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If you teach astronomy, you probably know Powers of 10, an old film by Charles and Ray Eames to illustrate vast range of length scales in the Universe.  (To see it on the official web site, you seem to have to register, but youtube has it too.)  Well, the American Museum of Natural History has created a new video along the same lines.

Powers of 10 from AMNH

It’s got a few big advantages over the old Powers of 10: it goes out to 100 times larger scales than the Eameses’ film, and it’s based on real data even out to very large scales, which of course wasn’t possible when Powers of 10 was made.

The new film only goes up in scale from the Earth, unlike Powers of 10, which also went down to the subatomic realm.  Whether that’s an advantage or a disadvantage is up to you.

Powers of 10 explicitly showed the length scale at all times: on the right is a running counter showing how many meters we’re looking at, and on the left is the same thing in other units.  Also, every factor of 10 is indicated by an outlined box.  The new video indicates the occasional milestone in length scale, but it doesn’t do it consistently throughout.  I think that’s a pretty big pedagogical disadvantage of the new film.  It’d be nice if someone added a counter like that to the film.  But it’s still pretty cool.

 In a comment on my earlier post about 3D movies, Phillip Helbig writes

In the latest Physik Journal (magazine of the German Physical Society), there was a two-page article on 3-D techniques. You mentioned three: colour, linear polarisation and the quarter-wave-plate model (your hypothesis was correct; that's how it works). The last is definitely the best of these three, but shares this problem with linear polarisation: the reflected image has to be polarised, so the screen has to be mirror-like, not just a white screen.

It’s nice to know that that’s what’s really going on!

Phillip goes on to say

There are two other techniques. One projects frames at twice the normal rate, altenately for each eye, and the glasses contain infrared-controlled LCD shutters which alternate at the appropriate rate. Probably the best system, but the glasses are more expensive.

I actually used a system that worked on this principle, way back in the 1980s, when I had a summer job working in Don Wiley‘s lab at Harvard.  It was a special computer with a huge monitor that rapidly switched between two images, along with a pair of glasses that plugged into the computer and alternately switched from opaque to transparent so that each eye was presented with one of the images.  This must have been a special-purpose, very expensive system back then.  I don’t remember how fast the switching was;  I’m sure it wasn’t fast enough to show movies and have it look good.  The lab used it to visualize big biological macromolecules.

Phillip again:

Another one is quite interesting: for one eye, use three primary colours, and for the other eye, use three OTHER primary colours. The filter for each eye only lets through the primary colours intended for that eye. (For a given perceived colour, there are many ways of mixing it out of narrow-band "primary" colours".

I’ve never heard of this.  What a cool idea.  The next time I teach our mathematical methods class, I’ll use it as an example of vector spaces and projection operators:

The spectrum of a light source is a vector in an infinite-dimensional vector space, but we only see color in a three-dimensional space.  Your visual system is in effect projecting from the big space down to the small space, so of course there are many different spectral shapes that are perceived as the same color.  The filters in front of each eye are additional projection operators.  By a clever choice of those operators, you can use different parts of the original, big vector space for each eye, and still present the entire three-dimensional space to each eye.

I bet you can mock up a not-very-many-dimensional model of how all this works.

Supposedly Sir Arthur Eddington said this, and supposedly he was at least partially joking.  I like to think he was only half joking, though, because there’s a pretty big nugget of truth in this supposedly backwards statement.  It’s really just an obnoxious way of stating another favorite adage of scientists: Extraordinary claims require extraordinary evidence.

If someone tells you the result of an experiment, and that result fits nicely in with a previously-established theoretical framework, you should be more inclined to believe it than you would be for a claim that does not fit into such a framework.  In so doing, you’re just being a good Bayesian reasoner, taking into account both your prior knowledge and the information contained in the new experiment.

Take, for instance, the idea that cell phones cause cancer.  Maine is considering a law requiring warning labels to this effect.  The epidemiological evidence is, to say the least, mixed.  I find the “don’t believe an experiment until it’s confirmed by a theory” maxim to be a pretty convincing argument against the idea tha there’s any risk: as far as I know, no one has proposed a plausible mechanism by which the microwave radiation emitted by cell phones could cause cancer.  As Bob Park has been pointing out in his What’s New column for quite a while now,

Cancer agents break chemical bonds, creating mutant strands of DNA. Microwave photons cannot break chemical bonds.

I’m terribly ignorant about biology, so maybe this argument is all wrong, but it sounds convincing to me.

