It occurred to me recently that the last time I bought a movie ticket was four months ago. After going through a chronological list of major film releases, I am pretty sure that I have not gone this long between movies since 2012. Here are the release months for films that I saw in various years. The maximum span here seems to be three.
An obvious problem with this list is that it is easy to watch a film one or two months after its release. If this had happened with the April 2013 film for example, then that would be an example of another four month gap. However, in this case, I happen to remember that I saw Iron Man 3 right when it came out. Another shortcoming is that the list omits movies that I saw in airplanes, people's houses or rented out venues. The latter type of cinema is something I have actually attended multiple times in 2017.
Four months instead of three is not much of an outlier. So I cannot really say whether this marks a sudden change in my interests. However, I can certainly mention two movies that I actively avoided.
If you're in the habit of searching Google for things that have to do with your favourite TV show, you may have come across an entire wiki devoted to it. Wikipedia certainly has its own articles about fictional universes but the fan wikis are supposed to report on them in a much more detailed and obsessive way. Even though you sometimes see them on Wikipedia, detailed descriptions of every scene in a movie are unencyclopedic. These belong on the fan wikis because "merely being true, or even verifiable, does not automatically make something suitable for inclusion" as stated in the relevant Wikipedia policy.
Most of these fan wikis are hosted on Wikia, a for-profit site that used to have the same look and feel as Wikipedia. By now, the look and feel has drastically diverged. Even though it still uses the same software, Wikia has been dumbed down and uses gimmicks like floating bars that follow you as you scroll down the page. However, I still use the site a great deal because the amount of information on it is truly vast. What I want to do now is explain the differences between the two interfaces and then give some ideas for wikis that haven't been created yet.
Lines drawn on a curved surface can be tricky. Consider one of the most basic facts about Euclidean geometry: that parallel lines never intersect. This does not hold on the surface of the Earth. If you and a friend stand one metre apart in some location on the Earth, you could both try drawing a line and heading due north. The lines would appear to be parallel during all stages of the journey but you would eventually find that they intersect at the North Pole. An observer watching from space would say that the lines don't look parallel but any measurement you could make without leaving the Earth would tell you that they are. This is because a sphere is locally flat. The fact that the lines cross can therefore be used to prove that the world is round. Similarly, measurements done in three dimensional space, might be able to prove things like that about the universe.
Now it's not just parallel lines that we have to worry about. If space were not flat, circle areas would appear to differ from and the sum of the angles in a triangle would appear to differ from . There is a wonderful formalism for doing calculus with lines drawn on a curved surface and there are two contexts in which people normally learn it. One is navigation and the other is general relativity. I want to take a shot at explaining it in the context of the two ant problem. This requires us to find the shortest distance between two points on a curved surface and prove it is the shortest. So if I hadn't already solved the problem, it might seem appropriate to use the techniques that were historically used to prove that a straight line is the shortest path between two points in flat space and that a great circle is the shortest path between two points on a sphere.
I never turn down a chance to be a smart-ass. One of the best things higher mathematics can teach you is how to go back and correct almost everyone who claimed to be teaching you math. It's almost impossible to a cover a decent amount of material in a math course without sacrificing correctness. This is true in grade school when you learn tons of stuff that isn't real math and it is true in grad school when writing one proof that is perfectly rigorous takes two weeks. Here are some common questions that need to be rephrased before they make any sense. The links point to where I found the questions but they could've come from anywhere. If they look like they were taken straight out of your high school calculus textbook, they probably were.
I've been remembering a lot of my dreams this month and in the spirit of full disclosure, I will tell you about them in all their random details! But first some fun facts. Humans dream during REM sleep, named after its "rapid eye movement", the stage of sleep most closely resembling wakeful neural activity. Various theories have been proposed for the regenerative functionality of REM sleep. Indeed, sleep deprived individuals and people trying out polyphasic sleep get less REM sleep, as the body favours the deeper stages in those circumstances. The image below, called a hypnogram, shows how the stages normally occur.
There are four or five cycles of REM sleep and they last for longer and longer amounts of time until the person wakes up. Movement of the eyes is presumably related to the fact that someone in a dream state feels mentally alert. I suppose the reason for the entire body not moving is the protection mechanism you hear about - where the body is physiologically immobilized during sleep. Even though this is supposed to wear off quickly upon regaining consciousness, some people report "glitches" where they wake up in total paralysis for several minutes. This has never happened to me but I think it would be really cool!