Homework, Coffee, Settlers of Catan, and Color-Coded Stuff: A Tale of a Night When I Didn’t Sleep

Leave a comment

9:39 PM

Cups of coffee: 0

M&Ms: 0

Homework done: None

Games of Catan: 0

 

The pattern is now familiar. I make a list of homework and a plan of attack, I get some M&Ms and make some coffee, and I sit down in front of my computer to document my sleepless night by writing random and rambling things about it, which shall then appear on my blog for all the world to see. Generally, these all-nighter chronicles begin with a remark that I wasn’t expecting to need to do this. That is certainly the case in this situation; I really thought that this semester wouldn’t call for any all-nighters. Academically, this is the lightest semester I’ve ever had. But around midterms, there’s no such thing as an academically light semester.

To be honest, this all-nighter probably isn’t necessary. I think that I could be ready to call it a night by about two O’clock or so. That’s really late for me, but it is much less drastic than pulling an all-nighter, especially since I don’t even need to be up at a reasonable time tomorrow. This semester, I only have morning classes on Mondays and Wednesdays, and tomorrow is a Tuesday. I prefer to be up at a reasonable time anyway, but I could make an exception to that habit if I felt it was necessary.

But, after giving the matter due consideration, I decided to pull an all-nighter. That way, I have all the time I need and don’t have to feel stressed about finishing by a certain time. Besides, it gives me an excuse to eat M&Ms, and it makes it possible for me to take the time for Catan breaks. Anyone who has been reading my blog regularly may have noticed a bit of a pattern lately, which is that I have a tendency to mention Catan quite frequently.

 

I didn't win. Life is tough.

I didn’t win. Life is tough.

11:26 PM

Cups of coffee: 1

M&Ms: 10 blue, 7 red, 3 yellow, 3 brown, 8 green, 8 orange

Homework done: All of my calculus homework and one single-spaced page of a paper that shall be double-spaced later

Games of Catan: 1. I lost. It wasn’t fair. I totally should have won.

 

I would say that I was making pretty good time, except that I’m supposed to have three pages of this paper done by midnight. That is, I’m supposed to submit a three-page draft online. Three pages really isn’t a big deal, especially because this draft isn’t going to be graded. The professor is just having us submit it to make sure that we actually have that much done. Originally, the paper was going to be due tonight, but now it’s due on Wednesday instead. Compared to certain papers from last semester, this will be quick and easy; it’s basically a paper on a project that was already presented in class today. But I’m a very slow writer. For me, any paper is a long paper. That’s a little ironic, considering just how much writing I do, even outside of schoolwork. I’m also very slow at math. I’m slightly proud of myself for being done with my calculus homework for tonight, even though it was a pretty easy homework assignment. It was on the partial derivative. Partial derivatives are pretty simple. Incidentally, I really don’t seem to have many yellow M&Ms here. That’s a little odd.

 

11:57 PM

Cups of coffee: Still just one

M&Ms:  12 blue, 9 red, 4 yellow, 3 brown, 9 green, 9 orange

Homework done: All of my calculus and that draft of that paper

Games of Catan: Still just one. I still think I should have won.

 

An incredible and very good thing as happened. As I logged onto the thingy to submit my paper draft, nothing went wrong. This is rare indeed. My college’s internet system doesn’t like me; whenever I try to log into something that’s through the college, it won’t accept my password the first few times I try. Sometimes, I keep on trying over and over and over and never even get in because it eventually blocks my access because of so many failed attempts to enter the password. This is extremely frustrating. But it didn’t happen tonight, which is good because I submitted that draft at 11:54, which was cutting it pretty close. The uncool part is that it’s a pretty lousy draft, but that’s not a big problem. I still have two days to finish it and clean it up, and I’ll probably be able to dedicate a significant portion of tonight to it. But I do have to concentrate on my algebra homework for tomorrow first.

 

Here's why the number of green M&Ms isn't a whole number.

Here’s why the number of green M&Ms isn’t a whole number.

1:57 AM

Cups of coffee: one and a half

M&Ms: 21 blue, 10 red, 8 yellow, 4 brown, 12 ½ green, 10 orange

Homework done: All of my calculus, that draft of that paper, and practically all of the computer assignment for linear algebra

Games of Catan: Just one. I really want to play another one now, but it isn’t time yet, according to my detailed plan for tonight.

