Now if we turn to _experience_, we find, as the sum total of our knowledge, that for the sake of expediency we approach everything with the presumption that it is _continuous_. This aggregate experience finds its expression in such sayings as "Nature makes no jumps," and similar proverbial generalizations. But we must emphasize the fact once more that in deciding matters in this way we deal solely with questions of expediency, not with questions of the nature of our mental capacity. =36. Measurement.= Measuring is in a certain way the opposite of counting. While, in counting, the things are regarded in advance as _individual_, and the group, therefore, is a body compounded of discontinuous elements, measuring, on the other hand, consists in _co-ordinating numbers with continuous things_, that is, in applying to continuous things a concept formed upon the hypothesis of discontinuity. It lies in the nature of such a problem that the difficulty of adaptation must crop out somewhere in the course of its attempted solution. This is actually shown by the fact that measurement proves to be an unconcluded and inconcludable operation. If, in spite of this, measurement may and must justly be denoted as one of the most important advances in human thought, it follows that those fundamental difficulties can practically be rendered harmless. Let us picture to ourselves some process of measurement--for example, the determination of the length of a strip of paper. We place a rule divided into millimeters (or some other unit) on the strip, and then we determine the unit-mark at which the strip ends. It turns out that the strip does not end exactly at a unit-mark, but _between_ two unit-marks. And even if the rule is provided with divisions ten or a hundred times finer, the case remains the same. In most cases a microscopic examination will show that the end of the strip does not coincide with a division. All that can be said, therefore, is that the length must lie _between n and n + 1 units_, and even if a definite number is given, the scientifically trained person will supplement this number by the sign ± _f_, in which _f_ denotes the possible errors, that is, the limit within which the given number may be false. We see at once how the characteristic concept of threshold, which has led to the conception of the continuous, immediately asserts itself when in connection with discontinuous numbers. The adaptation of the threshold to numbers can be carried as far as it is possible to reduce the threshold, but the latter can never be made to disappear entirely.