No need to be afraid, it is easy to use even if it must have been not
at all easy to 'prove'
on mathematical and logical grounds.
You can drive a car without being a car mechanic or and engineer at
Detroit, cannot you ?
You can use a house cleaning product without being a chemist ?
Well you can use these moves without being a topologist.
When trying to transform one
knot into another configuration, to find an 'equivalent' knot,
not allowed to undo and lay again the rope, no
re-threading of any part, no cutting
and no gluing, only 'smooth,
you may only 'move' it with Reidemeister's
If you want to apply the Reidemeister's moves it will
be that much easier if you
real rope knot.
It will have the added advantage of
'desensitizing' you about topology and there seems,
from past sorry experience on
Igkt forum, to be much need of that cure in the knotting
offense intended just as there is no offense intended in a medical
Similar trick it was that I used when writing what I have named the
Crossings (DSC) and the Great Sequence of Crossing ( GSC)
Which leads us to...
You need - it is compulsory it is in fact - to take
the greatest care in avoiding useless
get the only number of crossing that is useful :
number of crossings.
look at that to convince yourself that PLUS/MINUS is
equivalent to RIGHT/LEFT
which is equivalent to "Z" / "S".
Here is an easy trick to get the sign of the crossing :
Put one of your hand flat, palm down on the
strand that is in the
upper position in the
Strand is entering by the heel of the
hand and exiting by the
tip of the middle finger.
The lower strand in the crossing is supposed to enter the base of your
thumb and exit at its
- - - if you have to use your RIGHT hand to get the correct
configuration then it is a
crossing of sign PLUS.
- - - if you have to use your LEFT hand to get the correct
then it is a crossing
of sign MINUS
Another mnemonic trick that came to my mind :
Cross your forearms in front of you.
Only 2 ways to do that, just as it is for the strands in a crossing :
either RIGHT or
forearm goes in the Upper position ( that is the
one that is nearer to your trunk if
forearms are held more or less
vertical or the one nearer the sky if they are held more or
less horizontal ).
It is the direction pointed to by the
forearm to that is be retained as the
So the forearm which has the "upper hand" has its hand
the correct direction for
the letter and it is giving the "oblique bar"
of the letter :
is pointing to Your RIGHT
so it is "RIGHT"
and the left
forearm draw the
oblique bar of the Z.
is pointing to Your LEFT so it is "LEFT" and the
forearm draw the oblique
bar of the S.