Popular Science Monthly/Volume 24/December 1883/The Illusion of Chance



STUDY of the movements of events reveals dynamical, necessary sequences, and contemplation of the laws of probability, treated mathematically, generally involves a mental attitude at variance with theories of luck and premonition. It is believed that a rational treatment of the question will help to dispel superstitious ideas by disclosing the chain of continuity in all known actions. First, we will consider events mathematically, or as illustrating the laws of probability; and, second, as related to the practical question of success in life. The subject includes indirectly the question of ethics. Wrong or injurious action seems to disappear into a vast labyrinth. As we judge superficially or by immediate effects, we are easily misled into a belief that fraud may result in permanent gain, or that oppression will cure some political evils. It is important, for instance, that we have right ideas regarding the tendency in affairs whereby continued injustice or abuse of power comes to retribution. The jarring of the just relations of things leads to complications too subtile to be controlled, as the tyrants of history found by terrible experience, and the fact that our control is partial, as noticed definitely further on, should cause fear of the improper use of power. These truths well justify an examination of the subject.

Before considering the more complicated question of partial control in its relation to success, we will first glance at the simple or direct relations between familiar events, as seen in the calculable uniformity in the average results of great numbers of so-called games of chance. The numerical results of card-playing and dice-throwing, as examined by Professor Venn, have reaffirmed what is generally known —that resulting special aggregates, differing widely in number, show a narrow margin of difference when combined into an average of many such aggregates. "Let us suppose," he says, "that we toss up a penny a great many times; the results of the successive throws may be said to form a series. The separate throws of this series seem to occur in utter disorder. . . . But when we consider the result of a long succession we find a marked distinction; a kind of order begins gradually to emerge, and at last assumes a distinct and striking aspect."[1]

It is claimed that at one time about two hundred persons committed suicide annually in London, but it is possible that the increase of prosperity or the extension of moral influence might lessen the number. Human actions, when compared with games in which no skill is applied, thus disclose a marked difference in the fact that the average of many games shows a very small margin of departure from calculated uniformity, while during long periods human actions arising from like causes differ widely, owing to the evolution of intelligence, which gradually establishes extensive differences. Many natural phenomena go through long periods of growth and decline. But this method in nature may be far more difficult to trace than that in a game of cards. It is completely beyond our power to arrange the star systems in even a theoretical way that would seem in the slightest degree complete. In phenomena repeated at conceivable intervals, however, we may find the average as steadily maintained as that of great numbers of games. This is seen in the slight variations in the average of rainfall during a decade. If we extend the problem beyond the range of our short lives, we again find that apparently fixed averages slowly change. It would, therefore, require inconceivable lapses of time to discern the uniformity of average in these gradual changes during many centuries. As an illustration of this, there are good reasons for believing that the temperatures of the north and south temperate zones vary so greatly in ten thousand five hundred years that large portions of the globe now under cultivation will be covered by glaciers. Mr. H. B. Norton, in a lecture delivered before the Kansas Academy of Science,[2] makes a careful mathematical calculation based on the precession of the equinoxes. He thus estimates that the greatest variation in length between winters of the northern and southern hemispheres occurs at recurring periods of twenty thousand nine hundred and thirty-seven years. These great lapses of time are, he claims, accompanied by alternate deep submergence of the poles in accordance with the gradual change of the earth's axial inclination. He says:

"It thus appears probable that there have been many glacial periods in each hemisphere, and that the ocean, like a mighty pendulum, vibrates from pole to pole."

Herbert Spencer points out similar truths in that part of his philosophy concerning the rhythm of motion:[3] "Every planet, during a certain long period, presents more of its northern than of its southern hemisphere to the sun at the time of its nearest approach to him; and then, again, during a like period, presents more of its southern hemisphere than of its northern—a recurring coincidence which, though causing in some planets no sensible alterations of climate, involves in the case of the earth an epoch of twenty-one thousand years, during which each hemisphere goes through a cycle of temperate seasons, and seasons that are extreme in their heat and cold. Nor is this all. There is even a variation of this variation. For the summers and winters of the whole earth become more or less strongly contrasted, as the eccentricity of its orbit increases and decreases. . . . So that in the quantity of light and heat which any portion of the earth receives from the sun, there goes on a quadruple rhythm, that of day and night; that of summer and winter; that due to the changing position of the axis at perihelion and aphelion, taking twenty-one thousand years to complete; and that involved by the variation of the orbit's eccentricity, gone through in millions of years."

These phenomena illustrate the regularity of averages on an immense scale. The differences in temperature between unusually hot or cold seasons in a given year all offset one another when reduced to an average of a decade or of a century, just as we assume that the great differences between glacial and tropical temperatures manifest approximate uniformity in the long period above considered. It is thus clear that circumstances or the motions of events lead to sustained average results in spite of seeming irregularities. The slowness with which some great changes take place is equivalent to the establishment of permanent conditions as far as the short duration of our individual consciousness is concerned. The glacial period, whether due to the precession of the equinoxes or some other cause, involves a lapse of time far longer than is covered by the historical record of the earliest races, along down the line of mingled civilization and barbarity to the present time.

