time. Babbage showed in that most profound and eloquent work, The Ninth Bridgewater Treatise, that it was theoretically possible for human artists to design a machine, consisting of metallic wheels and levers, which should work invariably according to a simple law of action during any finite number of steps, and yet at a fixed moment, however distant, should manifest a single breach of law. Such an engine might go on counting, for instance, the natural numbers until they would reach a number requiring for its expression a hundred million digits. “If every letter in the volume now before the reader’s eyes,” says Babbage,5 “were changed into a figure, and if all the figures contained in a thousand such volumes were arranged in order, the whole together would yet fall far short of the vast induction the observer would have had in favour of the truth of the law of natural numbers.... Yet shall the engine, true to the prediction of its director, after the lapse of myriads of ages, fulfil its task, and give that one, the first and only exception to that time-sanctioned law. What would have been the chances against the appearance of the excepted case, immediately prior to its occurrence?”
As Babbage further showed,6 a calculating engine, after proceeding through any required number of motions according to a first law, may be made suddenly to suffer a change, so that it shall then commence to calculate according to a wholly new law. After giving the natural numbers for a finite time, it might suddenly begin to give triangular, or square, or cube numbers, and these changes might be conceived theoretically as occurring time after time. Now if such occurrences can be designed and foreseen by a human artist, it is surely within the capacity of the Divine Artist to provide for analogous changes of law in the mechanism of the atom, or the construction of the heavens.
Physical science, so far as its highest speculations can be trusted, gives some indication of a change of law in the past history of the Universe. According to Sir W. Thomson’s deductions from Fourier’s Theory of Heat, we