The Beginnings

The earliest physical proof of counting can be found in caves.  Since their discovery the purpose of cave art has been highly debated.  Were they merely artistic endeavors?  Ritualistic behavior?  Magic, of some sort, was surely involved because why else would they seek out such isolated locations to perform?  These interpretations seemed  to be reinforced by the discovery that flickering light, such as a firelight, allowed for the pictures to move and shift.  Cave art was, it seemed, the pre-historic movie theater and like the theater was constructed in darkness to allow for the best viewing.

This may still be the case.  As with most things there is another aspect to be considered: that of a calendar.  Not the kind we are familiar with that has a clear end and a set beginning, but one that is based on the seasons as observed.

in a 2022 study it was found that the reoccurring non-figurative signs not only were consistent across animal type but likely had a calendar function (An Upper Paleolitich Proto-writing System and Phenological Calendar, 2022, Bacon et all).  It had been known that the animals shown were both specific and associated with seasons prior to this study but the association of the non-figurative signs had not been considered as part of that.

Before an analysis of times can be done the calendar system must first be explained.  As previously mentioned this calendar was likely not based on a set and specific day to start nor did it have a defined ending.  We cannot be certain of this but this model depends on flora and fauna rather than astronomy which would be more relevant to humans without a reliance on agriculture.  The start of the season is based on the bonne saison, or the time when the rivers unfreeze, snow melts, and the landscape turns green.  This can vary from year to year but is a very clear sign of a new start.  The end of this calendar therefore cannot have a set day and counting the days becomes largely irrelevant during late winter.  This will place the start of the calendar sometime in late spring as the start of the paleolithic calendar.  Months would be calculated by lunar months rather than our system of weeks and an arbitrary number of days.

With this knowledge Bacon et all analyzed the markings versus an adjusted calendar (with 1 being may/ june) to where they and a third symbol (a Y marking) lay.  What they found was the overwhelmingly most line/ dot marks corresponded with mating and Y marks with birthing.  This was true across species.  The analysis showed that the markings could act as a predictive system for viewers, but what it did not do was give any indication of who was viewing or even allowed to view the art as it may have been restricted for various reasons. Given the clear and even distribution over both time and space it is unlikely that it was a tightly held secret but it may have been restricted to a specific class or group.

This may seem to be straying from numbers.  A calendar does not have much to do with numbers at first glance, particularly when it is seasonally based.  Numbers do not have to exist to track the moon or notice the rivers have unfrozen.  These things can have names without numbers, but the act of marking them down is clear proof that the artists were thinking sequentially and had a numerical system capable of expressing that.  It is the ability to mark an event that is in the future or the past sequentially that firmly places this in a numerical capacity.

Luckily this is not our only evidence for cardinality.  Notched bones have been found throughout the Upper Paleolithic.  The question is whether they can be determined to be decorative or quantificational and while we cannot answer with one hundred percent certainty we do know that some notches were cut all at once while others were done gradually over time. Those done over time are likely to be quantificational (The Roles of Materiality in Numerical Cognition 2015, K.A. Overmann).  Should that have not been the case the physical notches themselves provide discrete qualities that can be used as an external reference.  Adding a new notch over time stimulates the concept of cardinality by adding a plus one to the material artifact even if that is not the intent at the moment.

Another common find at paleolithic sites are beads with holes in them.  This allows them to sit on a string and to present themselves as a group despite the intention being purely decorative in most cases.  Being able to manipulate them allows for the free association of each bead to an object and allows for the concept of numbers to become decontextualized and abstract rather than firmly associated with one specific group.  But before that they are able to in themselves hold a meaning and allow counting without counting to occur, as happens with Rosary beads even today.

Strung beads in the paleolithic likely could provide a similar aid.  We do not, and cannot, know of the religious state of the paleolithic person but it is not farfetched to assume that strung beads could not be used to aid in oral history (each bead being associated with a specific part of the tale), travel time, or victories won.  Rosaries date rather late comparatively (showing up roughly 1200 CE) but show conclusively that beads can be used for purposes other than purely decorative. As with most things we must remember that objects often have more than one function and that we cannot fully understand exactly how people are using any object.

Other evidence exists with even less evidence of use.  Hand stencils were important for a large amount of time but it is difficult to prove that this was used in counting.  They do show finger positions that we associate with counting but they also show some associations that we do not (The Roles of Materiality in Numerical Cognition 2015, K.A. Overmann).  Is this learning associations with finger counting or did this serve an entirely different purpose?  We cannot know for sure.  What we can say is that an overwhelming amount show positions that would be suitable for counting.