A Brain for Numbers: The Biology of the Number Instinct by Andreas Nieder
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example, it leads toward how the brain constructs patterns in imagination and therefore in working memory’s manipulation of number and mathematics, in prediction necessary for the evolution of mathematics and number, and in how mathematics leads to that prediction in the real world, all the while based on quantity, space, and their symbolism. See also Devlin’s complementary description of mathematics in [4], which would include the study of the patterns of shape, motion, number, and cognition and behavior.
MIT PRESS, 2019, 376 PP, $34.95, ISBN 9780262042789 REVIEWED BY LARRY R. VANDERVERT
Nieder’s Philosophical and Theoretical Views
A
s the oft-quoted Nobel laureate Eugene Wigner observed:
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure even though perhaps also to our bafflement, to wide branches of learning [32, p. 14]. This may be the deepest mystery of the universe. And yet, as Wigner suggested, it allows us mere humans to peer far deeper into that universe than by any other means. All in all, the reader will find that Nieder’s approach in A Brain for Numbers: The Biology of the Number Instinct provides a wonderfully broad look into research on the evolution of brains as arbiters of fact and fiction in the world of number and mathematics. However, at the same time, much of this review will take issue with many of his arguments and conclusions.
A Weak Beginning? Nieder begins by defining mathematics as follows: ‘‘Mathematics is the science of quantity and space, plus the symbolism relating to quantity and space’’ (p. 3). The problem is that Nieder then goes directly into deep philosophical underpinnings of mathematics that take the mind far beyond the reaches of such a simple, limited definition. The reader would have been much better served by a more robust, ‘‘brain-amenable’’ definition. For example, as Steen has pointed out: Mathematics is the science of patterns. The mathematician seeks patterns in number, in space, in science, in computers, and in imagination. Mathematical theories explain the relations among patterns; functions and maps, operators and morphisms bind one type of pattern to another to yield lasting mathematical structures. Applications of mathematics use these patterns to ‘‘explain’’ and predict natural phenomena that fit the patterns [20, p. 616]. Steen’s definition would move the reader’s mind (and Nieder’s) directly toward important brain topics. For
Next, Nieder addresses two classic questions: Are numbers (and mathematics) a separate, independent part of the universe (mathematical Platonism, mathematical realism, or ontological realism) that humans can somehow learn to use to serve as an external, objective arbiter of what is fact and what is fiction? Or are they a part of the problem-solving human brain that has d
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