One hundred and thirty years after the work of Ludwig Boltzmann on the interpretation of the irreversibility of physical phenomena, and one century after Einstein's formulation of Special Relativity, we are still not sure what we mean when we talk of “time” or “arrow of time”. We shall try to show that one source of this difficulty is our tendency to confuse, at least verbally, time and becomin...

In our everyday lives we have the sense that time flows inexorably from the past into the future; that time has a definite direction; and that the arrow of time points towards a future of greater entropy and disorder. But in the microscopic world of atoms and molecules the direction of time is indeterminate and ambiguous. The true nature of time is somewhat mysterious. We creatures of time sens...

Dr. Blum's main thesis in this small volume is that from the origin of life, evolution has proceeded necessarily along certain channels, predetermined from without by the physical nature of the inorganic earth and by thermodynamic considerations from within. His interpretation of the free energy changes in biochemical reactions is particularly lucid. The exposition draws freely from the discipl...

Determining if two knots are not equivalent in an e cient manner is important in the study of knots. The arrow polynomial, which is calculated from a virtual knot diagram and is invariant under the Reidemeister moves, can be used to determine if two knots are not equivalent and determine a lower bound on the virtual crossing number. In this paper, we present the necessary data structures and al...