224 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1955 



In the case where open space appears to be required by the physical 

 characteristics of our neighborhood, we never will be sure of its 

 validity for the universe as a whole. The possibility should not be 

 overlooked that what we observe now is merely the metagalaxy — only 

 a step in the hierarchy of physical systems. The observed expansion 

 may refer only to this iimited, although large, material system; in 

 other parts of the world conditions may be different. The finite 

 intensity of the sky background has often been advocated to prove 

 the finiteness of the world. However, as shown by C. V. L. Charlier 

 on purely classical lines, an infinite world is compatible with a finite 

 intensity of the sky background if the universe is built on a hierarchical 

 principle, systems of each order (atomic nuclei, atoms, planets, stars, 

 clusters, galaxies, metagalaxies, etc.) being separated by distances 

 considerably greater than their diameters. Such a "hierarchically 

 diluted" infinite universe has a finite and small surface brightness even 

 in the absence of absorption or Doppler shifts. 



In the case of closed space the mii verse (the whole, or the observ- 

 able metagalaxy), with all its energy content, including radiation, is 

 bound to return to the initial state of nuclear fluid. This course of 

 events is likely to repeat itself, the universe oscillating without ex- 

 ternal loss, implying an unlimited age in the past and in the future 

 (time here meaning simply a succession of events, irrespective of its 

 numerical value). All the structural phases will return time and 

 again without, however, an "eternal recurrence of all things" in 

 Nietzsche's sense — the individual celestial bodies in successive oscilla- 

 tions would not be identical, nor would their inhabitants. On the 

 contrary, an milimited variety of combinations and of prospects of 

 evolution would be possible during each phase of the oscillation. 



Some have expressed disgust at the idea of an oscillating universe, 

 periodically repeatmg its general features (2). The present writer 

 cannot see why this great repetition should claim a lesser esthetic 

 value than, e. g., the annual succession of seasons so praised by poet 

 and layman. Besides, not only is the repetition never literally exact, 

 but, alas, we have no say in the matter — the Plan was laid down 

 without our being consulted beforehand. 



LITERATURE CITED 



1. Opik, E. Pop. Astron., vol. 41, p. 79, 1933 ; Harvard Reprint 84. 



2. Russell, H. N. Science, vol. 92, p. 19, 1940. 



3. F.OK, B. J. Observatory, vol. 59, p. 76, 1936. 



4. Chandrasekhar, S. Science, vol. 99, p. 133, 1944. 



5. BoK, B. J. Month. Not. Roy. Astron. Soc., vol. 106, p. 61, 1946 ; Harvard Re- 



print 284. 



6. Shaplet, H. Amer. Journ. Sel., vol. 243-A, p. 508, 1945, 



7. Ahrens, L. n. Nature, vol. 160, p. 874, 1947. 



