Various
Appletons' Popular Science Monthly, April 1899
GUESSING, AS INFLUENCED BY NUMBER PREFERENCES
By F. B. DRESSLAR
About two years ago a certain progressive clothing company of Los Angeles, California, procured a very large squash – so large, indeed, as to attract much attention. This they placed uncut in a window of their place of business, and advertised that they would give one hundred dollars in gold to the one guessing the number of seeds it contained. In case two or more persons guessed the correct number, the money was to be divided equally among them. The only prerequisite for an opportunity to guess was that the one wishing to guess should walk inside and register his name, address, and his guess in the notebook kept for that purpose.
The result of this offer was that 7,700 people registered guesses, and but three of these guessed 811, the number of seeds which the squash contained.
It occurred to me that a study of these guesses would reveal some interesting number preferences, if any existed, for the conditions were unusually favorable for calling forth naïve and spontaneous results, there being no way of approximating the number of seeds by calculation, and very little or no definite experience upon which to rely for guidance. It seemed probable, therefore, that the guesses would cover a wide range, and by reason of this furnish evidence of whatever number preference might exist. It is undoubtedly safe to assume, too, that the guesses made were honest attempts to state as nearly as possible best judgments under conditions given; but even if some of the guesses were more or less facetiously made, the data would be equally valuable for the main purpose in hand.
According to the theory of probability, had there been no preference at all for certain digits or certain combinations of digits within the limits of the guesses, one figure would occur about as often as another in units' or tens' place. It was argued, therefore, that any marked or persistent variation from such regularity in such a great number of cases would reveal what might be termed an unconscious preference for such numbers or digits for these places.
The purpose of this study, then, was to determine whether or not there existed in the popular mind, under the conditions offered, any such preferences.
After the very arduous and tedious task of collating and classifying all the guesses for men and women separately had been done, the following facts appeared:
In the first place, marked preference is shown for certain digits both for units' and tens' places. This statement is based on a study of the 6,863 guesses falling below one thousand. Of these, 4,238 were made by men and 2,625 were made by women. By tabulations of the digits used in units' place by both men and women, the following facts have been determined: 800 used 9, while but 374 used 8; 1,070 used 7, and 443 preferred 6; 881 used 5, and only 295 preferred 4; 862 chose 3, while 331 used 2; 577 ended with 1, while 1,230 preferred 0 as the last figure.
A tabulation of the figures used in tens' place shows, save in the case of 2 and 3, where 2 is used oftener than 3, the same curious preferences, but in a much less marked degree. To go into detail, 850 chose 9 for tens' place, while 559 took 8; 907 used 7, while only 637 selected 6; 748 took 5, while only 536 used 4; 601 used 3, and 634 chose 2; 728 used 1, as against 872 who used 0.
Were it not that the selections here in the main correspond with the preferences shown in units' place, the significance of these figures would be much less important; but the evidence here can not wholly be ignored when taken in connection with the facts obtained in the preferences shown in the case of the figures occupying units' place.
We are enabled, then, as a result of the study of these guesses, to say that under the conditions offered, aside from a preference of 0 over 1 to end the numbers selected, digits representing odd numbers are conspicuously preferred to those representing even numbers. How far this will hold under other conditions can not now be stated, but the facts here observed are of such a nature as to suggest the possibility of an habitual tendency in this direction. However, further investigations can alone determine whether or not this bias for certain numbers is potent in a general way.
The curve on the next page, exhibiting the results noted above, shows at a glance the marked and persistent preference for the odd numbers.
It will be noticed that of the digits preferred, 7 surpasses any of the others. Not only, then, do we tend to select an odd number for units' place when the guess ranges between one and a thousand, but of these digits 7 is much preferred. In connection with this fact one immediately recalls all he has heard about 7 as a sacred number, and its professed significance in the so-called "occult sciences." I think one is warranted in saying from an introspective point of view that there is a shadow of superstition present in all attempts at pure guessing. There appears to be some unexpressed feeling of lucky numbers or some mental easement when one unreasoned position is taken rather than any other.
It is impossible on the evidence furnished by this study to give more than hints at the probable reason for the preference here indicated. But it is worth while to glance backward to earlier conditions, when the scientific attitude toward all the facts of life and mind was far more subordinated to supernatural interpretations than it is to-day. In this way we may catch a thread which still binds us to habits formed in the indefinite past.
