Reading some of Susanne Langer again after many years and continuing to learn. She notes a large difference between language/words and mathematics/numbers, specifically that words can and do change meaning with context and over time while numbers maintain the same value (meaning) independently of context and time. Numbers used as complex symbols in mystic thinking, e.g., the Kabbalah, are codes and function as presentational forms, not numerical signs. So the same old questions arise of animal analogues and distinctiveness in human evolution; what are the roots here?
I found a 2009 Scientific American article about some research showing quantitative thinking in birds and monkeys. Some wild robins watched researchers put mealworms in holes drilled in logs and then went to the holes with the most worms to eat them. If the researchers surreptitiously removed some placed in a hole, the robins continued to search the hole for more. Monkeys showed the ability to choose between two sets of objects differing in number for the one with fewer objects. They have also shown the ability to match the number of beats heard to the number of objects seen. I am sure such reports are becoming common as we find ways to test such abilities in other animals beside ourselves.
No one is claiming that these animals count or use numbers symbolically, though Langer reviews a good amount of anthropological research showing that many primitive, preindustrial societies have words for 1, 2, and ‘more’, while clearly they can manage mathematically with larger sums. What I found surprising and curious was her hypothesis as to how humans came to count.
I do not remember this at all from my reading years ago but I find it remarkable now. She writes “the instrument of science is mathematics,” so that science could not flourish until the evolutionary appearance of “enumeration and calculation.” Further, mathematical “elements—similar units following each other in a series—are almost certainly first presented in the visual and kinesthetic perception of our own bipedal steps, under control of older cerebral mechanisms. Their expression belongs to the legs and feet, whose functions are amongst the least intellectual of our voluntary behavioral acts.” She goes on to explain that these same behavioral actions along with arms and hands compose rhythmic routines and subroutines, i.e., dance as an art form with special social relevance and transmitted inter-generationally as cultural memes as it were, so that counting and “fractions were danced for thousands of years without awareness of their relations to . . . steps.” With the advent of drumming the function of counting became centered in the hands (Mind v. III, pp. 209 and following).
This makes much sense to me. Remember my earlier post (2/16/14) of Bonobos can dance, e.g., they can keep the beat. And humans over a long history of gathering around fire and drum came to understand consciously, symbolically, the many rhythms to be found in the beat. Then from Pythagoras through other discoveries, e.g., of zero, to Newton and Leibniz (and beyond) science grew in its cultural roles. There is certainly more to find out here about these roots.