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.

Overwhelming Oddness

Here’s a short story I wrote for a tenth grade English class assignment. Before you read it, I want to mention a few things:

1. Back then, everything I knew about quantum mechanics came from second-hand reports of friends who had seen The Elegant Universe.
2. I had just finished reading Breakfast of Champions when I wrote this.
3. There’s a painfully obvious reference to a Matthew Arnold poem in here–can you find it?

How to Choose a School

(Updated on 04-03-2012.)

Prospective graduate students came to visit our physics department last weekend. For many of them, this visit marked the beginning of Decision Season. It’s a magical time of year: stressed-out prospectives are trying to figure out where they want to spend the next 5-7 years — older graduate students are trying to give them as much alcohol as possible — and everyone is trying to eat free food.

Since I recently went through this process myself about a year ago, I thought I would throw in my two cents about how to choose a school. (I think this whole post applies to college as well as grad school… so I’m just calling it “school.”) It’s a pretty daunting task to make such a big decision based on so little information, so I think most people love to hear advice about it.

The decision-making process can be broken into two steps: one in which you weed out schools that are bad, and another in which you select the best choice out of the ones that remain. There’s tons of advice about how to do the first step, and I’ve given links to some of my favorite advice sites at the end of this post. However, this part can hardly be called a decision; it’s more like a mechanical filtering process. The most frustrating part of choosing a school (to me) is picking between several good schools whose relative pros and cons seem to essentially balance out. Given the relative lack of advice pertaining to this step, I’d like to offer my own. So here’s the main idea:

Don’t Think Too Much

I’d like to now expound upon what I mean. First, here are three things that I believe to be true:

1. You’re ignorant. There are simply too many things that you cannot/don’t understand/know. The future and your own personality are too unpredictable. Can you really know what is best for you, or that a particular school will provide it? I don’t think so.
2. You’re making a bet on yourself. Individual people have individual reasons for going to school, but I think I can confidently assume that you are at least after knowledge, experience, and a good time. These things are highly personal endeavors. A teacher can present information to you, but you have to choose to learn. Professors can offer you research opportunities, but you have to take them. You can have fun, but not if you sit around doing nothing all day. In the end, it’s you that determines your success, not your school. Have some faith in yourself.
3. There’s no bad choice. Many people approach the decision-making process with the assumption that the school they choose will make a major impact on the rest of their lives. This is completely true. Unfortunately, most people also believe a corollary to this assumption — one which makes them think that if they choose the wrong school, it will have a major negative effect. While this can happen in some extreme situations, it’s pretty unlikely. For one piece of evidence, see the previous bullet point. For another, watch this awesome TED talk. I don’t want to profane it with an attempt to sum it up in one sentence. It’s pretty short, and you’ll be glad you watched it. Do it!

With the wrong attitude, the school search can turn into a hellish and stressful situation. While I think it’s totally reasonable to try to pick the school that seems to offer you the best experience, it’s also extremely important to realize that there’s almost no way you can make a mistake. So keep your favorite criteria in mind — reputation, location, aesthetics, stipend, atmosphere, faculty, etc — but don’t fret too much if you’re having a tough time picking a single school.

If you can narrow down your search to just two top schools, then it’s time to really “go with your gut.” If you’re choosing between two, they’re probably both pretty awesome. Your conscious mind is never going to be able to satisfactorily differentiate between the two. But you can turn to your subconscious mind instead. It’s been with you through the whole process, absorbing information and coming to its own conclusions. Here’s a trick to let it share its opinion: flip a coin. Heads is school X, tails is school Y. If you’re fine with the coin’s outcome, just stick with it. If you get a sinking feeling accompanied by a wish that it had landed the other way, then this is your subconscious talking to you. It’s that simple.

So, to repeat: don’t think too much! Think a little, but realize that thinking has limitations. Put your trust in yourself rather than your school. You’ll be fine no matter where you go.

Current grads: How did you pick your schools? Do you agree with my advice?

Further Reading

• Excellent advice from Cosmic Variance
• Some other good advice

Of Temples and Table Salt

Have you ever seen a diagram of a substance’s atomic structure (like the one below, for table salt) and wondered where it came from? If you haven’t, I’ll try to quickly explain why the existence of such a picture might be a mystery:

• Typical atomic sizes are between 30 and 300 picometers. A picometer is one thousandth of a nanometer, which is one millionth of a millimeter. Atoms are really small!
• Typical interatomic spacings in solids are bigger, but not by much; they are usually between 0.1 and 1 nanometers. So at the very least, we need to be able to detect things that are about 1 nanometer in size to determine the atomic structure of a molecule or material.
• The physical size of the average pupil prevents human eyes from seeing anything much smaller than a hair, which is about 0.1 millimeters wide– far larger than a nanometer! (Go here for an explanation.)
• In fact, the large wavelength of visible light prevents any optical device (including eyes and microscopes) from seeing anything smaller than a few hundred nanometers.
• X-rays have wavelengths comparable to interatomic spacings, but it is nearly impossible to build lenses for x-rays. Thus, x-ray microscopes don’t really exist.

So how do we know what anything looks like on such a small scale? Well, people have actually invented a whole bunch of clever methods for seeing very tiny things. I would love to talk about all of them, but for now I am just going to focus on one of the oldest and most widely-used techniques: x-ray diffraction. X-ray diffraction is a tool for determining the structure of a crystal, which is a solid material that has a repeating atomic structure. It’s true that not every material has a repeating structure, but many do. What’s even better is that many molecules can be tricked into growing in a crystalline form; for example, proteins can be stacked into periodic arrays. This allows x-ray diffraction to determine their molecular structures. This information is invaluable to physicists, chemists, biologists, doctors, and pharmaceutical companies. (Here is a big ol’ pile of protein structures.)

