Additional Math Pages & Resources

Wednesday, November 18, 2009

EZ come, EZ go

What is unusual about this paragraph? It looks ordinary. Study it - nothing is wrong with it. But it is unusual. Why? What suspicions form in your mind? What's odd about this string of words? Anything? If you work hard at it, a solution will dawn on you.

Give up? Or did you see the answer? If you didn't, perhaps this chart will give you a clue:

Letters in most languages are not evenly distributed throughout all the words, nor are they evenly used in a sentence or paragraph. If you study enough samples, you'll find some letters appear with much greater frequency than others. The English letter distribution appears in the table above.

Why does this matter?

It matters if you are a cryptographer - a person who does hidden or secret writing - a person who creates secret codes (or breaks or deciphers those codes). The study of the particular characteristics of your own language's frequency data, letter combinations, common patterns, etc. is known as cryptolinguistics.

This used to be the exclusive interest of governments (one against another) or subversive groups (against a government) but now is much more of a daily interest to citizens. We see it in two senses:
  • we want to protect our online transactions and privacy
  • we don't interference with things like watching movies or listening to music
That means we want our transactions to be protected, but we don't want to be hindered by Digital Rights Management (DRM) in our computers or televisions.

Here's one of 8 flow diagrams illustrating a logic path used to encrypt emails and emailed files.

The various symbols indicate a decision and action that you take depending upon how the data responds to your query.

When I was growing up, there were games that would help you learn to be better at creating and breaking codes. Scrabble™ of course is one of the games that helps you to understand how the English language works and it gives you an incentive to put together complicated words using letters that appear infrequently.

If you are good in math, you have excellent language skills, love Scrabble™, and tend to think in a logical manner, you might be a good cryptographer.

If you are like most people, you won't have a clue about decoding. Unless you have a secret decoder ring.

Secret codes are used all around you. The antique dealer marks items with both his cost, and a retail price. The cost is in code.

Most Excel Math™ products have a secret code on the back. Here's the code on the back of the 4th grade Teacher Edition on my desk:  9071809. Even though I am the editor, I can never remember how to decipher this code. It's put there by our printer. Can you do it?

Here is the answer to the problem posed in the first paragraph. Can you decipher it?
Bogstavet e vises ikke i første afsnit.

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