Poincaré's "Mathematical Creation" - via a review by Jim Holt of Nicholas Carr's "The Shallows"

I did not enjoy Nicolas Carr's "The Shallows - How the Internet Is Changing the Way We Think, Read and Remember" (in the US the strapline is the much brasher "What the Internet Is Doing to Our Brains".....), which seemed to veer between coherent scientific investigation and journalistic hyperbole.

There is an interesting review of The Shallows in the current issue of the LRB by science writer Jim Holt (who from his self-description comes across as someone who is not exactly an inveterate user of the Web). Holt's review gently and playfully points out several of the weaknesses in Carr's argument.

But this does not mean that Holt is calm about the impact of the Web on thought.

To cut a long story short, Holt argues that the connection between memory and creativity ought to make us wary of the web. What bothers Holt is the way that the Web allows you to avoid internalising facts and concepts, because you can look things up on demand, without needing to learn them, thereby denying your unconscious mind the chance to turn over learned facts and concepts to generate new ideas. This, Holt argues, is the process that is at the heart of creativity, which he illustrates with a short quotation from the French mathematician Henry Poincaré's essay "Mathematical Creation":

Having reached Coutances, we entered an omnibus to go some place or other. At the moment I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for conscience’s sake, I verified the result at my leisure.

Digging on the Web led me to the February 2ooo issue of Resonance, an Indian journal of science education, and the whole accessibly written essay by Poincaré.

 

 

 

Comments

[DJ]

Guy Claxton makes the same point (about the importance of the unconscious mind being able to turn over learned facts and concepts to generate new ideas) in some detail, and with more evidence -- dare I say there is a strong flavour of anecdote in the Poincaré piece? -- in a few of his books. Hare Brain, Tortoise Mind is probably the most accessible and direct on this point, though I love the broader scope of Noises from the Darkroom.