I went and saw Avatar in 3D last night.  Everybody told me it was visually amazing but the story was lame.  The first part is definitely true, but (probably in part because my expectations had been lowered so much) I was actually pleased by the story.  It’s totally formulaic, but I’m not sure that’s such a bad thing.  There are lots of things worse than a well-executed formula.

But that’s not what I want to talk about.  Naturally, after the movie was over, I had to try to reverse-engineer how the 3D glasses work.

To get 3D, you have to present slightly different images to the two eyes.  In the old days, the glasses had color filters on them, and the two images were presented on the screen in different colors. That has the significant disadvantage that you can’t use color to convey other information (i.e., color!).  So in modern 3D, the different images for your two eyes are projected onto the screen using two different polarizations.

The simplest way to do this would be to use horizontal and vertical linear polarizations.

[(Information for people who don’t know / don’t remember optics.  If you do know, then skip everything in brackets.) Light is a wave of electric  and magnetic fields.  The fields have to be perpendicular to the direction the light is traveling, but subject to that constraint they can be oriented in different ways.  Linearly polarized light just means light where the electric field is wiggling back and forth in a particular plane.]

The simple procedure would be to stick a filter in front of your left eye that only lets through horizontal polarization, and one in front of your right eye that only lets through vertical polarization.  Then project the two images onto the screen with the appropriately matched polarizations, and you’ve got it.

That’s not how it’s done, though.  One reason is that if you tilted your head, the polarizers wouldn’t be aligned right.  In fact, if you tilted your head 90 degrees, the image intended for each eye would reach the other one, which would have the disconcerting effect of flipping the image, so that stuff that was supposed to look close to you looked far away, and vice versa.  Even if you tilt your head less than 90 degrees, you’d get an unacceptable distortion.  This doesn’t happen — I tried it.

The solution to the head-tilting problem  is to use circular polarization rather than linear polarization.

[With circularly polarized light, the electric field rotates as the light propagates, so that the tip of the electric field vector traces out a spiral pattern.  In other words, it rapidly switches between horizontal and vertical as the light moves along.  There are two kinds of circular polarization, left and right, corresponding to clockwise and counterclockwise spirals.]

The images for your two eyes are actually projected on the screen in left and right circular polarizations.  Since a clockwise spiral is still clockwise no matter how you tilt your head, this solves the head-tilting problem.

So you might imagine that the 3D glasses just consist of a filter for each eye, one that lets through left circularly polarized light and one that lets through right circularly polarized light.  I think that is the general idea, but the details are a bit more complicated.  One way to see this is to take two sets of glasses and hold them up so that light passes through the left lens of one pair, followed by the right lens of the other.  (They’re not really lenses, of course; I’m just using “lens” to mean one of the two things in a pair of glasses.) In the simple picture I just described, you might expect to see no light at all get through: the first lens would block all of one polarization, and the second would block the other.

[If you’re just looking at a natural light source, it’s probably unpolarized, meaning that the electric field points every which way.  But even unpolarized light can be thought of as a combination of left and right circular polarizations, so the first lens would knock out half the light, and the second would knock out the other half.]

But that’s not what happens. Quite a bit of light gets through in this experiment.  Moreover, if you rotate one lens with respect to the other, the light that gets through changes from gray to yellow.  What’s up with that?

A couple of clues: First, the fact that the image changes as you rotate the lenses suggests that linear polarization is involved after all.  Second, there’s a fact you can dredge up if you’ve studied optics: it’s not easy to make a filter that passes one circular polarization and not the other.  What you can make is something called a quarter wave plate, which magically converts circular polarization into linear polarization and vice versa.  For instance, you can make a quarter wave plate that turns left circular polarization into horizontal linear polarization and right circular polarization into vertical linear polarization.

So now we can make a guess: each lens consists of two parts: a quarter wave plate to turn circular into linear, followed by a polarizing filter that just lets through one linear polarization.  The two lenses either have different linear polarizers at the back end (one horizontal and one vertical), or different quarter wave plates at the front (one that turns L/R into H/V, and one that turns L/R into V/H).  Either way should work.

Here’s one test of this theory.  Take two sets of glasses, and hold them up to a white light source, so that the light passes through one lens in the usual way, and then through another lens in the reverse direction.  According to the hypothesis, the light coming out of the first lens should be linearly polarized, and when it hits the second lens it should hit a second linear polarizer.  That polarizer will let light through if it’s lined up the same way as the first one, but block it if the two are perpendicular.  Sure enough, that’s what happens. When you rotate one lens with respect to the other, the amount of light that gets through changes, dropping to essentially zero when the rotation is 90 degrees.  This is true whether you’re using the left or right lens in each case.

