Any one whose disposition leads him to attach more weight to unexplained difficulties than to the explanation of facts will certainly reject my theory.

Maybe we have to accept that after reaching the deepest possible level of understanding science can offer, there will nevertheless be aspects of the universe that remain unexplained. Maybe we will have to accept that certain features of the universe are the way they are because of happenstance, accident, or divine choice.

More discoveries have arisen from intense observation of very limited material than from statistics applied to large groups. The value of the latter lies mainly in testing hypotheses arising from the former. While observing one should cultivate a speculative, contemplative attitude of mind and search for clues to be followed up. Training in observation follows the same principles as training in any activity. At first one must do things consciously and laboriously, but with practice the activities gradually become automatic and unconscious and a habit is established. Effective scientific observation also requires a good background, for only by being familiar with the usual can we notice something as being unusual or unexplained.

Not one of them [formulae] can be shown to have any existence, so that the formula of one of the simplest of organic bodies is confused by the introduction of unexplained symbols for imaginary differences in the mode of combination of its elements… It would be just as reasonable to describe an oak tree as composed of blocks and chips and shavings to which it may be reduced by the hatchet, as by Dr Kolbe’s formula to describe acetic acid as containing the products which may be obtained from it by destructive influences. A Kolbe botanist would say that half the chips are united with some of the blocks by the force parenthesis; the other half joined to this group in a different way, described by a buckle; shavings stuck on to these in a third manner, comma; and finally, a compound of shavings and blocks united together by a fourth force, juxtaposition, is joined to the main body by a fifth force, full stop.

The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. Nevertheless, it has been found that there are apparent exceptions to most of these laws, and this is particularly true when the observations are pushed to a limit, i.e., whenever the circumstances of experiment are such that extreme cases can be examined. Such examination almost surely leads, not to the overthrow of the law, but to the discovery of other facts and laws whose action produces the apparent exceptions. As instances of such discoveries, which are in most cases due to the increasing order of accuracy made possible by improvements in measuring instruments, may be mentioned: first, the departure of actual gases from the simple laws of the so-called perfect gas, one of the practical results being the liquefaction of air and all known gases; second, the discovery of the velocity of light by astronomical means, depending on the accuracy of telescopes and of astronomical clocks; third, the determination of distances of stars and the orbits of double stars, which depend on measurements of the order of accuracy of one-tenth of a second-an angle which may be represented as that which a pin's head subtends at a distance of a mile. But perhaps the most striking of such instances are the discovery of a new planet or observations of the small irregularities noticed by Leverrier in the motions of the planet Uranus, and the more recent brilliant discovery by Lord Rayleigh of a new element in the atmosphere through the minute but unexplained anomalies found in weighing a given volume of nitrogen. Many other instances might be cited, but these will suffice to justify the statement that “our future discoveries must be looked for in the sixth place of decimals.”

The present gigantic development of the mathematical faculty is wholly unexplained by the theory of natural selection, and must be due to some altogether distinct cause.

When there is publicity about [UFO] sightings that turn out to be explainable, the percentage of unexplained sightings goes up, suggesting that these, too, are caused by something in people’s psychology rather than by something that is actually out there. The UFO evidence forms no coherent residue; it never gets better.

When, in an experiment, all known causes being allowed for, there remain certain unexplained effects (excessively slight it may be), these must be carefully investigated, and every conceivable variation of arrangement of apparatus, etc., tried ; until, if possible, we manage so to exaggerate the residual phenomenon as to be able to detect its cause. It is here, perhaps, that in the present state of science we may most reasonably look for extensions of our knowledge