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MIT student blogger Yan Z. '12

An Asymmetric Discussion of Shoes, the Process of Moving, and 3D Glasses by Yan Z. '12

Physics problem included. Some assembly required.

Today I will tell you how to get into MIT. You get into MIT by wearing thick, waterproof shoes, because the road to MIT is paved with slush. (Yes, all of them. I tried.)

Slush blooms like grey wildflowers on concrete during murkily warm, precipitation-infatuated Januaries. This I gleaned from a morning of traipsing from car-to-door with luggage stuffed like roasted peppers (the stuffed kind, you know), ferrying the bare-stripped evidence of my baryonic selfhood in three suitcases, two boxes, and a broken laundry hamper mashed onto the cushions of a green car. (Is “green” somewhat of a creative-imagery let-down? To be specific, the car was nearly the exact color of the Green Party logo, but I thought that “Green-Party-green car” would be too much of a modifier sandwich.) Slush, puddled with motor juice under thin skins of ice, is the terror of unscotchgarded ankles in urban New England. Slush is a test of courage and moral fiber.

MIT is not a school for the daintily-shod. For that, I direct you to the sun-drenched, flip-flop-friendly sidewalks of that other school in Southern California, where the socially-repulsive pairing of socks with sandals is an acceptable solution to hard weather. (By “hard,” I mean “comparatively pleasant.”)

By the way, I’m sure some of you think that “shoes” is a metaphor for perseverance, academic ambition, or high SAT scores, but I urge you to read this literally. Forget having brilliant ideas or scientific ingenuity or whatever; you can’t pulverize a chunk of snow in your path by factoring large integers on a quantum computer in polynomial time, unless your shoe also runs Shor’s algorithm.*

*Inexplicably, as I was writing this, I mentally permuted a well-known tongue-twister into “Shoes solve Shor cells in the C shell.”

Long story shor(t), I moved out of Random Hall and into pika on Monday.

The purest of all unimportant joys may well be the clarity of knowing exactly what you own. To be precise, I have no clue whether I own any free will* or whether I still own my Intro to Solid State Chem. textbook after lending it out to some guy named Cappie, but there’s little point in chasing after the unanswerable. After the sad, sweet, soul-searching-and-room-searching process of moving out of Random Hall, I can list everything I own that interacts with photons and has never interacted with Cappie.

*Evidence against the existence of free will: I lost the game while writing this.

So I typed out this poem. Apologies to anyone who can read; after 1.5 years at MIT, I consider poetry to be a list of junk in my suitcases with line indentations partially inspired by e.e. cummings* and partially inspired by Python code.

*By “e.e. cummings,” I mean “the Wikipedia entry on e.e. cummings.”

Unmachinewashable sweaters,
Unmachinewashable electronics (laptop, etc.),
A problem set for
8.07 sublimated by Maxwell Stress Tensor puns (I was tired that week, alright?
I just couldn’t feel any sympathy for
how stressed and tense the electromagnetic field was.),
A mechanical caterpillar,
Name-brand ketchup (Heinz) as well as a phonetic ripoff of name-brand ketchup (Hunt’s),
Van Gogh flipbook in which the artist cyclically loses and regains his ear if
you flip it forwards and backwards in sequence,
Stephen Hawking’s Universe (although he’s been asking for
it back. Not that I wanted it in the first place, considering how much entropy he put in it.),
Stamps, the kind that last for-
ever supposedly. (Stephen Hawking hates these stamps because they violate all sorts of
physical laws when they fall into black holes.),
Five bottles of free hand sanitizer, courtesy of H1N1.

(In a moment of face-slapping irony, I realized soonafter that my list of possessions does not in fact include a room at pika, thanks to technical details of the housing system. For the past week, I’ve been sleeping in the back of Ruth’s room, storing my unmachinewashable luggage in Dave GradStudent’s room without his knowledge/consent, and waking up every morning in gorgeous pools of sunlight that softy obliterate my aversion to homelessness.)

