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.