Aristotle’s Philosophy of Fluid Mechanics

Aristotle’s Philosophy of Fluid Mechanics

Aristotle is often criticized by modern scientists for his allegedly naive, misguided or outright false statements regarding physical laws.  These criticisms typically fail to appreciate the amazing depth of insight characterizing Aristotle’s writings about the physical world, especially given that in his time there were no instruments for enhancing the human senses − instruments such as the telescope, the microscope, the spectroscope, the gyroscope, the hygrometer,  the thermometer, the barometer, the altimeter, and many others.

Other criticisms of Aristotle by scientists are based on his rejection of certain doctrines of modern physics, such as (a) his rejection of the concept of the void (or the perfect vacuum) as a real existent in the universe, (b) his rejection of ‘matter’ (the stuff of the physical world) as discontinuous (as required by modern quantum physics), (c) his supposedly naive assertion that the cosmos was filled with a uniform ether (generally believe to be disproved by the results of Michelson-Morley experiment), (d) that heavier bodies fall faster than lighter bodies (believe to be disproved by Galileo’s demonstrations).

Standing against the withering critique of Aristotle as a scientist, G. A. Tokaty, Emeritus Professor of Aeronautics and Space Technology, at The City University, London, in his book, A History and Philosophy of Fluid Mechanics (hereafter HPFM).  The seventh chapter of his book is entitled ‘Aristotle and the science of fluids’.  In this remarkable chapter, Tokaty has this to say about Aristotle as a scientist:

There is probably no parallel in the history of mankind to the influence of this one man, either in the vastness of his intellectual achievement or in the extent of his influence extending over two thousand years on the growth of scientific knowledge.  I should, however, deal only with his contributions to the subject of this book. . . . [H]e created an intense scientific curiosity, which accelerated the emergence of sciences. . .  [H]e succeeded  in the formation of certain basic laws of nature whose value to mechanics generally and fluidmechanics  [sic] in particular cannot be doubted. — Tokaty, HPFM, 1971, p. 17

Tokaty praises Aristotle for his formulation of the principle of continuity, a foundational concept in the modern science of fluid mechanics:

All branches of Fluidmechanics [sic] rest upon the continuity principle.  In brief, this is the principle that mass is indestructible and may be completely accounted for at different points of any fluid, at rest or in steady motion.  And Aristotle was the first to give this general formulation. “The continuous may be defined”, he wrote, “as the which is divisible into parts which are themselves divisible to infinity, as a body which is divisible in all ways.  Magnitude divisible in one direction is a line, in three directions a body.  Being divisible in three directions, a body is divisible in all directions.  And magnitudes which are divisible in this fashion are continuous.” — Tokaty, HPFM, 1971, p. 18

Tokaty honors Aristotle for his pioneering theories regarding motions, projectiles, and air resistance:

We, the aerodynamicists, are obliged to Aristotle for his pioneering concepts dealing with the motions of projectiles and air resistance.  It was he who pointed out, for the first time, that when a body moves in the atmosphere, the surrounding air becomes hot and, in certain circumstances, its (the body) even melts — yes, he said, ‘melts’. — G.  A. Tokaty, page 18.

Tokaty  praises Aristotle for being the first in recorded history to formulate, before Galileo (1564-1642), Huyghens [sic] (1629-1695),  and Newton (1642-1727), the concept of inertia:

We thus see that Aristotle was, really, the first, Galileo the second, Huyghens [sic] the third and Newton only the forth milestone in the history and philosophy of the law of inertia.  This alone give Aristotle a prominent place among the first fathers of general Mechanics and of Fluidmechanics [sic]. — G.  A. Tokaty, page 19.

Tokaty completes his chapter on Aristotle with Aristotle’s proof that ‘the free surface of water is a sphere.’

Just one more interesting point.  Aristotle was a good observer.  His eye noticed and his brain considered the fact that water or any other liquid never has an inclined surface.  ‘Why is this?’ he asked. [ Tokaty citing Aristotle’s On the Heavens, II, Iv, p. 162.] ‘Because then it must be spherical  If water is found around the earth, air around water, and fire around air, the upper bodies will follow the same pattern . . .’  And this is how he proved his proposition in regard to water:

Let βεϒ be an arc of a circle, whose center is α (Figure 3).  Then the line αδ is the shortest distance from α to βϒ.   Water will run towards δ from all sides until its surface becomes equidistant from the center.  It therefore follows that the water takes up the same length on all of the lines radiating from the center; and remains in equilibrium.  But the locus of equal lines radiating from the center is the circumference of a circle.  The surface of the water, βεϒ will therefore be spherical. — G.  A. Tokaty, page 21.

Screen Shot 2018-09-22 at 4.01.54 PM

Fig. 3. Aristotle’s scheme to prove that the free surface of water is a sphere.

[Image photo shot from Tokaty’s book HPFM, page 21]

NOTE:  What Aristotle was describing is today called the spherical cap.  Here is a page showing the computations of a spherical cap: 

Published September 22, 2018 @ 2:51  pm

Latest Revision: May 15, 2019 @ 6:35 pm


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