In reply to GrandpaBig:
With specific regard to hand written notation to describe the hand movements to tie a particular knot:
I have to inform you that it has been tried many times in the past - and all end the same way (they die a slow death and are forgotten).
Harry Asher attempted to introduce a hand written notation system in his book - "The Alternative Knot Book" - but again, it never caught on and died a slow death.
Why?
In my view, all of these hand written notation systems fail to take into account a 'reference frame'.
That is, the notation only has meaning to the person who wrote the notation.
From an outsiders perspective, there is no reference frame from which to make sense of the information.
For example, the notional concept of 'up', 'down', 'left' and 'right' can only have meaning within a defined reference frame.
Think of an astronaut in space... which way is up? Is there an 'up'?
For example, some attempts have used phrases such as; "form an underhand loop" (which is meaningless). Underhand implies there must be an 'over' hand... and again, which direction is 'under' and which direction is 'over'. If the knot is flipped over, 'under' becomes 'over', and 'over' becomes 'under' (and 'left' is exchanged with 'right'). The reference frame must be very clearly specified and then maintained by the knot tyer.
Most notation systems also fail to take into consideration the concept of chirality and the fact that all knots have a mirror image 'inverse' form. Eg... tie your favorite knot and then hold it adjacent to a plane mirror... and you will see its reflected 'inverse' form - which is equally valid.
I wish you every success in your endeavor to develop a user friendly hand written knot notation system!
If you succeed (I do believe anything is possible) - i will predict that it solves the reference frame problem and uses chirality to describe loop geometry.
...
In term of computer code - this is a different matter.
