are more digits."
This meant that Bill still understood, at least tacitly, sophisticated numerical concepts like place value. Also, even though he couldn't subtract three from seventeen, his answer wasn't completely absurd. He said "twelve,"
not seventy−five or two hundred, implying that he was still capable of making ballpark estimates.
Then I decided to tell him a little story: "The other day a man walked into the new dinosaur exhibit hall at the American Museum of Natural History in New York and saw a huge skeleton on display. He wanted to know how old it was, so he went up to an old curator sitting in the corner and said, T say, old chap, how old are these dinosaur bones?'
"The curator looked at the man and said, 'Oh they're sixty million and three years old, sir.'
" 'Sixty million and three years old? I didn't know you could get that precise with aging dinosaur bones. What do you mean, sixty million and three years old?'
" 'Oh, well,' he said, 'they gave me this job three years ago and at that time they told me the bones were sixty million years old.' "
Bill laughed out loud at the punch line. Obviously he understood far more about numbers than one might have guessed. It requires a sophisticated mind to understand that joke, given that it involves what philosophers call the "fallacy of misplaced concreteness."
I turned to Bill and asked, "Well, why do you think that's funny?"
"Well, you know," he said, "the level of accuracy is inappropriate."
Bill understands the joke and the idea of infinity, yet he can't subtract three from seventeen. Does this mean that each of us has a number center in the region of the left angular gyrus (where Bill's stroke injury was 20
located) of our brain for adding, subtracting, multiplying and dividing? I think not. But clearly this region—the angular gyrus—is somehow necessary for numerical computational tasks but is not needed for other abilities such as short−term memory, language or humor. Nor, paradoxically, is it needed for understanding the numerical concepts underlying such computations. We do not yet know how this
"arithmetic" circuit in the angular gyrus works, but at least we now know where to look.10
Many patients, like Bill, with dyscalculia also have an associated brain disorder called finger agnosia: They can no longer name which finger the neurologist is pointing to or touching. Is it a complete coincidence that both arithmetic operations and finger naming occupy adjacent brain regions, or does it have something to do with the fact that we all learn to count by using our fingers in early childhood? The observation that in some of these patients one function can be retained (naming fingers) while the other (adding and subtracting) is gone doesn't negate the argument that these two might be closely linked and occupy the same anatomical niche in the brain. It's possible, for instance, that the two functions are laid down in close proximity and were dependent on each other during the learning phase, but in the adult each function can survive without the other. In other words, a child may need to wiggle his or her fingers subconsciously while counting, whereas you and I may not need to do so.
These historical examples and case studies gleaned from my notes support the view that specialized circuits or modules do exist, and we shall encounter several additional examples in this book. But other equally interesting questions remain and we'll explore these as well. How do the modules actually work and how do they "talk to" each other to generate
conscious experience? To what extent is all this intricate circuitry in the brain innately specified by your genes or to what extent is it acquired gradually as the result of your early experiences, as an infant interacts with the world? (This is the ancient "nature versus nurture" debate, which has been going on for hundreds of years, yet we have barely scratched the surface in formulating an answer.) Even if certain