Between transferring addresses, splurging a weekend on Mystery Hunt, helping build a sounding rocket with an X-ray telescope (it’s going into outer space in 2011! As opposed to inner space, which is where mathematicians like to take dot products), cramming a 16-week class into 4 weeks, grading for the class that convinced me to major in Physics a year ago, not blogging, and sleeping five hours per night, I’ve been tossing a problem around in the liminal spaces between rational thought and crazy conjecture. I’m going to share it here, with the warning that it lurks around in a playground of optical physics and offers to give you plenty of brain candy if you follow it a bit further. (Don’t take candy from strange physics questions.)

A few weeks ago, my friend Aviv* went to see a certain movie and returned home with a pair of magical 3D glasses. They were magical not only because they’ll probably win an Academy Award for Best Inanimate Object in Cinema but also because of the strange way in which they filtered light. When Aviv looked in the mirror through his new glasses and closed his left** eye, he saw one lens of the glasses go dark while the other one remained transparent. Take a guess. Which lens was which?

*Aviv’s defining characteristics are (1) competence at both computer programming and roller-skating (he worked for Google and roller skates in Boston regularly without getting concussions) and (2) surviving on a diet consisting of only broccoli, strawberry yogurt, and chewy bars. Unrelatedly, the most bizarre thing that I’ve said to a mathematician recently was, “Did you know that if you cut up broccoli, you just end up with exponentially more broccoli than you had originally? That’s because broccoli is a fractal.”

**Left and right here will always be in reference to Aviv, not the mirror image of Aviv.

If you’ve read that 3D glasses usually work by polarization, the natural assumption is that the left lens went dark when Aviv closed his left eye. Imagine that the left lens is horizontally polarized while the right is vertically polarized. The light from Aviv’s closed (left) eye is horizontally polarized after it passes through the left lens, remains horizontally polarized when it bounces off the mirror at near-normal incidence, and gets completely blocked by the vertically-polarizing lens over Aviv’s open (right) eye. Thus, he doesn’t see any light from the area covered by the left lens of his glasses, whereas the vertically-polarized light from his right eye still gets through the vertically-polarized right lens.

Great! Problem solved. Now let’s go make a PBS special.

Except that exactly the opposite phenomenon happened. When Aviv closed his left eye, he saw the right lens go dark. That is, he could see his closed eye but couldn’t see his open eye in the mirror.

[EDIT: Just to be clear, I ruled out the possibility of the linear polarizing system described above as soon as he mentioned this. Avatar was released in three different 3D formats, according to Wikipedia, and two of them offer interesting solutions to Aviv’s question.]

After 15 minutes of Googling all possible combinations of “Avatar,” “3D glasses,” “what the heck, I thought I knew how light worked,” I stumbled upon a paper summarizing the technical specs of the Avatar glasses. (The discovery of this document is left as an exercise to the reader.) Quickly cobbling together a few scraps of peripheral 8.03 knowledge, I scribbled down a halfway decent explanation and went to bed. The next morning, I decided it was basically all wrong. Two hours later, I decided it could be workable with a few changes.

And then I decided that I simply needed more data.

Thus, gentle reader, I implore you to try the following tests and post your observations if you happen to have a pair of Avatar 3D glasses and a mirror within close reach:

1.Put on the glasses, look in the mirror, close one eye. Do you confirm Aviv’s observation?

2.Look at light reflecting off a surface at an angle of around 50-60 degrees from the normal. Close one eye. Close the other eye. Does the light disappear either way? If so, open the eye that doesn’t block the light, close the other eye, and tilt your head 90 degrees or until sufficiently uncomfortable. See if the intensity of light changes.

3.Repeat both of the above tests wearing the glasses backwards. (That is, face the outside of the glasses toward your eye.)

4.Repeat Test 1 with a reflective metal surface instead of a mirror.

In the meantime, I encourage you to comment here if you have an explanation. Scientific backing is appreciated but not necessary.

