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CRYPTIC SNIPPETS

 

Theseology--not to be confused with theology--is the study of how we should follow clues (as logic is the study of how we should reason). In cracking ciphers (cryptanalysis) we follow clues.1 These snippets of conversation raise questions not answered in this paper. By doing so they point to the need for this study called theseology. (For a book length treatment of the subject see T. Lai: The Art of Detection).


The Unobserved

It is hard to believe we can have knowledge about electrons. No one has ever observed an electron.

Back in the Middle Ages, if it is known that you can crack ciphers you are likely to be hauled before the Inquisition and charged with communicating with the devil. For, how else can you read a message you can't see?

You can't see the message but the person who wrote it...

Yes; but you are charged with communicating with the Devil, not with the author of the message.

Observations are Theory-Laden

How can observations be theory-laden? I open my eyes and I observe. Where does theory come in?

You will admit that if you are to crack this cipher (see below) you will have to introduce theory.

SBR SBCTU DBCKERVS FCGG WTTCXR SFH FRRJD YTHE SHUWI


Of course.

Would you believe that with this cipher I don't see SBR any more? but THE.

You mean the first three letter? Yes; I would too—if I had been translating back and forth over and over again.

No Foundation

If observations are theory-laden, how can we know anything at all? A house cannot stand without a solid foundation.

Cryptanalysis is possible even though observations are theory-laden ...

This only means what you obtain through cryptanalysis is not knowledge.

It is the other way around: knowledge is not like a house.

Ampliative Reasoning is Always Invalid

You say through cryptanalysis we know. How is this possible? You cannot see the hidden message, so you will have to reason to it. But reasoning can never lead to anything that we do not already know; ampliative reasoning is always invalid.

There is a choice to be made here: Either we do not know or knowledge is not obtained through reasoning. Since in cryptanalysis we obviously know we will have to conclude that knowledge is not obtained through reasoning.

You mean it is obtained by exercising our senses ...

We have already ruled that out since the message cannot be seen.

The Infinite from the Finite

Suppose in cracking a cipher we arrive at the proposition 'All S is in fact T.' Now how could we have arrived at this proposition if not by ampliative reasoning? For the proposition is universal but our evidence is finite.

We arrive at this proposition not by ampliative reasoning but by following clues.

What are clues?

Why is it that clues can lead to the truth?

Suppose in a cryptogram you see SB at the beginning of two words; what do you think SB could stand for?

One possibility is that it stands for TH.

Why?

Because many English words begin with TH.

What are clues then?

I'm sorry, I don't know.

A language is not just a pile of symbols; is it not?

No, it is not; a language has a structure.

English therefore has a structure.

Yes, English has a structure.

A structure has characteristics ...

What do you mean?

In English many words begin with TH.

Yes.

Every word has at least one vowel.

Right.

English has a structure and a structure has characteristics and that is why SB is a clue.

Now I see.

So clues are the characteristics of structures.

It seems so.

That's why clues can lead us to the truth.

I don't understand. Why?

Since clues are the characteristics of structures, if we have many clues we can reconstruct those structures of which they are the characteristics.

The Future

No one can avoid ampliative reasoning. Suppose you have intercepted another secret message from the same source tomorrow; will you not decipher the Ss as Ts as you have done today? But this is ampliative reasoning. Your are saying your theory works today, therefore it will work tomorrow.

I will not say my theory will work tomorrow. On the contrary, I will say most likely it will not work tomorrow ...

Not work tomorrow? Why?

Because the longer a cipher is in use, the more likely it will be changed ...

So you will not use your theory tomorrow ...

I will use my theory tomorrow.

I am puzzled. Why will you use it tomorrow if you think the cipher might change?

It's just a matter of not crossing a bridge before you come to it.

What do you mean?

I will use my theory tomorrow. If it works, there is no bridge to cross. If it doesn't work I will have a new cipher to break.

Going Beyond

Scientists make discoveries. By doing so they push knowledge beyond its current boundary. But when we follow clues we can't be doing this. A clue can only be a clue for something we already know.

Suppose you have invented a new kind of cipher and you have studied it carefully to find out its characteristics. Suppose another person has invented the same kind of cipher; would you be able to break it?

Of course; because I will be able to recognize the clues. But this supports my point; by breaking his cipher I have not discovered anything new.

Yes, you have; you have discovered this person has invented the same kind of cipher.

Okay; but you can't create a world and then discover God has done it before you.

True. But I can create a structure and then discover it is present in the world God has created.

Crucial Experiments

There are no crucial experiment. We cannot say either A or B and depend on a crucial experiment to rule out one of them. We cannot do this because it is never just A or B. The number of possibilities is infinite, so that ruling out any finite number will never take us any closer to the truth.

In cracking a cipher, when you have found a clue the number of possible interpretations of that clue is always finite. Indeed, in some instances it could have just two possible interpretations, so that if you can rule out one the other is likely to be right.

Why should the number of interpretations be finite? Why can't it be infinite?

Would you call anything a clue if it could mean anything at all?

Explanation

Given a body of facts we can always find some theory to 'explain' it. Indeed, we can always find more than one theory, and that's our problem.

Given a cryptogram, even if it is very long, we may not be able to find a single clue, and that often is our problem in cryptanalysis.

Relevant Evidence

Clues are found in the evidence. But what evidence is relevant depends on what theory we have accepted. Clues therefore cannot lead to the truth; they will only confirm what we have already accepted.

This view makes the assumption that given any body of 'evidence' one will always be able to find clues in it, clues which will eventually lead to a satisfactory solution. This assumption is false. There are ciphers around which have remained unsolved for centuries because no one knows where the clues are (for example, the Voynich manuscript).

Refutations

A theory always remains a theory. You can only refute it but you can never confirm it, that is, make it more likely.

Suppose in cracking a cipher I have the theory that S is in fact T. At the beginning when little is known, this theory will be very uncertain. At the end, however, when the whole message has been deciphered, even though one would not say it is absolutely certain, its certainty could be quite high.

Absolute Certainty

One difficulty philosophers have in explaining how knowledge is possible is that there is nothing we know absolutely for certain. When this is the case, where can we start?

In cryptanalysis we do not start with absolute certainty. In cryptanalysis the beginning is always uncertain. Is this combination of letters a clue? Is this series of symbols really a cryptogram? Is there a message to be found? These questions will not be easy to answer at the beginning. The situation of course will be different when we succeed. If at the end we find a hidden message together with the cipher used to encrypt it, then we can be a whole lot more certain.

A Large Body of Evidence

Some say to make scientific discoveries we need to gather a large body of evidence. Is there any truth to this?

In cracking ciphers there are many ways for looking for clues. One that is often tried first is to search for repeating patterns. Needless to say, if the intercepted message is too short repeating patterns will not appear. How long does the message have to be? It depends on how complex the cipher is. The more complex the cipher, the longer the message required.

Mistake

One characteristic of deductive reasoning is that you could have made a mistake and not know it.

In cracking a cipher, if you have made a serious mistake you will know.

How?

If you have made a serious mistake your investigation will come to a halt; you will not be able to find out more.

That's when you backtrack ...

That's right; you backtrack. If you can find the mistake and correct it, you can advance again. If not, you remain stuck.


Notes

1For an introduction to cryptanalysis see D. Kahn: The Code-Breakers (New York: Scribner, 1996)

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