Hey Judith,
I enjoyed your
posting on Celtic knots. I thought that I would try and respond in
kind. This one still seems relevant to me and I thought that everyone
would enjoy it, perhaps even John. Do you like it
John?
Judith said...
All physical Celtic knots (as opposed to pictures of
them) are made of the same three ingredients: a piece of long, thin
material, "empty" space, and the relations which create the pattern. There
are many distinctive patterns that can be created using these three ingredients,
one of which is represented in the photo. Clearly, we could recreate the exact
same pattern using a shoelace, a piece of ribbon, a leather strap, a willow
branch... anything that has a few basic properties such as
sufficient length, width, and flexibility. The material used doesn't really
matter beyond those basic requirements. What matters are the relations, which
are unique to each pattern. Interestingly, these relations can also be analyzed
and categorized (for example: relations of the physical material to "empty"
space, relations of physical material to itself, etc.). But the whole point (of
these particular relations and these ingredients) is the end result-- to
generate this particular design; this specific Celtic knot. Everything else
is entirely driven by that imperative.
Among the things that I find interesting about
these knots is that mathematicians study these knots using the branch of their
discipline called topology. Apparently this is the same branch of
mathematics from which Category Theory arose.
Everything is connected.
David
