"Great numbers are not counted correctly to a unit, they are estimated; and we might perhaps point to this as a division between arithmetic and statistics, that whereas arithmetic attains exactness, statistics deals with estimates, sometimes very accurate, and very often sufficiently so for their purpose, but never mathematically exact." (Arthur L Bowley, "Elements of Statistics", 1901)
"[…] statistics is the science of the measurement of the social organism, regarded as a whole, in all its manifestations." (Sir Arthur L Bowley,"Elements of Statistics", 1901)
"Statistics may rightly be called the science of averages. […] Great numbers and the averages resulting from them, such as we always obtain in measuring social phenomena, have great inertia. […] It is this constancy of great numbers that makes statistical measurement possible. It is to great numbers that statistical measurement chiefly applies." (Sir Arthur L Bowley,"Elements of Statistics", 1901)
"Statistics may, for instance, be called the science of counting. Counting appears at first sight to be a very simple operation, which any one can perform or which can be done automatically; but, as a matter of fact, when we come to large numbers, e.g., the population of the United Kingdom, counting is by no means easy, or within the power of an individual; limits of time and place alone prevent it being so carried out, and in no way can absolute accuracy be obtained when the numbers surpass certain limits." (Sir Arthur L Bowley,"Elements of Statistics", 1901)
"Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions. […] A curve is the totality of points, whose coordinates are functions of a parameter which may be differentiated as often as may be required." (Felix Klein, "Elementar Mathematik vom hoheren Standpunkte aus" Vol. 2, 1909)
"It is well to notice in this connection [the mutual relations between the results of counting and measuring] that a natural law, in the statement of which measurable magnitudes occur, can only be understood to hold in nature with a certain degree of approximation; indeed natural laws as a rule are not proof against sufficient refinement of the measuring tools." (Luitzen E J Brouwer, "Intuitionism and Formalism", Bulletin of the American Mathematical Society, Vol. 20, 1913)
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