Counting room

“ But these rumors were speedily verified by a party who had constituted themselves a committee to ascertain the truth or falsehood of the reports, and had marched up in a body to the counting-room of the agent. These now returned and announced that the counting-room was locked up, the agent being probably up at his house superintending the necessary arrangements for the reception of the body of the captain ”

“ In the system of counting every place, or column, counting from the right, has a value ten times greater than the one in the place or column nearest on the right. Thus in the number 36,542 the first figure on [71] the right represents “ones,” the next ten times as much or “tens,” the next ten times as much again or “hundreds,” and so on. We really read this number backward when we name it, for in handling it in any way we have to start with the last figure, representing the “ones.” The number really means two ones, four tens, five hundreds, six thousands and three ten thousands. ”

“ I noticed some of the company prepare their mouths and draw themselves up at the prospect of some agreeable forfeit. "Let us play at counting," said Charlotte. "Now, pay attention: I shall go round the circle from right to left; and each person is to count, one after the other, the number that comes to him, and must count fast; whoever stops or mistakes is to have a box on the ear, and so on, till we have counted a thousand." ”

“ But the one primitive method of counting which seems to have been almost universal throughout all time is the finger method. It is a matter of common experience and observation that every child, when he begins to count, turns instinctively to his fingers; and, with these convenient aids as counters, tallies off the little number he has in mind. This method is at once so natural and obvious that there can be no doubt that it has always been employed by savage tribes, since the first appearance of the human race in remote antiquity. ”

“ The process of counting is nothing but a setting up of a one-to-one correspondence between the objects to be counted and certain words, 'one,' 'two,' 'three,' etc., in the mind. Many savage peoples have discovered no better method of counting than by setting up a one-to-one correspondence between the objects to be counted and their fingers. ”

“ Such a child may count correctly from the point of view of a grown-up listener, without having any idea of numbers at all. The operation of counting, in fact, can only be intelligently performed by a person who already has some idea what the numbers are; and from this it follows that counting does not give the logical basis of number. ”

“ It is, that somebody besides the President of the Senate is to count, because, if he was to be the counting officer, the language would naturally have been that the President of the Senate shall open all the certificates and count the votes. ”

“ If a larger number than twenty is to be counted, as when, for example, a chief has to pay in tax for each door of his house, he calls in the aid of several men, who sit before him. One of these tells off his fingers and toes as the chief utters the names of the heads of the rooms; and when twenty have been counted in this way, a second man begins on his fingers, while the first continues to hold on to all his toes. A third and a fourth man may be used in the same way to complete the count ”

“ There can be little doubt that many of us were taught to count very badly, and that we were hampered in our arithmetic throughout life by this defect. Counting should be taught be means of small cubes, which the child can arrange and rearrange in groups. It should have at least over a hundred of these cubes—if possible a thousand; they will be useful as toy bricks, and for innumerable purposes. Our civilization is now wedded to a decimal system of counting, and, to begin with, it will be well to teach the child to count up to ten and to stop there for a time. ”

“ Sometimes people will speak of mere counting as one of the simplest operations in the world; but on occasions, as I shall show, it is far from easy. Sometimes the labour can be diminished by the use of little artifices; sometimes it is practically impossible to make the required enumeration without having a very clear head indeed. An ordinary child, buying twelve postage stamps, will almost instinctively say, when he sees there are four along one side and three along the other, "Four times three are twelve;" while his tiny brother will count them all in rows, "1, 2, 3, 4," etc. ”

“ Suppose we wish to know the number of inhabitants to a dwelling in New York. The same person cannot inhabit two dwellings. If he divide his time between two dwellings he ought to be counted a half-inhabitant of each. In this case we have only to divide the total number of the inhabitants of New York by the number of their dwellings, without the necessity of counting separately those which inhabit each one. ”

“ Counting by means of his fingers, without including the thumbs, the savage begins by dividing into fours instead of fives. Traces of this form of counting are somewhat numerous, especially among the North American aboriginal tribes. Hence the quinary form of counting, however widespread its use may be shown to be, can in no way be claimed as the universal method of any stage of development in the history of mankind.
In the vast majority of cases, the passage from the base to the next succeeding number in any scale, is clearly defined. ”

“ When the rebels started the new system of counting we used to bother them all we could by causing disappearances. One of the first attempts we made at this was to secrete about 150 men in the lofts and corners of the various buildings which then existed, as well as above the lower weight poles on the roofs of our cabins; the usual custom of hanging blankets to air on the eaves of our quarters enabling us to cover the men who were hidden there.
There was a great excitement and furore when the count showed the shortage and apparent escape. ”

“ In illustration and as an example it may be noticed that the eyes of the majority of persons convey the consciousness of numbers precisely, up to a certain point, without any operation of counting. Most people can say at a glance, of any small group of objects, that there are two, three, four, or even seven. With almost all individuals, counting, and counting from the beginning, becomes necessary when there are eight or more objects together. ”

“ If you once commit the addition table thoroughly, you have it fixed for life; whereas if you do not, you have to make the calculation over again every time, and thus lose a vast amount of labor. I have no doubt that there are some in this class who are in the habit of counting, who have ascertained that seven and eight, for instance, make fifteen, by counting up from seven to fifteen hundreds of times. ”