 

Normally, whether I’m staying up all night or just staying up really late, I don’t actually leave my room in the middle of the night. Tonight was an exception, though, because the aforementioned computer assignment for linear algebra required a computer program that I can only use on the computers in the math building. So I headed over there a little after midnight and spent about an hour and a half on that assignment. It was weird being outside at that time of night; for once, it was quiet. There were a few people in the math building, because that happens to be a favorite late-night-studying place and all-nighter place. The assignment in question was actually pretty cool; it had to do with ciphering. I made a slight mistake on a cipher that I was supposed to be deciphering, so it came out correct except for one word in the middle, which said ‘rMOk’. This amused me greatly. But I redid the exercise anyway, and it came out with real words that time. I couldn’t quite figure out how to do the last exercise, though, so I’ll have to do that one later. I’ll probably do it right before class, because that’s the only way I’ll have a chance to ask the professor about it.

 

3:08 AM

Cups of coffee: Two and a half

M&Ms: 31 blue, 14 red, 14 yellow, 14 brown, 22 ½ green, 18 orange

Homework done: All of my calculus, the draft for that paper, almost all of that algebra assignment, and the reading for my postmodernism class on Wednesday

Games of Catan: Still just one. But the time for game number two is near at hand. First, I have some algebra homework to do, but Catan is next after that.

 

Colored index cardsThere are five greatly awesome things that are within inches of my hands right now, all of which I have used quite a bit within the past few hours. The list is as follows: coffee, M&Ms, colored index cards, sharpies, and dry erase boards. A few minutes ago, I was surprised and confused to discover that my fingers were speckled, but a moment’s reflection enabled me to realize that this was because I had been using my fingers to erase numbers off of my dry erase board in order to replace them with other numbers. I love using dry erase boards to keep track of random and inconsequential details of my life. ‘Tis an entertaining thing to do. The appeal of colored index cards and sharpies, of course, is that they allow you to color code stuff, and color coded stuff is automatically cooler than non-color coded stuff. As a matter of fact, this point also can be extended to explain the coolness of M&Ms, and to relate to my interest in keeping track of M&M colors on my dry erase board. But coffee isn’t colorful. The coolness of coffee is independent of its visual appearance. Maybe someone should invent colored color-coded coffee. By definition, that would be incredibly cool, but I can’t actually think of a good purpose for it. I’ll have to think about this.

 

4:06 AM

Cups of coffee: Two and a half

M&Ms: 31 blue, 18 red, 14 yellow, 15 blue, 26 ½ green, 19 orange

Homework done: See above, plus just a couple algebra problems. But those couple that I did took a really, really long time.

Games of Catan: Two and a half. The website’s down, so that last game was aborted. That’s okay; it was making me really mad because I was losing really badly because nobody was rolling fours, sixes, eights, or nines, which just shouldn’t happen. People were basically just rolling tens every single time, which was very much in orange’s favor and did me no good at all. It was really unfair, especially since I had had a very similar problem in the previous game. Sometimes I wonder if other people have discovered ways to rig the dice on internet board games. It seems feasible, since those are just imaginary dice anyway. Presumably, if someone was really good with computers, they could figure out a way to trick the system. I’m not necessarily saying that’s what happens, I’m just saying that it sure seems like it.

 

101_9851Aside from the Catan problems which I have lamented in the previous paragraph, I’m also frustrated that this algebra homework isn’t going well. I still have several hours before class, but I don’t want to spend that entire time on this one homework assignment. At the rate I’m going, that’s how long it’ll take.

The weird thing is that it’s almost morning now, and it really doesn’t feel like it’s been that long since I got back from dance class at around eight O’clock. It’s no wonder I always feel tired; apparently nights go faster than days, and so one doesn’t get a lot of sleep by sleeping through the night. But it wouldn’t be any better to sleep during the day, since I have just determined that nights aren’t long enough for doing homework.

The only solution I can think of is that days just need to be longer. Since the length of a day is determined by the amount of time it takes the Earth to revolve around its axis, we just need to slow the Earth’s rotation. I wonder what kind of an impact this would have on the Earth’s climate. Of course, in order to minimize these effects, it is important that the Earth’s orbit around the sun should not be changed at all. I think years are a pretty good length.

