|A page from Einstein's notebook on the formulation of general relativity--|
see linke above to Prof. Norton's web-page
|Dirac's Relativistic Equation for the Free Electron|
There is one other beautiful equation I want to mention, which in my opinion is as important as the two above: Boltzmann’s equation for entropy (S) in terms of thermodynamic probability (W),
S= k logarithm(W)(k is the Boltzmann constant).
the Equation S= k logW
is at the top and the bust is of Boltzmann
or, you can’t unscramble eggs without doing work),
a physical law that, according to Einstein, will still be true many hundreds of years from now, even if all other theories are invalidated.
Why is science is explained mathematically? Or, as the renowned mathematical physicist, Eugene Wigner, puts it in his article, whence “The Unreasonable Effectiveness of Mathematics in the Natural Sciences"? The question was, of course, answered some 500 years ago by Galileo:
“The laws of nature are written by the hand of God in the language of mathematics.”We want to understand the world and to recognize, as Scripture declares, that God looked on His Creation and saw that it was good. When you see children playing with toy cars or other objects and arranging them neatly in a line, you see the first beginnings of a desire for order and sequence.
|Nautilus shell pattern illustrating the Fibonacci Sequence|
(from "Heritage Math", by Savannah Morrow)
I want to emphasize that the beauty of pleasing proportion comes from more than symmetry. Symmetry can be an element of beauty, but it neither a necessary element nor always a sufficient element. It is the apprehension of order, an order that appeals to our intellect, that is the core of beauty. This appeal to intellect distinguishes beauty from that which is simply good, according to St. Thomas Aquinas:
|The "Big Trees" of Yosemite Park|
(note the small size of the person
in the foreground.)
And all this became reinforced, later on when I became a Catholic (but more of that in a later blog) and saw that all of science was realized in Psalm 19a, “The Heavens declare the glory of God.”