Page 275 - J. C. Turner - History and Science of Knots

On Theories of Knots 265

what about Linguistic Science--can there be one?
In the vast new world of Computers, is it only the study of hardware
systems that constitutes Computer Science? Do the theories of the software
that drive them not qualify also to be under that umbrella? In the 1960s
and 1970s a continuous debate raged as to whether the theory and practice of
Computing could be called Science. Now most Universities in the world have
Computer Science Departments, even Schools of Computer Science.
Is Mathematics a Science? That seems harder to decide; if not, what
about part of it, such as Number Theory? This has been called `the most
exact Science'; but does it qualify* to be called Number Science? Some would
have us lump together mathematics, computer science, parts of philosophy
and the theoretical parts of science and engineering, and place them in a box
labelled the logical sciences; because, they would claim, they use the method of
logical deduction from axioms. That is patently wrong; or, at best a half-truth.
I claim that most new mathematics is arrived at empirically, by mathemati-
cians `playing with' their materials. They seek and find patterns, which they
then formulate as theorems (conjectures). Only after this experimental pro-
cess do they turn to the (often difficult, sometimes impossible) task of proving
the theorems, linking them to axioms via previously proved theorems. Any-
way, not all branches of mathematics, or the other subjects listed, have been
axiomatised.
It is evident that there are grey areas, between subjects which are univer-
sally labelled `Science' (such as Chemistry and Physics) and those which are
clearly `non-Science' ('Arts' subjects such as Greek and Latin).
Where does the study of Knots fit into this spectrum? Our next section
examines this question.

3. Is there a Science of Knots?
Under the first definition from the Collins Dictionary, it is impossible to deny
that the study of knots is a Science. There is a considerable body of knowledge
on the subject; and that has been organised systematically in a number of
ways, as we shall show below.
Under the second definition, however, the evidence has to be looked at
more closely before arriving at a decision. There is no doubt (in this author's
mind) that knots are phenomena which make up part of the material and
physical universe-even though, in order for them to exist, they usually are
first created by man or woman (they do occur naturally; for example, consider

`A distinguished mathematician of the last half-century, Freeman Dyson, is on record [3] as
believing that number theory is applied mathematics. He says: `You are not creating ideas;
you're just applying methods and using numbers as your experimental material.'