Why Does a Small Aperture Increase Depth of Field?

Photographers know that decreasing the aperture size on their camera will produce an image with a larger depth of field. Although it’s possible to take a great picture without understanding why this is true, it doesn’t hurt to know! All we need to figure it out is a little bit of geometry and physics, plus a little knowledge about how a camera works. This is a really fascinating topic for me; it shows how a single topic can have many different levels of understanding.

Click here to learn about aperture size and depth of field


The Two Cultures and a Call for Discussion

When I was a sophomore in college, I took a class about thermodynamics and statistical mechanics. Each chapter of the textbook (An Introduction to Thermal Physics by Daniel V. Schroeder) was preceded by an “amusing” quote about the subject material. One in particular caught my attention; it appeared before the chapter about entropy and the second law of thermodynamics:

“A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of Have you read a work of Shakespeare’s?”

This idea fit nicely with some things my friends and I had been talking about, such as the strange fact that many schools offer “science for humanities majors” classes but no corresponding “humanities for science majors” classes. We weren’t interested in taking watered-down humanities courses; we just thought that English majors should have to learn real science. It seemed like a dangerous double standard that could produce one-sided people unable to completely understand the world around them. So naturally, I wanted to read the book that this quote came from: The Two Cultures and the Scientific Revolution, by the British novelist C. P. Snow.

However, the library didn’t have it and my desire to read it quickly got buried under all the other things happening in my life. It’s always been floating around in the back of my head though, and I finally got a chance to read it last month. I can’t say that it quite lived up to my expectations. The book is full of vague generalizations (“If the scientists have the future in their bones, then the traditional culture responds by wishing the future did not exist.”), opinions stated as facts (“The only writer of world class who seems to have had an understanding of the industrial revolution was Ibsen in his old age”), and irrelevant stories about famous people. One of its most serious defects is that Snow never actually explains why a lack of communication between scientists and ‘literary intellectuals’ is bad—he says: “There seems then to be no place where the cultures meet. I am not going to waste time saying that this is a pity. It is much worse than that. Soon I shall come to some practical consequences,” but the consequences never come.

It seems that I am not the only person who was bothered by Snow’s argument (or lack thereof). His book (which was actually the printed version of a public lecture he gave at Cambridge in 1959) set off a huge controversy in the British press. His most famous opponent was F. R. Leavis, a literary critic who in 1962 made a scathing attack (also in the form of a lecture at Cambridge) against Snow and his ideas. Roger Kimball has described Leavis’s talk as “a devastating rhetorical fusillade. It’s not just that no two stones of Snow’s argument are left standing: each and every pebble is pulverized, the fields are salted, and the entire population is sold into slavery.” Leavis’s talk was published as The Two Cultures? The Significance of C. P. Snow, and I read this book too. It’s great—Leavis’s style is unlike anything I’ve ever read, and the cultural issues he brings up seem as relevant today as they did in the sixties.

Four years after his talk, Snow made a response in the form of another book (The Two Cultures: A Second Look, which is usually now included with The Two Cultures and the Scientific Revolution). In it, he expresses his surprise at the controversy he had created. He muses that:

“As the flood of literature mounted, two deductions became self-evident. The first was that if a nerve had been touched almost simultaneously in different intellectual societies, in different parts of the world, the ideas which produced this response couldn’t possibly be original.”

Truer words were never said. The Two Cultures and its surrounding debate are merely the most visible elements in a long string of literature that stretches from the deep past all the way to the present. I have now read quite a bit of it, and it has been a very interesting experience. (See Further Reading for a some of the best/easiest-to-find parts.) All this reading has caused me to think about a number of things that I don’t normally think about, such as:

  • What does it mean to be a scientist?
  • What is and what should be the role of science in society?
  • How does science affect nonscientific beliefs?
  • Is a scientific education sufficient for imparting culture?
  • What would a true synthesis of science and art look like?
  • Is there a “gulf of mutual incomprehension” between the sciences and the humanities? If so, is this bad, and if it is bad, what should be done about it?

And in another sense, I think that all these questions are manifestations of the following deeper questions:

  • How much, and what kinds of things, can humans know?
  • How should one live one’s life?
  • What does it mean to be human?

I think this is the “nerve” that Snow speaks about. I will probably share my thoughts on at least a few of these topics in later blog posts—but I would really like to have a conversation first. So please read some of these things and let me know what you think. If you’re having trouble finding The Two Cultures or The Significance of C. P. Snow, let me know and I may be able to help you out.

Further Reading

The list is virtually endless, so I’ll restrict myself to things available online for free.

  • The Four Ages of Poetry, by Thomas Peacock—a satire of the scientific/anti-poetic attitude the author felt was becoming prevalent. Published 1820. Available here.
  • A Defense of Poetry, by Percy Shelley—a response to Peacock’s satire that explains the virtues of poetry. Written 1821. Available here.
  • Science and Culture, by Thomas Huxley—a lecture given at the opening of a scientific school. His defense of science puts Snow’s to shame. Given 1880. Available here
  • Literature and Science, by Matthew Arnold—a response to Thomas Huxley’s talk. His argument is more effective and less cruel than Leavis’s. It is interesting to note that Arnold and Snow both gave their talks as Rede lectures at Cambridge. Arnold’s is from 1882. Available here.
  • The Value of Science, by Richard Feynman—some philosophy from everyone’s favorite physicist. This is a talk given in 1955. Available here.
  • ‘The Two Cultures’ Today, by Roger Kimball—a look back at the controversy from one of the best social critics around today. Published 1994. Available here.