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What is inertia

moved from talk:gyroscope

What is inertia and in what units is it measured?--Light current 02:16, 24 October 2005 (UTC)

My point was that inertia does not exist.;-) If it exists what are its units? How is inertia different from momentum or mass?--Light current 10:19, 24 October 2005 (UTC)

The definition I like is this one:

Inertia is really nothing at all. \"It\" was invented as the supposed cause of the non-accelerating state of rest / uniform motion. But then everyone knows that rest / uniform motion is the default, causeless state that automatically occurs when accelerational forces become absent. Inertia certainly is not a thing that \"resists\" acceleration prior to Newton\'s LAW I taking effect. Hold out a stone and then release it. Acceleration of the stone toward Earth is immediate and at it highest rate upon release. No \"resistance\", no hesitation, no \"inertia\". Any comments??--Light current 10:07, 26 October 2005 (UTC)

    • ADDED 06 December 2005** I disagree that "everyone knows that rest or uniform motion is the default." At least, they didn't know this in Newton's day. Aristotle thought rest was the default on earth and uniform motion the default in the heavens. But it is unification of heavenly and earthly laws that makes Newton's [and by default Galileo's] inertia so unique. The concept of rest and uniform motion being both the default for the heavenly bodies AND the earthly bodies was 'revolutionary'. The concept of inertia as a default state was the revolution of the millenium.
      • ADDED 01 December 2005**** This definition above is not saying that inertia doesn't exist. It is saying that inertia is an "idea", an "invention". An idea and an invention still exist even if they are not expressed in mathematical terms. The idea of "inertia" is present in Newton's first law and therefore is VERY real. The idea of inertia is the whole basis for the first law i.e. according to Isaac Asimov, inertia is the assumption upon which the first law is based. Assumptions cannot be proved and therefore do not need to be stated in mathematical formulae. Just because Newton starts with a "given", an unproved and unprovable "assumption" doesn't make that assumption non-existent. Yes it is an "imaginary concept", but "imaginary concepts" do exist. They are real. They are necessary to the formulation of any theory. One must start with an imaginary concept, a model, an assumption. That assumption becomes a real thing in the context of the theory. Without inertia being a real thing to Newton, a real assumption, a real concept then law one of Newton does not exist. They are integral. You can't say inertia doesn't exist and then say that the only thing that does exist is Newton's law one. You cannot separate the two. The idea comes before the law and creates the law. Without the idea of inertia there are no Newtonian laws of motion. Inertia was very real to Newton so it cannot be dismissed as imaginary today. His reasoning was that Aristotle postulated continual circular movement in the heavens and that laws on earth were different for Aristotle because Aristotle believed the earth was at rest. Newton knowing the earth was not at rest realized that the same laws in the heavenly bodies had to rule on earth. The same movement, inertia, existed in celestial bodies as existed on earth. It was from this reasoning more than the apple that made him believe that something on earth was making things come to rest. Take away the concept of inertia and you take away ALL of Newton's laws. Yes, inertia is a concept, a real concept, an assumption, a place to start for all of Newton's laws. Inertia is not a force as you describe above by calling it "a resistance". It is as you describe above "a default state". But only with this idea of a default state of inertia is the first law of Newton described. It was the assumption upon which the first law is based and it is the concept that is derived solely from the first law. The definition of the default state of inertia is derived as a concept from Newton's first law because it is the "given" that gave rise to Newton's first law. Inertia was Newton's way of describing the "default state". Aristotle had described the default state as "rest" (natural place). Newton contradicted or enlarged on the Aristotle default state and said that to the contrary the default state is "inertia" and upon this stone I shall build my laws of motion. Without the stone of inertia, Newton's laws do not exist. If inertia is an outdated concept, it has only become outdated since Einstein, but then we don't throw out Newtonian physics just because Einstein is more accurate. In the same way, we don't throw out the concept of inertia just because we understand things differently today since it was necessary for Newton's laws to exist.****voyajer 12/1/05

Actually, /I think the accn is almost constant.--Light current 17:57, 26 October 2005 (UTC)

  • Actually, you are fighting against your own definitions. When you describe inertia, it should not be described as a resistance to change, but as a default state maintaining its default state unless resisted.--voyajer 12/1/05


" If it exists what are its units? " Do radians/degrees exist then? I'm pretty sure angles exist, but radians/degrees are not units. They are dimensionless.

Actually, I don't think anyone has measured inertia. That is, in the first meaning of the word, not in the second meaning where inertia is considered the measure of how difficult it would be to change the inertia. But inertia in the sense of a tendency to maintain momentum would be a universal constant and a vector. I don't think the fact that we haven't measured it, doesn't mean it doesn't exist. And maybe someone has measured it and I don't personally know about it. Perhaps the measurement isn't useful scientifically. Added later that day: Actually, I've been mulling it over and inertia in its form in Newton's first law probably can't be quantified. Inertia is just a rule of the universe. It's like gravity. Gravity just happens when you get mass together. Why? No one knows. No one can really say what gravity really is. It's just a rule of the universe. You can quantify the effects of gravity, but you can't explain why it works. The same with conservation of energy (or any other conservation law) and universal symmetry. These are not quantified. They are concepts. They are the rules of the universe. Sometimes called the laws of the universe. Why do they exist? Where did they come from? What are they really? No one can say. It's just how the universe works. All we can do is tell you the effects. Inertia is a rule of the universe. In fact, inertia is probably a law. It's how things work. Once you get something in momentum, it stays that way until a force affects it. Obviously, a universal law is not meaningless. Voyajer 18:11, 8 December 2005 (UTC)

Imaginary concept

I suggest that inertia is an imaginary concept with no definition in physics. It has no units. Mass and momentum have units. But inertia is just lack of momentum. I think the article should be altered to reflect this fact. AS it stands the article is misleading.--Light current 22:28, 24 October 2005 (UTC)

Sorry inertia is not a lack of momentum. My carelessness. If inertia is a separate entity, what is the difference between it and mass? When calcluating the motion of rigid bodies, the quantity 'inertia' is never used. In fact its not used in any calculations that I know of.(Im not considering moment of inertia for rotation). Thats why I say its a misleading concept- a hangover from pre Newton days and should be described as such in this article--Light current 14:04, 25 October 2005 (UTC)

      • ADDED 01 December 2005*** Imaginary concepts are necessary to physics, they are necessary to theories, if you know anything about theoretical physics you will understand their necessity. In fact, without imaginary concepts, physics would not exist.***voyajer 12/1/05


    • Okay, so let's take this "imaginary concept" logic to the nth degree and see what you are really saying. Because right this moment you should hurriedly run over to the Euclidean Geometry page and state uncategorically that Euclidean Geometry does not exist. Well, how can it? Isn't a point without a size an imaginary concept? Isn't an infinitely straight line an imaginary concept? Isn't an infinitely sized plane an imaginary concept? Then by your logic, Euclidean Geometry does not exist. Do you get the fallacious reasoning yet?---voyajer 12/1/05


" If it exists what are its units? " Do radians/degrees exist then? I'm pretty sure angles exist, but radians/degrees are not units. They are dimensionless.

