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

Regarding Galileo, John Denker wrote:

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

Actually "... On Two New Sciences" was written while Galileo was under house arrest. It's true it had to be published in Leiden because publishers in France, Germany and Poland had refused, and Galileo was prohibited from publishing in Italy.

Don Polvani
Northrop Grumman Corp.
Annapolis, MD

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
Sent: Thursday, June 01, 2006 1:23 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] nifty pendulum, conservation, et cetera

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.

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