The Way of Science
Unit IV, Part 1 |
Unit IV, Part 2 |
Unit IV, Part 3 |
Unit IV, Part 4 |
Unit IV, Part 5 |
Unit IV, Part 6 |
APPENDIX #1: Quotes
The first three quotes, below, are all from Henri Poincaré.
Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house.
Speaking of mathematics, consider this quote.
The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it; and he takes pleasure in it because it is beautiful.
It may be surprising to see emotional sensibility invoked apropos of mathematical demonstrations which, it would seem, can interest only the intellect. This would be to forget the feeling of mathematical beauty, of the harmony of numbers and forms, of geometric elegance. This is a true aesthetic feeling that all real mathematicians know, and surely it belongs to emotional sensibility.
Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room, and it's dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it's all illuminated and you can see exactly where you were. Then you enter the next dark room...
That was Andrew Wiles, describing his [successful] seven-year struggle toward the proof of Fermat's Last Theorem. While we're at it, here's a quote from Pierre de Fermat himself.
I have found a great number of exceedingly beautiful theorems.
The next three quotes are all from the physicist Alan Guth's book, The Inflationary Universe.
Science is not a static body of dogma, to stray from which is to risk having one's epaulets stripped off in a ceremony of banishment from the scientific community. It is a self-correcting system of inquiry, in which errors - of which there are, of course, plenty - are sooner or later detected by experiment or by more careful analysis. Science is also a "bottom-up" system, in which grand pronouncements are arrived at not in an overarching, sui generis fashion but by building up inferences from many small cases. As a result science, while it can be exasperatingly detailed, is also pliant. Scientific findings, even the most imposing ones, customarily stumble into the world fraught with blunders that have to be worked out before they really begin to fly. They lack the satisfying, thunderclap certitude of religious and pseudoscientific dicta that admit to no error. But they are alive, and the withering of one branch of a theory does not necessarily mean that the theory as a whole is doomed.
As a leading cosmologist who was also a priest, Lemaître was often asked how he reconciled his faith in the Bible with the discoveries of modern science. "There is no conflict," he would invariably reply. "Once you realize that the Bible does not purport to be a textbook of science, the old controversy between religion and science vanishes... There is no reason to abandon the Bible because we now believe that it took perhaps ten thousand million years to create what we think is our universe. Genesis is simply trying to teach us that one day in seven should be devoted to rest, worship and reverence - all necessary to salvation."
To be sure, there have always been philosophers who maintained that the scientific enterprise has to do strictly with making accurate predictions or, even more strictly, with learning how to manipulate the forces of nature. Essentially this is a view of science as power. But many of the strongest minds in science and philosophy have objected to this position. They insist that science is primarily about knowledge, and that genuine knowledge is necessarily objective knowledge.
The empirical spirit on which the Western democratic societies were founded is currently under attack, and not just by such traditional adversaries as religious fundamentalists and devotees of the occult. Serious scholars claim that there is no such thing as progress and assert that science is but a collection of opinions, as socially conditioned as the weathervane world of Paris couture. Far too many students accept the easy belief that they need not bother learning much science, since a revolution will soon disprove all that is currently accepted anyway. In such a climate it may be worth affirming that science really is progressive and cumulative, and that well-established theories, though they may turn out to be subsets of larger and farther-reaching ones - as happened when Newtonian mechanics was incorporated by Einstein into general relativity - are seldom proved wrong. As the physicist Steven Weinberg writes, "One can imagine a category of experiments that refute well-accepted theories, theories that have become part of the standard consensus of physics. Under this category I can find no examples whatever in the past one hundred years." Science is not perfect, but neither is it just one more sounding board for human folly.
The last quote is from astronomer Carl Sagan.
It's a foreboding I have - maybe ill-placed - of an America in my children's generation, or my grandchildren's generation ... when, clutching our horoscopes, our critical faculties in steep decline, unable to distinguish between what's true and what feels good, we slide, almost without noticing, into superstition and darkness.
Unit IV, Part 7 |
Unit IV, Part 8 |
Unit IV, Part 9 |
Unit IV, Part 10 |
Unit IV, Part 11 |
Unit IV, Part 12 |
Unit IV, Exam
© copyright 2001, Michael Wirth and Sachiko Howard, New England College