I think you don't understand theoretical physics when you ask this type of question. Theoretical physics begins with abstracts, unquantifiables. When the "idea" of the atom was first suggested as a smallest particle, we had no idea if it really existed and only through thousands of years have we come up with ideas to explain it mathematically or to quantify it. Physics is not based on reality. Physics is where someone comes up with an imaginary concept and sees if it is useful to describe reality. Neils Bohr, a founder of Quantum Mechanics, said: ``There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature." Therefore, we do not have to know the "units" of inertia yet in order to say it exists as a useful idea upon which to build physics.Voyajer 18:21, 8 December 2005 (UTC)

Most things in physics only exist as "imaginary concepts" sometimes years and decades before they are proven. Most of physics is based upon imaginary ideas. Antiparticles were imaginary ideas. The fact that something has "units" doesn't mean it is real. Most theories in physics that turn out to be false start out by having units and having mathematics. The aether of the 19th century was described in "units" and had mathematical predictions. In more recent times, the tachyon (a particle faster than light) and the tachyon field are described in units. The speed of the tachyon is given and the strength of the tachyon field is given as 8.8 X 10 to the 8th volts per centimeter. Giving something "units" doesn't make it exist. On the other hand, dark energy and dark matter still have no units per se. They are theorized due to the need for more mass and energy to account for the expansion of the universe in its present state. The point is: The property of measurement (of having "units") does not make the thing real. What makes a thing "exist" in physics is solely the property of it being useful to explain reality. The idea of inertia is useful in physics. Voyajer 19:54, 8 December 2005 (UTC)

==UNIVERSALITY== http://arxiv.org/abs/physics/0211106


Emil Marinchev, Technical University of Sofia, Physics Department, 8 Kliment Ohridski St., Sofia-1000, BG, e-mail: emar@tu-sofia.bg

Abstract: This article is an attempt for a new vision of the basics of Physics, and of Relativity, in particular. A new generalized principle of inertia is proposed, as an universal principle, based on universality of the conservation laws, not depending on the metric geometry used. The second and the third principles of Newton's mechanics are interpreted as logical consequences. The generalization of the classical principle of relativity made by Einstein as the most basic postulate in the Relativity is criticized as logically not well-founded. A new theoretical scheme is proposed based on two basic principles:

 1.The principle of universality of the conservation laws, and
 2.The principle of the universal velocity.

It is well- founded with examples of different fields of physics.

Comments: 5 pages, 1 figure, Subj-class: General Physics, Key words:Universality, New Insight in Physics

http://arxiv.org/abs/physics/0211106

http://universality.hit.bg/

Original Languages

I would like to see the originals of the quotes used in the "History" section of this article. They seem to all have been originally written in Latin. The Buridan quote seems to come from Metaphysices, book XII, question IX. Unfortunately the only online edition of this text that I can find is scanned in so poorly as to be illegible (what a waste of effort!). I have no idea where the da Vinci and Galileo quotes come from. Can anyone provide me the original texts, or at least a citation so I know where to look for them? Thanks, Iustinus 20:04, 11 August 2005 (UTC)

Hooray! I've found the Buridan quote:
...proiectum post exitum a proijciente mouetur ab impetu dato a proijciente & mouetur quamdiu durat impetus fortior quam resistentia: et in infinitum duraret impetus, nisi diminueretur & corrumperetur a resistente cõtrario vel ab inclinante ad contrarium mótum
Now can anyone tell me where the Galilieo, and da Vinci quotes come from? There are also quotes from Kepler and Descartes: these have the source listed, but not the chapter or any other information, so that would be nice to have as well. Can anyone help?
-Iustinus 21:53, 4 January 2006 (UTC)

Iustinus, the Descartes quote looks like a rather mangled version of Principle 37 of Part 2 of The Principles of Philosophy. As it stands it seems nonsense. More later on the rest, but try Leonardo's Notebooks for da Vinci quote. --80.6.94.131 19:15, 11 January 2006 (UTC)A.Bellamy

I agree that knowing the true original quotes would be beneficial.. not sure how best to include them in the article without making things too verbose and hard to follow for the average reader, but I'm up for trying to figure it out. Out of curiosity, Iustinus, can you tell us where you found the Buridan quote (ideally, document/page/etc where it was originally written by Buridan, and a URL for the resource)? -- Foogod 20:31, 11 January 2006 (UTC)
I wasn't planning on putting them in this article, actually, but the one on the Latin Wikipedia. The English should have references, for sure, and I am glad that you are seeking to add them. I would love to have the entire quotes here, but agree that it would be impractical. The Latin version, on the other hand definitely needs to have the original quotes. What would be the point of translating the English back into Latin?
The Buridan quote was exactly where I had thought it was, In Metaphysicen Aristotelis Quaestiones Argutissimae' book 12, question 9 (towards the end). I never did find a legible text of this work online (as I mention above there IS a version available, but it's scanned at low resolution, making the fraktur print utterly illegible), but as it turned out my local university library had a copy of a modern (1964) edition. This volume doesn't seem to have an ISBN number, but its library call number, if that's of any use to you, is PA 3893 .M6B9
If you really want i could track down the relevant page in the illegible online version so you could link to it, but I don't think anyone will believe that it says what we claim it says ;) --Iustinus 00:53, 12 January 2006 (UTC)

The historical misunderstanding of inertia

    A.Bellamy comments: The historical misunderstanding of inertia

Just like the standard history of inertia and its modernity thesis of an anti-Aristotelian inertial-dynamics revolution, i.e THE Scientific Revolution, this article seriously misrepresents the history of dynamics, principally in its claim that the concept of inertia, as defined here as the tendency for motion to persist in the absence of external forces, was alien to the physics of Aristotle and historically novel to the 17th century, because by this time it was at least two thousand years old. Newton himself correctly attributed endorsement of this notion and his Principia's first law of motion both to Aristotle and also to the ancient Greek atomists and the Pythagorean Anaxagoras. Hence the article's first 'History' paragraph reproduced below is to be contrasted with Newton's own contrary view that immediately follows it:

WIKIPEDIA ON INERTIA AND ARISTOTLE: "The concept of inertia is alien to the physics of Aristotle which provided the standard account of motion until the 17th century. Aristotle, and his peripatetic followers, held that a body was only maintained in motion by the action of a continuous external force. Thus, in the Aristotelian view, a projectile moving through the air would owe its continuing motion to eddies or vibrations in the surrounding medium, a phenomenon known as antiperistasis. In the absence of a proximate force, the body would come to rest immediately."

ISAAC NEWTON ON ARISTOTLE: "All those ancients knew the first law [of motion] who attributed to atoms in an infinite vacuum a motion which was rectilinear, extremely swift and perpetual because of the lack of resistance...ARISTOTLE was of the same mind, since he expresses his opinion thus [in On The Heavens, 3.2.301b]: 'If a body, destitute of gravity and levity, be moved, it is necessary that it be moved by an external force. And when it is once moved by a force, it will conserve its motion indefinitely'. And again in Book IV of the Physics, text 69, [i.e. Physics 4.8.215a19] speaking of motion in the void where there is no impediment he writes: 'Why a body once moved should come to rest anywhere no one can say. For why should it rest here rather than there ? Hence EITHER it will not be moved, OR it must be moved indefinitely, UNLESS something stronger impedes it [My caps].' " [From one of Newton's Scientific Papers in The Portsmouth Collection, first published in Hall & Hall's 1962 Unpublished Scientific Papers of Isaac Newton.]

FURTHER COMMENT: The crucial error made by the current Wikipedia analysis of Aristotle's theory of projectile motion, in common with the ahistorical conventional history of inertia and dynamics, is that it crucially overlooks the fact that the context in question in Aristotle's Physics 4.8.215a14-19 is obviously that of a projectile with gravity, which therefore has a gravitational resistance to motion that must be overcome by some sufficiently strong countervailing force in order for motion against gravity to occur, just as it does in Newtonian physics, even if this is only by the force of inertia. But in the immediately following passage Physics 4.8.215a19 quoted by Newton above, as he and others analyse it, in the crucially different case of a projectile without gravity moving in a void where there is no resistance due to any medium, it would continue moving forever without any proximate force in the absence of any external impediment. This is because in Aristotle's dynamics bodies have no inherent resistance to motion other than a gravitational resistance to any counter-gravitational motion, whereas in Newton's they also have an inherent inertial resistance to all motion except uniform straight motion. The concept of inertia, first explicitly introduced into physics by Kepler in his 1607 Astronomia Nova, apparently generalising an innovation initially due to Averroes, was an auxiliary hypothesis of Aristotelian dynamics introduced in order to protect its basic law of motion from refutation by celestial dynamics. It was introduced in order to prevent the consequence of an enforced motion (i.e. F > 0) to which there is no other resistance such as gravity or an external medium (i.e. R = 0) being infinitely fast according to Aristotle's basic law of motion that average speed v @ F/R ('@' means 'is proportional to'), because v @ F/0 in such a case, which Kepler thought to be that of planetary motion propelled by rotating sunspecks to which there is no other resistance, neither by gravity nor by any external medium. The crucial anomaly in Aristotelian dynamics it resolved, formulated at least as early as the 6th century by Philoponus, was that Aristotle had posited the celestial spheres have a perpetual mover (F > 0) but encounter no resistance (R = 0), whereby they should move with infinite speed according to the dynamical principles of Physics and On The Heavens, but observably do not, even the stellar sphere taking 24 hours to rotate. In Kepler's original notion of inertia it is a non-gravitational resistance to all motion inherent in all matter universally and is proportional to the mass of a body, whereas in Newton's marginal revision of it, it is an inherent resistance to all motion except for uniform straight motion. In Newton's 2nd law a @ F/m in his creative development of Aristotelian dynamics, it is the resistance of inertia (i.e. m > 0) that prevents the acceleration of an enforced motion being infinite.


