The great question of the incompatibility of one of the attributes of the Creator—that of fore-knowledge, with the existence of the free exercise of their will in the beings he has created,—has long baffled human comprehension; nor is it the object of this chapter to enter upon that difficult question.

As, however, some of the properties of the Calculating Engine seem, although but very remotely, to bear on a similar question, with respect to finite beings, it may, perhaps, not be entirely useless to state them. [167/168]

It has already been observed, that it is possible so to adjust the engine, that it shall change the law it is calculating into another law, at any distant period which may be assigned.

Now, by a similar adjustment, this change may be made to take place at a time not foreseen by the person employing the engine. For example: when calculating a table of squares, it may be made to change into a table of cubes, the first time the square number ends in the figures —


an event which only occurs at the 99736th calculation; and whether that fact is known to the person who adjusts the machine or not, is immaterial to the result. But the very condition on which the change depends, maybe impossible. Thus, the change of the law from that of squares to that of cubes may be made to take place the first time [169] the square number ends in 7.

But it is known, that no square number can end in a 7; consequently the event, on the happening of which the change is determined, can itself never take place. Yet, the engine retains impressed on it a law, which would be called into action if the event on which it depends could occur in the course of the law it is calculating.

Nay, further, if the observer of the engine is informed, that at certain times he can move the last figure the engine has calculated, and change it into any other, in consequence of which it becomes possible that some future term may end in 7; then, after he has so changed the last figure, whenever that terminal figure arrives, all future numbers calculated by the machine will follow the law of the cubes. [169/170]

These contingent changes may be limited to single exceptions, and the arrival of such an exception may be made contingent on a change which is only possible at certain rare periods. For example: the engine may be set to calculate square numbers, and after a certain number of calculations — ten million and fifty-three, for instance, it shall be possible to add unity to a wheel in another part of the engine, which in every other case is immovable. This fact being communicated to the observer, he may either make that addition or refrain from it: if he refrain, the law of the squares will continue for ever; if he make the addition, one single cube will be substituted for that square number, which ought to occur ten million and five terms beyond the point at which he made [170/171] the addition; and after that no future addition will ever become possible, and no deviation from the law of the squares ever can occur.

13 December 2008