What is intelligence? What is the nature of creativity, thinking, learning, and even of mind?
In his latest book, Deep Thinking: What Mathematics Can Teach Us About the Mind, mathematician William Byers claims that all of these processes have a common root: Deep Thinking, something that we know as insight, that is, discontinuous "aha! thinking."
What is new in Byers' approach is his insistence that deep thinking is not exceptional and reserved for geniuses but the default condition of the mind. It is to be found whenever a problem is resolved by discovering a new approach. This happens when a child grasps a new conceptual system or a scientist develops a new paradigm.
Deep thinking can be difficult to access because it is more elementary than, and lives upstream of, rule-based, algorithmic thought. Thus creative insight, which is a paradigm of deep thinking, produces, but cannot be produced by, logical thought. Deep thinking is what you must rely on if you want to produce something that is truly original.
Evidence for this thesis comes from many disparate sources: the conceptual development of children, the history of mathematics and science, studies of the creative process, a reconsideration of the nature of learning, and the neurobiology of the brain.
The implications are enormous. To take just one example that is emphasized in the book: if real learning involves deep thinking, that is creative reframing, rather than merely accumulating and analyzing data, then teaching must be transformed so as to make this its primary goal.
A reconsideration of the nature of creative thought is vitally important in this day and age. There is a huge difference between human thought with its creative potential and the derivative and limited possibilities of machine thought. There is a trend in Western thinking that is very popular today, which maintains that the computer is potentially capable of just about anything and the human mind and brain are merely computational devices.
This book indicates where the fallacy lies in this approach. Deep thinking gets you out of the box; algorithmic processes, on the other hand, can only reveal new features of the box. In general any activity that is truly original is based on deep thinking; the child's mastery of the counting numbers is identical in kind to the thinking that produced Einstein's Theory of Relativity, Tolstoy's War and Peace, or Beethoven's Ninth Symphony.
The book retails for US$28 / £18 at all major bookstores. More information on the book can be found at: http://www.
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