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The encoding of Math problems vs. Secret Codes vs. Symbology

Think of a number. Any number. Write it down. Why does the number ‘look’ the way it looks? Why is the number 1 represented by a straight line? Why do two circles, one on top of the other mean ‘8’? The same goes for letters. The letter ‘A’ for example, has its roots in a pictogram of an ox head in Proto-Sinaitic script.

Who says it has to be like that? The images we use to describe words, letters, numbers and operations are just that. Images. Symbols. The collection of symbols that describe a group of objects are called symbologies. There can be different symbologies for the same group of objects. Individual items in a group of products, for example, can be symbolised using different kinds of barcodes. EAN-13 and UPC-E are the names of two important barcode symbologies.

Why are symbols used in the first place?

In the case of barcodes, the idea is to describe a lot of information about an object in a concise form. Another popular use is to hide information from human or digital ‘eavesdroppers’. Ever since Ancient times people have been concealing information. Julius Caeser, for example, is said to have used a substitution cipher for his communications with the army. Secret codes can also be seen as a form of symbology, if we use the word “symbology” in a loose way.

In my mind, though, symbologies are used for play! I really enjoy math puzzles, especially those where the purpose is to discover something hidden: a word, a number, an operator. In fact, as a young student, that was really what we were trying to do all the time. Many scientific papers seemed like gibberish to me - full of symbols that I had not a clue what they were trying to represent. The challenge of understanding different representation systems gave me a great sense of achievement. Not only did I succeed in solving the ‘puzzle’, often I also found out that really the language of symbols are just a clever ‘concealment’ of something. It’s like looking at an object through different ‘lenses’.

Cryptarithms

The fun and challenge of decoding different symbologies, using a few tools, mostly, but not uniquely mathematical tools has taken on many forms, especially throughout the last decades. One particular favorite is the cryptarithm challenge. Cryptarithms are math puzzles where each of the ten digits: 0,1,2,3,4,5,6,7,8,9 is encoded by a (usually) different letter. The object of the puzzle is, given a mathematical expression encoded into letters, to ‘break’ the code and uncover the cipher system. Many times the puzzle is ‘readable’ - the letters make up words! During this course, we will learn together about solving cryptarithms, deciphering unknown symbologies and other related math puzzles. I hope you will have as much fun as me…

Discussion

Use the discussion below, think a bit, and answer: why do you like solving puzzles?

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This article is from the free online course:

Maths Puzzles: Cryptarithms, Symbologies and Secret Codes

Weizmann Institute of Science

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