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Article #16993

Re: GRAVITY (John Baez)

#16993
From: john baez
Date: Mon, 16 Feb 1998 00:00
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In article <6cb0qc$3mt$1@agate.berkeley.edu>,  <bunn@pac2.berkeley.edu> wrote:

>When John said you should look in the "Physics," he was mostly going
>for comic effect, I think.  Either that, or he just misspoke.  The
>place where Aristotle really goes into detail about why heavy objects
>fall is in "On the Heavens," books 3 and 4.

My original post was indeed rather snide, but citing Physics instead of
De Caelo was an error on my part, not a deliberate joke.  

Here's a bit from book IV, part 2:

     Those of our predecessors who have entered upon this inquiry have
     for the most part spoken of light and heavy things only in the
     sense in which one of two things both endowed with weight is said
     to be the lighter. And this treatment they consider a sufficient
     analysis also of the notions of absolute heaviness, to which their
     account does not apply. This, however, will become clearer as we
     advance. One use of the terms 'lighter' and 'heavier' is that
     which is set forth in writing in the Timaeus, that the body which
     is composed of the greater number of identical parts is relatively
     heavy, while that which is composed of a smaller number is
     relatively light. As a larger quantity of lead or of bronze is
     heavier than a smaller-and this holds good of all homogeneous
     masses, the superior weight always depending upon a numerical
     superiority of equal parts-in precisely the same way, they assert,
     lead is heavier than wood. For all bodies, in spite of the general
     opinion to the contrary, are composed of identical parts and of a
     single material. But this analysis says nothing of the absolutely
     heavy and light. The facts are that fire is always light and moves
     upward, while earth and all earthy things move downwards or
     towards the centre. It cannot then be the fewness of the triangles
     (of which, in their view, all these bodies are composed) which
     disposes fire to move upward. If it were, the greater the quantity
     of fire the slower it would move, owing to the increase of weight
     due to the increased number of triangles. But the palpable fact,
     on the contrary, is that the greater the quantity, the lighter the
     mass is and the quicker its upward movement: and, similarly, in
     the reverse movement from above downward, the small mass will move
     quicker and the large slower. Further, since to be lighter is to
     have fewer of these homogeneous parts and to be heavier is to have
     more, and air, water, and fire are composed of the same triangles,
     the only difference being in the number of such parts, which must
     therefore explain any distinction of relatively light and heavy
     between these bodies, it follows that there must be a certain
     quantum of air which is heavier than water. But the facts are
     directly opposed to this. The larger the quantity of air the more
     readily it moves upward, and any portion of air without exception
     will rise up out of the water.

     So much for one view of the distinction between light and heavy.
     To others the analysis seems insufficient; and their views on the
     subject, though they belong to an older generation than ours, have
     an air of novelty. It is apparent that there are bodies which,
     when smaller in bulk than others, yet exceed them in weight. It is
     therefore obviously insufficient to say that bodies of equal
     weight are composed of an equal number of primary parts: for that
     would give equality of bulk. Those who maintain that the primary
     or atomic parts, of which bodies endowed with weight are composed,
     are planes, cannot so speak without absurdity; but those who
     regard them as solids are in a better position to assert that of
     such bodies the larger is the heavier. But since in composite
     bodies the weight obviously does not correspond in this way to the
     bulk, the lesser bulk being often superior in weight (as, for
     instance, if one be wool and the other bronze), there are some who
     think and say that the cause is to be found elsewhere. The void,
     they say, which is imprisoned in bodies, lightens them and
     sometimes makes the larger body the lighter. The reason is that
     there is more void. And this would also account for the fact that
     a body composed of a number of solid parts equal to, or even
     smaller than, that of another is sometimes larger in bulk than it.
     In short, generally and in every case a body is relatively light
     when it contains a relatively large amount of void. This is the
     way they put it themselves, but their account requires an
     addition. Relative lightness must depend not only on an excess of
     void, but also an a defect of solid: for if the ratio of solid to
     void exceeds a certain proportion, the relative lightness will
     disappear. Thus fire, they say, is the lightest of things just for
     this reason that it has the most void. But it would follow that a
     large mass of gold, as containing more void than a small mass of
     fire, is lighter than it, unless it also contains many times as
     much solid. The addition is therefore necessary.

