Do the ski gloves fit?

Stuart Dreyfus presents excerpts from Bellman, of dynamic programming fame, in RICHARD BELLMAN ON THE BIRTH OF DYNAMIC PROGRAMMING.

There’s a bit of research-related therapeutic talk here, and at least one provocative idea.

On logical scientific progress:

“Scientific developments can always be made logical and rational with sufficient hindsight. It is amazing, however, how clouded the crystal ball looks beforehand. We all wear such intellectual blinders and make such inexplicable blunders that it is amazing that any progress is made at all.
…
I strongly recommend the interesting study of these and related matters by Jacques Hadamard, the great French mathematician, in his book The Psychology of Invention in the Mathematical Field (Dover Publications, New York, 1945: paperback)”

On choosing your problem:

“Similarly, there are many questions that are difficult to answer, but hardly worth asking. The well-trained mathematician does not measure the value of a problem solely by its intractability. The challenge is there, but even very small boys do not accept all dares.”

…

“It is usually, if not always, impossible to predict where a theoretical investigation will end once started. But what one can be certain of is that the investigation of a meaningful scientific area will lead to meaningful mathematics. Inevitably, as soon as one pursues the basic theme of obtaining numerical answers to numerical questions, one will be led to all kinds of interesting and significant problems in pure mathematics”

A little Learning is a dang’rous Thing;
Drink deep, or taste not the Pierian Spring:
There shallow Draughts intoxicate the Brain,
And drinking largely sobers us again.
Fir’d at first Sight with what the Muse imparts,
In fearless Youth we tempt the Heights of Arts,
While from the bounded Level of our Mind,
Short Views we take, nor see the lengths behind,
But more advanc’d, behold with strange Surprize
New, distant Scenes of endless Science rise!
So pleas’d at first, the towring Alps we try,
Mount o’er the Vales, and seem to tread the Sky;
Th’ Eternal Snows appear already past,
And the first Clouds and Mountains seem the last:
But those attain’d, we tremble to survey
The growing Labours of the lengthen’d Way,
Th’ increasing Prospect tires our wandering Eyes,
Hills peep o’er Hills, and Alps on Alps arise!

from An Essay on Criticism

Featured for keeping me busy this semester.

Björn Ice-cool Borg, featured for keeping his calm on the court, no matter what.

Claude Elwood Shannon, featured for his cues on research.

• “The first one that I might speak of is the idea of simplification.
• “A very similar device is seeking similar known problems.
• “Another approach for a given problem is to try to restate it in just as many different forms as you can.
• “Another mental gimmick for aid in research work, I think, is the idea of generalization.
• “Next one I might mention is the idea of structural analysis of a problem.
• “Now one other thing I would like to bring out which I run across quite frequently in mathematical work is the idea of inversion of the problem.

Reference: Claude Shannon. 1952. Creative Thinking