Mensuration

“ It was evident that the goodness of the soil, the number of the people, their wealth, and the largeness of their contribution made such infinite variations between square and square as to render mensuration a ridiculous standard of power in the commonwealth, and equality in geometry the most unequal of all measures in the distribution of men. ”

“ PROTARCHUS: True.
SOCRATES: And in the productive or handicraft arts, is not one part more akin to knowledge, and the other less; and may not the one part be regarded as the pure, and the other as the impure?
PROTARCHUS: Certainly.
SOCRATES: Let us separate the superior or dominant elements in each of them.
PROTARCHUS: What are they, and how do you separate them?
SOCRATES: I mean to say, that if arithmetic, mensuration, and weighing be taken away from any art, that which remains will not be much. ”

“ He would not, therefore, judge as we do, nor have any idea of distance, outness, or profundity, nor consequently of space or body, either immediately or by suggestion. Whence it is plain he can have no notion of those parts of geometry which relate to the mensuration of solids and their convex or concave surfaces, and contemplate the properties of lines generated by the section of a solid. The conceiving of any part whereof is beyond the reach of his faculties. ”

“ Shall doctrine be taught a child? Yes! To have a specific doctrine clearly in mind does not fetter the young soul, any more than to be taught the apparent facts of geography and history, which may change either in reality or in his own interpretation as his mind matures. A doctrine is a practical and definite thing to work with; in later life to believe, and to approve of, or disbelieve, and disapprove of. If a man wishes to build a house, does it fetter him to know square measure, cubic contents, geometry, mensuration, and mechanical laws? ”

“ After all, this magic rule of averages which is invoked to cover up many troublesome and embarrassing situations is obnoxious to scientific accounting; it is a makeshift which carries with it a shiftless trust in the happy outcome of things—a trust which has been so often betrayed as to carry little weight. ”

“ For instance, that sum gives thirty-two letters per head to the population in the year; and, of course, as thousands of us can’t write, and thousands more don’t write, it follows that the real correspondents of the kingdom do some pretty stiff work in the writing way. But these are only the letters. If you include somewhere about four hundred and twenty million post-cards, newspapers, book-packets, and circulars, you have a sum total of fourteen hundred and seventy-seven million odd passing through our hands. ”

“ I quote this not to multiply examples of the waste of wealth, but to illustrate the insight which a few figures, such as those recorded by this meter, give us into the lives of the people. How much more does the account-book, a detective meter of every economic action, give us an animated photograph of the family life. Nothing is so calculated to stimulate social sympathy or to suggest questions for consideration. Like a doctor’s notes of his patients the facts are not for publication in any form which will reveal the identity of the subject ”

“ The test in each case is the effect of the book, picture or publication considered as a whole, not upon any particular class, but upon all those whom it is likely to reach. In other words, you determine its impact upon the average person in the community. The books, pictures and circulars must be judged, as a whole, in their entire context, and you are not to consider detached or separate portions in reaching a conclusion. You judge the circulars, pictures and publications which have been put in evidence by present-day standards of the community. ”

“ All of a sudden I fell to studying countenances, and soon flattered myself that I had made considerable progress in the science.
'There is no faith in countenances,' said some Roman of old; 'trust anything but a person's countenance.' 'Not trust a man's countenance?' say some moderns, 'why, it is the only thing in many people that we can trust; on which account they keep it most assiduously out of the way. Trust not a man's words if you please, or you may come to very erroneous conclusions; but at all times place implicit confidence in a man's countenance, in which there is no deceit ”

“ Thus, by taking a little trouble, the historian can apply one constant measure to his judgments of increase and decrease, as he reviews social changes. He must subdivide his community into enumeration units, and against each unit, at each convenient date, he must enter a record of his judgment that the trait, activity, interest, or relation under investigation can be predicated of a large or of only a small majority, of a large or of only a small minority, of the individuals composing the enumeration unit. ”

“ However, where statistical evidence is obtainable, no one dreams of estimating probability by the quantity of his belief. Insurance offices, dealing with fire, shipwreck, death, accident, etc., prepare elaborate statistics of these events, and regulate their rates accordingly. Apart from statistics, at what rate ought the lives of men aged 40 to be insured, in order to leave a profit of 5 per cent. upon £1000 payable at each man's death? Is 'quantity of belief' a sufficient basis for doing this sum? ”

“ Akin to the token which the enlarged use of statistics affords of the growing recognition of Politics as a true science, is the ever-increasing disposition, at the present day, to await, at any political crisis, whether legislative or administrative, the result of a patient examination of evidence as to the state of the facts and the previous history of the question. ”

“ The masses seem to be worth notice in three aspects only: first as the copies of great men, printed on bad paper from worn-out plates, next as a contrast to the great men, and lastly as their tools: for the rest, let the devil and statistics fly away with them! How could statistics prove that there are laws in history? ”

“ The mass of data that has not been seen, or very imperfectly seen, that has been misunderstood, or incorrectly recorded, the many pitfalls of omission and commission cause one at times to wonder at the temerity of those who feel confidence in what is termed the comparative method. ”

“ The magnitude of the task involved in a judicial review which requires a determination by the Court, in its independent judgment, of the correctness of the findings of fact as to value and income which the Secretary made, cannot be measured by looking alone at the volume of the evidence. ”

“ Under a complete system of state regulation not only are the forms and standards of uniform accounting established, but a staff of expert examiners is created to determine by periodical investigation, whether or not these standards are lived up to. ”