“ This method of counting is rapidly dying out among the natives of the island, and is at the present time used only by old people.18 Variations on this most unusual custom have been found to exist in others of the neighbouring islands, but none were exactly similar to it. One is also reminded by it of a custom19 which has for centuries prevailed among bargainers in the East, of signifying numbers by touching the joints of each other's fingers under a cloth. Every joint has a special signification; and the entire system is undoubtedly a development from finger counting. ”

“ The origin of the quinary mode of counting has been discussed with some fulness in a preceding chapter, and upon that question but little more need be said. It is the first of the natural systems. When the savage has finished his count of the fingers of a single hand, he has reached this natural number base. ”

“ If the countess holds the property, and the count continues to get the good of it, in a modest way; if the count does not do everything for himself, and earn his daily bread by manual toil, is not he mentally unbalanced to proclaim his theories to the world, and to change his mind so often on other points? ”

“ In six instances only do 2 people occupy one room; and in others the number varied from 3 to 9. In another court with 6 houses and 22 rooms were 84 people—again, 6, 7, 8, and 9 being the number living in one room, in several instances. In one house with 8 rooms are 45 people—one room containing 9 persons, one 8, two 7, and another 6. ”

“ They know, as soon as they reach 40, just how many there are, and it is hard to keep from counting the rest in a [Pg 531] group. Otherwise they do not feel any difference in counting Cards 8 and 9. Arranging the letters in words does not affect the speed of counting, so far as they can see, for in counting they do not notice the words at all.
When we average the records of all the subjects giving equal weight to each subject, though the number of tests may be different with the different men, we get the following table. Time given in thousandths of seconds. ”

“ Any such mode of counting, whether involving the use of the fingers or not, is to be regarded simply as an extraneous aid in the expression or comprehension of an idea which the mind cannot grasp, or cannot retain, without assistance. The German student scores his reckoning with chalk marks because he might otherwise forget; while the Andaman Islander counts on his fingers because he has no other method of counting,—or, in other words, of grasping the idea of number. A single illustration may be given which typifies all practical methods of numeration. ”

“ I count, but I count, in ordinary life, what I take to be real objects, existent quite apart from my counting. Suppose that I count ships seen from the shore. There, says common sense, are the ships, sailing by themselves, and quite indifferent to whether anybody counts them or not. In advance of the counting, the ships, in so far as they are a real collection, have their number. ”

“ On the whole, the grouping method refers mainly to concrete numbers and the counting method to abstract numbers. If we sort objects into groups of ten, and find that there are five groups of ten with three over, we regard the five and the three as names for the actual sets of groups or of individuals. The three, for instance, are regarded as a whole when we name them three. If, however, we count these three as one, two, three, then the number of times we count is an abstract number. Thus number in the abstract is the number of times that the act of counting is performed in any particular case. ”

“ Under the other system of counting, each clerk places on the table in front of him the ballot papers for each candidate in separate piles, makes them up into packets of fifty, placing an elastic band round each, and hands them over to the returning officer.
The work of the counting clerks is closely watched by an agent representing each of the candidates. All votes about which there is any doubt are referred to the returning officer. ”

“ When this noise had some time ceased, Giles Sharp, their Secretary, proposed to enter first into these rooms; and, in presence of the Commissioners, of whom he received the key, he opened the doors, and found the wood spread about the room, the chairs tossed about, and broken, the papers torn, and the [97] ink-glass broken (as has been said) ; but not the least track of any human creature, nor the least reason to suspect one, as the doors were all fast, and the keys in the custody of the Commissioners. ”

“ As a rule, however, the system has been none of these, but counting has been done by fives, by tens, or twenties, and this simply because it has been based upon the antique but persistent habit which man has of counting upon his fingers. ”

“ It is easy for any two people to count the number of men in a room and to agree as to the result; but ask them to say how many tall men, how many with black hair, how many blue-eyed, how many straight-nosed—and you will get a different result each time. ”

“ The fingers are, however, often employed in counting numbers far above the first decade. After giving the Il-Oigob numerals up to 60, Müller adds:8 “Above 60 all numbers, indicated by the proper figure pantomime, are expressed by means of the word ipi.” We know, moreover, that many of the American Indian tribes count one ten after another on their fingers; so that, whatever number they are endeavouring to indicate, we need feel no surprise if the savage continues to use his fingers throughout the entire extent of his counts. ”

“ The narrator was somewhat uncertain as to the order of many counts and made frequent use of a set of improvised counting sticks. We asked him why in later years the winter counts were designated chiefly by the deaths of the most prominent men, to which he replied that since his people were confined to the limits of the reservation nothing else happened worth remembering, and further, that the count ended with the death of White-calf because there were now no men living of sufficient worth to be honored with such mention. ”

“ Only once every four years are the electoral votes to be counted. In most cases the result is beyond all question decided, and the figures universally recognized before the counting begins. Doubtful cases of great importance may and probably will henceforth occur more frequently than formerly, but even then they are not likely to occur more than once or twice during the average official life of a judge of the Supreme Bench. ”

“ This suggests that mistakes in counting cannot be identified without an arithmetic calculus and this is plainly not true. Four types of mistakes in counting can occur:
Case C1. A child counting apples in a bucket says "one apple, two apples, four apples, five apples" and concludes that there are five apples in the bucket when there are in fact only four. In this case it is clear that the child has not learned how to count. The mistake can be identified and corrected by a parent or teacher.
Case C2. A person who has learned to count correctly makes a mistake through inattention. ”