Mar 07 2010

One critic's feisty defense of Avatar

Categories:

Film

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Airtalk had their annual roundup of critics at the Egyptian Theater to comment on the films nominated for the Academy Awards this year. I haven't yet seen Avatar, but I'm a pretty big admirer of James Cameron as a filmmaker. Most of the panel frankly hates Avatar, degrading it as a childish ripoff. This leads to the following comment by Henry Sheehan that I found interesting (Their audio was this horrible on the podcast. Not my fault.):

They're [the Avatar characters] are types. That's what Cameron likes to work with. Because among other things, all Cameron's movies are about movies, and the experience of watching movies. I can't go into everything that's good about Avatar right now. There's quite a bit. But, if you don't like the dialog, and you think it's silly: maybe it's not the film's problem. Maybe it's your problem.

This prompts a raucous response from some of the members of the panel, who snidely comment that the film is just a ripoff of Pocahontas. Sheehan goes on:

That's a typical problem regarding Avatar: that, at the real level, it's about indiginous people and about helping them out. And it's not about that in its final point. Yes, it uses that template. It's a consistent theme in Cameron's work. It goes back to the first Terminator film. And by the way, what most people don't like about the dialog in Titanic and Avatar is exactly what they did like in Terminator and Terminator 2.

"But no one nominated Terminator 1 or 2 for Best Picture or Screenplay", retorts one critic.

Right, because there's a bias against action films. But, Cameron started out saying that the survival of the human race is a real struggle, a bloody struggle, but it's a struggle worth taking in. And in a lot of ways what it has to fight is modernity, as represented by these robots from the future. Slowly over the years, film by film, Cameron has changed his mind. He no longer believes that the human race is worth saving. He doesn't think they've been good stewards of the world they've been given. He thinks, under those circumstance, they might as well go. It turns out that we are the robots. That's what he found out. We're not the flesh and blood creatures. Or if we are, we've expunged that from ourselves.

Unfortunately, the discussion has to wrap up at that point. (By the way, Charles Solomon is kind of an infantile horse's ass.)

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Feb 18 2010

This is why I hate NBC

Categories:

General

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Skip to 5:10 for maximum rage/time.

It's the 7th end, hammer rock, crucial shot for the US. Literally 1 second before the rock makes contact, they cut away to hockey. It's like if they cut away as the basketball was heading for the hoop at the buzzer.

God dammit. (US lost, anyway.)

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Feb 15 2010

Derive all the laws of mechanics in one blog post

Categories:

Science

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Introduction

The most basic law of nature that I know of is about probabilities. If you flip a coin, we say that the probability of getting heads is 1/2. The probability of getting tails is the same. The probability of getting either heads or tails is the sum

P(\text{heads or tails}) = P(\text{heads}) + P(\text{tails}) = 1.
(1)

Something has to happen, so the probability is 1 of something happening. The probability of getting two heads in a row is the product:

P(\text{heads then heads}) = P(\text{heads}) \times P(\text{heads}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}.
(2)

That is, an "and" proposition means to multiply the probabilities. Most grade school children can get their heads around this. It's an apparent mathematical fact, a point of logic,
and one might wonder why it would even end up being the subject of a discussion of physics.

Fine, so suppose that the things we are talking about are not flips of a coin, but some physical events, such as "the electron goes through hole A and hits a spot x on the wall behind the hole" and "the electron goes through hole B and hits a spot x on the wall behind the hole". We could call the probabilities of these things happening P(\text{A}) and P(\text{B}) . Now, we can tell very easily what P(\text{A}) is. Cover up hole B, and count how many electrons hit at x . That number divided by the total number of electrons you sent out is P(\text{A}) . Then do the same thing for P(\text{B}) : cover up A, count the number at x, divide.

Read the rest of this entry »

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Jan 22 2010

The north pole is melting. Why aren't we under water?

Categories:

Science

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Seemingly every day we hear about the terrifying eroding of the polar ice caps at the north pole. To some it's a sign of the apocalypse, to others a heartbreaking threat to the local ecosystem. To some it's even a trade route opportunity (???). But if that much ice is melting, and global warming causing the polar ice to melt will make water level rise, then why hasn't the water level been increasing?

The ice at the north pole is floating in the water. If you drop pieces of ice into a glass of water, and note the water line, then let the ice melt, you will see that the water line doesn't increase. Floating ice that melts doesn't contribute water. (Proof is below)

So what's the problem? The ice at the south pole is on land, and there's a hell of a lot more of it. When that goes, say goodbye to our coastal cities, hello to all manner of inclement weather and worldwide famine threat.

