We assume initially, each molecule is only capable of assuming a finite number of velocities...<math>0, \frac{1}{q},\frac{2}{q},\frac{3}{q},...\frac{… - Ludwig Boltzmann

Who sees the future? Let us have free scope for all directions of research; away with dogmatism, either atomistic or anti-atomistic!

If this be so—and hardly any physicist will contradict this—then neither the Theory of Gases nor any other physical theory can be quite a congruent account of facts, and I cannot hope with Mr. Burbury, that Mr. Bryan will be able to deduce all the phenomena of spectroscopy from the electromagnetic theory of light. Certainly, therefore, Hertz is right when he says: "The rigour of science requires, that we distinguish well the undraped figure of nature itself from the gay-coloured vesture with which we clothe it at our pleasure." But I think the predilection for nudity would be carried too far if we were to forego every hypothesis. Only we must not demand too much from hypotheses.

It is clear that every single uniform state distribution which establishes itself after a certain time given a defined initial state is equally as probable as every single nonuniform state distribution, comparable to the situation in the game of Lotto where every single quintet is as improbable as the quintet 12345. The higher probability that the state distribution becomes uniform with time arises only because there are far more uniform than nonuniform state distributions... It is even possible to calculate the probabilities from the relationships of the number of different state distributions. This approach would perhaps lead to an interesting method for the calculation of the equilibrium of heat.