87.74.30.128 17:45, 28 September 2005 (UTC) A.Bellamy 28 September 2005

        • ADDED 01 December 2005**** Bellamy has some nice points here, except that Aristotle believed that the heavens were a 5th element in which the laws on earth were not obeyed and in fact they contained separate universal laws. Therefore, quoting Aristotle's "On The Heavens" does not prove that he believed in inertia on earth. In fact, the truth is to the contrary. Kepler had hints of the idea of inertia but Galileo was the first to unify the laws for celestial bodies with earthly bodies and Newton was the first to generalize them.****voyajer 12/1/05

The concepts of Aristotle on force and motion can be summarize by the following equation: F = mv. To have motion you must have a force, versus today, to have motion you don't need a force i.e. principle of inertia. --24.202.163.194 00:33, 1 January 2006 (UTC)

So far as I can tell, Mr. Bellamy's points have not been fully addressed. The article still says that inertia was "alien" to Aristotelian, despite Bellamy's quotations which appear to show the contrary. The only attempt at a counterargument has been voyajers, and he only addresses the heavens. It is true that Aristotle believed the heavens were governed by different laws than was the earth, but that doesn't affect all of Bellamy's quotations. Could someone please address this? Either provide counterarguments here, or change the article? I would really like this article to reflect historical reality. --Iustinus 17:05, 5 January 2006 (UTC)


        • 06 January 2006: A. BELLAMY REPLIES TO VOYAJER'S CRITICISM OF 12 DECEMBER 2005

In spite of the promising opening complement, Voyajer's main criticism that Aristotle did not believe in "inertia on earth", whilst apparently uncritically accepting he believed in 'inertia in the heavens', fatally misunderstands the question at issue of whether the notion of 'inertial' motion (i.e. externally force-free and gravity-free motion) was entirely alien to Aristotle's physics, as Wikipedia and conventional histories claim. This is not the question of whether Aristotle's dynamics predicted 'inertial' motion on earth or in the heavens, for like Newton, Aristotle believed neither in 'inertia' on earth nor in the heavens in the sense of force-free 'inertial motion', since he believed all motion in both such regions is subject to forces such as gravity on earth or the prime mover that propells the eternally rotating celestial spheres of the heavens. In short, for both Aristotle and Newton 'inertial' motion is alien to both heaven and earth, as in modern physics, being only a purely theoretical ideal kind of motion.

Rather the key question is whether, like Newton's, Aristotle's dynamics also predicted hypothetically that there would be endless externally unforced motion in an infinite pure void without gravity if externally unimpeded, such as Newton correctly claimed it did in Physics 4.8.215a19-22, notably not mentioned by Voyajer. And rightly or wrongly, nor does any commentator I know of disagree with Newton that this is essentially a statement of 'the principle of inertia' or Newton's first law. Where they disagree is that unlike Newton (and Sir Thomas Heath in his 1949 Maths in Aristotle), they claim Aristotle denied the principle he stated.

As for Voyajer's general claim that quoting an argument from Aristotle's On The Heavens cannot prove what he believed about motion on earth, it entirely overlooks the fact that the passage in question (3.2.301b) concerns terrestrial bodies, being part of a reductio proof that sublunar bodies cannot possibly be weightless, because otherwise in violent motion they would be moved to infinity by any force whatever. This is because Aristotle's general law v @ F/R becomes v @ F/W for violent motion in which the body's gravitational weight becomes the resistance, and hence v @ F/0 for the violent (i.e. externally forced) motion of a weightless body, thus predicting infinite speed. But when this same law is also applied to the motion of the celestial spheres which Aristotle claimed to be weightless and to have no other resistance (i.e. R = 0) but to be moved by an unmoved mover (F > 0), then it predicts an infinitely fast rotation. But this is refuted by observation that such as the stellar sphere takes a day to rotate. This had become the leading problem of Aristotelian dynamics for Philoponus in the 6th century AD, which obviously presupposes both the heavens and earth were subject to the same core law of motion, v @ F/R, i.e. the unity of celestial and terrestrial dynamics, and whereby Philoponus replaced it by the universal law v @ F - R to avoid this problem. It eventually led to Averroes' (thus also Aquinas's) and Kepler's positing of inertia and inertially resistant mass to solve it whilst retaining the law v @ F/R, and then Newton's revision of Kepler's concept.

But the most important point about Aristotle's Heavens proof that a weightless body would be moved to infinity by violent motion, in spite of being invalid because it overlooks the fact that a resistant medium would prevent this, is that it clearly establishes that in Aristotle's dynamics, without their gravity bodies have no internal resistance to motion. Hence for example, it proves that the resistance to horizontal motion in Physics 7.5 that is measured by weight in its rule v @ F/W must be wholly due to gravity, since by Heavens 3.2.301b weightless bodies have no such internal resistance, rather than due to an inherent inertia that resists all motion and is measured by gravitational weight by proxy as commentators traditionally claim, thus invalidly attributing Kepler's theory of inertia to Aristotle. What it proves is the surprising fact that in Aristotle's physics bodies have horizontal weight or gravitational resistance to motion, and which became known as the 'inclinatio ad quietem' or 'tendency towards rest' on the horizontal in scholastic dynamics, as distinct from the 'tendency to a contrary notion' downward. The compounding of a horizontal uniform deceleration to rest with a continuing vertical uniform acceleration downward as the resistances to projectile motion under suitable parameters can explain the two and three stage non-parabolic projectile trajectories predicted by scholastic Aristotelian dynamics, such as depicted in Hall's The Science of Ballistics in the 17th Century, and which were possibly more realistic than Galileo's idealising parabolas. In short, the scope of gravitational resistance to motion in Aristotle's dynamics has been radically underestimated as merely a resistance to upward motion, whereas in fact it is virtually omnidirectional, resisting motion in ALL directions except for terrestrially centripetal straight downward 'natural' motion caused by gravity, or in Aristotelian terms, resisting all violent motion.

From the evidence of other translations and the logic of the argument, it seems Newton was immediately mistaken in apparently interpreting this motion in Heavens 3.2.301b as an externally unforced one after an initial push, and hence as an endless unforced motion, rather than as a violent continually externally enforced instantaneous motion, and whereby this passage was not essentially a statement of his first law. But more widely, since it establishes bodies have no non-gravitational internal resistance to motion in Aristotle's original dynamics, then it does also underwrite the counterfactual prediction by Physics 4.8.215a19-22 of an interminable externally unforced motion in a void quoted by Newton as his first law, because it establishes there would be no internal resistance to stop it.