“ There would have been no Decoration Day had the American kidnappers left us in Africa—our fatherland. The world must, therefore, hear from us upon these special occasions. So, like other elements of the population, we come to-day to make our annual report. We come, in company with the others, to review the past, to study the present, and, if possible, to forecast the future. In measuring the progress of any successful commercial enterprise, the mode of procedure is to compare beginnings with balance-sheets. Commercially speaking, it is to take an inventory. ”

“ The treatise of Achenwall, the German philosopher who originated the word, laid the foundation of many of the greatest reforms in modern legislation. Statistics are state facts, facts for the consideration of statesmen, such as they may not neglect with safety. It has been truly said that ‘statistics are history in repose; history is statistics in motion.’ If we neglect the one, we shall deserve to be neglected by the other. ”

“ The science of statistics, by which facts are so gathered as to embody truth, and so interpreted as to afford knowledge, is of recent origin. It is a singular fact that our young republic was the first government in the world to take a census at stated intervals. ”

“ Instead therefore of following the Account which had been communicated to me, I contented myself with relating, That it was reported, some Hamburghers had given a Sum of Money secretly to Count Steinbok. This Report became universal, and was founded on Appearances. An Historian is allow'd to insert Reports, as well as Facts, and when he publishes a general Report, an Opinion, merely as an Opinion, and not as Truth, he is neither responsible for it, nor ought to be accus'd in any manner for so doing. ”

“ Every ten years our Government takes a census. This happens to be the year in which it is done. It is also good policy for a science, especially if it is a relatively new one, to take a periodical account of stock. ”

“ In this department of mine the public may always rely upon finding exhaustive statistical tables concerning the finances of the country, the ratio of births and deaths; the percentage of increase of population, etc., etc.—in a word, everything in the realm of statistics that can make existence bright and beautiful. ”

“ We may prove that we are this and that and the other,—our Fourth-of-July orators have proved it time and again,—the census has proved it; but the Muses are women, and have no great fancy for statistics, though easily silenced by them. ”

“ The friends of a measure, or the promoters of an inquiry, though in the majority on a committee, can do no more than adduce evidence that exists, so that the business cannot suffer through them,—while those unfriendly to a measure, or hostile to an inquiry, may, from lukewarmness, or neglect, or possible prejudice, fail to present the proper evidence or recognize its just value, so that the business will suffer. ”

“ The last procedure requires discussion; the rest is self evident. In our business isolation is comparatively easy, inasmuch as any individual statement, any visual impression, any effect, etc., may be abstracted without difficulty. Much harder is the determination of its value. If, however, we clearly recognize that it is necessary to express the exact value of each particular source of evidence, and that the task is only to determine comparative valuation, the possibility of such a thing, in at least a sufficiently close degree of certainty, must be granted. ”

“ See, then, what we have to guard against in collecting sociological data—even data concerning the present, and, still more, data concerning the past. For testimonies that come down to us respecting bygone social states, political, religious, judicial, physical, moral, etc., and respecting the actions of particular causes on those social states, have been liable to perversions not simply as great, but greater ”

“ I know that table like a living thing, and yet I never saw it until to-day.”
“I suppose,” said Hugh, “that you base your system on the law of average?”
The professor laughed tolerantly. “No, I don’t. Law [225] of average,—that is child’s talk to me. Of course every table has its average, every wheel has its average, every croupier, you, I; every coup that is played, is an average with something that has gone before. Ah! these foolish system-players with their talk of average and probability and phenomenon. Why, every coup is a phenomenon as regards something that has gone before. ”

“ The cards with their spots are the evidence pro and con which each juryman has before him to interpret. Each person's decision on the number is his interpretation of the situation. The arguments, too, seem quite comparable to the arguments of the jury. Both consist in pointing out factors of the situation that have been overlooked and in showing how different interpretations may be possible.” Another man writes: “In the experiment it seemed that one man judged by one criterion and another by another, such as distribution, size of spots, vacant spaces, or counting along one edge. ”

“ In short, the more extended collection of economic data is now rendered possible by the better methods employed in census and statistical bureaus, and the resort to the work of verification of economic principles by the examination of these data is the one thing only which can redeem political economy from the baseless and common charge of being a set of impractical formulæ. ”

“ A single easy, simple sentence of plain Anglo-Saxon words contains a chapter of history that, in some instances, has taken days of labor to verify, and must have cost the author months of investigation to acquire; and though the public should justly estimate the labor bestowed on the facts which are stated, they cannot estimate the greater labor involved on those which are omitted—how many pages have been read—how many works examined—what numerous statutes, resolutions, speeches, letters, and biographies have been looked through. ”

“ Will a patient in the crisis of a given disease recover or not? That statistics are lying here in the background, and are thus indirectly efficient in producing and graduating our belief, I fully hold; but there is such a large intermediate process of estimating, and such scope for the exercise of a practised judgment, that no direct appeal to statistics in the common sense can directly help us. In sketching out therefore the claims of an Ideal condition of knowledge, we ought clearly to include a due apportionment of belief to every event of such a class as this. ”

“ The whole system of testimonials is a huge imposture. Granted that the sample is all that it is described as being, who can guarantee that what is served to the public in the face of severe competition will be up to the sample? ”

“ When we say that a statesman has "compiled an enviable record of achievement," or that a baseball pitcher has "compiled a 1.87 earned run average," we do not mean that those individuals have pulled together papers that show those results, but rather that they have generated or produced those results. ”