Mathematics has beauties of its own—a symmetry and proportion in its results, a lack of superfluity, an exact adaptation of means to ends, which is exceedingly remarkable and to be found only in the works of the greatest beauty. … When this subject is properly and concretely presented, the mental emotion should be that of enjoyment of beauty, not that of repulsion from the ugly and the unpleasant.

Speaking concretely, when we say “making experiments or making observations,” we mean that we devote ourselves to investigation and to research, that we make attempts and trials in order to gain facts from which the mind, through reasoning, may draw knowledge or instruction.
Speaking in the abstract, when we say “relying on observation and gaining experience,” we mean that observation is the mind's support in reasoning, and experience the mind's support in deciding, or still better, the fruit of exact reasoning applied to the interpretation of facts. It follows from this that we can gain experience without making experiments, solely by reasoning appropriately about well-established facts, just as we can make experiments and observations without gaining experience, if we limit ourselves to noting facts.
Observation, then, is what shows facts; experiment is what teaches about facts and gives experience in relation to anything.

The dance is four-dimensional art in that it moves concretely in both space and time. For the onlooker, it is an art largely of visual space combined with time. But for the dancer, and this is more important, the dance is more a muscular than a visual space rhythm, a muscular time, a muscular movement and balance. Dancing is not animated sculpture, it is kinesthetic.

The saying often quoted from Lord Kelvin… that “where you cannot measure your knowledge is meagre and unsatisfactory,” as applied in mental and social science, is misleading and pernicious. This is another way of saying that these sciences are not science in the sense of physical science and cannot attempt to be such without forfeiting their proper nature and function. Insistence on a concretely quantitative economics means the use of statistics of physical magnitudes, whose economic meaning and significance is uncertain and dubious. (Even wheat is approximately homogeneous only if measured in economic terms.) And a similar statement would even apply more to other social sciences. In this field, the Kelvin dictum very largely means in practice, “if you cannot measure, measure anyhow!”