Did Aristotle deny the principle of inertia he stated, as commentators claim ? I argue by reductio that they are wrong and Newton was right that Aristotle affirmed it. For if Aristotle had logically denied this counterfactual principle he stated, as his 20th century commentators such as Meyerson, Koyre and others claimed he did, and hence instead asserted that such a motion would be terminated, then he would have eliminated one of his intended refutations by reductio ad absurdum of the atomists' doctrine of motion in a void, namely on the ground that it is impossible because it would be interminable, and hence an absurdity because endless change is an oxymoron in Aristotle's anti-Heraclitean philosophy which defined all change as finitely completable. And the basic reason why Aristotle's dynamics variously predicted that a natural gravitational motion of a heavy body in a vacuum (Physics 4.8.215a29f) and an enforced motion of a weightless body (On The Heavens 3.2.301b) would both be infinitely fast was because it presumed bodies have no inherent internal resistance to motion other than that due to their gravity in violent (i.e. anti-gravitational) motion, and whereby R = 0 in its law of motion that average speed v @ F/R, and thus v @ F/0. And because a body completely deprived of its gravity would therefore have no internal resistance to motion whatever, thus there would be no dynamical cause that would terminate an externally unforced motion in a pure void. It would therefore be interminable, just as predicted in Physics 4.8.215a19-22, validly quoted by Newton as essentially an assertion of his Principia's first law of motion, albeit that for Newton, unlike for Aristotle, the continuation of such motion would be caused by the internal inherent force of inertia.

VOYAJER: "Kepler had hints of the idea of inertia but Galileo was the first to unify the laws for celestial bodies with earthly bodies and Newton was the first to generalize them."

KEPLER: No hint whatever inasmuch as his dynamics flatly denied the principle of 'inertial motion'. His positing that all bodies universally have a non-gravitational inherent internal resistance to all motion, which he dubbed 'inertia', entailed there could be no interminable externally unforced motion in a void, as Aristotle's dynamics predicted there would be, because it would be terminated by this inertia. His law v @ F/m becomes v @ 0/m in this case, and thus 'v' becomes zero. But Kepler's theory that bodies resist all motion is wrongly traditionally attributed to Aristotle, who presumed bodies have no such inertia whatever. The internal resistance to motion in all directions except straight downward in Aristotle's dynamics is due to gravity, not inertia. Newton's subsequent revision of Kepler's theory of inertia to exclude uniform motion from this inertial resistance restored Aristotle's ancient counterfactual 'principle of inertial motion'


        • 07 January 2006: A.BELLAMY REPLIES TO THIS COMMENT OF 1/1/06: "The concepts of Aristotle on force and motion can be summarize by the following equation: F = mv. To have motion you must have a force, versus today, to have motion you don't need a force i.e. principle of inertia."

1) "To have motion you must have a force, versus today, to have motion you don't need a force i.e. principle of inertia."

This slogan is the standard misrepresentation of the history of dynamics that creates the false impression that there was an anti-Aristotelian inertial-dynamics revolution that inaugurated a post-medieval modernity of science, culture and the Enlightenment. More generally it fuels the notion that scientific development is revolutionary rather than evolutionary, such as developed by Thomas Kuhn for whose model of scientific revolutions it was the original paradigm as the mother of all such. But this revolutionism tends to depend upon air-brushing out the continuity and missing conceptual links in the historical narrative that crucially reveal an evolutionary reformation of theoretical systems rather than wholesale revolution and their total replacement, such as key passages from Aristotle and Newton as we have cited above have been overlooked.

The radically false impression this slogan creates is that whereas all motion required a force in Aristotle's dynamics, it does not in Newton's and subsequent. But this invalidly contrasts Aristotle's theory of motion in the real world with Newton's theory of a purely ideal uniform motion in unrealisable circumstances, rather than with Newton's theory of motion in the real world in which he thought all motion is accelerated because it is perturbed by impressed forces such as multiple mutual gravities. The truth of the matter is that when like circumstances are validly compared with like, then in both Aristotle's and Newton's dynamics all motion in the real world has moving forces, and again in both dynamics the purely ideal continuing motion of a lone body in a gravity-free pure void would not require any external force, as Newton himself recognised in the passage quoted above. The main difference between them is that for Newton the perseverance of this ideal motion would be caused by an internal force according to Definition 3 of the Principia, namely by the inherent force of inertia, but like Newton's first law of motion which notably makes no mention whatever of inertia, Aristotle did not specify whether continuing externally unforced motion would be caused by any internal force anymore than Newton's first law did.

Thus in Newton's dynamics all motion, including ideal uniform motion, is caused by some force, either impressed forces or inertial force. As Newton expressed himself in his De Gravitatione... written just before the Principia:

'Force is the causal principle of motion and rest. And it is either an external one [i.e. vis impressa] that generates or destroys or otherwise changes impressed motion in some body; or it is an internal principle [i.e. vis insita or vis inertiae] by which existing motion or rest is conserved in a body and by which any being endeavours to continue in its state and oppose resistance... Inertia is force within a body, lest its state should be easily changed by an external exciting force.' [p148, Unpublished Papers of Sir Isacc Newton, Hall & Hall, 1962].

And as the leading 20th century Newton scholar Bernard Cohen finally admitted on page 98 of his 1999 A Guide to Newton's Principia:

'By virtue of his concept of the FORCE of inertia, Newton did not fully abandon the ancient notion that every motion must require a mover or some kind of moving force, even if a very special kind of internal force' [my paraphrasing],

thus rejecting the fundamental but logically invalid claim of his own 1960 Birth of a New Physics that Newton's Principia did abandon it because its first law of motion contradicted and rejected this ancient principle and so overthrew Aristotelian dynamics and founded a new physics. Elsewhere in the context of arguing that Newton had got his first law of motion from Descartes, Cohen had commented on Newton's own attribution of it to Aristotle's counterfactual principle of endless unforced motion in a gravity-free void, 'but Aristotle denied the void', as though he therefore denied this principle, thus illogically overlooking the fact that Descartes, whom Koyre and Cohen claimed first stated the principle of inertia, also denied the void, and as Newton also did for that matter, because it would have breached the Aristotelian principle of no action at a distance with respect to mutual gravitational attraction.

Finally, to scotch the idea that 'the principle of inertia' says "to have motion you don't need a force", a reading of the two main alternative candidates for such a principle, namely Newton's Principia's first law of motion and its Definition 3 of vis insita and vis inertiae, shows that the first law does not say that the perseverance of an externally unforced uniform motion would not be caused by any force and is thus force-free, and moreover Definition 3 shows that it would be caused by a force, namely by the internal inherent power or force of inertia. These two principles were translated into English in the 1999 Cohen & Whitehead translation of the Principia as follows:

"Every body perseveres in its state of rest or of moving uniformly straight ahead except insofar as it is compelled to change its state by forces impressed."

"Inherent force of matter is the power of resisting by which every body, so far as it is able, perseveres in its state of resting or of moving uniformly straight forward." [Newton/s following commentary defines the force of inertia (vis inertiae) as the same as inherent force (vis insita) ]

For logical clarification, the contrasting principles of inertia of Aristotle, Kepler and Newton are summarised in the following brief history of inertia, that is, of the notion of a non-gravitational inherent internal resistance to motion:

ARISTOTLE: Bodies have NO non-gravitational inherent internal resistance to motion of any kind, or in short, bodies have no inertia. (NB But they have an internal gravitational resistance to motion in all directions except for gravitational motion straight downwards to the centre of the Earth).

KEPLER: All bodies universally have a non-gravitational inherent internal resistance to ALL motion

NEWTON: All bodies universally have a non-gravitational inherent internal resistance to ALL motion EXCEPT for uniform straight motion, and this inherent force of inertia causes bodies at rest to remain so and moving bodies to have a tendency to persevere in moving uniformly straight ahead.

The fundamental error of the traditional history of inertia may be succinctly summarised as the error of mistaking Kepler's principle of inertia for Aristotle's because of mistaking Aristotle's virtually omnidirectional gravitational internal resistance to motion for a non-gravitational 'inertial' internal resistance to motion in ALL directions.


2) "The concepts of Aristotle on force and motion can be summarize[d] by the following equation: F = mv."