Although it would be nice if the number of days in a year was something a little nicer than 365 ¼. That’s such a random number. I would like to suggest 350. That’s close enough to the current year length that it wouldn’t make a big difference, but it’s easier to remember and it has more factors than 365 or 366. We could divide the 350-day year into ten months of 35 days each, which I think is a lovely length for a month to be, and ten is a nice number of months. And there will be exactly 50 weeks in a year, which would be convenient. It would also mean that holidays and birthdays would fall on the same day of the week every year, which is an appealing idea and would make it very easy to keep holiday traditions the same from year to year. And Advent would always be the same length, so Advent calendars could actually be Advent calendars instead of December calendars that call themselves Advent calendars.

It would seem that I don’t feel like returning to my algebra homework.

 

Between various math problems, you can see my M&M statistics.

Between various math problems, you can see my M&M statistics.

5:08 AM

Cups of coffee: Three and a half. Now my coffee is gone, but that’s okay, because I’ll be able to go and get some more from the cafeteria in just a couple hours. It is worth noting that, on days when I sleep, I hardly ever drink more than one cup of coffee.

M&Ms: 43 blue, 22 red, 19 yellow, 24 brown, 38 ½ green, 26 orange. This is a final count; my M&Ms are now gone.

Homework done: All I have accomplished since the last update was another couple paragraphs on that paper.

Games of Catan: Two and a half.

 

It’s still dark and will be for a while, but I hear birds singing. Some people on campus complain about how loud the birds are, and I am puzzled by their annoyance. Personally, I don’t mind the birds nearly as much as I mind the leafblowers and lawn mowers, which are also noises that one hears almost constantly on this campus, and frequently right under one’s window when one is trying to do homework.

I think I’m going to go take a shower now. After that, I have to get back to my algebra homework, and then I’m allowed to take a break to check tumblr.

 

6:26 AM

Cups of coffee: Still at three and a half.

Homework done: See above, plus a couple more algebra problems.

Games of Catan: Still at two and a half.

 

I actually didn’t take a shower shortly after five, like I said I would, because my roommate was in the shower. In my residence hall, we have suites, and each suite has its own shower. I definitely prefer that to a communal bathroom, but it’s more than a little annoying hearing water running when I’m trying to do homework. It’s weird how some noises, like showers and squeaky doors, drive me crazy, while other noises, like ticking clocks and the strangely loud hum of my desk light, don’t bother or distract me at all.

Right now, I’m a little annoyed at the world in general for the fact that it’s morning. I don’t know where all the time went last night. I was expecting that I’d get more done. Now I still have homework to finish and stuff to study for midterm exams later this week, but I have lost the quiet and solitude that the nighttime offers.

 

7:34 AM

Cups of coffee: A little more than three and a half. I just came back from breakfast in the cafeteria, and I brought back a cup of coffee with me. Coffee is good stuff.

Homework done: None since I last gave an update, actually. Unless I’ve done a couple algebra problems since then. I can’t remember how many I’d done before that point. I’m still less than halfway done with what I have due today.

Games of Catan: Two and a half

 

This is what one of my dry erase boards looked like by morning.

This is what one of my dry erase boards looked like by morning.

Today’s sunrise was disappointingly nonspectacular, but that’s okay, because now that the sun’s up, it’s a really beautiful day. Maybe it’s a bit chilly, but it’ll probably be really nice in a few hours.

Next on my agenda is the game I like to play where I use a random number generator to get twenty random digits and then try to memorize them in under a minute. Lately, I’ve only been doing this once a day. I’m on a good streak now, though. I’ve gotten a perfect score four out of the last five times. This may not be an achievement that means anything to anyone besides me, but I am rather proud of it. I just hope I can keep this streak going. Considering the fact that I haven’t sleep in over a day and I’m dead tired, my brain might not be at its best this morning, though.

I really wish I was playing Settlers of Catan right now. And I really wish I was winning.

 

9:13 AM

Cups of coffee: Four and a half

Homework done: More algebra, but I’m still not done with today’s assignment yet. I am actually making progress; it just really takes that long. Seriously, math is hard.

