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July 19, 2005

Is it harder to think in the abstract than in specifics?

Glenn Reynolds (a.k.a. "Instapundit") criticizes Daniel Pink's A Whole New Mind for encouraging people, perhaps indirectly, to seek out "holistic" and "right-brain" approaches to problems that will be appealing because they seem "easier than those tiresome traditional linear approaches with all their steps, increments, and well, work." Reynolds cautions that:

[G]enius . . . has more to do with perspiration than inspiration. And while our workplaces may be too unfriendly to right brain thinking, they're a lot friendlier than they used to be. . . . In fact, it's arguable that most business management could benefit from a more traditional approach to balance sheets and bottom lines: More thinking inside the Income Statement, and less effort to think "outside the box."

I think part of Reynolds' criticism stems from a problem with Pink's distinction between "logical" and "holistic" modes of thought. I've said before that I think Pink's analysis is insightful and well worth reading, but this distinction has limitations.

Consider instead a different distinction, that between thinking at different levels of abstraction (see previous posting). Imagine an engineer faced with the problem of designing an electronic calculator. She might start with low-level electronic components, such as resistors and capacitors, and attempt to combine them together into a calculator. This would require a detailed understanding of circuit design at a low level of abstraction (i.e., a high level of specificity).

If, however, the engineer had available existing components for adding, multiplying, and performing other arithmetic functions, she could design a calculator by combining those existing components together. She might not need to know anything about the internal guts (e.g., resistors and capacitors) of the components she used. This would require an understanding of circuit design at a higher level of abstraction.

Finally, if the engineer had access to an existing electronic calculator, she would not need to know anything about circuit design. But imagine that she programs the calculator to not only perform arithmetic, but also to solve equations. This would require a yet more abstract understanding of mathematics and programming.

Is it any "harder" or "easier" to solve problems at any one of these levels of abstraction than at the other? Yes, but only in the sense that it is easier to make an existing calculator add 2+2 than it is to design from scratch a calculator for adding 2+2.

But that is comparing apples and oranges. Once the calculator exists, it poses problems at a higher level of abstraction that are just as complex in their own right as the problems that existed at the lower level of abstraction before the calculator was built. Science and engineering are fractal in this way; there is no loss in resolution as you move among layers of abstraction.

Let me take a stab at using this analysis to harmonize Pink's original argument and Reynolds' criticism of it. We need to use both "logical" ("left-brain") thinking and "holistic" ("right-brain") thinking at every layer of abstraction. As Pink's Abundance, Asia, and Automation make it impossible for people in the U.S. to compete at their current level of abstraction using logical thinking alone, they will either need to use holistic thinking at that level of abstraction, or move up a level, where it will be possible for them to succeed using only logical thinking until the same forces kick in at that level at some point in the future. Then the whole game starts over again, and Pink will be able to write about the Neo-Conceptual Age and its progeny, ad infinitum.

Posted by Robert at July 19, 2005 10:22 AM
category: Human Creativity | Philosophy of Computing

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