I'm kind of persuaded by those that suggest that math ability like other cognitive abilities are biologically-given, innate structures. The argument (at least with those who view mathematics as a cognitive module of our mind/brain) is that both language and mathematics have the property of "discrete infinity" and since this property may be unique in the biological world, perhaps our mathematical ability may have developed as a by-product of the language faculty.
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The classic illustration is the system of natural numbers. That brings up a problem posed by Alfred Russell Wallace 125 years ago: in his words, the “gigantic development of the mathematical capacity is wholly unexplained by the theory of natural selection, and must be due to some altogether distinct cause,” if only because it remained unused. One possibility is that it is derivative from language. It is not hard to show that if the lexicon is reduced to a single element, then unbounded Merge will yield arithmetic. Speculations about the origin of the mathematical capacity as an abstraction from linguistic operations are familiar, as are criticisms, including apparent dissociation with lesions and diversity of localization. The significance of such phenomena, however, is far from clear; they relate to use of the capacity, not its possession. For similar reasons, dissociations do not show that the capacity to read is not parasitic on the language faculty.
Some simple evo-devo theses: how true might they be for language?http://ebooks.cambridge.org/chapter.jsf ... 817755A013Regarding the "reality" of time, I'm kind of sympathetic to these ideas:
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Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role at all. I summarize here this point of view, explaining why I think that
in a fundamental description of nature we must “forget time”, and how this can be done in the classical and in the quantum theory. The idea is to develop a formalism that treats dependent and independent variables on the same footing. In short, I propose to interpret mechanics as a theory
of relations between variables, rather than the theory of the evolution of variables in time.
“Forget time”http://www.fqxi.org/data/essay-contest- ... i_Time.pdfQuote:
It is not only Newton's laws that can be obtained in this timeless way. There is an interpretation of Einstein's general relativity in which it and time arise in much the same way. I will not claim that time can definitely be banished from physics; the universe may be infinite, and black holes present some problems for the timeless picture. Nevertheless, I think it is entirely possible indeed likely that time as such plays no role in the universe.
The nature of time
http://www.fqxi.org/data/essay-contest- ... f_Time.pdf
29 Jul 2012, 10:39 am
