My hypothesis is that the Kryptos Sculpture represents an elegant proof of what has become the central philosophical problem in the notion of “intelligence” in the broadest sense today, and has enormous implications in the future of mankind. The issue confronted the creator of this artwork: could an example be created to prove whether the human element of covert intelligence could ever be replaced by computers? Could we wrap this whole notion into a form that illustrates itself by example? in effect: a complete proof if true? In an Artwork? At Langley?
This was all in good fun, reinforced by the strong fellowship of the crypto community in the NSA and CIA. They belong to an ancient fraternity, and they honor that tradition by facing intellectual challenges. Historically, when a major discovery is made, the invisible college is informed in code. In this anonymous arena, ideas must create their own defense, and demonstrate truth so explicitly, that the verdict of the college is always unanimous. The rivalry of the members ensures their mutual vitality and that of the college.
Consistency with the theme would suggest honoring examples and symbols of the triumph of the human element over the unknown, light over dark in the history of the CIA. In the beginning, there were the twins: WW and WW. CAMP X and HYDRA are symbols for the COI and OSS, later TORCH perhaps. The CIA saw illumination at the end of a tunnel in Berlin in the form of a cable, echoing Carter’s triumph. PBJOINTLY, GOLD, REGAL, STOPWATCH all figure as images in my mind. The Russians were impressed and publicly acknowledged a new peer had arrived in the chess game. Each of these successes seemed to result from cooperation, ingenuity, and inventiveness. It was these victories that ensured the early survival, and fostered the growth of the CIA.
Within the American national security complex the NSA has a reputation of representing the brute force approach: mechanistic, computational intelligence gathering, which sees its parallel in philosophy as the Computational Theory of Mind. In a closed system if all the variables are known, and all operations giving rise to the formal system consistent, and if you have enough memory, or enough Turing tape, everything is both knowable and solvable. In human terms it’s like possessing an eidetic memory and infinite computational ability. When Deep Blue beat Kasparov, it was one for them, philosophically speaking.
Over at Langley, it is and was, a little more touchy-feely. For altogether too many reasons to list, the CIA represents the intuitive model of data analysis. Underlying this approach is a belief that data without the benefit of the context of the intentions of the humans that create it is basically useless. I am going to demonstrate a proof of why. Kryptos was presented to the CIA, but really the NSA, to illustrate the same point.
To serve my thesis, I present the following information, mostly edited from Wikipedia:
In 1880 Emil du Bois-Reymond made a famous speech before the Berlin Academy of Sciences outlining seven “world riddles” some of which, he declared, neither science nor philosophy could ever explain. He was especially concerned to point out the limitations of mechanical assumptions about nature in dealing with certain problems he considered “transcendent”. A list of these “riddles”:
- the ultimate nature of matter and force,
- the origin of motion,
- the origin of life,
- the “apparently teleological arrangements of nature,” not an “absolutely transcendent riddle,”
- the origin of simple sensations, “a quite transcendent” question,
- the origin of intelligent thought and language, which might be known if the origin of sensations could be known, and
- the question of freewill.
Concerning numbers 1, 2 and 5 he proclaimed: “ignoramus et ignorabimus“: “we do not know and will not know.”
On the 8th of September 1930, the mathematician David Hilbert pronounced his disagreement in a celebrated address to the Society of German Scientists and Physicians, in Königsberg: “We must not believe those, who today, with philosophical bearing and deliberative tone, prophesy the fall of culture and accept the ignorabimus. For us there is no ignorabimus, and in my opinion none whatever in natural science. In opposition to the foolish ignorabimus our slogan shall be: Wir müssen wissen — wir werden wissen! (‘We must know — we will know!)
Hilbert worked with other formalists to establish concrete foundations for mathematics in the early 20th century. However, Gödel’s incompleteness theorems showed in 1931 that no finite system of axioms, if complex enough to express our usual arithmetic, could ever fulfill the goals of Hilbert’s program, demonstrating many of Hilbert’s aims impossible, and specifying limits on most axiomatic systems.