45 responses to “An Asymmetric Discussion of Shoes, the Process of Moving, and 3D Glasses”

  1. Yan says:

    @ Shawn:

    That’s certainly possible, since Avatar was released in 3 different 3D formats, according to Wikipedia. The IMAX version probably used linear polarizers. See:

    I’m going to guess that Aviv’s glasses were one of the other two types.

  2. Yan says:

    @ Michael:

    “But the right eye lens, which is vertically polarized, has no trouble seeing the vertically polarized light which bounced off of the left lens, then off of the mirror, and now has come through the right lens.”

    This means that the open eye sees the light that gets reflected off the other lens but not the light that is transmitted through the other lens (which has the wrong polarization after going through the filter). In this case, Aviv shouldn’t actually see his closed eye since it’s under the lens. (Instead, we expect him to see the glare off of the lens.) Similarly, he should also be able to see his right eye.

  3. Ahana says:

    The first time I saw Aviv, he was roller blading, so (1) is =). Add microwave fish-things to his diet, but I am sure he never really eats them.

    Why did you decide to move out of Random Hall, Yan? :(

    The polarization bit was very enjoyable!

  4. genius ('18) says:

    “Scientific backing is appreciated but not necessary.”-LOL Yan!! You never cease to amuse and amaze me. Excellent post as usual! That story about the 3D glasses seems really interesting. I would think it would have to probably do with the physiology (spell checked?) of the brain?

    BTW: speaking of “Scientific backing”, I got an interesting ReCaptcha: step provable!Recaptcha is so awesome!!!(Invented by an MIT grad- Do MIT grads invent everything awesome? Two of my best teachers are MIT grads! Betcha CalTech has nothing that can beat that!)

  5. @genius (’18): My reCaptcha=”case panaceas”. Fascinating…lol! Sounds like something every law enforcement officer and shipper/mover would love to have to solve their problems. Just curious, have you seen the NovaScienceNOW clip about the guy who invented reCaptchas? It was very cool smile I envy your two teachers from MIT; the only alumnus I know even vagely is my EC,who is actually a parent of a younger student at my school. Lucky person!

    PS When you sign your name as “genius(’18)”, does that mean that your estimated MIT graduation date would be 2018? (I don’t think it’s 1918, although that would be really funny…) That would place you in…7th-9th grades, barring acceleration? Awesome! :D Hope you end up at MIT. Good luck!

    (PPS Yes, you did spell “physiology” right. raspberry)

  6. Michael says:

    Very interesting. I’m pretty rusty on optics, but here’s my (probably-incorrect-but-works-for-me-for-now) explanation. (Yes, that is much worse than Green-Party-green).

    As the environment’s light bounces off the glasses (before bouncing off the mirror), a portion of it is not reflected towards the mirror due to the polarization of the lens. Let’s call this one-half. So one-half of the light goes directly to the eye through the polarization, the other half bounces off toward the mirror. Thus, when it comes back, it is polarized even further so that the lens itself (or its mirror reflection) is greatly darkened in respect to the lens’ eye. (Between one-quarter and zero, according to the one-half polarization I am assuming; again I’m rusty on optics here). So because the light is already polarized before being reflected towards the mirror (and back again), it is further reduced, thus the eye would hardly be able to see the lens in front of it.

    Therefore, the left eye can only (or mostly) see the right lens, and the right eye can only (or mostly) see the left lens. When Aviv closed his left eye, he could not then see the right lens, because only his left eye could see his right lens.

    As I think about it, if this is true, then the right eye should see the left lens as semi-dark, but not as dark as the left eye would see the left lens. I’m wondering, is this true? (I would check, but I don’t have any of the magic 3D glasses.

  7. Yan says:

    @ Michael:

    Just to clarify, are you still assuming that the lens are polarized perpendicular to each other?

  8. Vladimir says:

    I haven’t read the whole post (or all the comments), but it seems you are assuming they use linear polarization, which is incorrect. At least when I watched Avatar, they used RealD technology, which uses circular polarization.

