ADDRESS DELIVERED AT ANNUAL MEETING. 25
thought in the Middle Ages. They did not imitate their master
in the study of nature; they contented themselves by studying
him.
The danger is just as present with us as it was with them ;
there is so much to impress, delight, and satisfy us in the marvels
of modern science, that perhaps all of us, most certainly the
beginner, may easily allow the feeling to get the mastery, that
there is nothing left to do, nothing even that needs doing.
And then in instructing others (and we all, if we know a
little more of anything than those around us, cannot help doing
that, even though we may never venture to count ourselves as
teachers) it is tempting to human nature to dwell on how much
we know, and but slightly on how little we know (which may be
the more important of the two) and that is a lesson that finds
too apt a pupil in a beginner.
It is one of the most hopeful elements in the best teaching of
science, that such wise efforts are made to encourage the student
to work out problems for himself. It is no easy matter; it is
wonderful what pains the average boy will take to avoid think-
ing. He will perform the marvellous feat of learning a proposi-
tion of Euclid by heart, without understanding it, and he will go
through life with two or three adjectives in his vocabulary
which he uses with persistent inappropriateness to save himself
the terrible trouble of thinking out what he means.
But even if we escape from these elementary forms of satis-
faction, I am not sure that we have exhausted the dangers.
May I try to set before you two habits of mind which are
not easy to define, for the words that seem naturally to explain
them are themselves of such uncertain meaning (at any rate in
common speech) that they need definition before we use them.
Idealism and realism, at any rate in their older senses,
express the two modes in which one may regard scientific as
well as other matters. One may dwell upon the general or on
the particular, and I want to urge that the more idealism there
is in our thought, the more one seeks for the general, the more
progress one can make. It is easy to recognise a proposition of
Euclid as true of the particular circles and triangles drawn on the
black-board, but it is a distinct sign of progress to prove the pro-
position with the figures upside down ; beyond that lies the