How To Solve Doppler Effect Problems

If you’re having difficulty solving classical Doppler shift problems on your physics homework, you’re not alone! Many textbooks portray the Doppler shift formula in confusing ways that obscure real understanding. It is often stated as either several different formulas (one formula for a moving source and stationary observer, one formula for a stationary observer and moving source, etc) or one formula with a cruel and impossible-to-remember sign convention (for example, “source velocity is positive when the source moves in the direction of the emitted wave”).

I prefer to use what one of my past professors used to call the “Method of Thinking” to solve Doppler shift problems. (This is just one use of a more general Method of Thinking, in which you simply think about a problem to find the answer.) The basic ingredients are one easy-to-remember “incomplete formula,” two simple rules, and an instruction to think:

1. , where the velocities are relative to the medium and stands for either plus or minus. The following two rules determine which sign to choose. (The formula is written in a general way to emphasize that the Doppler shift formula applies to many kinds of waves, but it is good to think of sound as a representative example. In that case, the wave speed is the speed of sound and the medium is air.)
2. If the source and receiver move towards each other (and one is stationary), the observed frequency increases.
3. If the source and receiver move away from each other (and one is stationary), the observed frequency decreases.
4. Think!

Examples

1. Suppose the observer is stationary with respect to the medium and the source moves towards it. Then and Rule 2 tells us that the frequency must increase. So the correct formula to use is . We choose the minus sign because shrinking the denominator of a fraction makes it grow.
2. Suppose the source is stationary with respect to the medium and the source moves away from it. Then and Rule 3 tells us that the frequency must decrease. So the correct formula to use is . We choose the minus sign because shrinking the numerator of a fraction makes it decrease.
3. Suppose both the source and observer are moving with respect to the air. This situation involves a little bit more Rule 4 than the first two examples. The trick is to imagine a third entity (call it “The Phantom”) at rest with respect to the air. The Phantom listens to the sound emitted by the source (call this “Stage 1″) and emits an exact copy to the observer (call this “Stage 2″). Thus, The Phantom is both an observer and a receiver. In Stage 1, The Phantom hears a frequency given by , where the sign is determined as in the previous examples. In Stage 2, the observer hears a frequency given by , where the sign is determined as before. Inserting the equation for the Phantom frequency into the equation for the observed frequency gives the correct formula. Note that the top of the Phantom frequency fraction will cancel with the bottom of the observed frequency fraction.
4. If the source and the observer are at rest relative to the ground, there can still be a Doppler shift if the medium is moving. This is equivalent to the previous case. (This means that on a windy day, your voice could appear to be lower or higher.)

It is not useful to remember the specific equations; instead, try to learn the process that leads to them. This allows you generate formulas as you need them from a few basic concepts, instead of cluttering your head with multiple and/or confusing equations. Note: this is a good example of the power of the physicist’s mode of thinking.

Continue forward to learn where Rules 1, 2, and 3 come from!

The Franck-Hertz Experiment

This picture is from a class (Experiments in Modern and Applied Physics) that I took at Rutgers back in my junior year.

It’s not a spaceship or alien technology; it’s a special mercury vapor triode I was using to recreate the famous Franck-Hertz experiment.

You can enjoy it as it is, or read further for an explanation of the physics behind the picture.

Back To School

Classes have started up again, so posts will probably become a little less frequent than before. In case you’re wondering, most of my time in the next few weeks will be spent doing this.

Rippled Ice

My current blog header is a crop from this photo, which was taken after a snowstorm at Rutgers in early February 2011. I wanted to get pictures of the snowy campus, but by the time I got out of class, everything had begun to melt. I walked by a wooden handrail and found this: some very thin rippled/bubbly ice floating on a slightly less thin layer of melted water. (The dark lines are the spaces between painted wooden boards.) There are a few spots where you can see air bubbles trapped between the ice and the water below it. I don’t know what physical processes produced this interesting texture, but I sure would love to. Does anyone have some insight?

The Missing Link: Point Particles, Extended Objects, and the Center of Mass

I’d like to make one more post about Newton’s Laws of Motion before I temporarily abandon them. There are two closely-related issues that I want to address:

1. There is a glaring problem with Newton’s Laws as I have portrayed them in my last two posts (Why Are Newton’s Laws of Motion Important? and Variations on Newton’s Laws of Motion).
2. Many students in introductory physics classes get the impression that physics cannot possibly apply in the real world because we always replace real objects with point particles.

In the process of addressing the problem with Newton’s Laws, I will simultaneously show that the aforementioned physics students could not be further from the truth; Newton’s Laws of Motion do apply to objects in the real world, and this is true because of the fact that we can replace extended objects with point particles (not in spite of it)!

Continue forward to see what allows me to make these claims!

Variations on Newton’s Laws of Motion

I would like to explore Newton’s laws in a bit more detail, especially the connection between the two different versions that I introduced in my previous post. Whereas that post focused on “higher-level” aspects of Newton’s laws, this one will explain some of the supporting details. (I’m also sort of making this post for the sake of completeness: I made a claim in my previous post, and I want to prove it. You shouldn’t believe anyone’s claims unless they have proof, including me.)

Just as a reminder, Newton’s Laws of Motion are:

1. If there is no net force on an object, it will have no acceleration.
2. If there is a net force acting on an object with momentum , then .
3. If object 1 exerts a force on object 2, then object 2 exerts a force on object 1 with the same magnitude but opposite direction.

I plan to turn them into:

1. The other two laws are valid in only in inertial reference frames. These special frames really do exist, and they are easy to identify.
2. There is an equation () that can determine the position and velocity of an object at any time in the past or future.
3. The momentum of a system is conserved if no forces act on it.