  9. Yan says:

    @ Vladimir:

    Read the whole post, please. I entertain the possibility of but never assume that they use linear polarization.

  10. Sreyan says:

    @Yan: are the glasses you have circular or linear polarizers?

  11. Sreyan says:

    Sorry im posting again, but i dont have the glasses anymore, could you tell me what happens when you try closing one eye and tilting your head? if you tilt your head and the same phenomena holds true, then you have a circular polarizer, otherwise you have a linear polarizer.

    I think. raspberry O.o

  12. Michael says:

    @ Yan

    Yes, that’s what I was assuming. As an after-thought, I was considering mentioning that, but I didn’t really want to post twice in a row. But I was assuming that closing the left eye makes the right lens disappear, and vice versa. I was also assuming (as I think you did before you made the PBS special) that the left lens was horizontally polarized, and the right lens was vertically polarized.

    But I just did a little more reading and I think I could explain my idea better and with more correct physics terms. When light hits the left (horizontally-polarized) lens, it allows in (theoretically) only horizontally polarized waves, and what is reflected back off of the surface of the lens (or what light then goes toward the mirror) is only vertically polarized waves (those waves prevented from entering the eye initially). Therefore, when the waves hit the mirror and come back to the left eye, they are unable to pass through the horizontal polarization because they are not horizontal, they are vertical (which is why they didn’t make it through in the first place). But the right eye lens, which is vertically polarized, has no trouble seeing the vertically polarized light which bounced off of the left lens, then off of the mirror, and now has come through the right lens.

    To test this, I suppose you could try looking at a left lens of the glasses with a separate (but similar) pair of glasses on to see if the same held true, as it wouldn’t seem that the mirror would have too much of an effect on the angle of incidence.

    Anyway, that’s my theory, but like I said, I’m pretty rusty with physics, so I’m not expecting too much that I’m right. Maybe just food for thought.

    P.S. Thanks for creating some very interesting blog posts; they’re always fun to read.

  13. Sreyan says:

    There’s only one explanation to this that I can think of. There has to be an inversion in the plane of polarization when the light strikes the mirror. Thus, when the vertically polarized light from the left eye hits the mirror, it becomes horizontally polarized and the right eye has no difficulty in seeing the closed left eye. However when the horizontally polarized light leaves the right lens, it hits the mirror and becomes vertically polarized and obviously the light is obstructed and the right lens is the one which infact appears black.

    Whether or not an inversion in the plane of polarization of light occurs at the surface a mirror is unknown to me, but its the only logical explanation for whats happening.

  14. Gyncdrory says:

    This forum is alive? If yes, please remove this topic and my account.

  15. Anonymous says:

    great opening sentence. smile

  16. shawn '11 says:

    That’s weird. Over winter break my little brother had a couple pairs of 3D glass from Avatar laying around his room, so I decided to take that opportunity to teach him about optics. For part of this lesson I used a mirror and one of the glasses and I observed exactly what I expected–When I closed my left eye I saw my left eye go blank, so I could only see my open eye.

    …maybe we had different glasses?

  17. Yan says:

    @ s:

    Nope, I actually meant to write “daintily-shod.”

  18. Anonymous says:

    Mirrors can reverse the direction of circular polarization. The kids at Harvard figured that out…

  19. Anonymous says:

    I love your writing.

  20. Sreyan says:

    @Yan, have a look at this Youtube vid and find out whether you have a lens which uses circular polarization, if yes, then i guess that explains things…. smile
    I wish I could get hold of one of these glasses again, absolutely amazing stuff!
    Brilliant blog Yan! This problem’s got me gripped since yesterday!

  21. Yan says:

    @ Sreyan:

    Sadly, I don’t have a pair of 3D glasses either. Maybe I’ll go look for some tomorrow.

  22. Keri says:

    A few things:
    – I have a pair of the 3D glasses, if you’d like to borrow them.
    – I also own circular polarizer filters for my camera lenses.
    – As (I hope) anyone with the two would feel tempted to do, I decided to layer the two and rotate the filter.

