Page 189 - J. C. Turner - History and Science of Knots

PART IV. TOWARDS A SCIENCE OF KNOTS?

This Part contains five chapters which deal with aspects of
knot study in which respectively behaviour testing, mathe-
matical modelling (two kinds), experimentation, and com-
puter aided design of knots is involved.
The first chapter describes tests and results from many ex-
periments, dating from the mid-nineteenth century, designed
to find out how knots behave under load.
The second chapter traces the history of mathematical mod-
elling of knots, and studies of their topological properties,
from the time of C. F. Gauss in the early 1800s up to the
present day.
In the third chapter the question is asked whether the study
of knots can reasonably be called a Science. It is argued that
there is much work to be done on the modelling of knots
outside the field and the narrow constraints within which
topologists choose to work. Knot classifications in various
encyclopedia of knots, produced since the 1930s, are briefly
described. And the ideas and works of A. G. Schaake, who
since the 1980s has developed an extensive new theory of
braiding processes, are reviewed.
The fourth chapter describes studies made by D. Mandev-
ille (1910-1992), of a process which he called trambling. `To
tramble' is to produce a sequence of real knots by altering