The Greeks considered the even numbers as representative of the feminine principle, and as belonging and applying to things terrestrial. To them the odd numbers were endowed with a masculine virtue, which in time was strengthened into supernatural and celestial qualities. The same belief was prevalent among the Chinese. With them even numbers were connected with earthly things, partaking of the feminine principle of Yang. Odd numbers were looked upon as proceeding out of the divine and endued with the masculine principle. Thirty was called the number of earth, because it was made up by the addition of the even numbers 2, 4, 6, 8, and 10. On the other hand, 25, the sum of the five odd numbers 1, 3, 5, 7, and 9, was called the number of heaven.
It is generally true that, as lower peoples developed the need of numbers and the power to use them, certain of these numbers came to be surrounded with a superstitious importance and endued with certain qualities which led at once to numerical preferences more or less dominant in all their thinking connected with numbers.
It would certainly be unjustifiable to conclude from the evidence at hand that the preferences shown in the guesses under consideration are directly traceable to some such superstition; and yet one can scarcely prevent himself from linking them vaguely together. Especially is this true when some consideration is given to a probable connecting link as shown in our modern superstitious notions. I have found through a recent study of these superstitions that where numbers are introduced, the odd are used to the almost complete exclusion of the even. For example, I have collected and tabulated a series of more than sixty different superstitions using odd numbers, and have found but four making use of the even. Besides these specific examples there are many more which in some form or another express the belief that odd numbers have some vital relation with luck both good and bad.
It would be impossible to define precisely or even approximately just what sort of a mental state the word "luck" stands for, but one element in its composition is a more or less naïve belief in supernatural and occult influences which at one time work for and at another time against the believer. In its more pronounced forms, the belief in luck lifts itself into a sort of a blind dependence upon some ministering spirit which interposes between rational causes and their effects. In a way one may say that the more or less vague and shadowy notions of luck which float in the minds of people to-day are but the emaciated and famishing forms of a once all-embracing superstition, and that these shadows possess a potency over life and action oftentimes beyond our willingness to believe.
There is another interesting and somewhat curious thing to be noticed in connection with these guesses. There is a persistent tendency to the duplication of digits, or, if one thinks of the numbers as at first conceived in terms of language, a tendency to alliteration. For example, the numbers 111, 222, 333, 444, 555, 666, 777, 888, and 999 occur oftener by sixty-seven per cent than any other combination possible in the tens thus represented. That is to say, other things equal, one would have a right to expect 334 or 332 to occur as often as 333. But the fact is, in this particular case, 333 occurred forty-eight times, while the other two put together occurred only three times. Here, however, we have the combined influence of the preference for the odd over the even and the digital sequence. Still, if we select 444, we find that this number, made up though it is of three digits in general least selected of all, the preference for alliterative effect is strong enough to make the number occur 28 times to 14 times for both 443 and 445. If we take 777, we find that it was used more times than all the other combinations from 770 to 779 inclusive, put together.
Therefore, under conditions similar to those presented for these guesses, one would be safe to expect these duplicative or alliterative numbers to occur much oftener than any other single number in the series.
It would evidently be unsafe to generalize upon the basis of this study, notwithstanding the large number of guesses considered. However, it seems to me that the results here obtained at least suggest a field of inquiry which promises interesting returns. If it be true, as here suggested, that odd numbers are preferred by guessers, advantage could be taken of this preference in many ways. Furthermore, as I suspect, it may be that this probable preference points to a habit of mind which more or less influences results not depending strictly on guessing. It has been shown, for example, that the length of criminal sentences has been largely affected by preferences for 5 or multiples of 5 – that is to say, where judges have power to fix the length of sentence within certain limits, there is a strong probability that they will be influenced in their judgments by the habitual use of 5 or its multiples. Here it would seem that unconscious preference overrides what one has a right to consider the most careful and impartial judgments possible, based upon actual and well-digested data.12
Another thing is noticeable in these guesses. The consciousness of number beyond 1,000 falls off very rapidly. The difference in the values of 1,000 and 1,500 seems to have had less weight with the guessers than a difference of 50 had at any place below 1,000. And so, in a way, 1,000 seems to mark the limit of any sort of definite mental measurement. This fact is more and more emphasized as the numbers representing the guesses increase until one can see there exists absolutely no conception of the value of numbers. For example, many guessed 1,000,000, while several guessed more than 10,000,000. Guessing means, with many people, no attempt at any sort of reasonable measurement, but rather an attempt to express their guess in such a way as to afford them the greatest amount of mental relief. And this relief can not be wholly accomplished without satisfying number preferences. Therefore, guessing is likely to exhibit, in a greater or less degree, some habitual lines of preference subject to predetermination. It may be that much practical advantage has been taken of these facts in games of chance where number selections play an important part.
