This is how numbers came to be: when survival depended on the concept of quantity

"God created the integers; the rest is the work of man." Leopold Kronecker (1823-1891)

A monkey accustomed to receiving a daily amount of food appropriate to its lifestyle is forced to fast . If offered a pile of fruit and another even larger pile, the hungry monkey chooses the larger pile, eats until it is satisfied, and leaves some food behind. Then, when it returns to its normal diet, if offered the same options, it chooses the smaller amount. The laboratory animal has experienced lack, abundance, and sufficiency , and has chosen the latter.

What determines your assessment—when you are given the choice—is that small part of your brain called the hypothalamus , which is responsible for several vital functions, including regulating hunger . Humans share this regulatory function with other higher animals , but they have a frontal brain area that allows them to process and conceptualize the generalized experience of the urgent need for food: hunger.

Roughly speaking , we can say that throughout the evolution of the branch that would lead to the species Homo, the comparative concepts of little or nothing, enough, much, and too much were formed. Therefore, it is very likely that this comparative concept started from the stomach, that is, from the daily need for food, and that, thanks to the complex activity of the cerebral cortex, it extended to other assessments of our ancestors' habitat. This was not an abstract exercise. It was about evaluating how to survive in the face of the experience of cold, warm, hot, scorching, or in the face of the experience of darkness, clarity, light, splendor, etc. This is the premise for a conceptualization that is difficult to place in time through a sequential paleontological analysis. However, the result of this long process (from the empty stomach to thought) can be seen in Homo sapiens of the Middle Paleolithic, more than thirty thousand years ago: the concept of quantity .

When we speak of quantity, we refer to something measurable and whose measurement can be shared with others. Little, much, etc., will remain in everyday life as useful and common, though subjective, terms valid for the individual, valid in a qualitative discussion about topics on which one can reach relative agreement. They are an implicit common denominator. The human group realized that, for the indispensable cooperation or division of tasks for survival, it was necessary to express quantity in conventional and understandable terms. The fingers were probably the first instruments used to communicate small quantities. We still use them today, using more or less versatile codes, which change, like all codes, with the passage of time and from one culture to another.

In any case, the main limitation of expressing oneself through gestures lies in their instantaneous nature: they cannot be frozen in time. What the hominid had quantified, perhaps in a conversation with an equal, ceased to be perceptible immediately afterward. Perhaps they invented the game of rock, paper, scissors, but a code that could be recorded and that would last still remained to be devised…

That we were approaching the concept of number is merely a declaration of intent on the part of the narrator. The scenario described so far is the result of the interaction of studies in paleontology, neuroscience, ethology, and biology. Even so, as plausible as it may seem, this scenario is merely hypothetical . Therefore, we must be cautious about everything related to such remote times!

However, as we approach prehistory and truly historical periods, we have more solid information. Bone finds that present notches and incisions that can be interpreted as signs used for counting date back to between 35,000 and 20,000 years ago. The best-known— the Lebombo bone , found in South Africa, and the Ishango bone, near Lake Edward—already offer us a complex representation in which we can assume that notches of different sizes and positions correspond to different values. Beyond the purpose of such complex incisions (lunations? A calendar? A number game?), what they reveal is probably a well-established counting tradition . Engraving a notch on a rigid support, a vertical mark that resembles an extended finger, meant counting an objective entity. Therefore, it can be assumed that this method was in use thousands of years ago, to the point of reaching a level of elaboration as complex as that shown in the African finds mentioned above.

Likewise, it is reasonable to assume that the earliest and most widespread type of incision used readily available, perishable materials , such as a wooden stick, or ephemeral ones, such as a charcoal line on a pebble. For this reason, such documentation is impossible to find, as it exists only in the retrospective reasoning of experts. However, we can review the numerous marks preserved on fossil bones or stones, interpreted as decorative until they were discovered and dated in the second half of the 20th century. In this case, scholars reasoned, the scratches and notches dating back to the Upper Paleolithic could confirm a more basic primitive activity of calculation . It is not difficult to imagine a system for recording goods stored in a warehouse, such as harvested fruit, in which each item would correspond to a confirmatory notch. Through recording, the heap (i.e., the vague quantity: little, much, etc.) becomes a formal quantity, subject to verifiable addition or subtraction. Now we're getting closer to the concept of number.