Gödel’s incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert’s program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert’s second problem.
[ed: I suggest the Kryptos creators have extended the problem to the world of cipher, code, and language itself as a formal mathematical systems]
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an “effective procedure” (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.
Minds, Machines and Gödel is J. R. Lucas’s 1959 philosophical paper in which he argues that a human mathematician cannot be accurately represented by an algorithmic automaton. Appealing to Gödel’s incompleteness theorem, he argues that for any such automaton, there would be some mathematical formula which it could not prove, but which the human mathematician could both see, and show, to be true.
As Einstein did so often, he had already demonstrated the proof succinctly in plain English years before, but as the great instructors always do, posed it poetically. “The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift.” This comment was directed squarely at Hilbert. Both of them had anticipated the earliest computer by 15 years.
Lucas wrote several books on the philosophy of science and space-time. In A Treatise on Time and Space he introduced a transcendental derivation of the Lorenz Transformations based on Red and Blue exchanging messages (in Russian and Greek respectively) from their respective frames of reference which demonstrates how these can be derived from a minimal set of philosophical assumptions.
In The Future Lucas gives a detailed analysis of tenses and time, arguing that “the Block universe gives a deeply inadequate view of time. It fails to account for the passage of time, the pre-eminence of the present, the directedness of time and the difference between the future and the past. Instead he argues in favor of a tree structure in which there is only one past or present (at any given point in space-time) but a large number of possible futures. “We are by our own decisions in the face of other men’s actions and chance circumstances weaving the web of history on the loom of natural necessity”
Gödel, Escher, Bach: An Eternal Golden Braid also known as GEB, is a 1979 book by Douglas Hofstadter exploring common themes in the lives and works of logician Kurt Gödel, artist M. C. Escher and composer Johann Sebastian Bach, GEB expounds concepts fundamental to mathematics, symmetry, and intelligence. Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of “meaningless” elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of “meaning” itself.
Given the previous, my working hypothesis is that if K4 were solvable by any known crypto system, or the result of any sequenced mathematical system which a computer or human genius could solve, it would have already been solved. I possess an experimental observation in support of this in that the most powerful computers on the planet, and the women and men that operate them have had 25 years, with no signs of success.
Ed Sheidt knew it would come to this. So did Sanborn. I believe it was the plan. That’s why it was necessary to control the timeline on the overhead views of the site, and the Morse transcription, since they needed to protect that information to ensure Kryptos would fulfill its goal as represented by my hypothesis: to make a point about covert intelligence and operations being inherently a human science. They gave out the necessary info long ago, however, and still, no solve. In the meantime, it has become a time machine. Through natural human curiosity, it generates the energy to sustain itself. When we try to solve the enigma, we enter into self-created worlds of what we think it might be about: the history of cryptography, the story of the OSS, Berlin, Tut, whatever. There is no evidence of what the form and context of “the answer” might really be.
I’ve tentatively suggested that any known system of attack, using any language will fail. There is a context that needs application that only a human can conceive. Something that is “not present” in the context of Hilbert space: i.e.: all that can be known and modeled by a computer. We have been informed by Sanborn, since the beginning and repetitively since that: the installation reflects a broad spectrum of elements which are to be taken as a whole. The creation of disparate elements requiring re-contextualization in spatial terms, perhaps in Cartesian space, was the central defense mechanism of the sculpture and the source for several clues. There’s no way to reduce what might be hidden between rocks, recycled pennies, or maps into a data input that can exist in the same Hilbert space as the “text” of K4.
Thus, we need to really figure the Morse Strata out, since as humans, we can intuit something that might be missing, the “lack of” something as itself a signifier. What is the message covered by the rocks? We need to explore doubled letters and palindromes as signifiers and potentially as punctuation. The “e” strings could be prosigns, ellipsis dots, numbers: anything really. We should convert it back to morse and explore different directional contexts.