This claim is historically false. It mistakes Kepler's law of motion F = mv for Aristotle's F = Rv, and thus overlooks what was in retrospect one of the the most important conceptual developments in the history of physics and Aristotelian dynamics in two millenia, namely the introduction of the notion of inertial mass m as another resistance to motion in addition to those of gravity, the medium and friction.

F = mv or v @ F/m was not Aristotle's law of motion. The latter was that 'average' speed v @ F/R (or F = Rv), where R is resistance to motion, BUT it did not posit any kind of internal resistance to motion m like Kepler's 'inertia', but only resistance due to the medium and to gravity in anti-gravitational violent motion. (The Lyceum's Aristotelian Mechanica also posited the third resistance of friction, which saved v @ F/W from refutation by the slower speed of a cart without wheels than one of the same weight with wheels when pulled by the same force, namely by enabling such as v @ F/(W+f) compared with v @ F/W.)

Rather F = mv, or v @ F/m, was Kepler's crucial revision of Aristotle's law. Thus to characterise Aristotle's law as F = mv air-brushes out a vital conceptual innovation in the history of physics that was crucial to its evolutionary development into Kepler's and Newton's dynamical laws, namely the introduction of 'the force of inertia', a new resistance to motion in addition to those of gravity, the medium and friction.

The thesis that Aristotle's law was F = mv can easily be refuted by reductio from Aristotle's Physics. Thus when there is neither of these two resistances to motion, such as in natural gravitational motion in a void as analysed in Aristotle's Physics 4.8.215a29f (i.e. free-fall), where the body's own Weight becomes its motive Force and R = 0 because there is no medium, then Aristotle predicts the speed would be infinite because v @ F/R then becomes v @ W/0. But it would not be infinite if bodies also had an internal 'inertial' resistance to motion m as in Kepler's law. For if they had, then v @ W/R would then become v @ W/m rather than v @ W/0. Thus F = mv could not possibly have been Aristotle's law because v = F/m would have predicted finite speed when Aristotle predicted infinite speed in the same circumstances in which v @ F/0 according to his law v @ F/R and its only two possible parameters for R, gravity and the medium.

Kepler accepted Aristotle's core law v @ F/R, but introduced the notion of inertia into physics as an internal resistance to all motion in all bodies universally specifically in order to avoid its empirical refutation by the observably finite speed of celestal motion when it is presumed to have a motive force (F > 0) but no resistance (R = 0), as both Aristotle and Kepler supposed it did. For in such dynamical circumstances v @ F/0 and so v is infinite. But the massive cosmological refutation of Aristotle's law by the observation that the stellar sphere was not infinitely fast but took 24 hours to rotate had led Philoponus in the 6th century to replace it by the alternative law v @ F - R, whereby speed is not infinite when R = 0. But in the 12th century Averroes rejected Philoponus's law and restored Aristotle's. He saved it from this celestial refutation by positing that in spite of being weightless the stellar sphere had an inherent internal resistance to motion, whereby R > 0 and thus its speed not infinite. Kepler then generalised this notion to become that of a non-gravitational internal resistance to all motion inherent in all bodies universally, including the planets that are propelled by the rotating sun's sunspecks but to whose orbital motion there is no resistance in his celestial dynamics, and dubbed it 'inertia'.

Thus just as many concepts in physics, such as perturbing hidden planets, dark matter, parallel universes and a plethora of exotic elementary particles, are invented to save some core theory from empirical refutation given other factual assumptions, so the notion of inertia in its original meaning of an internal resistance to some kinds of motion inherent in all bodies also arose as a problem-solving auxiliary theory of Aristotelian dynamics to save its core law from refutation by celestial motion. Newton subsequently adopted it with the marginal revision that the inherent force of inertia resists all motion EXCEPT uniform motion (which he thought probably did not exist anywhere because all motion is accelerated by the multiple gravitational forces in the universe), and synthesised it with his revision of the scholastic Aristotelian auxiliary theory of impetus of Avicenna and Buridan as developed by Benedetti and Galileo to form his own highly idiosycratic concept of 'the force of inertia' that both causes uniform motion to persevere, like impetus, and resists non-uniform motion, like inertia.

Finally it should also perhaps be noted that because the average speed v of any uniformly accelerated motion from rest is proportional to the acceleration, Newton's law a @ F/m entails v @ F/m for uniformly accelerated motion from rest, and also that on Newton's law, if bodies did not have any resisting force of inertia and so m = 0, then in a void any force would move them with infinite speed, just as in Kepler's and Aristotle's physics, thus revealing the Aristotelian historical rationale of the notion of inertial resistance to motion.


Mr. Bellamy, I have appreciated your comments here]. I wish someone would make as earnest an attempt to argue the other side, so that I could more easily judge between your arguments and theirs. But I do have a couple of complaints:

  1. I wish you would use more standard Wikipedia-type formatting, especially signatures (--~~~~) and indentations (: :: ::: and so on), bullet points (* ** *** and so on) and the like. While your at it, why not get an actual wikipedia account? That would make things easier both for us and for you.
  2. I confess that I have trouble following your arguments at time. Would you mind providing a simplified summary explaining (in, say, one sentence each) how each of the major figures believed inertia (or its equivalent) worked? For instance, as the wikipedia article stands now, I would expect the following:
  • Aristotle believed that without an external force, any object would naturally come to rest.
  • Philoponus disputed this, saying that motion would be sustained by some other force (which however might dissipate). Averroes supported Aristotle on this, Occam supported Philoponus.
  • Buridan described a momentum-like concept under the name impetus, which he viewed as causing continuous moton.
  • Kepler first used the term inertia, but to him it only referred to a resistence to motion, never a resistence to stopping.
  • Galileo: A body moving on a level surface (horizontal motion) will continue in the same direction at constant speed unless disturbed.
  • Descartes: Everything, which is simple and undivided, remains, as far as it is on itself, always in the same state and never changes except by external causes.
  • Newton: Every body continues in its state of rest or of uniform motion in a right line unless it is compelled to change that state by forces impressed on it.

Now, obviously you disagree with this summary. Could you please write your own version, explaining each (in your opinion) important change or innovation in the theory? That would help me a lot.
One more thing: do you have anything to add to Talk:Inertia#Original Languages? --Iustinus 17:01, 7 January 2006 (UTC)

8/1/06 BELLAMY TO IUSTINUS: Thanks. Will respond shortly.

9/1/06 BELLAMY TO IUSTINUS 7 JANUARY

Thanks for your interest and appreciative comments. I analyse your comments into 6 points I shall try to deal with. Could you possibly please kindly provide your e-mail address to mine to correspond off-line so as not to take room in this space?

Immediately I offer the following response to your fourth point:

IUSTINUS: "Would you mind providing a simplified summary explaining (in, say, one sentence each) how each of the major figures believed inertia (or its equivalent) worked?"

REPLY: Perhaps the most important point to make here is the Joadian one that 'It all crucially depends upon what you mean by 'inertia' !', because unfortunately there is much confusion and equivocation about this in the literature, in which it can variously mean 'interminable motion', 'motion in a void', 'entirely force-free motion', 'externally force-free motion', 'an internal resistance to motion', etc and upon which the truth or falsity of both conceptual and also historical claims about it depend.

However, for summary logical clarification I added a section to my Reply 1 to the Comment of 1 January 2006 that summarises the contrasting 'principles of inertia' of Aristotle, Kepler and Newton with respect to the original historical meaning of the term 'inertia' as first introduced into physics by Kepler to mean a non-gravitational internal resistance to motion inherent in bodies. I reproduce it here:

ARISTOTLE: Bodies have NO non-gravitational inherent internal resistance to motion of any kind (but they have an internal gravitational resistance to 'violent' motion, that is, motion in all directions except for gravitational motion straight downwards to the centre of the Earth, which is 'natural' motion).

KEPLER: All bodies universally have a non-gravitational inherent internal resistance to ALL motion

NEWTON: All bodies universally have a non-gravitational inherent internal resistance to ALL motion EXCEPT for uniform straight motion, and this inherent force of inertia causes bodies at rest to remain so and moving bodies to have a tendency to persevere in moving uniformly straight ahead.

