Interesting Stuff

I have some wild rice. The instructions on it say to boil some water in a saucepan, stir in the rice, cover, reduce heat to a simmer, and wait a while. When I stir the rice into the boiling water, I also stir in some butter and a spice mix (sugar, powdered soy sauce, onion, sesame seeds, garlic, and some other stuff). I mix everything thoroughly, cover it (so I can’t see what happens), reduce the heat, and wait.

When the rice is done, I uncover it, and all the sesame seeds are in a ring around the edge of the pan. The ring is maybe an inch thick; the pan is about 8 inches in diameter. The butter and sugar are mixed throughout and not clustered in any place, but the other spices, like the sesame seeds, seem to be in higher concentrations in the ring and lower concentrations in the center of the pan. I have a gas-powered stove, if that makes a difference.

Why does this happen?

Suppose you could create the specification for your ideal programming language. It must be possible to implement (it can’t solve undecidable problems, etc), but other than that the sky’s the limit. What would you put in it (what kind of syntax, intrinsics, etc)? For what sort of applications would it be used? What other features would it have? Would the interpreter/compiler do anything unusual? Tell me anything you want about your ideal language and the tools that go with it. You’re welcome to answer some of these questions if you don’t have answers to all of them.

I’ve been asking variations of this question to all sorts of people, and it’s fascinating seeing where they agree and where they don’t.

A coworker and I were having a discussion about general relativity, and wandered down a tangent in which our understandings of the universe differed. We both agree that each others’ explanations are plausible without any hard data against which to test predictions (and we didn’t have real data to back up any of our claims). Does anyone want to weigh in on this debate? Have cosmologists considered this idea and come to a conclusion one way or the other?

Is space itself expanding, or are the things in space just moving away from each other? →

Define a “hub” to be a vertex that shares an edge with every other vertex (such as the middle of a star graph, or any vertex in a complete graph). Suppose we have the adjacency matrix of an undirected, unweighted graph with V vertices (so our input has size V^2). Find an algorithm with running time o(V^2) that can determine whether a hub exists in the graph, or prove that no such algorithm exists. Note the use of little-o notation: the algorithm must be asymptotically faster than (big) O(V^2).

My bet is that no such algorithm exists, but I can’t figure out how to prove it.

I’ll be at Mudd tomorrow, btw.

1. My can of soup says to put in a bowl, cover loosely, microwave, and then let stand for a minute. I do all of this in a plastic bowl with a flimsy plastic lid that can be sealed shut (but I don’t seal it). When I take the soup out of the microwave, the lid is not only sealed on, but bowed in from lack of pressure (lack of atmosphere?) inside the bowl. The soup is still hot (I don’t think it has cooled much). What’s going on?
2. My shower has a smooth, clear, glass door. When I shower, the water covers it with a smooth, even layer, so I can still see out pretty clearly. When I touch my finger to the glass, the water “runs away” from my finger and leaves the glass nearly dry in the vicinity. This is so strong that the water will actually flow up to “escape” my finger’s vicinity. New drops of water that hit the glass while my finger is touching it also move away (though at a slower pace, since they can’t flow as easily without more water around). When I remove my finger, the film of water returns to the way it was before. This isn’t dependent on something I’ve put on my finger; it works with all 10 fingers/thumbs, both elbows, my tongue, and at least one toe. I don’t have a water softener. What is happening?
3. Galileo showed that all objects fall at the same rate, no matter how much they weigh. I have a bowl full of Cheerios and put some raisins on top. The Cheerios and raisins are about the same size, but the raisins are denser. I put my hand over the top of the bowl and shake it. I would expect all objects in the bowl to fall at the same rate when I shake, and keep the raisins on top. Instead, they gradually migrate towards the bottom. What’s going on?
4. There is a doorway with the sun shining through it onto a wall (with the shadow of the doorframe on the wall). I stand several feet in front of the door so that the side of my shadow nearly touches the side of the door’s shadow. The part of my shadow closest to the door’s is mirrored, so it appears that the side of my arm is coming out of the doorframe. This occurs even if I move around slightly (it appears as though the door’s arm is moving in the opposite direction). The shadows need to be within a couple inches of each other to get this to work. What is going on?

The world is a strange and fascinating place.