Today, we wonder what to tell our children about
mathematics. The University of Houston's College of
Engineering presents this series about the machines that
make our civilization run, and the people whose ingenuity
The book, The Beginner's
Guide to Constructing the Universe, is by math
teacher Michael Schneider . I
doubt I'll see the universe quite the same after reading
it. It's all about mathematics.
For Schneider, math takes three forms: secular, symbolic,
and sacred. We learn secular math in grade school.
"If pens cost $1.25 each, how many will ten dollars buy?" --
that sort of thing.
Schneider's concern is with the way symbolic mathematics
flows from nature into our art and technology. We sense
the number 6 in the hexagons of a honeycomb; 3 in the
triangular form of clover; 5 in a cat's pentagonal face;
octagonal 8 in the pattern of spider legs. Earth as a
whole evokes the number one. We take nature's symbolic
forms and build them into our science and our designs.
Mathematics becomes sacred when we let it transform our
consciousness. That transformation reflects in the
religious use of symbolic math -- the Holy Trinity
harmonizes the numbers one and three. The Day of Rest
dramatizes the number seven. Schneider doesn't press the
point. We can become mathematical mystics if we wish. But
his business is to open our eyes to numbers in nature and
then help us to understand our response to those numbers.
So the book deals in the rich symbolic content of the
numbers one through ten. Those symbols show themselves in
two ways: directly in nature, and in art and technology
as they mirror nature.
The essential symbol of each number is a polygon with
that many sides -- triangles, squares, pentagons,
hexagons. The polygon with two sides is only a line. The
polygon with one side reduces to a point -- the center of
a circle. Schneider then shows how to build up every
other polygon from intersections of circles -- so each
number is in fundamental harmony with every other number.
Take the number five: On one level, nature shows us fives
in starfish, human fingers, the face of a sand dollar and
the cross-section of an apple core. We then carry those
geometric themes over into the art and science of our own
The natural spiral is constructed from a pentagram, and
we find those spirals in whirlpools, fingerprints, and
the vortex eye of Jupiter -- in galaxies, red cabbage,
and the chambered nautilus. That same spiral is also shot
through our art and technology. You can use a pentagram,
for example, to generate the golden section -- that
essential proportion of classical architecture.
After Schneider has done that with each number from one
to ten, I find myself back at his starting point -- which
is education. We might well weep for the poverty of a
math class that never takes us beyond secular
mathematics. The full value of math, like any other
knowledge, only comes clear when we finally weave it back
into the fabric of our whole being. And Schneider has
given us just a hint -- of how we might do that for our
I'm John Lienhard, at the University of Houston, where
we're interested in the way inventive minds work.