🚀 go-pugleaf

baez@math.ucr.edu (john baez) writes:

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

The interesting point is that there was no concept of density for
Aristotle, yet his elucidation makes clear that he partially
understood the difference between mass and density.  This is, as
Aristotle himself points out, a vast advance on the previous
opinions.  

Aristotle thinks that "absolute mass" is a meaningless concept; that
we can compare two masses of gold or two of wood, but not one of gold
and one of wood.  When we do that, we are speaking of the heaviness of
gold itself, or wood itself--and then we are (in modern terms) really
speaking about density.  Aristotle isn't totally right; of course we
can compare the masses of lumps of different materials.  But it's key
to realize that where Aristotle says "light" and "heavy" he is usually
referring to what we call density, not what we call mass.

Denser objects do fall faster through non-vacuum media than less dense
objects.  Most of the cited passage, where it uses "heavy and light"
in fact refers exactly to more and less dense (as Aristotle's own
explanation makes clear).  In the atmosphere, for example, there is no
void, all the empty spaces are filled with air.

Now, the difference in density between a gold sphere and a wood one is
negligible compared with the density of the air, so when you drop
them, they both appear to fall at the same time.  But they do not fall
at equal rates; the wood one is slightly more bouyant than the gold
one; the difference is just to small to notice.  But put them in
water, whose density is closer to that of wood and gold, and the
difference is immediately obvious.

Another example is air bubbles in fluid.  Because of the way surface
tension works, big bubbles are less dense than small bubbles.  And so,
as differently sized air bubbles rise through fluid, the bigger ones
(being less dense) rise faster.  This is hard to notice in water, but
it's really obvious in shampoo.

Now it's not just density that matters.  The shape of the objects and
the viscosity of the fluid also matters.  So things are quite
complex.  But in fluids of uniform viscosity and objects of uniform
size and shape, density in fact has exactly the right properties
Aristotle thinks it should.  

The point here is that Aristotle was not totally right about the
matter, but he was in fact right about the point where he is usually
accused of being wrong, and that he was not some arrogant
anti-experimentalist, but rather someone who argued on the basis of
experience that Platonic anti-experimentalism was wrong.

Thomas