I will not try to explain to you that, to define the relation 1+1=2, *Principia Mathematica* needed/used 150 pages of difficult Set Theory definitions..

And was seriously *dented* by far fewer, but resounding pages

from Goedel, where Hilbert & Frege also tried hard but failed.

Yes, defining the "simple" is ... not so simple!!

(And these were bright thinkers amongst bright thinkers!)

Can you see the shaping of "knot" definitions et cetera as activities

in this realm of deliberation, distinguishable from just putting up

a knot-form for consideration of (possible) practical use?

In fact, I might suggest that it is as well a fit to a "theory" (and

maybe a better name), philosophical --but *beside* "practical"--

heading that one simply explores the *knot space* of structures

that can be roughly conceived as points in some vast matrix,

a knot universe (multi-dinensioned). Some things can be stated

and projected as series: the

*overhand* ("pretzel"), and next

a dble.overhand and so on, but then in the multiple forms one

has different orientations (anchor bend, stangle knot, ...?) of the

same topology.

Considerations of which seemingly "simple" things can quickly

be frustrating (to me, at least), as interconnections abound.

Of course, the mere

*mention* of some aspect is not throwing

things off; that is different from where the thread topic focuses

on that aspect, in contradistinction to something "practical".

--dl*

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