17 entanglements

2  coins. pennies.  baby toy with 2 suns

glass held by hand

tie

cube tied

hair dryer cord

phone cord

hair braiding

twisted rope, gas station air pump

coil up ropes, ship docking

electrical extension cords

computer cord, power, LAN

head phone, DNA, belt

pastries  (demo via a large paper towel, slit in the middle)

SU(2)/S)(3) double covering picture

Electron spin 1/2, using SU(2) representation

untangle chains, bike chains

group game of untangling hands: why we must let go (¼ chance of a trefoil knot) – this is something different

The tie is definitely isomorphic to SU(2)/SO(3):

create a configuatration space where 2 rotation is needed to bring back to  identity .

tangling, untangling.

Wilzek generalize it to spin 1/N?  identity of exchange.  Is this concept connected?  Not geometrically, as I have reasoned once.

Now how does the 2-coin problem isomorphic to the tie problem?

The 2^nd coin serves to previde a reference to distinguish the orientation of the 1^st coin, and make the situation so that going quarter of the way leads the two coin to face each other, showing that they are equivalent to one rotating 180-deg.

Relative rotation of 180-deg is done via absolute rotation of 90-deg, because both coins can be thought of as traveling/