## 2 A Quantitative Description of a Communication System
### Looking for a Proper Language Scale  
We see the scale of a language as the set of finite symbols that \"best\" serves to represent a written message. The qualification \"best\" refers to the capacity of the set of symbols to convey the message with precision in the most effective way. Take for example the western natural languages. Among their alphabets, there are only minor differences; too few differences to explain how far from each other those languages are. As [PERSON] (1977) observes, some letters may be the basic units of a language, but there are other units formed by groups of letters. [PERSON]'s syntactic structures [PERSON] (1977), later called context-free grammar (CFG) [PERSON] (1977) offers another representation of natural language structure. The CFG describes rules for the proper connections among words according to their specific function within the text. Thus, CFG is a grammar generator useful to study the structure of sentences. [PERSON] himself treats a language as an infinite or finite set of sentences. CFG works at a much larger scale than the one we are looking for in this study. Regarding natural languages it is common to think that a word is the group of characters within a leading and a trailing blank-space. At some time a meaning was assigned to that word, and thereafter the word's meaning, as well as its writing, evolves and adopts a shape that works fine for us, the users of that language. [PERSON]'s principle of least effort [14] and [PERSON]'s reading ease score [20] certainly give indications about the mechanisms guiding words, as written symbols, to reduce the number of characters needed to be represented. From a quantitative linguistics perspective, this widely accepted method for recognizing words offers limited applicability. Punctuation signs, for example, have a very precise meaning and use. The frequency of their appearance in any western natural language compete with the most common words in English and Spanish [21]. However, punctuation signs are very seldom preceded by a blank-space and are normally written with just a single character, which promotes the false idea that they function like letters from the alphabet; they do not. They have meaning as well as common words have. Another situation revealing the inconvenience of this natural but too rigid conception of words, is the English contraction when using the apostrophe. It is difficult to count the number of words in the expression \"they're\". How many words are there, one or two? See [PERSON] _et al._[21] for a detailed explanation on English and Spanish word recognition and treatment for quantification purposes. Intuitively the symbols forming a description written using some language, should be those driving the whole message to low entropy when computed as the function of the symbols frequency. In this situation the message is fixed as fixed is also the text and the quantity of information it conveys. Then, there appears to be a conflict: while the information is constant because the message is invariant, any change to the set of symbols considered as basic units, alters the computed message entropy, as if the information had changed; it has not. To solve this paradox, we return to the question asked at the beginning of this section about the meaning of \"best\" in the context of this discussion. From the point of view of the message emitter, the term \"best\" considers the efficiency to transmit an idea. This is what [PERSON]'s work was intended for: to determine the amount of information, estimated as entropy, needed to transmit an idea. From the reader's point of view the economy of the problem works different. The reader's problem is to interpret the message received to maximize the information extracted. In other words, the reader focuses on the symbols which turn the script as an organized, and therefore easier to interpret message. If the reader is a human and there are words in the message, the focused symbols are most likely words because those are the symbols that add meaning for this kind of reader.