Page 303 - J. C. Turner "History and Science of Knots"

294 History and Science of Knots

Leaving those somewhat facetious comments aside, we believe we have
presented a reasonable case for the affirmative-The Study of Knots may be
designated a Science! We believe that this Chapter, allied with the evidence
of many of the other Chapters in this book, strongly supports our view. More-
over, we believe we have shown that the field of this Science is much wider than
the restrictive one of the topological knot theorist; to use Schaake's words, it
must be broad enough to deal with `real knots', as well as `hypothetical ones'.
It seems pertinent here to give the following quotation, from a discussion
about the position which the science of number occupies with respect to the
general body of human knowledge:*

It seems to me that what Philosophy lacks most is a principle of
relativity ...
A principle of relativity is just a code of limitations: it defines
the boundaries wherein a discipline shall move and frankly admits
that there is no way of ascertaining whether a certain body of facts
is the manifestation of the observata, or the hallucination of the
observer. Tobias Danzig

In these terms, I have tried to shed light on what might be a principle of
relativity for the Philosophy of Knots.
Whether you will agree with me or not on the above issues, I know I
can assert, without any doubt, that whatever it is called, the study of knots
will continue to fascinate and exercise the minds of men and women for as
long as humankind exists. That is assured because knots will always be useful
to them; because knots are beautiful and mysterious objects; and because
the expanding fields of knot studies will pose ever more complex problems,
challenging our descendants to solve them.

10. References

1. C. W. Ashley, The Ashley Book of Knots
(Doubleday, New York, 1944) 620 pp.
2. C. L. Day, The Art of Knotting and Splicing
(Dodd, Mead and Company, New York, 1st edn. 1947; Naval Institute
Press, Annapolis, Maryland, 2nd edn. 1955) 225 pp.
3. D. J. Albers, `Freeman Dyson: Mathematician, Physicist, and Writer',
The College Mathematics Journal, MAA 25 No. 1 (January, 1944)
2-21.

*In:`The Two Realities ', from Number- The Language of Science (Doubleday, 1954) 232-
253.