Page 323 - J. C. Turner - History and Science of Knots

Trambles 313

superseded. What took their place was 25 closely related bends arranged as if
inscribed on two sides of a single coin or medallion (Fig. 8). Desmond Man-
deville called it the Tramble Talisman. Previously unpublished, it is another
useful tool. You have already met most of the knots. Newcomers are:
front side ... Wh (Whatnot, #1407), the unstable form of the Jinx;
Kn (Knobble, #1424);
rear side ... Cf (Counter Fisherman);

The 15 front-side bends, those which share a common frontier or corner, con-
vert directly one into the other. They are all like-handed. Opposite handedness
can be an obstacle to trambling. Indeed the limited scope for trambling from
bends on the front of the Talisman to the 10 other bends on the back was
due to a change in handedness. Such changes could, however, be effected via
Bends C, G, L and R, which is why they are shown on the front (where they
belong) and also penetrating through in places to the rear.
Desmond claimed [7] to have tested out every one of the 70 possible
Talisman tuck-transformations. Each worked in both directions, 140 in all.

The Tramble Drum

Perhaps a world map of bends would actually be a sphere, as several bends
were later found to leak around the rim of the Talisman connecting front with
rear. Desmond Mandeville began work again and in 1986 made a simple drum-
shaped model (Fig. 9 shows it flattened out) of certain knot relationships he
was confident he had established [8].
It was a six-sided cylinder, divided in half to give 12 faces around, plus two end
plates. An A-prefix replaces the usual # Ashley reference. Only symmetrical
bends were used, except perhaps L, so Sheet Bends were omitted. Most were
like-handed. The sole newcomer is: Cl (Corrickle, #1451);
but note that P (Parallel Ends) was Z (the iZZard) in the Alphabend.

The full Carrick (Ca) proved to be more of a nexus than either the Reef
or Granny; and so it was imagined lying at the centre of the cylinder, from
where it could readily be tucked to give any one of the other 14 bends.