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Galileo
Philosophy is written in this grand book, the universe, which stands
continually open to our gaze. But the book cannot be understood
unless one first learns to comprehend the language and read the
letters in which it is composed. It is written in the language of
mathematics, and its characters are triangles, circles, and other
geometric figures without which it is humanly impossible to understand
a single word of
it.
--- The Assayer (Il saggiatore), 1623
Act one, scene four
Valentine: When your Thomasina was doing maths it had been the same
maths for a couple of thousand years. Classical. And for a century
after Thomasina. Then maths left the real world behind, just like
modern art, really. Nature was classical, maths was suddenly
Picassos. But now nature is having the last laugh. The freaky
stuff is turning out to be the mathematics of the natural world.
Tom Stoppard's "Arcadia"
Faber and Faber paperback edition, 1993, p. 44-5.
Mathematics
Mathematics as an expression of the
human mind reflects the active will, the
contemplative reason, and the desire for
aesthetic perfection. Its basic elements
are logic and intuition, analysis and
construction, generality and
individuality. Though different
traditions may emphasize different
aspects, it is only the interplay of
these antithetic forces and the struggle
for their synthesis that constitute the
life, usefulness, and supreme value of
mathematical science.
R. Courant, 1941
in What is Mathematics?
Lasers
Laser beams reflected from the moon,
allowing measurement of the moon's distance,
is only one illustration of the
spectacular quality of laser light.
There are many others, as well as myriad
everyday uses for the laser. But for
several years after the laser's invention,
colleagues used to tease me about it,
saying, "That's a great idea, but
it's a solution looking for a problem."
The truth is, none of us who worked on the first lasers
imagined how many uses there might eventually be.
This illustrates a vital point that cannot be overstressed.
Many of today's practical technologies result from basic
science done years to decades before. The people involved,
motivated mainly by curiosity, often have little idea as to
where their research will lead. Our ability to forecast
the practical payoffs from fundamental exploration of
the nature of things (and, similarly, to know which of today's
research avenues are technological dead ends) is poor.
This springs from a simple truth: new ideas discovered
in the process of research are really new.
Charles H. Townes
How the Laser Happened,
p. 4.
Charles Townes, with Nikolai Basov and Alexander Prokhorov,
is winner of the 1964 Nobel prize in physics.
Zen Proverb
True beauty is a deliberate, partial breaking
of symmetry.
The Dynamics of Ambiguity, Giuseppe
Caglioti, p. 55.
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