur Leonard de Vinci'' *Duhem, Pierre, ''History of Physics'', Section IX, XVI and XVII in ''The Catholic Encyclopedia

* * * * * * * * * * * {{DEFAULTSORT:Theory of Impetus Natural philosophy Classical mechanics Obsolete theories in physics