Page 300 - J. C. Turner "History and Science of Knots"
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On Theories of Knots 291
T U
LEVEL
THE RKT
Fig. 13. The Evolution Tree for String Runs of Regular Knots [25], [15, Pamphlet
6]. It shows the way string-runs can evolve upwards, from the trunk. For example,
to construct by cylindrical braiding a 5 Part/8 Bight Turk's Head, one has to, in
effect, pass through the 1P/1B, 1P/2B, 2P/3B, and 3P/5B forms first. Note that
the whole tree grows from the `forms' 0/1, 1/0 and 1/1, using mediant additions.
8.2. Quotations from `Knots-Facts and Fallacies'
In 1992 Schaake published, privately, a pamphlet [15, Pamphlet 8] called
Knots-Facts and Fallacies, in which he set out many of his views on what a
`real knot theory' should consist of. He made many scathing remarks about
what he called the `classical knot theory of hypothetical knots'-and even in-
cluded inflammatory opinions about mathematicians. We will pass over the
latter; but we feel it is instructive to include here some of the former kind of
