Wilhelm Ostwald's Happiness Formula

This is a reprinted version of Ferenc Szabadváry, “Wilhelm Ostwald's Happiness Formula”, in Journal of Chemical Education, Volume 42, Issue 12, December 1965, pp. 678–679. Translation by Ralph E. Oesper.

Wilhelm Ostwald (1853-1932) was one of the outstanding personalities of chemistry. Though he made important discoveries such as his “dilution law” and his clear exposition of catalysis, his greatest accomplishment was perhaps his recognition of the relations between observations that had been made in the second part of the 19th century and his explanation of these connections. He brought together the findings of Guldberg and Waage, of J. W. Gibbs, of van't Hoff and Arrhenius, and arranged them into a systematic whole which ever since has been taught under the title physical chemistry, a discipline that is now viewed as the basis of all other branches of chemistry. His great goal became "a chemistry without substances," i.e., the system of those general concepts and relationships (laws of nature) that can be applied to all substances without dependence on their nature. Physical chemistry really was created from the application of the laws of thermodynamics for explanation of chemical events. Ostwald was not satisfied to limit the validity of thermodynamics to physics and chemistry. His fine success in this area and his lively imagination misled him to the belief that phenomena and occurrences in physiology, psychology, and sociology, in fact even in art, could be explained through the thermodynamic laws. In 1907 he stated: “There is no problem that cannot he solved by means of the laws of thermodynamics.” Ostwald held that in reality everything consisted of energies. However, it is not entirely clear what he meant by energy. He employed and operated with this concept usually in a completely material sense. He took the field especially against atomism; he believed that atoms did not exist, that they were merely relics of ancient mystic tenets. Unfortunately he put forth this contention at a time when the atom, after being no more than a mental picture for thousands of years, was in fact becoming accessible to scientific experimentation. Ostwald was finally convinced of the reality of atoms by the work of Jean Perrin on the Brownian movement (1908). The extremes to which Ostwald extended his thermodynamic philosophy are well illustrated by his “Happiness Formula,” in which he sought to express a state of mind in mathematical terms. Its genesis was a spell of depression from which he sought to escape into a happier state, and for this he thought it necessary to discover the laws of happiness. After several weeks of intense cogitation directed to this goal, he believed that the solution was as follows:1 He proceeded from the fact that all life is characterized by liquid equilibrium in which a continuous energy stream flows through the system. Every conscious experience is proportional to the total energy flow. If the experience is welcome, i.e., in harmony with the will, it produces a pleasant or happy feeling; when it is unwelcome, i,e., opposed to the will, it produces displeasure or unhappiness. The proportional energy in the first case is represented by A, in the second case by W. One feels happy or not depending on whether (AW) is positive or negative.

“At first I thought that I had thus found the solution that I had been seeking snd I was rather unsatisfied with the scanty finding that in order to be happy it was necessary to make the total of the welcome activities and experiences as large as possible, and the sum of the unwelcome ones as small as possible. However, people are usually intelligent enough to do that without any science. But then I remembered that formerly the mere overcoming of difficulties and hindrances had produced positive feelings of happiness, which now were not nearly so strongly felt of course. Consequently, the energy activity itself must contain a source of happiness and this likewise must be brought under the sought law. The total energy participation is the sum of the welcome and the unwelcome, hence (A + W). Since all pleasurable sensations cease, when (AW) as well as (A + W) equals zero, both constituents must be bound to each other as factors of a product and not perhaps as the members of a sum. If a factor k is also introduced, which expresses the conversion of the energetic event into the psychological, the result is the happiness formula (Glücksformel), in which G represents the degree of happiness: $G = k(A-W)(A+W)$ Expressed in words, the formula states that happiness is proportional to the excess of (AW) of the energy involved that is in accord with the will and to the total amount (A + W). In order that the happiness assume a highest possible value, both factors (AW) and (A + W) must be as large as possible. Of the two, the total energy activity (A + W) is under our control only to the extent that we preserve our health by leading a physiologically suitable life, because illness represents diminution of energy. The energy stream is most independent of us in childhood and early adulthood and inevitably decreases with advancing age. This falling-off usually starts to became noticeable between the 40th and 50th year of life and comes more and more into the foreground in later years. In youth (A + W) is accordingly large and intense happiness can be attained even though the other factor (AW) is decreased by notable values of the resistances W. If (AW) once becomes negative, the high value of (A + W), likewise a high negative result, brine about a marked feeling of unhappiness. Youth therefore is characterized by vehement fluctuations between intense feelings of happiness and unhappiness. If the total involvement of energy decreases with advancing age, the product necessarily becomes smaller, and to insure an adequate feeling of happiness the person must primarily see to it that the second factor (AW) becomes as large as possible, i.e., that the resistances are as small as possible. Accordingly, the kind of happiness enjoyed in youth is much different than that enjoyed in maturity and old age. The young exhibit heroic happiness, i.e., the powerful activation of the total energy, and are capable also of overcoming great resistances. The quiet happiness of the aged on the other hand resides in the avoidance of resistances, in the peaceful enjoyment of fruitful activities that are in accord with the will.”

Ostwald maintained of course that the possession of this formula enabled him to keep the feeling of unhappiness away from himself. The reader is at liberty to try it on himself and determine whether he can succeed as well as Ostwald in this endeavor.

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1. Ostwald, W., Annalen für Naturphilosophie, 4, 419 (1905). [This reference does not appear to be correct. The page number should be 459. See here. —Ed.]