I’m treading familiar ground but perhaps not to all of us when I discuss the differences between inductive and deductive reasoning. Sherlock Holmes is the quintessential example of deductive reasoning and if you’re not familiar with the character then the analogy is useless to you, if you are then perhaps you are still slightly confused. It’s not just about being smart and picking up on things that others wouldn’t. Holmes would spout forth endless minutae about the various types of soil samples their locations in London to flesh out his conclusion and that is nothing more than deductive reasoning at work. If I’ve seen 50 farmers with that type of mud on their shoes then by golly, that fella right there is probably a farmer.

Let’s do the definitions quick and then get into the meat of why I expect anyone to care.

Reasoning: –noun 1. the act or process of a person who reasons. 2. the process of forming conclusions, judgments, or inferences from facts or premises. the reasons, arguments, proofs, etc., resulting from this process.

Deduction: -noun reasoning from the general to the particular (or from cause to effect)

Induction: -noun reasoning from detailed facts to general principles

Take the time to look it up elsewhere if you will, you’ll find a very fascinating story of birds or events or what have you. I’ll give you my own example and then relate the debate to cryptology.

Passing through a field, two friends see an animal print in the mud. The deductive fellow would compare it to his field guide which has been prepared by countless observers noting countless animal prints and he then compares the unknown particular to the well-documented general and determines it is likely probably a pink and yellow unicorn. Now his friend wasn’t paying attention because he’s more of an inductive thinker and has been trying to reconstruct the nature of what could generate an imprint like that. (Classically, folks would argue that the inductionary would see a unicorn with a hoofprint and assume that all hoofprints are made by unicorns. This is mainly due to a fundamental misunderstanding about the nature of inductive reasoning and due to the fact that we are all indoctrinated into subscribing to deductive reasoning and trained to regard inductive rationale with misplaced prejudice and scepticism.)

Cryptologists, especially in the military, often are faced with an abundance of text that has been encoded by similar means. Once you’ve seen enough substitution ciphers (or watched enough Wheel of Fortune) they become manageable. Vigenere ciphers, Enigma ciphers, definitely all of the analog ciphers have been in use so long historically that not only have methods been developed to crack them but your cryptoanalyist is constantly examining and comparing ciphertext that has been enciphered in similar manners and sometimes with the same keywords. The field is practically founded on deductive reasoning, oh, and a little math.

K1-3 used standard methods that would fall prey to the standarized military attacks.

K4 is different. We know it’s unique and that the masking method is probably not known. We know it’s plaintext is in English. We know it is solvable. We know there are clues in the earlier sections of the sculpture. We know that there is a technique at work that has altered the letter frequency to even out the counts and move them away from standard plaintext values. We know there are 97 letters. We know that before an deciphering can occur, the masking technique must be conquered. We know that it has resisted almost 20 years of attempts by the CIA, the NSA and the assorted hobbyists and amateurs grinding away on it. It must be difficult but not impossible. It must not use standard enciphering techniques, or at least at first otherwise someone would have solved it. We know it hasn’t been solved due to the fall-out over people claiming to be the first solvers for K1-3. We all know the score now. It doesn’t count unless you announce it first. Otherwise it seems like you’re just trying to rain on someone else’s parade. We need to use induction or intuition to assemble all of the details about what the masking accomplished and any hints given. We must then develop hypothesis and test them. We need to redefine inductive reasoning into something more useful than just “jumping to conclusions”. We need some good ideas!

K4 is essentially the only one of its kind (unless recycled by Sanborn in later pieces) and we have no deductive process that will help reach a solution. It will be through inductive reasoning and intuition that it is solved, if ever.

It’s a technique, something reversable, which makes it an algorithm of sorts. If we can try to discover the rules, then we can uncover the true K4. Otherwise, and I can’t exaggerate this enough for anyone reading, WE ARE JUST WASTING OUR TIME UNTIL WE FIGURE OUT THE MASKING. Sure, I’ve tried this and that but it’s only been about 3 weeks for me whereas some folks have spent over a decade trying to fit a round peg into a square hole.

So drop your cipher or try and finish up that last method you’ve been dying to try. For me, my last so-called “cipher” attack will be to attempt to force a foursquare solution. I’m hoping that if I try and solve K4 as is as well as shifted one letter over then I’ll be able to retrieve at least some plaintext and that can form the basis for further efforts.

After that, I will attempt to learn or come up with possible ways to hide a message in K4.

Good luck and good night!

Kryptos Fan

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