Page 273 - J. C. Turner "History and Science of Knots"

264 History and Science of Knots

special, singled-out properties. Some of these properties will grab the attention
of investigators-excite them in a way which directs their efforts to understand
the properties more clearly, more deeply. Often, with growing knowledge of
the objects, they begin to gain some kinds of control over the objects. They
learn how to manipulate them in ways which have interesting, maybe useful,
consequences. They make hypotheses about them, such as: `If I do this to
these objects, and that to those ones, the results will be such and such.' Then
they work out experimental methods for testing their hypotheses.
Testing of hypotheses proceeds essentially in one of two ways:
(i) Experiments are made with the actual objects. Results of the exper-
iments will then suggest answers to the queries, or settle the hypotheses one
way or another. Confidence in one's conclusions will depend on many factors,
such as experimental design, sample sizes, accuracy of the observations, and
so on.
(ii) If mathematical descriptions of the objects and their relationships are
sufficiently well-advanced, mathematical models of the objects can be manip-
ulated in ways suggested by the hypotheses. Other kinds of model, iconic or
analogue, may be used similarly. Results obtained by observing changes in the
models can then be used to confirm or deny hypotheses.
When using mathematical or other types of models, their suitability must
always be kept in question. Experiments must be made with the objects
themselves, to test whether the real processes correspond closely with the
changes and processes occurring with the models. If they do, then confidence
will be gained in the validity of the modelling: and answers to hypotheses,
gleaned from the models, will be considered to be new knowledge about the
objects, with a fair degree of justification. If they don't, the validity of the
models will be in doubt, and they must be improved before further use.
When much of the above is done, or at least well-started and moving along
the indicated lines, it is permissible, in our view, to claim the title `Science' to
apply to this universe and its methods of study.
To summarise, it is generally agreed that the key elements involved in
developing a science are making observations on a set of objects, establish-
ing descriptions and definitions of key characteristics, classifying the objects,
modelling processes and relationships involving the objects, and making and
testing of hypotheses about them. And revising the models when necessary.
As to the objects of study, the second dictionary definition would seem to
restrict the field to the material and physical universe, although, in parenthe-
ses, it extends this to include any particular branch of the knowledge gained.
We find this restriction puzzling, old-fashioned maybe, and unacceptable. Does
the Dictionary writer find Biology hard to classify as a Science? What of the
Social Sciences, such as Economics and Psychology? Can the study of money
markets, or labour movements, or social deviants be said to be science? And