Sir Francis Bacon and Codes

from Digital Codes and Converters, the 1961 Ph.D. Thesis of F.G. Heath at the Victoria University of Manchester. Read optically for a colleague many years ago, it is provided here as interesting; touching upon the authorship of Shakespeare and other Elizabethan texts and poems. It also shows how cryptography then awaited the computer to create the modern digital world of information.

1.2 Sir Francis Bacon

There are reports going back to 200 B.C. (Polybius: a semaphore) for instances where combinations of symbols having only a few alternatives have been made into an alphabet. The man who undoubtedly wrote the first proper description of such a code was Sir Francis Bacon.

Bacon was primarily interested in ciphers, and in 1605 wrote “Of the Advancement of Learning” which describes vaguely a cipher termed OMNIA PER OMNIA, the best possible, and mentions that it is quintuple infolded but gives no useful details. In 1623 he described this cipher precisely in “De Augmentibus Scientiarum” written in Latin. Fortunately, a contemporary English translation exists, prepared by Gilbert Wats in 1640, and facsimiles of the important pages are shown in Figure 1.1.

Bacon claims that he invented this cipher himself, observing that if a binary property is used, then five symbols give 32 alternatives (25) which is sufficient for 24 letters of the alphabet (v and j were not separate at that time). He then constructed two slightly different type fonts, assigning to each type font one of the binary alternatives. Then, by using these two separate sets of type he made each five letters of an innocent message carry five binary digits which identified one letter of the ciphered message. It will be noticed in Fig. 1.1 that if we replace a by 0 and b by 1 that the simple binary sequence is obtained.

Figure 1.1 Code of Sir Francis Bacon. (a) above and (b) below

This might seem to be the point where Sir Francis Bacon leaves the story, having provided a binary code for the early telegraph engineers. Such is not the case. Bacon used another cipher (where a keyword indicates significant phrases) and in 1894 Dr. Orville W. Owen in the U.S.A. prepared the second volume of his book” The cipher story of Sir Francis Bacon” about this system, assisted by Elizabeth Wells Gallup. In the winter of 1895-6 Mrs. Gallup studied the binary cipher which has already been described, and found that it was incorporated in the first folio editions of Shakespeare’s plays. She naturally set about deciphering messages and a summary of the career of Sir Francis Bacon as revealed in them in Ref. 2. If the deciphered messages are true, then history books need a complete revision for the period of Elizabeth 1.

The various ciphered messages may be summed up as follows:-

Elizabeth, while imprisoned in the Tower, married Leicester secretly and gave birth to two children, the first Francis Bacon, the second Richard Deveraux, afterwards Earl of Essex.  Francis was cared for from birth by Mistress Ann Bacon, and was reared and educated as the son of Nicholas Bacon (Lord Keeper of the Great Seal of England). At sixteen he found out his true parentage, and was sent to France, returning two years later. In Mrs. Gallup’s own words, “The proofs are overwhelming and irresistible that Bacon was the author of the delightful lines attributed to Spencer – the fantastic conceits of Peele and Greene – the historical romances of Marlowe – the immortal plays and poems put forth in Shakespeare’s name, as well as the Anatomy of Melancholy by Burton”.

There is no point joining the argument* as to the truth or otherwise of Mrs Gallup’s decipherment: in Vol. III her publishers give a summary of her career and show that she was not a person to promote false knowledge lightly. During one spell in the British Museum she damaged her eyesight, partly by overwork and partly by the poor lighting. Three things are worth noting however.

*However, the news is not so good, since The Shakespearean Ciphers Examined: An analysis of cryptographic systems used as evidence that some author other than William Shakespeare wrote the plays commonly attributed to him, OUP, William F. Friedman 2011 suggests (I believe) that the notion of a typographical code in print was impractical given the state of typesetting in Elizabethan England.


Bacon, from childhood, was intended for a public career. At that time all diplomatic, and much personal correspondence was committed to cipher. Among the substantial benefits incurred upon mankind by Bacon was the invention, while in France, of what is known as Baconian or Bi-lateral Cipher, which is adaptable to a multitude of means and uses. It may not be generally known that this Cipher is the basis of nearly every alphabetical code in use in telegraphy, and in the signal service of the world. It is in brief, an alphabet which requires only two unlike things for its operation. These may be two slightly differing fonts of type on a printed page, as illustrated in the example given at length in his De Augmentis, published not long before his death; or it may be a dot or a slight disfigurement in a single font, or the alternating dot and dash or short and long sound space of the Morse telegraphic code, or the alternating long and short flash of light as in the heliographic system; the “wig-wag” of a flag or signal light, or two coloured lights alternately displayed; in short any means whatever alternating two unlike or unequal signs, sounds, motions or things. Under the rules of of arithmetrical progression almost innumerable alphabets can be constructed, by these means undecipherable without its particular key. It has no limitations upon its usefulness, and has never been surpassed in security, ingenuity or simplicity. Bacon himself called this the Omnia-per-omnia, the all-in-all cipher, and the name is completely descriptive [though bi-literal in now used-ED].

(Extract from Ref. 2)

The second point of interest is a forward in volume 3 by Mrs Gallup’s publishers which contains the statement “she has either deciphered it from the labors of Francis Bacon, or it is a creation of her own. There is no middle ground”. The idea of signal/noise ratio would not be familiar in 1910, and we ought to just check that the deciphered messages have a low probability of being “noise” generated between two different type fonts used at random.

It turns out that the publishers were correct, since Mrs Gallup deciphered 500 pages, all intelligible and consistent, giving perhaps 30,000 letter (coded) or 150,000 letters in the original plays. this situation can only arise once in 2150,000 or 1050,000, and it is obvious that lopping off a few 0’s for various reasons will not make the noise hypothesis tenable.

It may seem strange that Mrs Gallup’s work has left such a small impression: her name will not be found in its alphabetical place in the Encyclopedia Britannica for instance. It appears that her work is considered erroneous by scholars because one of her decipherments was a particular translation which did not exist in Bacon’s time3. Whatever the truth of this, Mrs Gallup’s book is interesting, the fascinating part of the story (to an electrical engineer) being that all this evidence in the Bacon v. Shakespeare controversy was written down in five digit binary code.

Although direct evidence is hard to find, there seems little doubt that Gauss was the man who applied Bacon’s code to a telegraph system, date around 1833. It does not seem that Gauss deviated from his other work for long enough to describe this work in detail: reference 7 states that Gauss and Weber proposed the five-digit code for telegraphy, and 1833 is given as the date, but the only paper published by Gauss and Weber at that time was on Terrestrial Magnetism


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