So the answer’s got to be version 2 of the hypothesis: both lenses have the same kind of linear polarizer at the back end (let’s say vertical), but they have two different quarter wave plates at the front end: one converts left circular polarization to vertical and one converts right circular polarization to vertical.

You can try a bunch of other similar tests, flipping the orientations of the two lenses various ways.  I think they’re all consistent with this theory, with the exception of one thing: sometimes, as noted above, the way the light gets through depends on color.  The most dramatic example is if you send white light through, say, the left-eye lens backwards, and then through the right-eye lens forward.  The result is a nice, rich purple.  What’s up with that?

According to the theory I sketched, the experiment I’m describing consists of sending the light through four elements: a linear polarizer and quarter-wave plate for the first lens, and then a quarter-wave plate and a linear polarizer for the second lens:

LP1  QWP1  QWP2  LP2

The two quarter wave plates next to each other form something called (not surprisingly) a half wave plate.  A half wave plate rotates linear polarizations by 90 degrees — that is, turns horizontal into vertical and vice versa.  In that case, we’d expect this sequence to let through no light at all: the first linear polarizer lets through only (say) vertical, then the HWP turns it to horizontal, and the second linear polarizer blocks horizontal.  So we should see black, not purple.

I think the explanation is that a quarter wave plate (or a half wave plate) can only be designed to work perfectly at one wavelength [i.e., one color].  The glasses are probably designed to behave correctly in the middle part of the visible spectrum, which means they’ll be imperfect at the two ends.  So this particular combination of lenses would do a good job at blocking out light in the middle of the spectrum (yellow, green) but not so good at  blocking out light at the edges (red and violet).  That seems consistent with what I observe.

I guess this must mean that the 3D effect is only perfect for light in the middle of the spectrum, and for other colors some of the image meant for one eye actually reaches the other.  Presumably this imperfection isn’t very noticeable “in the wild.”

One experiment I wish I’d tried during te movie: put the glasses on upside down, so that the image meant for the left eye goes to the right eye and vice versa.  This should have two effects:

1. Make you look even goofier than the other people in the room wearing 3D glasses.
2. Show you the picture inverted in depth (close stuff looks far and far stuff looks close).

If you try this during a 3D movie, let me know if it works (particularly #2 — I’m pretty confident about #1).

Having written about the speculation, I suppose I should finish the story.  In a few talks yesterday, the CDMS dark matter detection experiment announced its latest results.  I didn’t hear the talks (at least one was streamed on the web, but I was in bed by then.)

They saw two events in their detector which look like what you’d expect from dark matter particle interactions, but two isn’t enough to conclude anything.  The group has elaborate procedures for calculating how many background events (i.e., events that look like dark matter but aren’t) might be seen.  Two is more than the expected number, but not by all that much: they estimate there’s a 23% chance of getting two background events.  To say they’d seen dark matter, that probability would’ve needed to be a tiny number.

Of course, it’s possible that these were dark matter events.  If so, I guess it means that the experiment is right at the edge of having sufficient sensitivity to detect dark matter particles.  This’d be great, because then future experiments would presumably be able to provide a real detection.

The group said they were planning to post a paper on the arXiv, but it’s not up yet.  Maybe they meant they’d submit it yesterday, and it’d appear today, or maybe they just didn’t get everything finished when they said they would.  I imagine it’ll be up soon.  In the mean time, there’s a brief summary of the result on their web site.  For those who want a bit more detail and can’t wait for the paper, JoAnne Hewett from Cosmic Variance was liveblogging one of the talks.

Having spread an unfounded rumor about the CDMS dark matter search last week, I thought I’d point out what’s actually happening.  This is oldish news, so some of you probably already know it, but for those who don’t, according to the CDMS web site,

The CDMS collaboration has completed the analysis of the final CDMS-II runs, which more than doubled the total data from all previous runs combined. The collaboration is working hard to complete the first scientific publication about these new results and plans to submit the manuscript to arXiv.org (http://arXiv.org) before the two primary CDMS talks scheduled for Thursday, December 17, 2009 at Fermilab and at SLAC. Jodi Cooley, the CDMS analysis coordinator and a professor from Southern Methodist University, will present the talk at SLAC at 2 p.m. PST, and Lauren Hsu, a scientist from Fermilab, will present the talk at Fermilab at 4 p.m. CST. A Web cast of Cooleys talk will be available on the CDMS Web site.

