hurricane preparedness

A few days ago, Yasha told us that there was going to be a hurricane: we'd likely lose electricity, and there might be flooding.
Mitka:  "But why didn't we know about this before now?"
Yasha:  "Because we live under a rock."

me:  "There's nothing to do to prepare for loss of electricity, right?  We should get flashlights or something?  Oh, you probably have flashlights already, because you have everything.  Do you have batteries, too?"
Yasha:  "Yeah.  All my batteries are currently in my lasers."

Today, Mitka did some homework with classmates.
Mitka:  "Harvard's closed tomorrow, so there's no class and Eric and I might get together and do some work."
me:  "If Harvard's closed tomorrow, that probably means it won't be pleasant to walk outside."
Mitka:  "What?  No.  They're probably closed because they'll lose electricity.  And the professors have to drive to campus."
me:  "If people can't drive to campus, you probably won't want to walk.  I mean, in the snow it's fine to walk even when it's not safe to drive---not while the snow is actually falling, but afterward---but..."
Mitka:  "It's not snow.  It's just water."
me:  "Right.  Exactly."

Mitka went to Whole Foods to buy "water and batteries and stuff".
me:  "We decided we'd fill pots with water, remember?  The thing you were actually supposed to buy is cereal."
Mitka:  "But we might not have pots.  I think I'll buy some water anyway."
me:  "We might not have pots?  How would we not have pots?"
Mitka:  "I meant we might not have enough pots."

Mitka:  "Don't forget to move the violin upstairs."
me:  "I just did."
Mitka:  "Oh, okay."
me:  "I mean, during this conversation."

Mitka:  "You know, if there's flooding, your mattress is on the floor."
me:  "Oh.  That's true, I didn't think of that.  I thought, 'Oh, the only valuable thing we have downstairs is the violin.'  But the mattress cost a lot of money, and it's directly on the floor."
Mitka:  "I have a cover thing that might help keep it dry."
me:  "No, I don't think that will help much."
Mitka:  "We can try dragging it upstairs later."

I went to Whole Foods with him, to help carry stuff.  We got one gallon of water, lots and lots of juice, some fruit, cereal, bread, and cheese.  In the checkout line, I loaded juice into my backpack.
me:  "You're buying... a dry salami?  But you don't normally buy salami."
Mitka:  "Yeah.  So we don't starve.  A hurricane is a good excuse."

When we got outside, Mitka remembered that he'd meant to buy toilet paper---we only had one roll left.  The RiteAid was closed.
Mitka:  "Do you want to go back to Whole Foods?  Or we could go to CVS or something."
me:  "I don't really feel like doing anything."
Mitka:  "Okay, but if the stores are out for a week, toilet paper is something we really wouldn't want to run out of."
me:  "That's true."

Mitka:  "We might not have internet tomorrow!  How are we ever going to entertain ourselves?"
me:  "Oh, maybe I should go get my books from my office."

We got home, and MIT had sent a notice.
me:  "MIT is closed tomorrow.  I think I'm gonna go get my books."
Mitka:  "They're not locked, are they?"
me:  "No, no.  They're closed, and I don't expect to go to campus tomorrow, and it'll probably be raining anyway.  I'll just go now and get my books."
Mitka:  "Do you want to borrow my bike?"
me:  "No."
I went up and put my shoes on.
me:  "Okay, bye.  Oh, I'll also get toilet paper."

Decorating!

Some days ago, I mentioned that when I'm older, I might have multiple rooms that are mine. (One can dream, I know.) Hannah said that she didn't find having one's own space to be particularly valuable. I countered, saying that I find it nice to be able to set up my room the way I like it so it is comfy to be there. Hannah said that she doesn't really get anything out of being able to control a space, though she conceded that she does need a space where she can be without anyone else. I suggested that then she wouldn't mind me decorating her room. She declined.

A few days later, Hannah decided that she will decorate her room herself. She did this by printing out a 3 foot by 3 foot photo of her general life advisor on twelve sheets of paper and putting it up on her wall.  I found this to be hilarious, but it made Mitka uncomfortable because having large portraits of revered figures gave him unpleasant associations.

His own room is decorated with artworks, some of them just printed out, and some of them more fancy. Mine has a three-panel painting of Venice, a poster I got with my admission to MIT for undergrad that I kept around for four years, a clock made out of a video card, a calendar, and a large collection of trinkets, pictured below.

Hölder and rural

First I mentioned that my advisor, being German, has a pristine pronunciation of the name Hölder.  Later, Yasha was having trouble saying the word rural.  He kept saying rural over and over because it wasn't working, and I said rural over and over to demonstrate how it was done, and then I started saying Hölder over and over.  Mitka pointed out that rural and Hölder have mostly the same sounds.  Yasha concluded that rural should have only one syllable, and if he just rhymes it with the word curl, it works out fine.