CONCERNING WEASELS
By WILLIAM E. CRAM
Why is it that while popular fancy has attributed all sorts of uncanny and supernatural qualities to owls and cats, and that no ghost story or tale of horrid murder has been considered quite complete without its rat peering from some dark corner, or spider with expanded legs suddenly spinning down from among the rafters, no such grewsome association has ever attached itself to the weasels, creatures whose every habit and characteristic would seem to suggest something of the sort? Now, fond as I am of cats, I should never think of denying that they are uncanny creatures, to say the least. But, suppose it was the custom of our domestic tabbies to vanish abruptly or even gradually on occasion, like the Cheshire cat after its interview with Alice, that would at least furnish some excuse for the general prejudice against them, but would really be no more than some of our commonest weasels do whenever it serves their purpose. I remember one summer afternoon I was trout-fishing along a little brook that ran between pine-covered hills. As I lay stretched on the bank at the foot of a great maple I saw a weasel run along in the brush fence some distance away. A few seconds later he was standing on the exposed root of the tree hardly a yard from my eyes. I lay motionless and examined the beautiful creature minutely, till suddenly I found myself staring at the smooth greenish-gray root of the maple with no weasel in sight. Judging from my own experience, I should say that this is the usual termination of any chance observations of either weasels or minks.
Occasionally they may be seen to dart into the bushes or behind some log or projecting bank, but much more frequently they vanish with a suddenness that defies the keenest eyesight.
In all probability this vanishing is accomplished by extreme rapidity of motion, but if this is the case then the creature succeeds in doing something utterly impossible to any other warm-blooded animal of its size. Mice, squirrels, and some of the smaller birds are all of them swift enough at times, but except in the case of the humming bird none of them, I believe, succeed in accomplishing the result achieved by the weasels. The humming bird, in spite of its small size, leaves us a pretty definite impression of the direction it has taken when it darts away; but when a mink, half a yard in length and weighing several pounds, stands motionless before one with his dark coat conspicuous against almost any background, and the next instant is gone without a rustle or the tremor of a blade of grassA weasel, it leaves one with an impression of witchcraft difficult to dispel; and best appreciated when one sees it for one's self. Nor is the everyday life of the weasel quiet or commonplace; his one object in life apparently is to kill, first to appease his hunger, then to satisfy his thirst for warm blood, and after that for the mere joy of killing.
The few opportunities I have had for observing these animals have never shown them occupied in any other way, nor can any hint of anything different be gained from the various writers on the subject, while accounts of their attacking and even killing human beings in a kind of blind fury are too numerous and apparently well authenticated to be entirely ignored. These attacks are said usually to be made by a number of weasels acting in concert, and the motive would appear to be revenge for some injury done to one of their number. There seems to be something peculiar about the entire family of weasels. The American sable or pine marten is said to have strange ways that have puzzled naturalists and hunters for years. In the wilderness no amount of trapping has any effect on their numbers, nor do they show any especial fear of man or his works, occasionally even coming into lumber camps at night and being especially fond of old logging roads and woods that have been swept by fire; but at the slightest hint of approaching civilization they disappear, not gradually, but at once and forever, and the woods know them no more. If there is anything in the theory of the survival of the fittest, why is it that not one marten has discovered that, like other animals of its size, it could manage to live comfortably enough in the vicinity of man? The mink and otter still follow the course of every brook and river and manage to avoid the keen eyes of the duck hunter, while for six months in the year their paths are sprinkled with steel traps set either especially for them or for the more plebeian muskrat. If a pair of sables could be persuaded to take up their quarters in some parts of New England they could travel for dozens of miles through dark evergreen woods with hollow and decaying trees in abundance, while at present there are almost no traps set in a manner that need disturb creatures of their habits. Partridges, rabbits, and squirrels, which form their principal food, are nearly if not quite as abundant as before the country was settled, so that it would certainly not require any very decided change of habits to enable them to exist, but evidently the root of the matter goes deeper than that, and, like some tribes of Indians, it is impossible for them to multiply or flourish except in the primeval forest.
