I've read that when Newton made this remark, he may have been making
fun of someone - Halley, perhaps - for beilng short!

However, the naive interpretation is so much more comforting.

Copernicus, Galileo, and Kepler were giants.

Copernicus boldly proposed a simpler and more straightforward
understanding of the Solar System - which depended on the Earth being
simply one of its moving parts, rather than the center of the Universe
- at a time when such a notion was simply incomprehensible and
unimaginable to most people.

Galileo took important first steps in studying the physical world, he
first turned a telescope to the heavens, and he saw confirmation of
Copernicus' insight in the moons of Jupiter.

Kepler accurately worked out the shape of planetary orbits, and made
many other important studies.

And then came Newton, modestly noting that he could have not achieved
what he did, if he had not had the groundwork laid by these three men
to build upon.

What did Newton do? Did he engage in vandalism upon what Copernicus,
Galileo, and Kepler had wrought, as one contributor to this forum
keeps claiming?

Of course, to most of us here, that's so badly wrong as to be
ludicrous.

Newton worked out the laws of mechanics. Using the various
conservation laws for linear momentum, kinetic energy, and angular
momentum, one could work out the motions of interacting bodies to high
accuracy.

Okay, so now that we have computers, that let some people cheat at the
roulette table. So what?

There are those who believe that the chief consequence of Man's
technical progress has been the development of ever deadlier weapons
of war. And for the number two consequence, they will poiont to the
human misery attendant on the Industrial Revolution, as businessmen
found they needed less labor for production.

But others will blame these things on social and political factors,
judging science and technology instead by their potential - often
realized in many ways - to better the lives of humanity.

The same amount of land can feed more people. Diseases can be cured
that once could not be. And we live lives of luxury and convenience
instead of back-breaking toil.

Two other giants to remember, of course, are Euclid and Archimedes.

If it weren't for Leibnitz also inventing Calculus - and, unlike
Newton, revealing it to the world - perhaps Newton's contribution to
the world might have ended up as a dead end instead of a watershed.

But because we _did_ have Leibnitz, we then had Euler and Gauss... and
Laplace, who developed the modern science of celestial mechanics,
resting on the foundation laid by Newton, which the location of
Neptune be predicted by means of perturbation theory.

Tiny effects of Neptune's gravity, causing unexpected deviations of
the orbit of Uranus from what would be expected if only Jupiter and
Saturn were causing noticeable small deviations from the orbit,
strictly following Kepler's laws, that Uranus would have had around
the Sun were it and the Sun alone, let astronomers calculate where
Neptune must be located, so that they could point their telescopes
that way and find it!

If anyone doubted Newton's law of universal gravitation, his other
laws of mechanics, or the validity of the calculus, this achievement,
impossible without all these things being true, would have dispelled
anay remaining doubt.

The satellites in the Global Positioning System send radio reports of
their time and their position which enable recievers on Earth with
computers attached to determine their location with accuracy. The
reports from those satellites had to include corrections reflecting
Einstein's General Theory of Relativity - not just the much simpler
Speicial Theory of Relativity - for this to work properly.

Einstein, Le Verrier, James Watt... they, and many others, all stood
upon the shoulders of Isaac Newton. Our modern world simply would not
have been possible without his achievements.

John Savard