Where Did Humans Learn Geometry?
In Plato’s dialogue Meno, Socrates illustrated his view that certain foundations of knowledge are innate rather than learned.1 He took an untutored slave boy and, with a series of sketches in the sand, got the boy to deduce the Pythagorean Theorem by his own reasoning (see Encarta).
In a modern version, Harvard scientists found that basic concepts of geometry are understood by untutored tribespeople of the Amazon rainforest. LiveScience reports:
While high school freshmen sometimes struggle with parallelograms and the Pythagorean Theorem, people deep in the Amazon quickly grasp some basic concepts of geometry.
Although these indigenous tribes had never seen a protractor, compass, or even a ruler, a new study found they understood parallelism and right angles and can use distance, angles, and other relationships in maps to locate hidden objects.
The finding suggests all humans, regardless of language or schooling, possess a core set of geometrical intuitions. (Emphasis added in all quotes.)
Their research was published in Science.2 The authors referred to the Meno story at the end of their paper, feeling they had done Socrates one better – because his slave boy already possessed Greek language and familiarity with lines and shapes, and their Amazonian tribe did not. The researchers did not speculate, however, on how this uniquely human capability evolved:
Our experiments, in contrast [to Socrates], provide evidence that geometrical knowledge arises in humans independently of instruction, experience with maps or measurement devices, or mastery of a sophisticated geometrical language. This conclusion is consistent with paleoanthropological evidence and with previous demonstrations of a right-hemisphere competence for nonverbal tests of geometry in split-brain patients. Further research is needed to establish to what extent this core knowledge is shared with other animal species and whether it is available even in infancy or is acquired progressively during the first years of life. There is little doubt that geometrical knowledge can be substantially enriched by cultural inventions such as maps, mathematical tools, or the geometrical terms of language. Beneath this fringe of cultural variability, however, the spontaneous understanding of geometrical concepts and maps by this remote human community provides evidence that core geometrical knowledge, like basic arithmetic, is a universal constituent of the human mind. Constance Holden in Science3 also wrote up this story about possible “cognitive universals” but mentioned a couple of skeptics who think interpretation of the results is difficult. Even so, they seem to point to at least a “general reasoning ability” that has only been demonstrated in humans. Cognitive neuropsychologists are very interested in the study.
1In Socratic philosophy, Truth (with a capital T) was self-existent, and was intuitively known – merely recalled – by humans, not learned by experience. Socrates argued against the world of flux portrayed by Heraclitus, who taught that a man could never step in the same river twice. To Socrates and Plato, by contrast, experience could only speak of material objects, not abstractions or concepts. Material objects may be in a state of flux but Truth is eternal.
2Dahaene et al., “Core Knowledge of Geometry in an Amazonian Indigene Group,” Science, 20 January 2006: Vol. 311. no. 5759, pp. 381 – 384, DOI: 10.1126/science.1121739.
3Constance Holden, “Hunter-Gatherers Grasp Geometry,” Science, 20 January 2006: Vol. 311. no. 5759, p. 317, DOI: 10.1126/science.311.5759.317a
Pythagoras, Socrates, Plato, Aristotle, Cicero, the Stoics and many other great thinkers in the classical world – probably the majority of the famous philosophers (Democritus and Lucretius being exceptions) – believed in intelligent design. They were non-evangelical, pagan philosophers to whom the intrinsic order and design of the universe and life was self-evident. Their concepts of the Designer differed, but they all pointed to design as coming from an intelligent source.
Most of the classical philosophers were also absolutists. They believed that outside of the mind of man there existed an unchanging truth beyond the mere objects accessible to the senses. Evolutionists will find little support for relativism and materialism among the ancients. History does not support their contention that intelligent design is a conspiracy by evangelical Christians. The burden of proof should be upon the modern sophists who claim geometry is an artifact of the mindless, materialistic process of natural selection.
So the stone-age indigenous peoples of the rain forest comprehend geometry. Fascinating. Tell us, Darwinists, how did this evolve? Be sure to include your axioms.