The common weasel or ermine, which is the only kind I have seen hereabouts, would seem to have everything on its side in the struggle for existence, and when one happens to be killed by some larger inhabitant of the woods it must be due entirely to its own carelessness. Nevertheless, they do occasionally fall victims to owls and foxes, and I once shot a red-tailed hawk that was in the act of devouring one. Still, these casualties among weasels are probably few and far between. Fortunately, however, they never increase to any great extent. Occasionally in the winter the snow for miles will be covered with their tracks all made in a single night, and then for weeks not a track is to be seen; but usually they prefer to hunt alone, each having its beat a mile or more in length, over which it travels back and forth throughout the season, passing any given point at intervals of two or three days. This habit of keeping to the same route instead of wandering at random about the woods is characteristic of the family, the length of the route depending to a certain extent on the size of the animal. The mink is usually about a week in going his rounds, and may cover a dozen miles in that time, while the otter is generally gone a fortnight or three weeks. When it is possible the ermine prefers to follow the course of old tumble-down stone walls, and lays its course accordingly. In favorable districts he is able to keep to these for miles together, squeezing into the smallest crevices in pursuit of mice or chipmunks. All the weasels travel in a similar manner – that is, by a series of leaps or bounds in such a way that the hind feet strike exactly in the prints made by the fore paws, so that the tracks left in the snow are peculiar and bear a strong family resemblance. On soft snow the slender body of the ermine leaves its imprint extending from one pair of footprints to the next, and as these are from four to six feet apart, or even more, the impression left in the snow is like the track of some extremely long and slender serpent with pairs of short legs at intervals along its body. I have said that the ermine is the only true weasel I have found in this vicinity, but this is not strictly true, at least I hope not. One winter I repeatedly noticed the tracks of an exceedingly large weasel – so very large, in fact, that I was almost forced to believe them to be those of a mink. The impression of its body in the snow was quite as large as that made by a small mink, but the footprints themselves were smaller, and the creature appeared to avoid the water in a manner quite at variance with the well-known habits of its more amphibious cousin, while, unlike the common weasel, it never followed stone walls or fences. I put my entire mind to the capture of the little beast, and set dozens of traps, but it was well along in the month of March before I succeeded. It proved to be a typical specimen of the Western long-tailed weasel, though I can find no account of any other having been taken east of the Mississippi. Its entire length was about eighteen inches; the tail, which was a little over six, gave the effect at first glance of being tipped with gray instead of black, but a closer inspection showed that the black hairs were confined to the very extremity and were partly concealed by the overlying white ones; the rest of the fur was white, with a slight reddish tinge, and much longer and coarser than that of an ermine. Since then I have occasionally seen similar tracks, but have not succeeded in capturing a second specimen. In all probability the least weasel is also to be found here if one has the patience to search carefully enough; none, however, have come under my observation as yet. All the small weasels that I have seen have proved on close inspection to be young ermines with thickly furred black-tipped tails; in the least weasel the tail is thinly covered with short hair and without any black whatever. Late in the autumn or early in the winter the ermine changes from reddish-brown to white, sometimes slightly washed with greenish-yellow or cream color, and again as brilliantly white as anything in Nature or art; the end of the tail, however, remains intensely black, and at first thought might be supposed to make the animal conspicuous on the white background of snow, but in reality has just the opposite effect. Place an ermine on new-fallen snow in such a way that it casts no shadow, and you will find that the black point holds your eye in spite of yourself, and that at a little distance it is quite impossible to follow the outline of the weasel itself. Cover the tail with snow, and you can begin to make out the position of the rest of the animal, but as long as the tip of the tail is in sight you see that and that only. The ptarmigan and northern hare also retain some spot or point of dark color when they take on their winter dress, and these dark points undoubtedly serve the same purpose as in the case of the ermine.
An old hunter, one of the closest observers of Nature I have ever known, once told me that female minks hibernated in winter in the same manner as bears, though it was his belief that, unlike the bears, they never brought forth their young at that season. At first I refused to take the slightest stock in what he said; the whole thing appeared so absurd and so utterly at variance with the teachings of those naturalists who have made the closest possible study of the habits of minks. Since then, however, I have kept my eyes open for any hint that might have the slightest bearing on the subject, and to my surprise have found many things that would seem to point to the correctness of the old hunter's theory. To begin with, he said that late in the winter he had repeatedly known female minks to make their appearance from beneath snow that had lain undisturbed for days or even weeks, the tracks apparently beginning where he first observed them, the difference in size between the two sexes being sufficient to make it easy to distinguish between their tracks at a glance; and, moreover, since he first began trapping he had noticed that while the sexes were about equally abundant in the autumn, the females always became very scarce at the approach of winter and remained so until spring, when they suddenly increased in numbers and became much the more abundant of the two.
This is also the experience of trappers in general, and may be verified by any one who cares to take the trouble to look into the matter. Evidently no one has ever discovered a mink in a state of hibernation; at any rate, no such case appears ever to have been reported; but this does not necessarily prove that it is not a regular habit among them.
The cry of the mink is seldom heard, even in places where they are fairly abundant, as they have evidently learned that the greatest safety lies in silence. It is a peculiarly shrill, rattling, whistlelike scream, that can be heard at a considerable distance.