Lightman's A Sense of the Mysterious
Another of the books I've completed in recent weeks — but only get around to mentioning now — is A Sense of the Mysterious, by Alan Lightman. Lightman is known as a physicist turned novelist, and he has taught both subjects at MIT. As a physicist and writer of fiction I feel a certain kinship.
Lightman's writing is at times exquisite; at worst it is better than most. His insights can be brilliant, too. It's a small book, and not all the essays I found to be equally good, but all were still excellent ruminations about topics scientific and literary and personal. Here are a few quotations that I wanted to save; as usual, there are more at my Science Besieged book note.
I've been thinking a great deal lately about the "scientific method" for Ars Hermeneutica; watch this space for further thoughts as they develop. Meanwhile, here Lightman touches on the subject with observations that I can't argue with.
All of which led me to question the meaning of the "scientific method." Since high school, I had been taught that scientists must wear sterile gloves at all times and remain detached from their work, that the distinguishing feature of science is the much-vaunted "scientific method," whereby hypotheses and theories are objectively tested against experiments. If the theory is contradicted by experiments, then it must be revised or discarded. If one experiment is contradicted by many other experiments, then it must be critically examined. Such an objective procedure would seem to leave little room for personal prejudice.
I have since come to understand that the situation is more complex. The scientific method does not derive from the actions or behavior of individual scientists. Individual scientists are not emotionally detached from their research. Rather, the scientific method draws its strength from the community of scientists, who are always eager to criticize and test one another's work. Every week, in many journal articles, at conferences, and during informal gatherings at the blackboard scientists analyze the latest ideas and results from all over the world. It is through this collective activity that objectivity emerges.
So how could I reconcile the Popperian view of science, with its unbudging demand for objective experimental test, against the Polanyian view, with so much emphasis on the personal commitment and passions of individual scientists? The answer, perhaps obvious but at first shocking to a young scientist, is that one must distinguish between science and the practice of science. Science is an ideal, a conception of logical laws acting in the world and a set of tools for discovering those laws. By contrast, the practice of science is a human affair, complicated by all the bedraggled but marvelous psychology that makes us human. [pp. 35–37]
In this next excerpt he touches on something that I think is at the heart of how science works: the contingent nature of scientific truth.
Something of the power of pure mathematics can be seen by its permanence. We often use the terms objective and subjective to distinguish between those things existing outside our minds versus those produced in our minds, things with reality and permanence versus things that shift and dissolve with each new point of view. Paradoxically, mathematical results, which we deduce in our minds, last forever. Gone is the civilization of ancient Greece, but not the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle equals the sum of the squares of its two legs. Euclid's theorem that the angles of a triangle sum to 180 degrees will always be true. New branches of mathematics have been developed, including new branches of geometry, but the angles of a Euclidean triangle will always sum up to 180 degrees.
Science, by contrast, is constantly revising itself, constantly changing its theories and results to give better approximations to physical reality. An example is the theory of light. The wave nature of light was first revealed in the mid-seventeenth century by the experiments of th Italian scientist Francesco Maria Grimaldi. Grimaldi discovered that the concentric circles of darkness and light produced by light emerging from a small hole are similar to the crests and the troughs of overlapping waves of water. In the mid-nineteenth century came Maxwell's fully quantitative theory of light as an electromagnetic wave. Maxwell's equations, however, did not correctly explain all phenomena of light. In the early twentieth century, experiments suggested that light does not always behave as a continuous wave; it sometimes acts as a group of discrete particles, or "quanta," called photons. In the late 1940s, physicists produced a new quantitative theory of light called quantum electrodynamics, replacing Maxwell's equations. In the 1960s, scientists went even further and proposed that the phenomenon of light is deeply connected to other fundamental forces. The theory of light was modified once again. Scientists have differing opinions about whether humankind will ever find the ultimate laws of nature, or whether such final truths exist. But there is no disagreement that the history of science is the history of an endeavor constantly revising and refining its laws. Scientific theories do not have the staying power of pure mathematics. [pp. 70–71]
By the way, I can relieve your sense of suspense and say now that I am one of those scientists who believe humankind will never settle on the ultimate laws of nature; science is far too restless a discipline. There are fundamental reasons that go very deep, but this isn't the essay to discuss them.
Finally, this excerpt, which is about the character of mathematical proofs — in some sense the artificiality of mathematical proofs — something that will resonate with anyone who has taken upper-level math courses and read those dreaded words: "the details are left for the interested reader to show." I'll come back to this sometime when I talk more about what's wrong with the way we teach science and mathematics, something else I've been pondering for Ars Hermeneutica.
Mathematical proofs are not only about mathematics. They are about mathematicians as well. Euclid's proof [that there is no largest prime number — an example in the previous paragraph] is revealing for what is absent, as well as for what is present. There are no unnecessary elements, no false starts, no wrong turns. Undoubtedly, the first attempted proofs of the conjecture were clumsy, and Euclid must have thrown out a lot of good papyrus before he produced the proof that the handed down tot eh ages. Indeed, the ideal proof in mathematics shows no traces of the mortal path of trial and error that led to it. Johann Carl Friedrich Gauss, the great German mathematician, often called the "Prince of Mathematics," refused to publish his mathematical proofs until he had fashioned them into works of disembodied perfection. A cathedral is not a cathedral, he said, until the last scaffolding is down. When one looks at a proof by Gauss, it is impossible to tell where his reasoning began. Gauss wanted it that way. Pure mathematics is often compared to an art form, but it is a peculiar art form. A mathematical proof is a beautiful painting in which the viewer is not supposed to see the brushstrokes of the artist. That absence and simplicity is part of the aesthetic. [pp. 75–76]