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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).
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