We need to start looking at shapes. Sanborn as an artist will express himself in mathematical terms consistent with that of his craft, which takes the form of the math of nature. Pi, Phi, phi, and e. The Golden Ratio. Sanborn has slyly tried to create a notion that he has no mathematical skill. There is a 30 year record of his public work that suggests a very high level of geometric skill. I’m not great with numbers either, but when you understand Pi and Phi, numbers are pretty much just placekeepers. Consider the 3,4,5 right triangle- how good do you really have to be at math?
This should apply both to text and design. To decrypt Kryptos, we are going to have to model the activities of those who discovered the Archimedes palimpsest: we will have to look through the book, to see the scroll. Both the book and the scroll will deliver information based upon their original proportion and orientation, and this understanding is what will make the scroll legible. The process of making medieval manuscripts from old scrolls gives us a model for an overall matrix transformation as well.
An expert on Medieval palimpsest like Tiltman would inform us that there was a time when deviations from the truly beautiful page proportions 2:3, 1:√3, and the Golden Section were rare. Many books produced between 1550 and 1770 show these proportions exactly, to within half a millimeter. Ed Sheidt lectured about medieval printing guilds, secrecy and methods of steganography and encoding systems in the middle ages. In those days, the great thinkers of the day were under the patronage of powerful political leaders. They performed a role similar to what the CIA does for the Executive Office: they were the eyes and ears. In royal courts around the world, there was a secret fraternity of alchemists, poets, and scribes, a communications and intelligence network. Among the 3 estates, this fraternity was “outside the loop.” The modern notion of diplomatic immunity owes itself to this ancient entente cordiale. Their symbolic tools are the Key and the Quill.
A Palimpsest is a text that survives as traces of original ink from vellum or papyrus scrolls, which were subsequently reused by later scribes. The process involved cutting the scrolls, which could be 20 ft or more, into pre-defined lengths, washing and otherwise effacing the previous text, stacking them at a 90 degree orientation to the original text, and folding the stack into a gather. The gathered stack is folded like a newspaper and sewn together at the fold to make a Folio, or the pages are cut individually, stacked and sewn together at the binding to form a Codex. Palimpsest parchment sheets typically retained their original central fold in the new binding, but each was ordinarily cut in half, making a quarter (“quarto”) volume of the original folio, with the overwritten text running perpendicular to the effaced text.
The new text was often a hymnal or liturgical piece, relating to monastic worship. Ironically, the content of the texts remaining in palimpsest under these rather common and ordinary books, authored by the great Greek and Roman philosophers, statesmen and scientists, would have been quite radical and destabilizing to the Monks’ world view indeed.
For example, in the Archimedes Palimpsest pictured above, diagrams are clearly visible in certain sections of this 10th century manuscript. Through X-Ray analysis, the entire manuscript contained three of Archimedes’ most important mathematical treatises: “The Method”, “The Stomachion” and “On Floating Bodies.” They were not known to exist prior to their discovery in palimpsest.
I suspect that Sanborn takes pride and satisfaction from the parallel: lurking under the foundations of ritual and dogma are often radical and destabilizing ideas. That is very image he intended for Kryptos- as an architectural palimpsest- with successive generations of strata built one on top of another- and underneath, hidden knowledge struggling to break free, be rediscovered, brought back up from undergruund: decrypted?
In the context of the would-be code breaker in the field “Palimpsest” is rich with meaning and imagery in a much broader sense than the first phrase that it unlocks as passkey on the Vigenere table. It doesn’t just open the door to the first part, but rather suggests a technique-It provides a directive from Sanborn and he seems to be saying something between the lines: “eventually, you will reuse the Palimpsest section plaintext to provide the structure for later decryptions.” Logically, the keys discovered here will remain consistent, are to be relied upon, despite an expanding universe of maybes and “unknown unknowns.”