Page 254 - A Mind For Numbers: How to Excel at Math and Science

Chapter 13: Sculpting Your Brain

1 DeFelipe 2002.
2 Ramón y Cajal 1937, 309.
3 Ramón y Cajal 1999 [1897], pp. xv–xvi; Ramón y Cajal 1937, p. 278.
4 Ramón y Cajal 1937, 154.
5 Fields 2008; Giedd 2004; Spear 2013.
6 Ramón y Cajal 1999 [1897].
7 Bengtsson et al. 2005; Spear 2013.
8 Cajal could clearly plan well—witness his construction of the cannon. But he couldn’t seem to make the
connection with the bigger picture consequences of his actions. Taken up with the exciting task of
blowing up a neighbor’s gate, for example, he couldn’t make the obvious prediction that he would be in
deep trouble as a consequence. See Shannon et al. 2011, with their intriguing finding that functional
connectivity in troubled teens connects the dorsolateral premotor cortex to the default-mode network (“a
constellation of brain areas associated with spontaneous, unconstrained, self-referential cognition” p.
11241). As troubled teens mature and their behavior improves, the dorsolateral premotor cortex instead
appears to begin connecting with the attention and control networks.
9 Bengtsson et al. 2005; Spear 2013; Thomas and Baker 2013. As Cibu Thomas and colleagues note (p.
226), “the evidence from animal studies suggests that the large-scale organization of axons and dendrites
is very stable and experience-dependent structural plasticity in the adult brain occurs locally and is
transient.” In other words, we can make modest changes in our brain, but we can’t indulge in wholesale
rewiring. This is all commonsense stuff. For a terrific popular book on brain plasticity, see Doidge 2007.
The best technical approach to this topic is Shaw and McEachern 2001. It is fitting that Cajal’s own
work is now gaining recognition as foundational in our understanding of brain plasticity (DeFelipe
2006).
10 Ramón y Cajal 1937, p. 58.
11 Ibid., pp. 58, 131. The ability to grasp the key ideas—the gist of the problems—appears to be more
important than verbatim ability to memorize. Verbatim as opposed to “gist” memories seem to be
encoded differently. See Geary et al. 2008, 4–9.
12 DeFelipe 2002.
13 Ramón y Cajal 1937, p. 59.
14 Root-Bernstein and Root-Bernstein 1999, pp. 88–89.
15 Bransford et al. 2000, chap. 3; Mastascusa et al. 2011, chaps. 9–10.
16 Fauconnier and Turner 2002.
17 Mastascusa et al. 2011, p. 165.
18 Gentner and Jeziorski 1993.

Chapter 14: Developing the Mind’s Eye through Equation Poems
1 Plath 1971, p. 34.
2 Feynman 2001, p. 54.
3 Feynman 1965, 2010.
4 This section is based on the wonderful paper by Prentis (1996).
5 Excerpts from the song “Mandelbrot Set,” © Jonathan Coulton, by kind permission of Jonathan Coulton.
Lyrics excerpted from song fully given at http://www.jonathancoulton.com/wiki/Mandelbrot_Set/Lyrics.
6 Prentis 1996.