Page 324 - J. C. Turner "History and Science of Knots"

Rambles 315

Summary
When trambling's innovator Desmond Mandeville died, at the age of 82, few
knot tiers understood trambles. Many were bemused by them. He had devised
shorthand symbols akin to chemical formulae for trambling techniques [11],
but even his keenest followers struggled with the cryptic language and failed
at fluency in it; no doubt it deterred many practical knotters, being too much
like topological knot theory.
Topology is a mystery to even erudite knot tiers. They are surprised to
hear that its practitioners do little or no real knot tying, and that it isn't
easy-mathematically -to sort out a Reef Knot from a Granny knot. Knot
theorists transform imaginary knots, without any tucking or untucking. They
have no use for ends, unless those ends stretch to infinity; whereas Desmond
Mandeville sought an ergonomic explanation of knot relationships [12]. You
cannot tramble without ends, or with just the two ends of a single piece of
cord. Trambling uses both stands and wends. Tension, flexibility and friction
too-subjects not in any topology syllabus-also intrude. If knot theory is
mental gymnastics, then trambling is free-for-all wrestling.
Both, nevertheless, are pure research done for its own sake. Practical uses
may occur later. Meanwhile each seeks in its own way to unravel what the
19th century mathematician Tait [16] called `beknottedness'.
Trambling shines new light on knots and makes it possible to interpolate
or extrapolate where others may lurk in the shadows. Trambles open up
untrodden areas for puzzle addicts to explore. They might also add to scientific
knowledge. Knot classification is becoming significant in the understanding of
polymers, DNA and other enzymes, and the logic of space [17]. So put aside
those molecular models made from sticks and balls. Take a couple of cords
and try trambling.
Desmond Mandeville left detailed notes [13], his correspondence and pub-
lications. These include a trio of testing parlour games, one of which is like a
point-to-point (steeplechase) horse race [14].

Acknowledgements

The writer gratefully acknowledges Mrs. Norah Mandeville's help, making her
late husband's trambling research available to him.
Knotting Matters is the quarterly journal of the International Guild of
Knot Tyers, published in Suffolk, England.
Rob Chisnall's cartoon `Now the What Goes Where' originally appeared
in Knotting Matters, Issue No. 3 (April 1983), page 3.