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Engravings with marks and incisions which may represent numbers have been known since the Paleolithic period. Number is a concept and may have various equivalent symbolic representations and diverse notations. The Latin term “numerus” essentially referred to the Roman numerals condensed into a letter of the alphabet, or some other symbol, a quantity. Plato had already understood that doing a sum was nothing more than calculating what a number would become. As signs, representations of numbers may be either declarative or votive and are created by means of a code. Numbers may also either be cardinal or ordinal. In any case, a number is a sign, which may be understood as an index and codified by a symbol or an icon.

Many of the drawings and engravings which have survived from the Stone Age show sketches of animals, lines and, in a number of cases, if not an indication of a precise number, at least the idea of “many”, which is expressed by means of the repetition of a pattern associated to a zoomorphic icon: sets or collections of marks, cuts, signs - for example, the sign of multiple lines associated to the roe deer on rock 13 of Canada do Inferno[1].

It is known that nomadic herdsmen developed an oral language for numbers [2] but it was only when they became more sedentary, during the Neolithic period, that these settlements established written number systems. In any case, number is thought, an abstraction [3] and it is understood as a form of being. If we remember Euclid: one is that which makes it possible to say that each being is said to be singular, individual and the numbers are a multiplicity constituted by units.[4] The monad represents unity. Also, for the Jews, God is One [5] and for Seneca, multiple divinities are aspects of a single God [6].

A natural number may be represented by a set of marks, cuts, stones - or a symbol and this is defined as a vaguely codified sign. [7]
Abduction is a process which is an attempt to clarify the meaning of a sign, establishing hypotheses and complemented by deduction - for example, on one of the rocks at Penascosa there are at least seven sketches of animals with alternate heads [8] - Is it to associate genus or suggest movement? Man resolves the problem of counting by creating natural numbers, by means of the concept and the practice of making a direct correspondence between something and a symbol [9], possibly mediated by an object: such as a, a mark in the sand or a engraving on stone. A message, as a system of meanings, is the significant form that the destinatary, based on pre-established codes, makes sense of  [10].

If you showed a citizen of ancient Rome and a contemporary European the cypher III, the former would interpret it as 3 and the latter, probably as 111. This difference is justified by the positional value of the algorisms [11] and by the norm of interpretation, the dominant usage. There are two interpretations for the concept of number: as cardinal or ordinal. While cardinal represents the number of elements in a set or collection where we may use Cantor’s definition: a set is a collection of any objects you can think of considered as forming a whole [12], an ordinal number signifies the position of an element in the collection, once a meaningful interpretation has been adopted, an order. We have the very wide definition of number proposed by Russel in 1901 [13]: the number of a class is the class of all the classes similar to it.

For example, the comet drawn on rock 3 at Canada do Inferno [14], may be seen as a vector, a directed entity, or as a set of straight lines forming a number. Here is a table with the first four natural numbers, cardinal and ordinal, with their corresponding terms in some European languages:

There is a clear distinction between the words which designate a cardinal number and its corresponding ordinal number in the case of 1 and 2, which begins to disappear from the number 3 on. This illustrates that three is the first representation of many. Even today the first digits do not have the same probability of occurrence in the numbers found in real life[15], the number 1 appears with greatest frequency, about 30 percent, while the number 9 only appears somewhere in the order of 4 percent.

In the bible, the Book of Numbers is so called because of the command given to Moses [16], intended to make a census of the whole community of the sons of Israel by family, and the numbers take on symbolic meanings[17]. Since Descartes, the mathematical discourse, the Mathesis universalis, studied series of numbers, figures, stars, sounds etc.[18], and even today Mathematics is defined as the science of patterns [19].

Calculation comes from the Latin word calculus, which means little stone, as the Romans did not have a generative number system, that is, capable of performing arithmetical operations and so had to make calculations with little stones or marks in the sand. The Chinese used the abacus and number systems with lines, crosses and other cursive features.

The meaning of a number may be declarative or votive. Or, more commonly, signs may be commemorative, serving to remind us of something, if they were already learnt by experience, or simply indicative, if the relation is not obvious, but hypothetical [20]. Aristotle had already clarified that a number is a number of something, or rather a specific index, while Plato, in The Republic [21], anticipated that calculus and arithmetic dealt entirely with numbers and were sciences suitable for reaching the truth.