We're hard-wired for geometry

Excerpts from news items about the one topic, a South American tribe "who lack written language and who have never seen a maths book" yet who "do well on basic geometry tests" (in fact "identical to the score for US children" on the same tests) which "suggests geometry may be hard-wired into the brain." If so, this is another problem for the `blind watchmaker' to explain. My comments are bold and in square brackets.

Geometry ability may be innate, ABC/Reuters, 20 January 2006 ... Amazonian hunter-gatherers who lack written language and who have never seen a maths book do well on basic geometry tests, researchers say in a study that suggests geometry may be hard-wired into the brain. Adults and children alike showed a clear grasp of concepts such as where the centre of a circle is and the logical extension of a straight line. This was despite not having words for these concepts, the researchers report today in the journal Science. Professor Stanislas Dehaene ... and colleagues tested 14 children and 30 adults of an Amazonian group called the Munduruku, and compared their findings to tests of US adults and children. "Munduruku children and adults spontaneously made use of basic geometric concepts such as points, lines, parallelism, or right angles to detect intruders in simple pictures, and they used distance, angle, and sense relationships in geometrical maps to locate hidden objects," they write. "Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms." Geometry is an ancient field and Dehaene's team postulated that it may spring from innate abilities. "Many of its propositions -- that two points determine a line, or that three orthogonal axes localize a point -- are judged to be self-evident and yet have been questioned on the basis of logical argument, physical theory, or experiment," the researchers write. There was no way the Munduruku could have learned these ideas, they add. "Most of the children and adults who took part in our experiments inhabit scattered, isolated villages and have little or no schooling, rulers, compasses, or maps," they write. "Furthermore, the Munduruku language has few words dedicated to arithmetical, geometrical, or spatial concepts, although a variety of metaphors are spontaneously used." ... They designed arrays of six images, each of which contained five conforming to a geometric concept and one that violated it. "The participants were asked, in their language, to point to the weird or ugly one," the researchers write. "All participants, even those aged 6, performed well above the chance level of 16.6%." The average score was nearly 67% correct, identical to the score for US children. "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," they conclude. ...
We're hard-wired for geometry: Tests with Amazon villagers hint at innate geometrical sense, MSNBC, Daniel B. Kane, Jan. 19, 2006 WASHINGTON - Even if you never learned the difference between a triangle, a rectangle and a trapezoid, and you never used a ruler, a compass or a map, you would still do well on some basic geometry tests, according to a new study. Using a series of nonverbal tests, scientists claim to have uncovered core knowledge of geometry in villagers from a remote region of the Amazon who have little schooling or experience with maps and speak a language without the mathematical language of geometry. ... For thousands of years, people have wondered if the basics of geometry came naturally to all humans or if they were something you had to learn through instruction or cultural experiences. According to Plato's writings, Socrates attempted to determine how well an uneducated slave in a Greek household understood geometry, and eventually concluded that the slave's soul "must have always possessed this knowledge." [See also Livescience. This is another example of "Wallace's paradox, the apparent evolutionary uselessness of human intelligence" which "is a central problem of psychology, biology, and the scientific worldview" and is explained away by Darwinists as "exaptations: adaptive structures that are `fortuitously suited to other roles if elaborated", but which Pinker admits are "just an avowal of faith by people ... who believe in natural selection" and "can hardly fail to be true":

"`I hope you have not murdered too completely your own and my child.' So wrote Darwin to Alfred Russel Wallace, the biologist who had independently discovered natural selection. What prompted the purple prose? Darwin and Wallace were mutual admirers, so like-minded that they had been inspired by the same author (Malthus) to forge the same theory in almost the same words. What divided these comrades was the human mind. Darwin had coyly predicted that `psychology will be placed on a new foundation,' and in his notebooks was positively grandiose about how evolutionary theory would revolutionize the study of mind ... But Wallace reached the opposite conclusion. The mind, he said, is overdesigned for the needs of evolving humans and cannot be explained by natural selection. Instead, `a superior intelligence has guided the development of man in a definite direction, and for a special purpose.' ... Wallace became a creationist when he noted that foragers-'savages,' in nineteenth-century parlance-were biologically equal to modern Europeans. Their brains were the same size, and they could easily adapt to the intellectual demands of modern life. But in the foragers' way of life, which was also the life of our evolutionary ancestors, that level of intelligence was not needed, and there was no occasion to show it off. How, then, could it have evolved in response to the needs of a foraging lifestyle? Wallace wrote: `.... Natural selection could only have endowed savage man with a brain a few degrees superior to that of an ape, whereas he actually possesses one very little inferior to that of a philosopher.' [Wallace A., "Natural Selection and Tropical Nature," 1895, p.202] Wallace's paradox, the apparent evolutionary uselessness of human intelligence, is a central problem of psychology, biology, and the scientific worldview. Even today, scientists such as the astronomer Paul Davies think that the `overkill' of human intelligence refutes Darwinism and calls for some other agent of a `progressive evolutionary trend,' perhaps a self-organizing process that will be explained someday by complexity theory. Unfortunately this is barely more satisfying than Wallace's idea of a superior intelligence guiding the development of man in a definite direction. ... Stephen Jay Gould, in an illuminating essay on Darwin and Wallace, sees Wallace as an extreme adaptationist who ignores the possibility of exaptations: adaptive structures that are `fortuitously suited to other roles if elaborated' ... `Objects designed for definite purposes can, as a result of their structural complexity, perform many other tasks as well. A factory may install a computer only to issue the monthly pay checks, but such a machine can also analyze the election returns or whip anyone's ass (or at least perpetually tie them) in tic-tac-toe.' [Gould S.J., "The Panda's Thumb," 1980, p.50] I agree with Gould that the brain has been exapted for novelties like calculus or chess, but this is just an avowal of faith by people like us who believe in natural selection; it can hardly fail to be true. It raises the question of who or what is doing the elaborating and co-opting, and why the original structures were suited to being co-opted. The factory analogy is not helpful. A computer that issues paychecks cannot also analyze election returns or play tic-tac-toe, unless someone has reprogrammed it first.' (Pinker S., "How the Mind Works," [1997], Penguin: London, 1998, reprint, pp.299-301)

I have added this to a new section of my "Problems of Evolution" book outline, PE 14.1.8 "Man ... Uniqueness ... Mathematics."]

Stephen E. Jones, BSc (Biol).
"Problems of Evolution"