On Aristotle, Newton and a 500 Pound Gorilla (Friction)

    The physics/astronomy of Plato/Aristotle/Ptolmey/(and later the Church) is often 
held up as famously wrong in many introductory physics/astronomy courses.  However, in 
some ways this may be a bad rap [see the Footnote below].  Newton's [and the giants 
(Copernicus, Galileo, and Kepler) on whose shoulders he said he stood] triumph was in 
some sense the ability to temporarily put the 500 pound gorilla of friction in the 
closet and imagine motion in the absence of friction. (Once done the systematic influence
of the gorilla could be incorporated.) 
    Consider Newton's Law of Inertia which says, in part, that a body in uniform 
[constant velocity = speed + direction] motion will naturally remain in this state unless acted 
upon by an outside influence.  Aristotle, on the other hand, said that the natural state of an 
object is at rest, that all objects seek this state, and that a constant outside action is required to 
keep an object in motion.
    In the words of W. Wolf "Lets go to the video tape" and consider what we observe in 
real life.  If I want to move a chair across the room I have to push on it continuously or else it 
quickly comes to rest.  Indeed to keep anything moving horizontally, near the surface of the 
earth, one has to keep pushing/pulling it or it will come to rest.  Our every day world is 
dominated by friction (of various kinds) that robs the energy of motion from an object 
(turning it to heat that is often difficult to account for) until it inexorably grinds to a halt.  
Thus Aristotle indeed summarized the world, as he knew it and as most of us know it.   
The leap of intellect that Newton et. al. realized was that: 1) the reason such objects 
came to rest could be attributed to an external frictional forces that always opposed the 
motion; and 2) in the absence of  such messy (every day) forces, the object could proceed in 
uniform motion never coming to rest.
    Really the only place that the ancients could observe objects where friction was 
negligible was in the regular motions of the planets across the sky.  Although the planets 
showed variations in their motion (speeding up, slowing down or even reversing direction for 
brief periods) these motions were exquisitely reproducible and regular and showed no signs of 
slowing down.  Aristotelian logic dictated that some constant outside action must be at work 
to keep these objects moving.  The church, which embraced the Aristotelian/Ptolemaic 
universe, could perhaps see the hand of god or angels in this constant outside push that kept 
the planets moving.
    Newton et. al. realized that the planets didn't slow down because there was no 
friction acting on them (there is no air and hence no air friction in space).  [Newton's precise 
ideas on this are not known to this author.]  Thus the planets were free to continue their 
motion undiminished.  At the same time Newton et. al. realized that the planets moved, 
approximately, in circular orbits about the sun.  A circle is not straight-line motion, so 
Newton knew there must be an external action (force) that bends the planets motion into a 
circle, and this force must pull toward the sun (the circular orbits center).  The quantification 
of this force was provided Newton's Universal Law of Gravity.  This law of gravity allows 
the understanding (or rather the mathematical prediction) of the dances of the planets in all 
their exquisite detail.  It is important to realize however, while the law of gravity provides us 
with the mathematical ability to explain and predict the motions of celestial bodies, it gives us 
no hint as to why is there gravity, and why it obeys this specific mathematics.  
This last point was emphasized beautifully by Robert Feynman (a true geniuses, and 
wonderful character in the history of modern physics).  He said, in effect, that as far as 
fundamental understanding goes, we had not come that far.  He noted that the ancients 
believed that angels pushed the planets along their paths in the sky and that now we only 
know that the angels actually push toward the sun.
In introductory physics courses there is a tendency to relegate the 500 lb. friction-
gorilla, for the most part, to the closet and to discuss in detail the easier case of frictionless 
motion.  The closet door is often opened only to consider the easiest case of a constant sliding 
surface frictional force.  As emphasized by the experience-based philosophy of Aristotle, true 
frictionless motion is rather uncommon in every day life.  This is done for the very good 
reason that the inclusion of air friction in the equations of motion for an object moving 
through the air (for example) makes them mathematically very difficult to solve.  Indeed in a 
full treatment (including the variation of air density with height) the equations becomes 
impossible to solve exactly analytically (that is to say with a paper and pencil using 
algebra/calculus).  As a mater of fact it was to solve the problem of a bullet traveling through 
air that the first electronic computer was constructed the at the U. of Penn. in the 2nd World 
War era (near the same time one was constructed in England to crack the German Enigma 
code-machine messages).
    If another part of this discussion we will consider some simple cases of air-frictional 
(drag) forces on objects.  Some typical approximations for the drag force will be solved 
analytically.  Also a simple numerical method of solving the equations of motion will be 
illustrated.  The numerical method could be generalized to cases that can not be solved with 

Footnote.  The Platonic philosophy of science elevated pure abstract reasoning to a holy 
pedestal.  At the same time it viewed experimental observation with extreme prejudice.  This 
stance is unequivocally deserving of the label as a very bad idea. Consider the classic Plutonic 
example of the observation of the shadow of a hand cast against a cave wall by a flickering 
campfire providing a poor guide to understanding the shape of the hand.  Plato used this to 
argue that observation was horribly fallible, could not be trusted and that pure abstract reason, 
regarding the essence of the hand, was the only true way to proceed.  Clearly the choice here 
is of a horrendously bad experiment being chosen to discredit the entire method of inquire.  
For a counter example consider the use of a distant, well defined light source (like the sun) 
and the observation of the shadow cast on a flat surface close to the hand.  This shadow would 
provide a rather good image of the morphology of the hand (given the constraint that one is 
precluded from looking directly at the hand).