Der (un)eingeschlagene Pfad

ZusammenfassungIn einer ersten, durch den Physiker Freeman Dyson inspirierten „Common-Sense“ Kolumne vergleicht der Wirtschaftsinformatiker Edy Portmann die Geschichte von Analog- mit der von Digitalcomputer und fordert abschließend, mit einem gewagten Blick in die Zukunft, sein Schicksal als humanistischer Prophet heraus.

At Lunch with Freeman Dyson

This is the story of a minor discovery in mathematical game theory. It concerns the prisoner’s dilemma game, which, played once, involves little strategy. But consider the iterated prisoner’s dilemma (IPD) game. In the IPD, there is information in the previous plays, which each player can use to devise a superior strategy that remains self-interested.

Dyson’s classification and real division superalgebras

It is well-known that unitary irreducible representations of groups can be usefully classified in a 3-fold classification scheme: Real, Complex, Quaternionic. In 1962 Freeman Dyson pointed out that there is an analogous 10-fold classification of irreducible representations of groups involving both unitary and antiunitary operators. More recently, it was realized that there is also a 10-fold classification scheme involving superdivision algebras. Here we give a careful proof of the equivalence of these two 10-fold ways.

Rank partition functions and truncated theta identities

In 1944, Freeman Dyson defined the concept of rank of an integer partition and introduced without definition the term of crank of an integer partition. A definition for the crank satisfying the properties hypothesized for it by Dyson was discovered in 1988 by G.E. Andrews and F.G. Garvan. In this paper, we introduce truncated forms for two theta identities involving the generating functions for partitions with non-negative rank and non-negative crank. As corollaries we derive new infinite families of linear inequalities for the partition function p(n). The number of Garden of Eden partitions are also considered in this context in order to provide other infinite families of linear inequalities for p(n).

Looking Back at Kinesiology’s Future: The Need for Both Focused Frogs and Visionary Birds

This essay reflects on the status of kinesiology amidst the current pandemic and Black Lives Matter movement. Utilizing the metaphor coined by mathematician and physicist Freeman Dyson, I contend that the continued success of kinesiology is more plausible if we prepare more visionary birds, those with broader range and a variety of interests, to supplement the more narrowly focused frogs who currently dominate the field. Implicit in the essay is the contention that the field would benefit if it took a more interdisciplinary approach to the study of physical activity, sport, exercise, and other human movement forms as advocated by the American Kinesiology Association and individual scholars in the field. More specifically, I argue that the social sciences and humanities should be provided a more prominent place in kinesiology curriculums and serve as an academic core for all students in the field, irrespective of career aspirations and goals.