-------------------

12/18/2011 Justin Coslor -- Knot Theory Ideas

Perhaps Knot Theory models could be computed by treating the
string as a numberline, and mark its intersections (crossings)
and loops or angle changes (of various radiuses) along the 
numberline representation, similar to a timeline. In that manner,
large knots are made out of combinations of smaller knots that 
occur in a series (one after another) along the string numberline,
*similar to how various prime numbers or prime number equations 
occur in series when representing a computer file or hard drive 
as a single gigantic number.

(*Note: for that kind of prime substitution data compression 
the prime ordering could skip over the first 10,000 or so 
prime number orderings such that the 10,001 prime number is 
represented by the number 1, and so on since the first 
however-many small prime numbers substituted for their 
ordering numbers do not provide a smaller representation, 
because they need to make accomodations for the syntax 
markers ("p" and ",").)

Some knots when laid flat on a table look like the same knot 
but are opposites such that when flipped over they look the 
same from both sides, while other knot pairs look different 
when one is flipped. Those could be called equivalents or mirrors. 

The Knot Theory numberline representation technique could be 
applied to many other topics such as alternative route mathematics, 
and terrestrial/aquatic/aerial/space navigation, and can represent 
curvatures as straight lines. Besides navigation, knots are 
related to the shape of time. In navigation there are an infinite 
number of different velocity models for every knot theory 
numberline model (i.e. speed up here, slow down here, speed up 
some more here, etc, in various ways but in the same space 
knotwork path).

-------------------