    They’re definitely circular polarizers in the glasses. One’s positioned horizontally, the other vertically – at the very least, they’re 90 degrees out of phase with one another. I rotated the filter while over the left lens until all light was blocked from passing through, then moved it over to the right lens, where the maximal amount of light passed through the lens and filter.

    For reasons I can’t figure out or remember(?), though, everything is in shades of dark red and brown with the polarizing filter over the lenses of the glasses.

    That was fun. Now I want to go eat a sandwich or something.

  23. Sreyan says:

    @Keri, but as Yan said there are two or three different kinds of 3D Glasses being used for watching Avatar. However i guess only the circular polarizer fits the bill coz there has to a reversal in the plane of polarization.

    Problem solved i guess. =)

    my reCaptcha: “fractals the”

  24. Michael says:

    Light travels in waves, so that horizontal and vertical refer to how the tiny light particles move. It’s like a jumprope which can either wave (or snake) side-to-side or up-and-down. Since light particles are so small, you wouldn’t notice this movement with the unaided eye. But this is where polarizing lenses come into play; a polarizing lens will cancel out one of those patterns so that you only see the other.

    However in this case, the wave patterns are circular in motion (still a viable pattern with a jumprope wave model). The only difference is, instead of side-to-side and up-to-down, you have clockwise or counterclockwise. So while one lens deals with clockwise wave motion, the other deals with counterclockwise, and because they are opposite, you can have two different images (the left eye and the right eye, which gives you 3D/stereoscopic images).

    Because the light waves themselves, smaller than your eye can recognize, are moving either side-to-side, up-to-down, or circular (one direction or the other), the glasses will be able to handle the difference, but when you take them off you will just see normal light. It is essentially the same thing as normal light, just that the wave patterns are oriented in different ways, though the whole image itself as seen on the screen without the glasses, as you observed, does not appear sideways (just probably very fuzzy in parts). I hope that made some sense, Abishek, it was kind of a long explanation (my bad).

    The question I’m thinking about now is: how does the circular polarizing lens work specifically on these 3D glasses? Does it use birefringence only? Birefringence and linear polarization?

    Good way follow up to my response by asking another question. It got me looking at another level of depth which I had previously overlooked (about seeing the eye behind the lens). So thanks! And I see now why you asked about what type of polarization I was assuming.

    @Anonymous (who posted the “Harvard kids” link):
    Thanks for posting the link; it is a good explanation. The funny thing is, I’d actually thought of the same thing while driving home in the car, but when I got on eagerly to say something, you’d already posted nine minutes earlier. Also, I couldn’t help but feel like the whole “kids at Harvard” thing was a jab against MIT, so in the interest to quell any rival claims, I would like to note that the Harvard site actually references a 1968 Berkley text book for its explanation, and that beyond that one does not have to presume that it was even Berkley which had the original explanation. But thanks for pointing out the link =)

  25. Sreyan says:


    Note we are using circular polarizers here, your link provides an explanation on the working of linear polarizers. Using a linear polarizer, the intuitive case happens: With the left eye closed, in the mirror the right eye sees it self, but the left lens is black.

    It’s because we’re using circular polarizers that the plane of polarization reverses on reflection and the counterintuitive thing happens…

  26. Mario ('14?) says:

    Would mirrors be able to reverse the circular polarization of light? For example, if the polarization were ccw and cw for the lenses, would the ccw light hit the mirror and become cw polarized, sorta like how left hands “become” right hands?

  27. abhishek says:

    at sreyan:the intuitive case is indeed the blocking of left and right as you have said…but the mirror image is again laterally inverted….so the final effect is the one observed by yan.

    and if the glasses were circular polarized..that would mean of the 2 images projected on the screen in the movie hall, one would have to be horizontal and the other verical…which is clearly not the case if you take off the 3d glasses and view the images.