In any case, it's a good physics problem.

Diagram

Suppose a mass \Delta m goes from solid phase to liquid. How does the water level change? The water level is the volume of liquid plus the volume of the solid that is submerged. Let

V_s = the volume of the solid

V_{ss} = the volume of the solid that's submerged

\rho_s = the density of the solid phase

\rho_L = the density of the liquid phase

The volume occupied by \Delta m before it melted was \Delta m/\rho_s . V_{ss} can be found by applying Archimedes' principle: the weight of the solid is equal to the weight of water displaced
by the solid, for something floating in static equilibrium. This implies

V_s \rho_s g = V_{ss} \rho_L g
(1)

so that the volume that determines the water level is

V = V_L + \frac{V_s \rho_s}{\rho_L}.
(2)

The volume occupied by \Delta m afterward is \Delta m/\rho_L . So, the change in volume that determines the water level is

\Delta V = \Delta V_L + \frac{\rho_s}{\rho_L} \, \Delta V_s = \frac{\Delta m}{\rho_L} + \frac{\rho_s}{\rho_L}\left(-\frac{\Delta m}{\rho_s}\right) = 0.
(3)

Now, this proof does not work if the ice is touching the bottom of the glass, or the sides of the glass. It does, however, work for any substance that will float in solid phase (i.e. any substance that expands when solidifying).

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Jan 08 2010

The more I know, the less I understand

Categories:

Science

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Every year I am assigned to teach the "general interest" class in wave matter to non-science majors. I don't mind this assignment, as the material is interesting despite the facile treatment given in the class. We cover general wave phenomena (wave creation, propagation aspects, Doppler shift, bow waves) and then move on to talk in detail about sound and light.

It's light that's got me in a bind. When I was first tasked with explaining such things as why the sky is blue, why water looks blue (from inside it), refraction, dispersion in rainbows and prisms, absorption, and stimulated emission, I really didn't think much of it. The 'explanation' is just a list of facts and analogies:

  • Higher frequency light (shorter wavelength) scatters more from gas molecules (hence blue photons scatter during the day in all directions)
  • ... on the other hand, blue light scatters less from liquid molecules
  • light refracts (bends at an interface between two media) due to velocity change in concordance with Fermat's principle (alternatively, and somewhat more satisfactorily, from Huygen's principle)
  • Dispersive media have frequency-dependent velocities, making red refract more
  • light is absorbed by an atom whose electron orbitals have the same energy difference as the photon's energy E=hf
  • Stimulated emission is likely to occur with excited atoms in the presence of another photon of the same energy

With each passing year, I started to internally inquire why the hell any of these things really happens. Nitrogen molecules have a higher scattering cross-section for blue photons than red. How come? Light takes the path of least time. Why the hell would that be, particularly when a ray of light is viewed as a stream of photons? Photons in a laser cavity stimulate emission of identical photons (statistically) because they are bosons, but by what mechanism do they do that?

Now, I don't feel like such a fool. I'm going to reckon that a large number of physicists do not know the answers to these questions, not in the least because they are actually rather difficult to ascertain, and aren't covered in undergrad or graduate courses. But this doesn't absolve me, because the answers are knowable.

The first clue, and I suspect the last, lies with good ol' Feynman. While his fairly enjoyable lecture series at Cornell was recently put up online by Bill Gates, of much more interest is a series of lectures given at the University of Auckland about quantum electrodynamics. QED, as it's unfortunately abbreviated, can answer the questions of which way the photons go in optical experiments, how photons interact with electrons, how electrons interact with other particles, and such. These are the answers I sought, but the QED lectures are for a general audience, and just left me hungry for the real theory. His explanation about the probability amplitudes as vectors in the complex plane that obey certain rules of addition and multiplication was all well and good, but he never says how to calculate these amplitudes.

So, going into my fourth time teaching a class about why the sky is blue, I actually do not know the answer. I know only the proximate cause: blue light scatters more from air than red light does. But this is not the ultimate cause, and it's odd that it took me this long to be really curious about it.

By the end of the term, I must answer the following questions:

  • How does Fermat's principle come from a quantum theory of photons?
  • What determines the scattering cross-section of a photon with matter?
  • What is the quantum mechanical explanation of an electron confined in an atom? How does the presence of a (non-virtual) photon influence the probability of spontaneous emission of such an electron?
  • What determines the effective wavespeed of light in a medium, such that a dispersion relation v=v(f) arises?

And finally...

  • WHY THE HELL DO I HAVE TO THINK ABOUT THESE THINGS?

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