The fundamental error of the traditional history of inertia may be succinctly summarised as the error of mistaking Kepler's principle of inertia for Aristotle's because of mistaking Aristotle's virtually omnidirectional gravitational internal resistance to motion for a non-gravitational 'inertial' internal resistance to motion in all directions.

INERTIA AS INTERNAL RESISTANCE TO MOTION: To further extend this analysis for you, of the Wikipedia 9 major figures you list, only 3 of them posited the existence of any such inertia so far as I know, namely Averroes, Kepler and Newton. The rest - Aristotle, Philoponus, Occam, Buridan, Galileo and Descartes - did not so far as I can tell, and so their principles of inertia could be summarised as the same as that of Aristotle, namely that bodies have no inertia. And although Annaliese Maier argued that bodies have a non-gravitational 'inertial' internal resistance to motion in Buridan's and Oresme's scholastic dynamics [The significance of the theory of impetus for scholastic natural philosophy 1955], as Buridan put it according to Ernest Moody's 1966 rebuttal of her thesis, 'Prime matter does not resist motion[1966 Galileo and his Precursors]. Maier claimed this alleged inherent inertial resistance would prevent the permanent conservation of impetus and thus of interminable motion in a void, even in spite of the elimination of gravitational resistance to motion, because this inertia would destroy impetus, thus scuppering Duhem's thesis that scholastic impetus theory was the origin of Newton's-inertial-dynamics. But her own textual evidence from Oresme clearly showed she had mistaken the Aristotelian gravitational horizontal tendency towards rest for a non-gravitational inertia, because Oresme clearly said it was their WEIGHT, and hence gravity, that caused it:

"For the reason why such things as men or animals experience work or effort inmoving themselves or other heavy things is that their WEIGHT inclines them towards rest or to be moved with some other contrary motion" Oresme: De caelo et mundo

INERTIA AS HYPOTHETICAL INTERMINABLE EXTERNALLY UNFORCED MOTION IN A VOID: However, if the principle of inertia is taken to mean the thesis that externally unforced motion would continue in the absence of any resistances such as those of the medium or of gravity or other external impediments, as in a pure void, then 6 of the 9 people you list clearly endorsed it, namely Aristotle, Occam, Buridan, Galileo, Descartes and Newton, whether or not they believed a void existed and hence that such motion was possible. As I understand them, for Aristotle, Occam and Descartes this is simply because such motion would be conserved in the absence of any resistance, whereas for Buridan and Galileo it is caused by the internal force of (Avicennan) impetus that (unlike self-decaying Hipparchan impetus) is permanently conserved in the absence of any resistance to motion. But for Newton the perseverance of uniform motion would be caused by the internal force of inertia, a kind of proxy for impetus in this specific historically novel capacity as a motor that Newton gave it, as distinct from its other original capacity as a resistance to motion and thus as a brake, which Newton restricted to being a brake on accelerated motion but not on uniform motion. Newton rather confusingly split up the Avicennan (i.e. non-Hipparchan) concept of impetus eventually developed by Benedetti and then Galileo in his Dialogo and Discorsi into those of 'the force of inertia' and 'quantity of motion' (mv) and redefined 'impressed force' as 'the impressing force'.

As for Philoponus, Averroes and Kepler, for Kepler all bodies have an internal resistance to all motion, so externally unforced motion would be impossible even in a pure void because inertia would prevent it even without any gravitational resistance to motion. The same may apply to Averroes insofar as he may have held all bodies have a non-gravitational inherent resistance to all motion, but not if he only attributed such inertia to the stellar sphere or to heavenly matter in general but not to sublunar bodies, which would therefore have no inherent resistance to motion in a void when deprived of their gravity, as suggested by Aquinas's analysis of his views in his Commentary on Aristotle's Physics [Book 4, Lecture 12, 535].

The case of Philoponus is problematic. Richard Sorabji's 1988 Matter, Space and Motion speculates that because he subscribed to the (Hipparchan) theory of self-decaying impetus, then projectile motion must terminate even in a void when the impetus has expired, thus removing Aristotle's 'refutation' of the void on the ground that it would permit interminable motion. But unless Philoponus posited a non-gravitational internal resistance to motion like Averroist or Keplerian inertia, then why should externally unforced motion in a void without gravity terminate just because its impetus has, and indeed why should externally unforced motion in a void need any impetus anyway ? In Aristotelian dynamics the only reason for positing internally impressed force or impetus is to explain the projectile violent motion against gravity of heavy terrestrial bodies in the real world as opposed to in a void without gravity (that is, in a pure void without natural places towards which bodies gravitate as distinct from a mere vacuum with natural places and hence with gravity), and this is because some motive force is required to overcome their countervailing resistance of gravity. For otherwise in a pure void where they have no gravity their externally unforced motion would be endless as in Physics 4.8.215a19-22, rather than dynamically impossible as in the immediately preceding passage Physics 4.8.215a14-19.

So far as I am aware, Sorabji has produced no clearly valid argument nor evidence to date that Philoponus claimed projectile motion in a pure void WITHOUT gravity would terminate, or indeed that it would require any impetus. For the alleged evidence of this in Philoponus's Physics, 644, 16-22 he cites in his 2004 The Philosophy of the Commentators 200-600 AD notably does not show this. It only shows that Philoponus maintained that a projectile violent motion AGAINST COUNTERVAILING GRAVITY (i.e. "contrary to nature"), rather than a projectile motion in a pure void WITHOUT GRAVITY, would no longer move against gravity once its impetus had become too weak to overcome gravity. But this is just what Aristotle claims in Physics 4.8.215a14-19, except in his case the motive force against gravity is the air rather than impetus, so projectile violent motion against gravity in air ceases when the air's motive power weakens (and projectile violent motion against gravity in a vacuum without any air to move it against gravity is completely impossible).

Thus Sorabji's 'evidence' is logically irrelevant to the issue of whether unforced motion in a void without gravity would be interminable. For the Philoponus passage he cites does not deal with the crucially different dynamical case at issue of externally unforced motion in a pure void without gravity that is thus neither natural nor contrary to nature, that is an 'inertial' motion, and which Aristotle claims would be endless in the immediately following passage Physics 4.8.215a19-22. In fact Sorabji's evidence shows Philoponus evidently mistook this latter passage to be "another argument to show that nothing moves contrary to nature [i.e. against gravitatioal resistance] in a vacuum", rather than an argument to show there cannot be unforced gravity-free motion in a pure void without any resistance, i.e. an 'inertial' motion that is neither natural nor contrary to nature, because it would be interminable. Moreover Sorabji's citation of this evidence is notably perverse inasmuch as he himself does not make this same mistake, for he claims of this very same passage that "Aristotle's objection unwittingly presupposes inertial movement independent of force", hence agreeing with Newton and other commentators, contra Philoponus, that it deals with a case of 'inertial' motion. It seems Sorabji fails to notice that Philoponus did not interpret it to be a case of 'inertial' motion. The upshot of this is that not only does Sorabji's Kuhnian thesis that Philoponan physics was a new paradigm that overthrew Aristotelian science to become the origin of modern physics fail for the simple reason that eventually both the older Galileo and Newton rejected it, but it has yet to evidentially establish its key thesis that Philoponus denied the principle of inertia because he maintained against Aristotle and Newton that external unforced and unresisted motion in a pure void would terminate.

Of course inasmuch as Philoponus's law of motion was v @ F - R, then certainly in a pure void where R = 0 and so v @ F, if also F = 0 such as if the force of impetus were zero, then it would predict zero speed and so no motion. However, the crucial question is whether Philoponus intended this law to be applied to motion in a pure void without any resistance to motion, as distinct from only being applied to motion in the real world or in a vacuum with gravity, just as we may ask whether Aristotle intended his law v @ F/R to be applied to celestial motion, as Philoponus did to refute it ?


