Aristotle principles of dynamics

Today's note is a guest note by Grzegorz Koczan. Aristotle is quoted as saying: ""There is no great genius without some touch of madness." And he is also quoted as stating that "Anybody can become angry - that is easy, but to be angry with the right person and to the right degree and at the right time and for the right purpose, and in the right way - that is not within everybody's power and is not easy." Finally, he is quoted to say that "Jealousy is both reasonable and belongs to reasonable men, while envy is base and belongs to the base, for the one makes himself get good things by jealousy, while the other does not allow his neighbour to have them through envy." I like Aristotle!

Aristotelian physics

Aristotle principles of dynamics

Grzegorz M. Koczan

Information about the origin and purpose of this note: The note was made available by the author (Dr. G. M. Koczan) to Professor Arkadiusz Jadczyk for popularization, discussion and verification by publishing it on the professor's scientific blogs.

Aristotle is the author of a series of coherent writings on physics written around the same time, which are now consolidated and known as the work of Physics (Aristotle 350 BC, Leśniak 1968). In this work, Aristotle gave several proportions of the motion of bodies. It is difficult to explain why these proportions are currently so poorly exposed and why only one of them is usually analyzed. A selective analysis of proportions, however, leads to an wrong or misunderstood Aristotle principle of motion. Based on the translation of Physics, the author proposes a broader and more coherent system of reconstruction of Aristotle principles of dynamics (Koczan 2021, 2023).

Aristotle proportion of motion in Book VII of Physics can be represented quite faithfully by the following proportionality. Namely, the ratio of the distance s to the time t is proportional to the ratio of the driving factor (force F) to the measure of the body quantity (mass m): s/t~F/m. In Book IV of Physics, there are proportions that can be expressed by the proportionality of the motion time t to the density of the medium d: t~d or equivalently in the form s/t~1/d. In Aristotle, the density of the medium is a measure of the resistance of the medium, so often the proportion from Book IV is written in the form: s/t~F/f, where f is the measure of resistance. Both reconstructions (s/t~F/m and s/t~F/f) of Aristotle dynamics are known from the history of physics and are current reconstructions, but practically they have never been confronted simultaneously.

The author decided to simply combine both proportionalities resulting from Aristotle's proportions into one proportionality, which can be expressed as: s/t=F/(fm) or equivalently F=fmv using the velocity symbol v=s/t. The resulting relationship is equivalent to the original proportions, except for the equals sign. The physical truth of the obtained equation F=fmv now depends on the interpretation of the measure of resistance f, as well as the force F. If f is interpreted ad hoc literally as a resistance force, then the equation under consideration will not be confirmed in physical reality. However, if f is just a drag coefficient proportional to the density of the medium, and F is the force driving the motion (i.e. the force opposing the drag, and thus de facto equal to it), then the equation will have the correct physical sense. Such an equation describes the movement of a body under the influence of a strong resistance proportional to velocity, according to Newtonian dynamics. This agreement is based on quasi-stationary states. Thus, the equation F=fmv can be called Aristotle second principle of motion, which is physically correct for quasi-stationary or stationary states.

From Aristotle's second principle of motion follows the law of rest, or Aristotle zeroth principle of motion. It says that in a medium with resistance to motion, the body tends to rest if there is no force driving the motion. The zeroth principle (law of rest) is true and is consistent with Aristotle Physics.

The most difficult situation in the analysis of the equation F=fmv is when f=0 and F=0, because then the velocity can have any value (including infinite or zero). It is not true that Aristotle in a similar context rejected all non-zero values of velocity (infinite and finite), because he was aware of the indestructibility of motion and postulated the eternity of circular motion. Thus, in the present situation, the body can, according to Aristotle, move uniformly in a circle or be at rest. It is worth adding that in the macroscopic sense, rest can be treated as a circular motion with a radius approaching zero, and locally a radius approaching infinity can be treated as a rectilinear motion (generalized circle). In this way, Aristotle first principle of motion can be described based on uniform circular motion.

Aristotle's zeroth, first and second principles still need to be supplemented with the third principle, which tells us what the drag coefficient f depends on. As already mentioned, the drag coefficient depends directly on the density of the medium d. In addition, the greater the density ρ and the greater the weight of the body, the lower the drag coefficient. Thus, Aristotle third principle of motion has the form of proportionality f~d/ρ. This proportionality in the context of the density of the medium d is undoubtedly consistent with Aristotle Physics, and in the context of the density of the body ρ, one can have some doubts whether Aristotle did not mean F here.

1. Arystoteles (350 p.n.e.), tłum. Leśniak K. (1968), Fizyka (Physics), Corpus Aristotelicum 184a‒267b, PWN Warszawa.

2. Koczan G. M. (2021), [Aristotle's Defense: reconstruction of his dynamics not contradictory to the observation], preprint, www.researchgate.net/publication/356554413, DOI:10.13140/RG.2.2.10119.52647.

3. Koczan G. M., monograph submitted in April (2023) for review: [DEFENSE OF ARISTOTLE'S “PHYSICS” – Mathematically unified reconstruction of consistent with observation Aristotle's dynamic], Wydawnictwo SGGW.

P.S.1. 09-07-23 7:19 My wife likes this great gospel song. This is for her. And it is Sunday today anyway.

How Great Thou Art - Lyrics

Oh Lord, my God
When I, in awesome wonder
Consider all the worlds Thy hands have made
I see the stars, I hear the rolling thunder
Thy power throughout the universe displayed

P.S.2. 7:31 

Beatitude is God’s aim for humanity; get this supreme

good for thyself first that thou mayst distribute it entirely to thy

fellow-beings.

He who acquires for himself alone, acquires ill though he

may call it heaven and virtue.

Sri Aurobindo

P.S.3. 8:14 The double compactified universe with the conformal infinity cap (double Dupin cyclide) connecting our space-time with its polar opposite universe:

P.S.4 19:52 Light circulating at infinity and never entering Minkowski space - see the notes - tomorrow will describe in details. There are two focus points.

 ParametricPlot3D[{(2 Sin[u])/(2 - 

     Abs[Sin[u]] Cos[v]), (2 Abs[Sin[u]] Sin[v])/(2 - 

     Abs[Sin[u]] Cos[v]), (2 Cos[u])/(2 - 

     Abs[Sin[u]] Cos[v])}, {u, -Pi, Pi}, {v, -Pi, Pi}, 

 Mesh -> {0, Range[-Pi, Pi, Pi/30]}, MeshStyle -> {Blue, White}, 

 MeshStyle -> Directive[PointSize[Large]], Background -> Black, 

 Boxed -> False]