Sunsets at the Beach and Streetlights in Windshields

Some time ago, Hannah asked me if I knew the explanation of the effect one sometimes sees while driving at night, where streetlights look like they have rays of light emanating from them in two opposite directions, which rotate as you drive by. I didn't know, but, after a conversation, we decided that it's very related to the phenomenon that causes the reflection of the sun in the ocean at the beach to look like a path of light heading out to the horizon rather than a small circle of light like one would expect from a mirror.

The thought is that the ocean is choppy rather than flat, and so the surface of the water is often tilted away from the horizontal, up to some maximal angle that depends on how big the waves are. The sun is way brighter that anything else that the ocean might reflect, so, even if only a small portion of the light hitting your eye from a particular point came from the sun, it will drown out any other stuff reflected from there.

If the ocean were flat, there would be some point in the water where light from the sun would bounce off and hit your eye, so you'd see the reflection of the sun there. However, if you move that point in the water either towards the sun or towards you, it doesn't take a very big change in the angle of the water to compensate for the change to ensure that light from the sun still hits you after bouncing off. Since the ocean is choppy, we can expect there to be a little piece of water surface somewhere around there at the right angle to do that for you. It helps that the sun is a reasonably sized disk, so there's some room for error. So, we can expect to see a bright path in the water heading from you towards the sun.

OK, but why don't we see a reflection of the sun everywhere else, too? The problem is that, as you move the point in the water to the side, the angle of the water needed to bounce that light back to you quickly becomes quite large. When that angle becomes larger than the maximal angle of the waves, you stop seeing a reflection of the sun. So, you'd expect the path of the light to be fairly narrow, though it would get wider with a choppier ocean, and also it would get a bit wider near the point of "true" reflection.

So, what's this have to do with windshields? Well, light entering glass gets bent according to Snell's Law. When the two sides of the glass are flat and parallel, like in a windshield, once the light leaves the glass, it gets bent back to the same direction it was originally going. (A lens, on the other hand, exploits having the two sides of the glass be at angles to each other in order to make a net change in the direction of the light.) However, nothing is perfectly smooth and flat, and so some light will hit an imperfection in the surface of the glass where the surface is at a slightly different angle.

Like with the ocean, we can assume that there's a maximum angle of the imperfections in the glass. The details of the double-refraction are different, but the result is the same as with the ocean: after going through the glass, the light will be off by at most a small angle from where it is "supposed to" go. In fact, if we turn the ocean into glass and turn the sun into a streetlight that is below the surface rather than above it, we should see the same "path of light" effect that we see at the beach, though with a thinner path since the glass is less "choppy" than the water.

The only problem left is that the ocean is horizontal, whereas (unless you're very bad at driving) a car's windshield is not, and it's a bit tricky to do 3D rotations in your head to convert one to the other. Fortunately, there's a convenient trick for figuring out which direction to expect the line of light to point. At the beach, the path of light follows the line joining your feet to the point in the water where you'd expect to see the "true" reflection of the sun. You can think of your feet as a magical solar light path attractor: The path of light from the sun will point towards your feet wherever you go.

With a car windshield, we can do the same thing. Instead of your feet, you need to imagine a line from your eye that is perpendicular to the windshield. Since windshields are tilted, this line will go upwards and forwards from your eye and probably hit the plane of the windshield above the actual windshield itself. That point is your magical streetlight line of light attractor: You can expect that the line of light from the streetlight will stay pointed towards your magical line of light attractor as you drive by.

Now, being a theorist, I haven't actually gone out and verified that the direction of the line of light is as I described. I'd be curious to hear if folks see it.

Playing Soccer, with applications to Being Yourself

Some days ago, Hannah commented on the uselessness of the suggestion, "Just be yourself," since it's not like you were considering an alternative.

I figured that, a lot of time, "Just be yourself" falls into the same category as "I'm sure everything will turn out fine" and associated conversation-ending platitudes that secretly mean, "I support you, but I don't really feel like listening to you talk about your problems right now." Naturally, it would feel frustrating to hear that, particularly since there's a bit of hypocrisy in talking like you support someone without actually doing anything to support them. However, I also feel that, on occasion, "Just be yourself" can be meaningful advice.

In a cool paper, folks were asked to do a soccer drill either while paying attention to what they were doing, or while being asked to simultaneously do a distracting task. As one might expect, the novices did best when they focused on the soccer drill. However, surprisingly, the experienced players did better when they had to do a second task at the same time, but only when using their dominant foot.

The mechanism suggested in the paper is that, as people practice a skill, it becomes an unconscious "automated" process. For experts, focused attention on the task interferes with this unconscious process, hurting performance.

Extrapolating wildly from this study, I'd argue that we are experts at tasks like talking or behaving appropriately in social situations (despite plenty of entertaining evidence to the contrary), and so focused attention can likewise be counterproductive.

For example, focusing on impressing someone could lead to bragging, and thereby have the opposite effect. On the other hand, attention is useful when trying to behave in a new manner: For example, a novice at giving lectures might benefit from paying attention to their talking speed. The phrase "Just be yourself" could then be a way of saying, "You're more like an expert than a novice at this particular task, so paying attention to your behavior is more likely to hurt you than to help."