Iustinus, I hope this analysis helps summarily clarify the pre-history of Newton's complex and even perverse notion of the force of inertia. My apologies for any extent to which it is defects of my exposition whereby you find my arguments are difficult to follow. But I would point out that Newton's concept of the force of inertia is arguably a leading candidate for the most idiosyncratic, incoherent and unintelligible concept in the history of physics, as perhaps implicitly recognised by the English Department for Education's teacher-recruitment publicity campaign poster with the challenging question 'Could you teach inertia to kids ?'(e.g. How does a body remember where it came from so it can go straight, Miss ?). In effect it posits that bodies have inside them a force that acts as both a motor and also a brake of motion, a motor of uniform motion and a brake on accelerated motion.

I suggest the main difficulty of understanding it stems from the fact that it rather confusingly revised and fused together two very different auxiliary theories of Aristotelian dynamics, namely the theory of impetus and the theory of inertia, each invented to deal with entirely different problems. Very briefly, impetus was invented to provide the otherwise missing motive force in terrestrial projectile motion without which Aristotle's rule for violent motion v @ F/W would become v @ 0/W, hence speed would be zero and so no motion; but with the internal force of Impetus it becomes v @ I/W. But the internal inherent force of inertia was originally invented to provide the otherwise missing Resistance to celestial motion without which it would be infinitely fast because v @ F/R became v @ F/0 given the presumption that R = 0 because there is neither gravitational resistance nor a resistant medium in the heavens. I suggest the idiosyncratic and apparently relatively 'irrational' nature of Newton's complex concept of the force of inertia in itself means it can best be understood in terms of its historical problem-solving rationale in relation to these two different problems of Aristotelian dynamics.

But whatever, I am sorry to say I find the Wikipedia main explanation of inertia essentially unintelligible or false for numerous reasons, especially after its first sentence. Can YOU understand it ?:

"In physics, inertia is a historical concept and a perceived property of matter that eventually was developed by Isaac Newton to explain the default state of matter in terms of bodies tending to remain in motion or to remain at rest unless acted upon by a force. We today adopt a two-fold definition of inertia. One definition is the world-view of Newton, his assumption of a tendency toward maintaining momentum that lead him to write his laws of motion. This first definition of inertia as "a tendency to maintain momentum" is therefore not described in mathematical terms but considered the default state or universal law of matter and is integrated into Newton's first law. However, in its broader second meaning, inertia has been redefined to be more mathematically useful as the measure of how difficult it is to change the momentum of a body in terms of inertial mass, often referred to as "a body's resistance to change". "

Just consider a few problems of the very first sentence - surely all concepts in physics are historical ? how can inertia possibly be perceived ? surely the default state of matter in Newton's cosmology is to be in accelerated motion due to multiple gravitational forces ? surely it should refer to uniform motion rather than motion in general ? and surely it should say impressed force since the force of inertia keeps bodies in uniform motion ? etc. The remainder is surely simply bizarre.

--80.6.94.131 19:15, 9 January 2006 (UTC)A.Bellamy


Interesting subject!

Interesting subject! There is enough stuff above to create an article just for this subject. I suggest you do one, if it's not already done: is it? Title? 'Before, during and after Newton', or else. It would be easier to discuss all those interesting points that you have introduce.
Regarding 1), I did not know that it was a slogan.
As for 2), it does not say that's what Aristotle said, just that his concepts could be interpreted nowadays with this formula. 1) & 2) have to be read together, not separatly.
Finally, in the theories of physics used nowadays, there is no such thing as a medium who resist to the motion of an object, and if it where so, that would be considered as a force, force in the sense that it is use nowadays. --Aïki 17:49, 7 January 2006 (UTC)


10 JANUARY: A.BELLAMY REPLIES TO AIKI 7 JANUARY AS ABOVE

Thanks for the appreciative suggestion, to be considered ! I reply in bracketed inserts to your comments in quotes:

AIKI: "Regarding 1), I did not know that it was a slogan."

[The typical phraseology of the 20th century literature on the alleged inertial-dynamics and scientific revolution tends to be the 'forced versus force-free motion' mantra of the ilk 'in Aristotle's dynamics motion requires a force but not in Newton's', which seems to me fair game for being termed a 'slogan' or 'mantra'. But as such it is not merely simplifying, but of course seriously falsifying, because in neither dynamics is there any force-free motion in the real world, and moreover in an externally force-free pure void for which Aristotle predicted interminable motion, then continuing motion would be caused by the internal force of inertia in Newton's dynamics.

The two main errors of this mantra are first that it invalidly compares the behaviour of a body that is wholly unperturbed by gravity in Newton's dynamics with that of a body with gravity that brings it to rest or prevents its motion in Aristotle's dynamics, that is, it compares the behaviour of a body under two crucially different sets of dynamical initial conditions; and secondly it wholly overlooks the role of Newton's FORCE of inertia. These errors are illustrated in such as the following example of this mantra from pp17-18 of Stephen Hawking's 1988 A Brief History of Time, but into which I have inserted the crucially different initial conditions it omits and that hopefully make its invalid malcomparison, and thus its anti-Aristotelian prejudice, somewhat clearer:

'Before Galileo and Newton people believed Aristotle who said that the natural state of a body [WITH GRAVITY] was to be at rest and that it moved only if driven by a force or impulse [TO OVERCOME ITS GRAVITY]...but after them we believe whenever a body is not acted on by any force [AND SO NOT BY GRAVITY] it will keep on moving.' [NB Slightly paraphrased]

Newton's criticism of this exposition based on his comments quoted above would presumably be that in both ancient atomist and Aristotle's dynamics a body without gravity not acted upon by any force would also keep moving.

At least since the publication of Westfall's 1970 Force in Newton's Physics, which argued the dynamics of the Principia was based on two forces rather than one, namely 'impressed force' which causes uniform acceleration and the 'force of inertia' which causes uniform motion and also rest to persevere, it has increasingly come to be accepted that the 19th century positivist view that the only force in Newton's dynamics was impressed force, such as portrayed by Mach, is seriously mistaken. Perhaps one of the most forceful ways to illustrate this error is simply to ask what is the force by which the body is said to be "carried in uniform motion" along the sides of the parallelogram in Newton's exposition of the famous 'parallelogram of forces' in the Principia's Corollary 1 of its prefatory axiomatics ? Newton's parallelogram of forces is surely a parallelogram of inherent forces. It seems it was Cohen's acceptance of Westfall's analysis that eventually by 1999 forced him to concede Newton did not abandon the fundamental principle of Aristotelian dynamics that all (actual) motion requires a mover, and from which it would seem to follow that by the same token he had previously claimed Newton's dynamics wholly overthrew Aristotelian dynamics to found a new physics because it breached this principle, then rather it was a continuation and development of it, thus arguably dispelling the leading myth of post-medieval scientific modernity in a fundamental dichotomy between 'yesterday' and 'today' that the 'forced versus force-free motion' mantra asserts.

AIKI: "As for 2), it does not say that's what Aristotle said, just that his concepts could be interpreted nowadays with this formula."

[And nor does my text say the formula F = mv is what Aristotle said, but just that his concepts CANNOT POSSIBLY be interpreted by that formula, neither nowadays nor at any time, if m here denotes inertially resistant mass. This is crucially because they provably did not include any concept of bodies having any inertial resistant mass m, a much later innovation. Hence the Keplerian formula F = mv contradicted Aristotle's two different predictions of infinite speed when there is no gravitational resistance to motion (Physics 4.8.215a29f and Heavens 3.2.301b), which both presumed there is no inertial resistance to motion either, whereby R = 0 in Aristotle's law v @ F/R.]

AIKI "1) & 2) have to be read together, not separatly." [Why ?]

On medium

AIKI: "Finally, in the theories of physics used nowadays, there is no such thing as a medium who resist to the motion of an object [Then how come some bodies float in water ?], and if it where so, that would be considered as a force, force in the sense that it is use nowadays."