  28. Anonymous says:

    @abhishek: that is not how circular polarization works. the image never has to be horizontal or vertical, it has to be either VERTICALLY or HORIZONTALLY Polarized.

  29. s says:


  30. Interesting- all properties of light seeming abstranlansic after pre-inflationatory covergence; I wonder if this heads to the variable speed of light theory as a proponent of the “evoltuion” of light, and by extension, the omnipresent formation of a single unifying matter base, say something of a particle, which subserts even planck measurements and disects particle interaction on a partial-scale.

    I also wonder how I managed to make that all one grand-sentence….

  31. D says:

    So….I’m reading this post and the comments and pretending I understand what polarisation is. I only know what it implies but have not yet done an in-depth study of it. Anyone else like me?

    Anyway, Such new things make me even more impatient to get into college. I’m on vacation (I finished my finals in November) and cannot wait for the ‘busy’ college life. I’m also kinda tired of not exercising my brain as much as I think I should. And yet I have 7 more months of vacation ahead of me! Oh well.

    Recaptcha: activate Smith. LOL.

  32. Emily says:

    I’m not sure if it helps with anything, or if there’s an obvious explanation to it, but depending on which way you look through the glasses changes what you see through them. If you have two pairs of the glasses, (yes, I did manage to convince my friend to give me his glasses too) and hold them so both of the glasses are 90 degrees apart, you can still see through them fine (although everything looks a little bit blue). However if you face them towards each other and at 90 degrees they act like you would assume they would – one eye cancels out one eye and the other cancels out the other. But if you put the one facing away from you behind the one facing towards you, all of the eyes cancel out all of them!

    I think I’m going to go to sleep now. Maybe my brain will be able to comprehend this when it’s not midnight.

  33. Justin says:

    @Emily: Interesting. =)

    As we call it in Malaysia, this conversation in getting so ‘chim’! Anyway I don’t get it, honestly. It’s interesting, though, I might read on that sometime.

  34. yin says:


  35. C2 says:

    Wow… @ Yin… I am very surprise too!!
    Alright, here is what you needÔºö
    2-写2个考试 (第一个你可以选这3个其中一个:SAT Reasoning, ACT, TOEFL, 如果英语不太好就选TOEFL. 第2个是必要的:数学1级或2级,和科学科的其中一门:物理,化学,生物,哪个都可以。在这个网页可以有比较仔细的说明:在那里报名考试等等


    Wow… you have no idea how long it took for me to type this up…

    I am going to buy my rubber boots today =D , hopefully, they can get me into MIT.

    VERIFICATION: aura sentences

  36. c2 says:

    @ yin

    How do you type Chinese in this website, I tried to help you and typed a whole bunch of instructions… then I don’t think it was accepted… Hope they don’t think I am trying to post anything bad…

    Well, on the other hand, I should get some rubber boots and hopefully they can help me get into MIT…

  37. Yan says:

    @ D:

    No worries. I probably didn’t know what electricity was before coming to MIT. I’m too tired at the moment to attempt to explain polarization, so let’s ask Mr. Feynman about it:

    @ cd:

    Comment approved!

  38. Winnie says:

    I learn so much from MIT blogs 8D I knew I should have taken my 3d glasses out of the cinema…

  39. Ammar'14 says:

    It’s been a really long time since I last worked out a real-life physics problem, thanks for reminding me of the wonderful feeling of the challenge!

    I think you should be more careful with what you post here, I’m pretty sure the sales on waterproof shoes worldwide have raised dramatically since you posted this.
    Sort of how Randall Munroe of xkcd can hijack whole advirtising campagins and bring hundreds of people from around the nation to a location of his choosing with a well-placed comic.

  40. C2 says:


    YAY, thanks =D Hope that was helpful…

    And… it is C2 (not cd T-T)… BTW, this is the second time.. =O

    That was a funny comment, xD. Nice one, because that could actually happen~!

  41. Festering says:

    Hmm. Both the lenses are dark when I wore mine. How odd.

  42. Festering says:

    Please disregard my previous comment. I was being pranked.