Re: [Phys-l] nifty pendulum, conservation, et cetera

[John Denker <jsd@av8n.com>]

Bob LaMontagne wrote:

> I don't mean to hijack this thread, 

Not a problem.  The content of this thread has been as much about
history as anything else (although one might not know it from the
Subject: line).


> I remember the old Physical Science
> text by Holton making a big distinction between N1 and Galileo's Law of
> Inertia. As I remember, Galileo claimed that as long as a rolling object did
> not change it's distance from the center of the Earth it would not speed up
> or slow down. N1 applies to true straight line motion.

I don't know where that's coming from.  Galileo was waaay smarter
than that.

There are all kinds of legends about Galileo, such as that he was
the first real experimental physicist ... and therefore wasn't a
theorist, and didn't know much about theory.  Horsefeathers!  He
was a formidable theorist, and quite skilled in the mathematics
of his day.

He had all three bases covered:
 -- He knew about the mathematically-perfect parabola, about
  conic sections, and geometrical constructions.
 -- He had his experimental data, and he knew it did not
  exactly fit the parabola, partly due to random error of
  measurement, and partly due to systematic effects such
  as irreducible friction.  He discussed this.
 -- He knew on theoretical physics grounds that the mathematical
  parabola could not possibly be the right answer if the
  trajectory became long enough to cover distances on the order
  of the radius of the earth.  I suspect he even knew the right
  answer ... but he didn't blurt it out.  He did explictly say that
  the parabola was the right answer on laboratory scales and not
  on cosmic scales ... and he even explained *why* he wasn't going
  to say anything about the latter -- namely because he didn't want
  to get burned at the stake.


It's spooky reading Galileo's 1638 book _On Two New Sciences_.  Galileo
died a year before Newton was born, but much of Galileo's book reads
like a letter to Newton.
 -- Hey, look at this, you can take ratios of infinitesimals.
 -- Uniform straight-line motion of a free particle.
 -- Square-law motion of a uniformly accelerated particle.
 -- Parabolic motion compounded of unaccelerated motion in
  the horizontal direction, plus uniformly accelerated motion
  in the vertical direction.
 -- The magnitude of the resultant is given by adding the
  magnitude of the components /in quadrature/ (i.e. the root
  of the sum of the squares) which we nowadays explain in
  terms of vectors.
 -- The aforementioned hints about orbits being non-parbolic
  trajectories.

Perhaps more striking are the Galilean ideas that Newton did
not follow up:
 -- Conservation of energy.
 -- Things that look suspiciously like the principle of virtual
  work.
 -- Things that look like the beginnings of measure theory,
  250 years ahead of their time.

Galileo obviously knew about energy and conservation of energy;
Newton concentrated on forces and momentum, and apparently thought
momentum was "the" conserved quantity, to the neglect of energy.

What's even more amazing is that Galileo never wrote an equation
in his life.  Viète (sometimes called "the father of algebra) was
a generation ahead of Galileo, but the development of symbolic
algebra was not completed until Descartes, after Galileo had done
his work, and algebraic ideas spread slowly.  In any case, algebra
was just not part of Galileo's bag of tricks.  He relied on words
and on geometric constructions.

As far as I can tell, if the subject is the *laws* of motion,
Galileo was all over it, like seeds on a strawberry.  OTOH if we
are talking about the *equations* of motion, that's Newton.

============================

BC wrote:

> >  2) History is strange and complicated.

> I think T.S. Kuhn explains some of this.

Yes indeed.

> G.G. .... Wow! Better than I thought.

There's a lot of that going around.

I guess people are justifiably skeptical when they hear of Galileo's
work, and they naturally assume it couldn't possibly be as good as
it's cracked up to be ... but really it is that good;  indeed it is
better than most people realize.

It really is spooky reading.

 1) One sees the passage I quoted a couple weeks ago, about how we
  don't need any philosophical baloney about cause and effect, we
  just need to correctly predict and describe the behavior.  Wow,
  indeed;  that's the epoch right there.  That's the beginning of
  science as we know it.

 2) One sees Galileo's drawing of the interrupted pendulum.  Wow.
  That demo is still nifty, still worth doing today.

 3) One sees Galileo's drawing of a parabola ... I mean THE parabola.
  The beginning of physics as we know it.  Uniform motion in the
  horizontal direction, plus uniformly accelerated motion in the
  vertical direction, plus independence of the two components ....
  Wow.

 4) And there's the weight plus pulley plus larger weight on an
  inclined plane.  That demo is still worth doing today.  Principle
  of virtual work.

 *) Lots of other stuff.

===============

I am not suggesting that everybody go out and read the book, or
assign it to students.  It's full of pre-modern mathematics that
puts people to sleep.  But it's good to remember the book exists.

It's amusing to wonder what he might have accomplished if he
hadn't been arrested.