But another thought pushed itself into these deliberations: it was a memory of the calculation of averages as it is understood in probability theory. The rules of probability begin with cold, almost shameless nonchalance in the propensity of events to go one way at one time, a different way at another, or indeed to turn into the opposite of what they are. So one essential aspect in the formation and consolidation of an average is that the higher and special values are far fewer in number than the average ones, that in fact they hardly ever occur, and that this is true also of the disproportionally low ones. Both the high and the low remain, at best and at worst, marginal values, and this is the case not only according to the manual of calculation but also in experience wherever chance-like conditions prevail. This experience may have been obtained from hailstorm insurance and mortality surveys; but there is a clear correspondence between the low probability of marginal values and the fact that in history, too, one-sided arrangements and the unalloyed realization of exorbitant ambitions have rarely lasted. And if that seems but half the story from one point of view, from another we may consider how often, thanks to the same statistical law, the human race has been spared the enterprising mania of genius no less than the ravages of inflamed stupidity incited to action. Without deliberate intention, Ulrich kept on extrapolating from the idea of probability to spiritual and historical events, and from the mechanical concept of the average to mediocrity in the moral sphere; and so he arrived at the two-sidedness of life with which he had begun. For the limits that are set on ideas and emotions, and the changes to which they are subject, their futility, the mysterious and treacherous connection between their meaning and the manifestation of its opposite—all this and the like of it is already given as an inherent consequence of the supposition that one outcome is as likely as another. But this supposition represents the fundamental idea from which probability theory draws its substance, and is that discipline’s definition of chance; that it also characterizes the course of events in the world therefore permits the conclusion that life would not be much different from the way it is if everything were immediately left to chance.

Agathe asked if equating the course of the world with chance wasn’t a capricious way of wrapping the truth in gloom, amounting to romantic pessimism.

“Anything but that!” Ulrich replied. “We began with the futility of all high-hearted expectations and thought there was a treacherous secret behind this. But if we now compare that futility with the rules of probability, we can explain this secret—which we could call, playing mockingly with its famous opposite, the “preestablished disharmony” of creation—very unpretentiously by the fact that nothing happens to contradict it! Evolution is left to itself, not saddled with a spiritual organizing principle; apparently it operates randomly; and while these premises all but exclude the True, they do at least constitute the foundation for the Probable! At the same time, out of this concept of probability, we can explain mediocrity as the statistical average that is the world’s sole stabilizing factor and whose highly undesirable increase is palpable all around us. So there’s nothing Romantic about this, and maybe not even anything gloomy; rather, whether we like it or not, I would say it’s an adventurous possibility!”