So they will be releasing results on (roughly) the date mentioned in the original rumor, and they do plan on having a paper available.  The part that’s apparently not true is the part about Nature.

I’ve heard some people speculating about the likelihood that the new results will contain something big and exciting, such as a claimed detection of dark matter.  I don’t know the folkways of this particular culture well enough to know whether the way this data release is being handled suggests a big result or not.  (I understand a bit about the astronomy and astrophysics culture, but dark matter detection experiments have mostly inherited the culture of particle physics, which is quite different.)

Anyway, like lots of other people I’ll be going to the arXiv the day the article is supposed to appear to find out.

As I mentioned a while ago, my Dad was awarded the Wallace H. Coulter award for lifetime achievement by the American Society of Hematology.  The award ceremony was this past week at the meeting in New Orleans.  Here’s the Society’s announcement about the award.

I just updated my previous post to make clear that the rumor about CDMS having detected dark matter probably isn’t true.  Thanks to the people who pointed out the update to the place I got the rumor from, which includes an email from an editor at Nature indicating that they haven’t accepted such a paper. Sorry for my credulousness.

Brent Follin, in a comment to my post, makes some observations about the Nature editor’s email:

It seemed a little strong and personal to be an actual email from someone writing a professional email, but it did point out that December 18th is a Friday, and Nature is published on a Thursday (with the articles normally released by Wednesday's evening news). So this rumor could be true, but I doubt the Nature publication (which makes me doubt the rumor). Also, Dr. Sage seemed pretty pissed about the mention of an "embargo", which she says is unfounded–that authors can, for instance, post on Arxiv before the publication date.

A couple of comments:

First, I agree with Brent that the tone seems very odd.  Maybe he just had a bad day.  Second, I went and checked out Nature‘s embargo policy.  It’s true that the policy allows posting on the arXiv, but it forbids talking to the press until a week before publication.

I’m not sure how that policy serves a useful purpose:  journalists can read the arXiv, you know!  Is it really better for them to see the article but not be able to talk to the authors for clarification?   But it’s their journal, so they can do what they want.

UPDATE:  Never mind.  It looks like the whole thing’s not true.  See the “important update.”  Sorry!  (I agree with Brent in the comments to this post that the tone of the email from the Nature editor is quite odd, by the way.)

A rumor is apparently going around that the CDMS experiment may be about to announce that they’ve directly detected dark matter particles.

CDMS is one of several experiments that try to observe dark matter particles directly interacting with their apparatus as they pass through.  These experiments are always placed deep underground to shield them from “ordinary” cosmic rays; this one is in a mine in Minnesota.

Evidence for the rumor: The collaboration had a paper accepted in Nature.  Nature usually only publishes high-profile results.  If CDMS had a non-detection to report (even if it set a new and interesting upper limit), Nature would be less likely to accept it. Nature articles are embargoed until publication, meaning that the collaboration can’t release the results or talk about them until December 18.  Members of the collaboration have canceled seminars before that date and scheduled talks at a number of universities to take place on that date.

So it definitely sounds like they have something exciting to say.  If they really have directly detected dark matter particles in the lab, needless to say this would be a Really Big Deal.

There’s a good post on RealClimate about the nature of certainty and uncertainty in science.  The hook for the post is a Wall Street Journal Op-Ed headlined “The Climate Science Isn’t Settled.”  The point of the post is to explain why this phrase is almost always a misleading rhetorical trick:

The phrase "the science is settled" is associated almost 100% with contrarian comments on climate and is usually a paraphrase of what 'some scientists' are supposed to have said. The reality is that it depends very much on what you are talking about and I have never heard any scientist say this in any general context – at a recent meeting I was at, someone claimed that this had been said by the participants and he was roundly shouted down by the assembled experts.

The reason why no scientist has said this is because they know full well that knowledge about science is not binary – science isn't either settled or not settled. This is a false and misleading dichotomy. Instead, we know things with varying degrees of confidence – for instance, conservation of energy is pretty well accepted, as is the theory of gravity (despite continuing interest in what happens at very small scales or very high energies) , while the exact nature of dark matter is still unclear. The forced binary distinction implicit in the phrase is designed to misleadingly relegate anything about which there is still uncertainty to the category of completely unknown. i.e. that since we don't know everything, we know nothing.

Although the author is (naturally) most interested in talking about climate science, the post is really about the nature of science in general, and a lot of what it says applies more broadly.  In particular, creationists and relativity-denialists (who, astonishingly, still exist) talk in very similar ways to those described here.