Civilization advances by
extending the number of important operations which we can perform
without thinking about them.
Alfred North Whitehead
Introduction to Mathematics (1911)
...it is certain that the real function of art is to increase our
self-consciousness; to make us more aware of what we are, and therefore
of what the universe in which we live really is. And since mathematics,
in its own way, also performs this function, it is not only
charming but profoundly significant. It is an art, and a great art.
John W.N. Sullivan
There is one very good reason to learn programming, but it has nothing
to do with preparing for high-tech careers or with making sure one is
computer literate in order to avoid being cynically manipulated by the
computers of the future. The real value of learning to program can only
be understood if we look at learning to program as an exercise of the
intellect, as a kind of modern-day Latin that we learn to sharpen our
All deep things are song. It seems somehow the very central essence of
us, song; as if all the rest were but wrappages and hulls!
There's music in all things, if men had ears:
Their earth is but an echo of the spheres.
The pleasure we obtain from music comes from counting, but counting
unconsciously. Music is nothing but unconscious arithmetic.
Gottfried Wilhelm Leibniz
Music is everybody's possession. It's only publishers who think that
people own it.