Have you heard of the branch of pure mathematics called topology? Up until a couple of days ago I had not. Topology is a branch of mathematics that deals with shapes. Different shapes can be deformed or reworked into one another. The topologists are interested in so called "closed" forms that have a fixed extent or limit.
After reading a general description, I'm still reasonably certain I have only the slightest grasp of what it means--certainly in a mathematical sense. But its relevance just might extend well beyond the abstruse world of higher math.
Topology is in the news because Grigory Perelman, a Russian mathematician, some three years ago, informed the world he'd solved this mathematical problem known among mathematicians as the Poincare conjecture. Then the Russian disappeared. The world's foremost mathematicians continued the Russian's work and now, three years later, have reached a "cautious optimism" regarding Perelman's conclusions. Many are now suggesting that not only is it a remarkable achievement in mathematics--but of human thought itself.
Dr. William Thurston of Cornell has said, "You don't see what you're seeing until you see it, but when you do see it, it lets you see many things." Thurston goes on to say that, "curiosity is tied in some way with intuition." For most of us non-mathematicians this easily sounds like obscure gobblygook, but just possibly there may be something else to consider....
That something else is the two words curiosity and intuition. Where do they come from? Why do some people appear to have more of it than others? Does one need curiosity before intuition takes place or might it be the other way around? Why or how did Albert Einstein for example, sitting in a trolley car in Vienna, come up with the idea that time itself depends on where the observer is? Was he merely bored as he traveled back and forth from his dull job at the patent office? And will the latest mathematical discoveries get us any closer to an understanding? Are you curious?
Will the rising cost of a barrel of oil--and the difficulty of having easy alternatives--stimulate new energy sources? Is it scarcity that will push and develop our curiosity and intuition? History is full of examples where shortages led to new inventions as well as new energy sources.
The writer Deborah Blum, in an article in The New York Times, remarked that President Bush's veto of the embryonic stem cell legislation follows a fairly consistent pattern of those that have opposed medical and scientific "progress" on religious and moral grounds.
In the 11th and 12th century the Christian church warned individuals that using medicine to treat illness indicated a "lack of faith." As recently as the 19th century cries of "Satanism" were shouted when doctors began using chloroform to reduce the pain of childbirth.
Religious benightedness and incurious rulers have always been with us. But dogged persistence followed by evidence and success more often than not triumphed over ignorance.
To what degree does a vibrant, creative society encourage curiosity and respect intuition? To what degree does it ultimately demand evidence? What will we learn next about the Poincare conjecture?