Solution to the Cryptography Challenge

On 13 Nov. 1787, Thomas Jefferson wrote to William Stephens Smith, John Adams' secretary, about the newly adopted Constitution of the United States; he felt that the delegates in Philadelphia had overreacted to Shays' Rebellion in Massachusetts. The sentence which begins "The tree of liberty" is one of my favorite quotes, and it is this sentence I encrypted.

" ... God forbid we should ever be twenty years without such a rebellion. The people can not be all, and always, well informed. The part which is wrong will be discontented in proportion to the importance of the facts they misconceive. If they remain quiet under such misconceptions it is a lethargy, the forerunner of death to the public liberty. ... And what country can preserve its liberties if their rulers are not warned from time to time that their people preserve the spirit of resistance? Let them take arms. The remedy is to set them right as to facts, pardon and pacify them. What signify a few lives lost in a century or two? The tree of liberty must be refreshed from time to time with the blood of patriots and tyrants. It is its natural manure. ..."

If you want to read the full text of Jefferson's letter, you can find it here: http://www.monticello.org/site/jefferson/tree-liberty-quotation

If you are unfamiliar with Shays' Rebellion, here is a link to an excellent article: http://en.wikipedia.org/wiki/Shays_rebellion

How the Code Works

This code may be nearly impossible to solve in the usual way - backwards, starting with the coded message and working back to the original. This is why I tried to emphasize, in my clues and in personal conversations, that you should try to solve it forwards : think about building your own code, and see where that leads you.

If you are designing a code which you hope to use for more than one puzzle; if your key can be used to encrypt any sentence in the English language; then what one feature does the key absolutely have to have? It has to contain all 26 letters of the alphabet. Now hold that thought.

The two concepts I kept hammering over and over were "easy" and "simple". The simplest code to use is a letter-substitution code of some kind, like the ones you find in the newspaper (and at the RG). I can use this code "from memory", meaning that I can keep the key in my head, without needing to have it written down somewhere; a child can use the code with only pencil and paper - and might even be able to figure out the key. People suggested several ingenious mechanisms at the RG, many of which would have been even harder to crack than my own - but they often required keeping track of multiple tables at once, which would have made them complicated for an adult to use without a computer, let alone a child.

So the key has to be something which contains all 26 letters of the alphabet, and is easy to remember.

Two people got it as soon as I phrased the issue that way. Most of us can not remember a random arrangement of 26 letters - I certainly can't; but if the letters form a sentence - particularly one you might have encountered before - the task of remembering becomes much easier. There is a familiar sentence, used to test the keys on a typewriter, also used by people practicing their handwriting, which was actually highlighted in an episode of The Simpsons last season! The sentence, of course, is

The quick brown fox jumps over the lazy dog.
But we're not quite done yet. I said that there was one little twist, and I told a few people that if they knew what I was doing when the code occurred to me, it would be a huge clue. I was actually putting a title on a recordable DVD, although if I had been using Twitter, the same logic would have applied. If you've ever done either of those things, or contacted a business via a website which allows you only a few hundred characters for your message, then you have had to deal with the question of what constitutes a "character". In most or all such applications, a space counts as a character.

It was pointed out to me that the code would have been much easier to solve if I had left spaces between the words - which is why I didn't. But there were two possible assumptions, and most people made the wrong one, as I suspected they would. The fact that there were no spaces might have meant that I had simply run all the words together; but it could also have meant that the spaces were there, but encrypted, like the letters.

So now you just number the letters and the spaces in the key sentence, in order. One of the nice things about this system - and the thing which makes it so hard to solve backwards - is that since several letters (and the spaces) are duplicated, you have choices when you encode, and your choices can be completely random. For instance, the first word in the Jefferson quote, like the first word in the key, is "the"; but instead of encoding it "1 2 3", I could use the number for the "t" in the first appearance of "the" in the key, the "h" from the second "the", and the "e" from an entirely different word. When you have the key, however, there is no ambiguity at all: every different number which corresponds to an "e" is decoded as an "e", no matter which one you felt like using when you encoded the message.

Easy. Simple. You just have to forget about the usual way you solve codes, and start from scratch.

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There is an apocryphal story which I have heard in two versions, one about Christopher Columbus, the other about the architect Christopher Wren (designer of St. Paul's Cathedral in London). I will tell you the Columbus version:

When Columbus returned from his voyage to America - having become the second or third European, and perhaps the fifth human, to "discover" the New World - his rivals criticized all the attention he was getting. "What did he do?", they asked. "Just sailed West. Anyone could have done that!"

In reply, Columbus gave them an egg, and asked them to stand it on its end. They all tried, carefully balancing the egg with their fingers, but it invariably slid down on its side. Eventually, they turned to him and said, "It can't be done."

Columbus took the egg and crunched it against the table, flattening one end; then he removed his hand, and the egg sat upright and did not topple over.

"That's not fair!", they cried. "You didn't tell us that we were allowed to do that!"

"That's my point," Columbus replied. "Once you know how to do something - once you know which 'rules' aren't rules at all - it always looks easy."