Page 320 - J. C. Turner "History and Science of Knots"

Trambles 311

Welcome back. You have completed a tramble. This route can, with
practice, be covered in two minutes or less. Desmond Mandeville did it between
stations on London's underground train system. And it can be reversed.

Mapping the Bends

Desmond Mandeville came to believe that trambles were a serious and sub-
stantial field of study. He demonstrated many more of them [4], going off in
all directions over an immense range.
There are at least a dozen distinct routes from Reef Knot to Granny Knot
[5, 6]. But there is no direct route, short of untying and starting afresh, from
the Reef to the common Sheet Bend. Each attempt only produces the left-
handed (wends opposed) variant. Shaw found this-look back at Fig. 1(a)-
(b). So the Reef is close-measured in tucks-to some knots, but remote
from others; although it can be a bridge between seemingly unrelated far-off
neighbours.
Bends are not simply strung together like beads; they have cross-linkages
too. He charted one such network. The map (Fig. 7), based upon the Al-
phabend, covered a small zone around the full Carrick Bends (Co)(Ca), and
revealed an almost crystalline symmetry and logic.
All the knots are reversible. That is, if both stands are shortened to become
wends (and wends lengthened into stands), a similar knot results. A Reef (R)
treated this way is another Reef (R'). Similarly G' and J' are bends created
from G and J, and Hc, Hc' are forms of the half Carrick Bend (#1444). L
and L', single Carrick Bends (#1445), are in practice identical.
But swap just ONE stand and wend for a different knot to appear. The
Reef turns into a Thief (R, T'). Fl is the Flemish or Figure of Eight Bend
(#1411) and Fl', M', V are derived from Fl, M, V.
All knots have a mirror-image, and this handedness has to be taken into
account in trambling. Bends on the left of the chart are left-handed, those on
the right are right-handed, except for certain neutral ones (R, R'; T, T'; L, L';
and Fl, Fl').
Si is the so-called left-handed Sheet Bend (#1432), but the name has
nothing to do with handedness. It hints at an inferior performance (which irks
left-handers like me). The basic tramble is shown by a broad line. It does not
stop at Si or Hc, which are intermediate steps to other bends.