In deference to those who are too cautious to accept any doctrine of averages in nature, it is well to give full weight to an opinion in a letter from Professor C. H. Hitchcock, regarding the glacial period. He thinks that every agency must be considered, including "obliquity of orbit, precession of the equinoxes, axial variation, and elevated planes at the north." He adds, "If you can prove that in an ice age at the north the climate about the south pole was ameliorated, then the fact that it is somewhat colder there now may be of service." Beside the variation in ocean-level, we may consider it probable that, when the earth cooled from its primeval molten state, it was left with slight excess of elevated surface at points either north or south of the equator, and that in time this resulted in difference of temperature, in ice accumulation, in axial variation due to unequal attraction. Professor Hitchcock's suggestion of many causes is valuable because it calls attention to the possibility or probability of a vast and connected ring of variations, each related to the other, so that ultimately we can only understand the facts as illustrating the instability of the homogeneous as taught by Herbert Spencer. But the oscillation is manifested in so many other ways that, even when it fails as applied to a special series of geological facts, we are still justified in believing it as an underlying truth not demonstrated in this case, owing to our want of definite knowledge concerning the glacial period.

Having thus glanced at mathematical considerations, we now pass to the identity pervading widely different phenomena. In addition to this law by which exceptional events are found to accord with a certain average, we further find identity in various kinds of action. When the ice on the river is rent with a sound like the booming of cannon, we detect some resemblance to the rumbling of an earthquake. Hence the theory may be that the subterranean sound involves the cracking of rocky strata. The motion of a small whirlpool, of a tornado, of the solar system, and hypothetically of great extents of nebulous matter, discloses an undercurrent of identity indicating that we should not value the event in itself, but the wide play of phenomena so represented. We may further conclude that the material universe, as far as known, is of value as standing for something beside optical appearances and mechanism. Aside from this representative value, concerning sidereal systems, men of genius may discern direct practical power in small things, as in the following instances: Watt applies to a wider use the lifting power of steam, as seen in the upward motion of a tea-kettle cover,[4] and Edison applies the lessened friction between electrified metal and rough paper to the general purpose of reducing the friction of machinery—at present this principle is used to increase the sounding power of the telephone. Many things appear trifling because we fail to see in them the wonderful analogies awaiting disclosure and the possibilities of development, so that lack of perception or combining power is the main condition of our helplessness in the presence of many forms of material action or phenomena.

In direct opposition to the idea of mastery through knowledge and continuous effort, we find the belief in luck, the central idea of which is that a bias in our favor may pervade events. The notion of natural order in events, followed regardless of persons, substitutes for the illusion of luck the truth of a mere coincidence between what we like and what results. Such favorable coincidences when not read aright have wrecked the lives of some men who might otherwise have developed useful powers. A careful study of such a fortunate turn of events reveals some unpleasant but irresistible facts—that a sustained favorable coincidence is very rare and likely to be of doubtful permanent value, because there is not a proper development of personal quality whereby no injury will result from prosperity. The fortunate person tries to swim in a sea of new conditions which he has not reached by a natural process of growth. The phrase "always lucky" is open to two objections not easily set aside, owing to the profound complexity of events: that the person may have skill, tact, agreeableness; and that there may be error, owing to the special or restricted view of the person judging. Belief in luck is directly and practically objectionable, because it leads to submission in matters requiring action.

Another singular but essentially superstitious idea at times gains credence. A connection between two events is affirmed strongly in proportion to lack of evidence, or it is assumed that an event has necessary relation to personal welfare. This was well illustrated by an occurrence in the central part of Illinois during the presidential contest between Lincoln and Douglas. Two flag-staffs, about two hundred feet high, had been put up in the Court-House Square of the town. Just before the election the staff in honor of Douglas fell, owing to a defect in the timber. It was at once thought that this foreshadowed the defeat of Douglas, and when the result seemed to verify this prophecy the superstitious impression became stronger than ever.

Our tendency to fill the unknown with imposing possibilities is a natural and perhaps justifiable effect of the profound mysteries of life and being which stimulate our curiosity and imagination, but there is absurdity in postulating connections between special events which are much better explained by means of the usual physical factors and the reason. With some persons the supposed relation between death and thirteen at table seems impressive, because it is assumed that there is interference owing to unknown laws of action or association. It may seem incredible that any well-educated person should hold this belief seriously, yet beyond the shadow of a doubt it has influenced many who were able in action, if not in dealing with questions of causation. As death and thirteen at table are both quite common, it follows that the concentration of attention upon this or any usual number must result in the observation of many coincidences. An absence of the coincidence is easily overlooked, because the allowance of one year for the death to occur causes the prophecy to be forgotten. The disclosure of this or any other causal connection at once deprives the superstitious idea of its assumed value. This is evident in a like instance if we maintain that spilling salt has relation to calamity because it indicates carelessness and nervousness. Nature never overlooks carelessness, and nervousness may arise from consciousness of impending trouble; hence statistics might show (if we could eliminate other influences) that persons who spill salt or upset things are more liable to disaster than others. The rejection of a natural cause is unfortunate, because it is one form of the belief that an imagined relation is objective. It is assuming that an event will necessarily conform to a prophecy made entirely without reasonable data. George Eliot pointed out this absence of reason by saying, in effect, that some people are surprised at the presence of an evil which they have done everything to produce, and at the absence of a wished-for result which they have done nothing to attain.

  1. "The Logic of Chance," by John Venn, M. A., p. 6.
  2. Published in "The Popular Science Monthly," October, 1879.
  3. "First Principles," pp. 256, 257.
  4. The story has been discredited, but the truth is applicable.