this bend is not simple.
We enter into a very complex subject here, knot4u !
What is "simplicity' is debatable, and it is not a simple matter at all, that is for sure ... I use the word in a restricted, quantitative sense, that has to do with the number of
elements , and the number of
relations between elements, an entity has. You know Newton universal gravitation equation, Maxwell s equations, ( in their antisymmetric tensor form), Einstein gravitational field equations... They are "simple", in that they relate a few quantities with a few relations, yet, in a broader sense they are not simple, not at all !
We can easily say that a tetrahedron or a cube, for example, are the simpler Archimedes polyhedra. However, our evaluation might depend upon the machine and the language we use to describe them. We can actually
count simplicity, by counting the number of bits and bytes a particular computer, with a particular program that is able to describe a thing, will use. (Computational complexity : A relevant web book, at (1) , and a simple article, at (2)). But what happens with another computer, and with another compute language ? In some computers and some computer languages a thing can be described with a shorter, more economical in bits and bytes program than another thing, so we can argue that the former is simpler than the later... but, in some others, the order of simplicity count can well be reversed ! And the matter can be vastly more complicated than that, because brains evolved to understand the difference between a cow and a tiger, not between the symmetric sheet bend and the ABoK#1406 ! For a cat, a mouse is a much simpler thing than either a tetrahedron or a cube, that is for sure.
In the field of knots, to count complexity in an objective way, should we include only the geometrical elements of a knot, or also the steps - tucks or whatelse -, we have to follow to tie this knot ? Should we count only the 3D geometrical elements of the tied knot, or also the physical mechanisms needed to keep this 3D machine in a static equilibrium ? A knot simple in geometrical elements count, but complex in physical mechanisms count, is it a simple or a complex knot ? You tell me...
At the end of the day, what counts are not semantics, but our lives... and lives, being so short, should better be interesting to live. This bend is an interesting thing, and when we learn interesting things, we feel we live longer...
1)
http://www.cs.princeton.edu/theory/complexity/bookWebNov06.pdf2)
http://pespmc1.vub.ac.be/COMPLEXI.html