     Of those who deny the existence of a void some, like Anaxagoras
     and Empedocles, have not tried to analyse the notions of light and
     heavy at all; and those who, while still denying the existence of
     a void, have attempted this, have failed to explain why there are
     bodies which are absolutely heavy and light, or in other words why
     some move upward and others downward. The fact, again, that the
     body of greater bulk is sometimes lighter than smaller bodies is
     one which they have passed over in silence, and what they have
     said gives no obvious suggestion for reconciling their views with
     the observed facts.

     But those who attribute the lightness of fire to its containing so
     much void are necessarily involved in practically the same
     difficulties. For though fire be supposed to contain less solid
     than any other body, as well as more void, yet there will be a
     certain quantum of fire in which the amount of solid or plenum is
     in excess of the solids contained in some small quantity of earth.
     They may reply that there is an excess of void also. But the
     question is, how will they discriminate the absolutely heavy?
     Presumably, either by its excess of solid or by its defect of
     void. On the former view there could be an amount of earth so
     small as to contain less solid than a large mass of fire. And
     similarly, if the distinction rests on the amount of void, there
     will be a body, lighter than the absolutely light, which
     nevertheless moves downward as constantly as the other moves
     upward. But that cannot be so, since the absolutely light is
     always lighter than bodies which have weight and move downward,
     while, on the other hand, that which is lighter need not be light,
     because in common speech we distinguish a lighter and a heavier
     (viz. water and earth) among bodies endowed with weight. Again,
     the suggestion of a certain ratio between the void and the solid
     in a body is no more equal to solving the problem before us. The
     manner of speaking will issue in a similar impossibility. For any
     two portions of fire, small or great, will exhibit the same ratio
     of solid to void, but the upward movement of the greater is
     quicker than that of the less, just as the downward movement of a
     mass of gold or lead, or of any other body endowed with weight, is
     quicker in proportion to its size. This, however, should not be
     the case if the ratio is the ground of distinction between heavy
     things and light. There is also an absurdity in attributing the
     upward movement of bodies to a void which does not itself move.
     If, however, it is the nature of a void to move upward and of a
     plenum to move downward, and therefore each causes a like movement
     in other things, there was no need to raise the question why
     composite bodies are some light and some heavy; they had only to
     explain why these two things are themselves light and heavy
     respectively, and to give, further, the reason why the plenum and
     the void are not eternally separated. It is also unreasonable to
     imagine a place for the void, as if the void were not itself a
     kind of place. But if the void is to move, it must have a place
     out of which and into which the change carries it. Also what is
     the cause of its movement? Not, surely, its voidness: for it is
     not the void only which is moved, but also the solid.

     Similar difficulties are involved in all other methods of
     distinction, whether they account for the relative lightness and
     heaviness of bodies by distinctions of size, or proceed on any
     other principle, so long as they attribute to each the same
     matter, or even if they recognize more than one matter, so long as
     that means only a pair of contraries. If there is a single matter,
     as with those who compose things of triangles, nothing can be
     absolutely heavy or light: and if there is one matter and its
     contrary-the void, for instance, and the plenum-no reason can be
     given for the relative lightness and heaviness of the bodies
     intermediate between the absolutely light and heavy when compared
     either with one another or with these themselves. The view which
     bases the distinction upon differences of size is more like a mere
     fiction than those previously mentioned, but, in that it is able
     to make distinctions between the four elements, it is in a
     stronger position for meeting the foregoing difficulties. Since,
     however, it imagines that these bodies which differ in size are
     all made of one substance, it implies, equally with the view that
     there is but one matter, that there is nothing absolutely light
     and nothing which moves upward (except as being passed by other
     things or forced up by them); and since a multitude of small atoms
     are heavier than a few large ones, it will follow that much air or
     fire is heavier than a little water or earth, which is impossible.

This was taken from

http://classics.mit.edu/Aristotle/heavens.36.ivpart2.html
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From: baez@math.ucr.edu (john baez)
Subject: Re: GRAVITY (John Baez)
Date: 1998/02/16
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