[Are you really trying to claim there is no such subject in modern physics as fluid mechanics that studies the resistance to motion by fluid media ? Or that according to modern physics there is no such thing as a terrestrial atmosphere whose resistance to motion could incinerate insufficiently insulated space shuttle's ? And nor does my text say the resistance of a medium was ever considered not to be a force in any sense. What are you trying to claim here ? However, I should perhaps clarify that both the variables 'F' and 'R' in my formula v @ F/R refer to forces, F being the motive force and R the resisting force.]

The comment does perhaps raise the issue of the changing recognition or not of various different resistances to motion in the history of physics and their analysis as forces. In fact I suggest the main development in dynamics from Aristotle to Newton was that of identifyimg what the various resistances to motion are and whether they should be subtracted from the motive force, as in Philoponus's v @ F - R, or whether it should be divided by them, as in Aristotle's v @ F/R. Note that in Euler's Newtonian law a = F/m, 'F' really refers to net force, that is, motive forces minus resisting forces, but if instead 'F' refers to gross force it can be expressed more fully as a = (F - R)/m to reveal its possible historical roots in both Philoponus's v @ F - R and Aristotle's v @ F/R. In Newtonian dynamics some resistances to motion, such as the buoyancy upthrust of a fluid medium, are to be subtracted from the motive force, but it is to be divided by others such as inertial resistance m. Stoke's Law for the terminal speed of gravitational fall in a fluid medium provides an interesting study in this problem, and some such as Stephen Toulmin have even claimed it is the modern vindication of Aristotle's law v @ F/R.

On this analysis it seems that both Aristotle and Philoponus may have discovered a part of the eventual 'Newtonian truth' in respect of the mathematical analysis of the role of resistance in determining the speed of motion and answering the key question of whether it divides or subtracts from the motive force.] --80.6.94.131 19:16, 10 January 2006 (UTC)A.Bellamy

On medium: answer from Aïki

1- For the existance of media, you are right. But I cannot remember why I added this part on medium, even after reviewing (rapidly,I admit) your texts! If I remember, I will come back to tell you.

2- What is the @ for? Doe's it means = ? (Please, if it is possible, give me a brief answer.) Thank you.
--Aïki 01:07, 11 January 2006 (UTC)

11 Jan Reply: As I say above in the 'Further Comments' section of my original contribution when I first introduced it, '@' means 'is proportional to', because I was not aware of the availability of the symbol 'α', as in ma α F, for example. Thanks, I should perhaps re-edit. Note that you cannot substitute '=' for 'α' because, for example, ma = F entails no deceleration without a Force, but in Kepler's theory of inertia (v α F/m) there would be, because internal inertia would stop an externally unforced motion. Newton's second law says that the change of motion (compelled in the first law) is proportional to the impressed force, which is interpretable as Δvm α F, but does not say whether or not there is any change of motion without an impressed force, such as there can be in Kepler's physics. It is only the first law that rules this out, and Definition 3 that explains it would be prevented by the internal force of inertia a la Newton. Of course Aristotle's mathematical physics, like Newton's, was actually a theory of arithmetical proportions rather than algebraic equalities. --80.6.94.131 17:50, 11 January 2006 (UTC)A.Bellamy

Is F = mv in Aristotelian dynamics?

AIKI, with respect to your acceptance of the standard view that F = mv represents the Aristotelian theory of the effect of a force, the following exposition may be helpful for yourself and others in explaining why its apparent implication that a constant force produces a constant speed in Aristotelian dynamics is mistaken.

DOES A CONSTANT FORCE PRODUCE A UNIFORM OR ACCELERATED MOTION ?

One of the traditional key claims of the mistaken thesis that Newton's dynamics overthrew Aristotelian dynamics is that in the latter a constant force produces a constant speed, whereas in Newton's it causes a uniform acceleration. But as usual this standard history misrepresents both of these dynamics by air-brushing them to produce the illusion of a revolution, when in fact Newton's dynamics was a revisionary development of the scholastic Aristotelian dynamics developed by Avicenna and the Paris school, and also of the new theory of inertia of Kepler's development of Aristotelian dynamics. For on the one hand this claim overlooks Newton's force of inertia, which causes uniform motion to persevere. And on the other hand, in scholastic Aristotelian impetus dynamics such as eventually adopted and developed by Galileo, primary forces such as gravity produce uniformly accelerated motion (in a void) by means of continually creating and impressing fresh successive and equal amounts of the secondary force of impetus within bodies. And because the internal force of impetus causes uniform motion to continue in the absence of all resistance, its uniform accumulation caused by gravity therefore produces uniformly accelerated motion.

Consequently the historical truth of the matter is that both Aristotelian and Newton's dynamics similarly posited two different kinds of force, namely a kind of primary or external force that produces uniform acceleration, such as gravity or Newton's concept of impressed force in general, and secondary internal forces that cause uniform motion to continue in the absence of all resistance, such as the force of impetus in Aristotelian dynamics or the force of inertia in Newton's development of Aristotelian dynamics. This development both revised and fused together the latter's two different auxiliary theories of impetus and Kepler's theory of inertia - the latter was an inherent resistance to all motion proportional to mass invoked to prevent infinite speed in the absence of any other resistance to a motive force - to form Newton's highly idiosyncratic hybrid concept of 'the force of inertia' that both causes (uniform) motion and resists (accelerated) motion.

Finally, it should be noted that in Aristotle's law of motion v @ F/R, v refers to the average speed of the whole motion from rest (i.e. d/t) rather than instantaneous speed and therefore does not distinguish whether the motion is constant or accelerated. And hence Newton's a @ F/m entails Kepler's v @ F/m. Aristotle's own separate supposition that a constant force produces a constant speed must be inferred (or not) from other analyses or as a logically implicit presupposition (Drabkin argued it was logically implicit in the rules of violent motion elaborated in Physics 7.5), but he certainly accepted gravitational fall was accelerated as a matter of fact, whatever the dynamical explanation. But whatever, it would seem that at least since the 10th century and Avicenna's impetus theory of projectile motion and of gravitational fall in which gravity is its continual primary projector, there was a specific variant of Aristotelian dynamics in which a primary propelling force produces a uniformly accelerated motion. The Avicennan impetus theory, subsequently adopted and developed by the Paris schools of Burdian et al in the 14th century and Galileo in his post-Pisan later mechanics in the 17th century, was apparently the third major auxiliary theory of Aristotelian dynamics devised to save its core theory that all real motion requires a conjoined motive force from refutation by identifying the force of projectile motion which has no apparent conjoined force. It replaced both Aristotle's original auxiliary theory of the air as the conjoined mover and then the Hipparchan-Philoponan impetus theory of an essentially self-decaying impermanent impressed internal force.

At the beginning of the 20th century, in his strenuous efforts to prove his alma mater Paris University (i.e. Buridan et al), rather than Galileo and Newton, had been the originators of allegedly anti-Aristotelian inertial-dynamics in the 15th century, the highly influential French philosopher and historian of science Pierre Duhem mistakenly miscast impetus theory as the revolutionary overthrow of Aristotelian dynamics because he claimed it contradicted its basic principle that all motion requires a 'contiguous' mover, by which he meant an external conjoined mover rather than a conjoined mover that may be either external or internal. But this restriction was patently mistaken, because it placed no such restriction on the mover, as patent in its various theories of the internal mover of gravity, of the internally impressed force of the air in projectile motion, and of the internal moving souls of the planets. In short, the idea of internal motive forces, both inherent (gravity) and contingent (impressed force) stems from Aristotle himself. Thus far from being the wholesale overthrow of Aristotelian dynamics that breached its most fundamental principle, rather its supplementary impetus theory was its saviour and further development that fully observed its core principle that all actual motion requires a conjoined mover. But unfortunately Duhem's crucial error was by copied by such as Kuhn and Cohen and others in portrayals of Newtonian physics as revolutionary.

--80.6.94.131 17:14, 13 January 2006 (UTC)A.Bellamy