“We are not stuff that abides, but patterns that perpetuate themselves. A pattern is a message,” the mathematician, philosopher, and cybernetics pioneer Norbert Wiener wrote in his landmark treatise on communication, control, and the morality of our machines. We are patterned messages, and we make and exchange patterned messages in order to describe, understand, and navigate what we are and world in which we are — this may be the defining feature of what makes us human. Ursula K. Le Guin captured this in her splendid meditation on the magic of human communication: “Words are events, they do things, change things. They transform both speaker and hearer; they feed energy back and forth and amplify it. They feed understanding or emotion back and forth and amplify it.”

But there is a special class of messages designed with a dual purpose — to feed and amplify understanding for some, while muddling and muffling it for others: cryptography, or the art-science of encoding and decoding secret messages. The mind capable of making codes, but especially the mind capable of breaking them, is one endowed with a singular combination of skills and dispositions that illuminate the nature of creativity itself.

One such mind belonged to Elizebeth Friedman (August 26, 1892–October 31, 1980) — the cryptography pioneer who helped defeat the Nazis with pencil, paper, and perseverance, and the heroine of Jason Fagone’s excellent book The Woman Who Smashed Codes (public library). Friedman worked closely with her husband, William, as the two laid the groundwork of contemporary cryptography. Along the way, they authored a number of papers designed to train government personnel in code-breaking, but brimming with broader insight into the qualities of mind and character that make this uncommonly difficult and creative endeavor possible.

Their insight into the art-science of code-breaking survives in a 1918 paper titled “An Introduction to Methods for the Solution of Ciphers,” composed by both Friedmans but published only under William’s name, like the vast majority of their joint work and even some of Elizebeth’s solo papers. Theirs, lest we forget, was an era long predating “the invention of women.”

The Friedmans write:

Deciphering is both a science and an art. It is a science because certain definite laws and principles have been established which pertain to it; it is also an art because of the large part played in it by imagination, skill, and experience. Yet it may be said that in no other science are the rules and principles so little followed and so often broken; and in no other art is the part played by reasoning and logic so great.

The work of deciphering, they argue, is the work of induction — applying generalized principles to a particular problem at hand, which requires that the code-breaker rest upon a set of assumptions. But this fundamental blindspot of inductive thinking is counterbalanced by unparalleled vistas of imagination, enlisting the same combinatorial faculty that governs all creative work. The Friedmans consider this uncommon marriage of logic and intuition at the heart of code-breaking:

If the special conditions of the problem approximate or conform closely to the generalized principles, the solution readily follows. But this is rarely the case, and [the decipherer] is forced to modify, not only his assumptions, but also his methods, and even to discard some of them. It is the facility and ease with which a decipherer is able to modify his methods and discard his assumptions, which differentiates the good decipherer from the poor one. Deciphering is not a process for a “one-cylinder mind.”

Likewise the part played by imagination and intuition can hardly be overestimated. The knowledge of the circumstances surrounding the interception of a message, of the correspondents, etc., furnishes a wide field for the exercise of the intuitive powers; and a shrewd “guess” will often result in more progress than a whole day’s painstaking labor. This faculty, so essential in deciphering, can be developed and trained. The exercise of the imaginative powers by attempting to assume whole words, given only two or three letters and their positions, will result in the stimulation of all the faculties concerned in the expression of ideas, will thus enlarge the decipherer’s vocabulary, and otherwise arouse those qualities of mind which are peculiarly needed in cipher work.

But the most crucial element of successful code-breaking is the same defining feature of success in any creative or intellectual endeavor: doggedness. Four decades after Tchaikovsky composed his timeless case for the supremacy of work ethic over inspiration, the Friedmans write:

Persistency is absolutely necessary for deciphering. Results are often secured only after seemingly endless experiment, and concentrated effort. It may be said that even after one has a thorough grasp of the underlying principles, patience and perseverance are the key-notes to success.

Echoing Lewis Carroll — “When you have made a thorough and reasonably long effort, to understand a thing, and still feel puzzled by it, stop, you will only hurt yourself by going on,” the brilliant logician and Alice in Wonderland author had counseled in his three tips on overcoming creative block — they issue a vital caveat that applies to all creative problem-solving:

Yet, too long application soon results in mental exhaustion, and in such a condition little progress can be made. The decipherer will actually save time by ceasing from his labors and attacking the problem afresh later. A few minutes of work by a rested and clear mind is worth as many hours by a brain which is dull from fatigue.

The Friedmans summarize the essential components of the code-breaking mindset:

The qualities upon which success depends in deciphering are interrelated — reasoning from laws must be balanced with facility in modifying those laws; imagination must go hand in hand with discretion; and intuition can never wholly take the place of concentration and perseverance. Finally, let it not be forgotten that many times the greatest ally the mind has is that indefinable, intangible something, which we would forever pursue if we could — luck.

In his biography of Elizebeth Friedman, Fagone offers a kindred summation of the code-breaker’s essential character traits:

This is the essence of codebreaking, finding patterns, and because it’s such a basic human function, codebreakers have always emerged from unexpected places. They pop up from strange corners. Codebreakers tend to be oddballs, outsiders. The most important trait is not pure math skill but a deeper ability to pay attention. Monks, librarians, linguists, pianists and flutists, diplomats, scribes, postal clerks, astrologers, alchemists, players of games, lotharios, revolutionaries in coffee shops, kings and queens: these are the ones who built the field across the centuries and pushed the boundaries forward, stubborn individuals with a lot of time to sit and think and not give up.

Complement with a wonderful, forgotten 1957 treatise on how intuition and imagination fuel scientific discovery, then revisit Nietzsche on how we use language — ordinary, uncoded language — to both reveal and conceal reality.