It is natural for man to relate the units of distance by which he travels to the dimensions of the globe that he inhabits. Thus, in moving about the earth, he may know by the simple denomination of distance its proportion to the whole circuit of the earth. This has the further advantage of making nautical and celestial measurements correspond. The navigator often needs to determine, one from the other, the distance he has traversed from the celestial arc lying between the zeniths at his point of departure and at his destination. It is important, therefore, that one of these magnitudes should be the expression of the other, with no difference except in the units. But to that end, the fundamental linear unit must be an aliquot part of the terrestrial meridian. ... Thus, the choice of the metre was reduced to that of the unity of angles.

Our children will enjoy in their homes electrical energy too cheap to meter. ... Transmutation of the elements, unlimited power, ability to investigate the working of living cells by tracer atoms, the secret of photosynthesis about to be uncovered, these and a host of other results, all in about fifteen short years. It is not too much to expect that our children will know of great periodic famines in the world only as matters of history, will travel effortlessly over the seas and under the and through the air with a minimum of danger and at great speeds, and will experience a life span far longer than ours, as disease yields and man comes to understand what causes him to age.

The faith of scientists in the power and truth of mathematics is so implicit that their work has gradually become less and less observation, and more and more calculation. The promiscuous collection and tabulation of data have given way to a process of assigning possible meanings, merely supposed real entities, to mathematical terms, working out the logical results, and then staging certain crucial experiments to check the hypothesis against the actual empirical results. But the facts which are accepted by virtue of these tests are not actually observed at all. With the advance of mathematical technique in physics, the tangible results of experiment have become less and less spectacular; on the other hand, their significance has grown in inverse proportion. The men in the laboratory have departed so far from the old forms of experimentation—typified by Galileo's weights and Franklin's kite—that they cannot be said to observe the actual objects of their curiosity at all; instead, they are watching index needles, revolving drums, and sensitive plates. No psychology of 'association' of sense-experiences can relate these data to the objects they signify, for in most cases the objects have never been experienced. Observation has become almost entirely indirect; and readings take the place of genuine witness.