It is no coincidence that IAU and Saha’s ionization formula are about the same age. Both events are related to World War 1 and connected with Germany though in entirely different ways.

Once sufficiently large number of stellar spectra had been obtained and empirically classified according to the Harvard scheme, it was inevitable that theoretical explanation would be forthcoming. The only surprise was that the breakthrough came from the far-off Calcutta which was nowhere on the world research map.

History chose the hour; the hour produced an unlikely hero: Meghnad Saha. Calcutta University had just become a research centre under Indian auspices. By a fortuitous combination of circumstances immediately after the war, the latest German language physics publications arrived in Calcutta as a personal library. While Europe needed time to resume scientific exchanges and activity, India seized the opportunity and produced two outstanding pieces of theoretical work: Saha’s ionization formula (1920), and Bose statistics (1926). It is to the credit of The Royal Society that it elected Saha as a member (1927) in spite of the government’s objections arising from Saha’s anti-British stance. Saha however was unable to carry out further observational and experimental work suggested by the theory.

Saha was a multi-faceted personality with strong views on political ideology, the role of science in a new nation and other topics. India’s charismatic Prime Minister, Jawaharlal Nehru, during 1947-1964 had a soft corner for sophisticated, suave, upper-crust people. Impatient and angry, confrontational rather than persuasive, Saha did not qualify.

Saha is justly regarded as one of the founders of theoretical astrophysics. Examination of his life and work is a rewarding exercise from various points of view: development of modern astronomy; Western science and the non-West; and political and social activism of a leading scientist and educator.

In this paper we study different types of planar random motions (performed with constant velocity) with three directions, defined by the vectors dj = (cos(2πj/3), sin(2πj/3)) for j = 0, 1, 2, changing at Poisson-paced times. We examine the cyclic motion (where the change of direction is deterministic), the completely uniform motion (where at each Poisson event each direction can be taken with probability ) and the symmetrically deviating case (where the particle can choose all directions except that taken before the Poisson event). For each of the above random motions we derive the explicit distribution of the position of the particle, by using an approach based on order statistics. We prove that the densities obtained are solutions of the partial differential equations governing the processes. We are also able to give the explicit distributions on the boundary and, for the case of the symmetrically deviating motion, we can write it as the distribution of a telegraph process. For the symmetrically deviating motion we use a generalization of the Bose-Einstein statistics in order to determine the distribution of the triple (N0, N1, N2) (conditional on N(t) = k, with N0 + N1 + N2 = N(t) + 1, where N(t) is the number of Poisson events in [0, t]), where Nj denotes the number of times the direction dj (j = 0, 1, 2) is taken. Possible extensions to four directions or more are briefly considered.