One consequence of successive combination is that the simplest marks will suffice to express any information. Francis Bacon proposed for secret writing a biliteral cipher, which resolves all letters of the alphabet into permutations of the two letters *a* and *b*. Thus A was *aaaaa*, B *aaaab*, X *babab*, and so on.[108] In a similar way, as Bacon clearly saw, any one difference can be made the ground of a code of signals; we can express, as he says, *omnia per omnia*. The Morse alphabet uses only a succession of long and short marks, and other systems of telegraphic language employ right and left strokes. A single lamp obscured at various intervals, long or short, may be made to spell out any words, and with two lamps, distinguished by colour, position, or any other circumstance, we could at once represent Bacon’s biliteral alphabet. Babbage ingeniously suggested that every lighthouse in the world should be made to spell out its own name or number perpetually, by flashes or obscurations of various duration and succession. A system like that of Babbage is now being applied to lighthouses in the United Kingdom by Sir W. Thomson and Dr. John Hopkinson. [108] *Works*, edited by Shaw, vol. i. pp. 141–145, quoted in Rees’s *Encyclopædia*, art. *Cipher*. Let us calculate the numbers of combinations of different orders which may arise out of the presence or absence of a single mark, say A. In these figures +---+---+ +---+---+ +---+---+ +---+---+ | A | A | | A | | | | A | | | | +---+---+ +---+---+ +---+---+ +---+---+ we have four distinct varieties. Form them into a group of a higher order, and consider in how many ways we may vary that group by omitting one or more of the component parts. Now, as there are four parts, and any one may be present or absent, the possible varieties will be 2 × 2 × 2 × 2, or 16 in number. Form these into a new whole, and proceed again to create variety by omitting any one or more of the sixteen. The number of possible changes will now be 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2, or 2^{16}, and we can repeat the process again and again. We are imagining the creation of objects, whose numbers are represented by the successive orders of the powers of *two*.