Laws of Form

The theme of this book is that a universe comes into being
when a space is severed or taken apart. The skin of a living
organism cuts off an outside from an inside. So does the cir-
cumference of a circle in a plane. By tracing the way we represent
such a severance, we can begin to reconstruct, with an accuracy
and coverage that appear almost uncanny, the basic forms
underlying linguistic, mathematical, physical, and biological
science, and can begin to see how the familiar laws of our own
experience follow inexorably from the original act of severance.
The act is itself already remembered, even if unconsciously,
as our first attempt to distinguish different things in a world
where, in the first place, the boundaries can be drawn anywhere
we please. At this stage the universe cannot be distinguished
from how we act upon it, and the world may seem like shifting
sand beneath our feet.
Although all forms, and thus all universes, are possible,
and any particular form is mutable, it becomes evident that
the laws relating such forms are the same in any universe. It
is this sameness, the idea that we can find a reality which is
independent of how the universe actually appears, that lends
such fascination to the study of mathematics. That mathematics,
in common with other art forms, can lead us beyond ordinary
existence, and can show us something of the structure in which
all creation hangs together, is no new idea. But mathematical
texts generally begin the story somewhere in the middle, leaving
the reader to pick up the thread as best he can. Here the story
is traced from the beginning.