Games of Catan: Two and a half. But I’m getting close to my next Catan break. This excites me greatly.

 

Here is a picture of outside, despite the fact that the picture doesn't look as pretty as it really is.

Here is a picture of outside, despite the fact that the picture doesn’t look as pretty as it really is.

I just opened my window. It’s so ridiculously beautiful out there today. The thing about Alabama is that you never know from one minute to the next what the weather is going to be like. On Sunday, it was nice like this, but yesterday, it was gloomy and wet and rainy and just really ugly. But then it suddenly cleared up in the middle of dance class, very shortly before it got dark. And last night it was pretty chilly. As clear as the weather is now, there’s no telling whether it’ll rain again. For all I know, it could snow tomorrow.

I’m trying to remember what I normally write in my all-nighter blog posts. I seem to recall that they aren’t normally about the weather, but right now, the weather seems to be the most noteworthy thing. I tried to take a beautiful picture from my window so that I could show the beautiful weather, but it didn’t turn out looking very beautiful because most of the trees still don’t have leaves yet. I’m guessing that will happen soon.

 

10:28 AM

Cups of coffee: I’ve stopped at four and a half.

Homework: A couple more algebra problems

 

CatanOkay, I admit it, I just played several consecutive games of Catan; I don’t even know how many because I lost count. Most of those games were ridiculously short because one person got all the luck and won before I’d even had a chance to do anything. It was getting quite frustrating. I mean, here I’ve been awake all night, working long and hard in an effort to learn stuff. I feel like the universe at least owes me a few lucky rolls. So I just kept playing until I finally won.

And now, here’s what I’m going to do: I’m going to put this on my blog, then I’m going to finish my algebra homework (which is finally almost done), and by then, it’ll probably be about time for me to get all my books and stuff together, go to the cafeteria for lunch, check my mailbox quickly, and then head off to math class.

 

 

Advertisements

Simultaneity Is Relative

3 Comments

HomeworkToday was the last day of January term, and the course I finished just a few hours ago was about relativity and spacetime and Einstein and physics and stuff. I took this class for two reasons: first, because I am interested in physics to some extent, even though I’m really much more of a literature- and-writing person than a math-and-science person, and second, because it would be cool to actually know what I’m saying when I start talking about the spacetime continuum and making up crazy science fiction theories. I’m not sure that this class has caused revolutionary developments in my science fiction ideas, but I definitely have gotten stuff out of it, and it’s cool that I can now say that I understand the concepts of Einstein’s relativity. Because of the coolness of these topics, I now present a summarized list of stuff I have learned.

1. Aristotle’s observations of gravity led him to believe that each of the four elements (earth, air, water, and fire) had a different natural tendency and that the tendency of any object was determined by its proportion of the elements. Earth is heaviest and its tendency is to fall. Water also has a tendency to fall, but it’s lighter than earth, so anything that contains a lot of the earth element will sink beneath the surface of the water. Air is light, so its tendency is to rise above earth and water. Fire is the lightest, and so it will rise even above air. Of course, according to Aristotle, every substance familiar to us is a combination of the four elements. For example, dirt is not pure earth; it just contains a much larger quantity of the element earth than any of the other elements. It is also worth noting that Aristotle believed in the existence of a fifth element called the aether, an idea which is similar to, but not the same as, the idea of the aether mentioned in the following paragraph.  Also, I personally feel that it is worth noting that Aristotle was wrong, because this is something that I like to note as frequently as possible.

2. For centuries, scientists have believed in the existence of a substance called the aether that fills all of space and acts as the medium through which light waves can travel. In the nineteenth century, there were many experiments that attempted to detect and describe this aether, the most famous of which was done by Michelson and Morley in 1887. All of these experiments failed to detect any such thing as aether, but it was Einstein who eventually proposed the idea that the aether did not, in fact, exist. This dissatisfied many physicists, but it made Einstein’s theories work out very nicely, and they turned out to be true.

3. The speed of light is 299,792,458 meters per second. This is the equivalent of 670,616,629 miles per hour. When I’m driving to or from dance class, I am driving at an average of only 0.00000000894 of the speed of light. (When I’m driving to or from church, I drive a bit faster than that because people drive crazy fast on that interstate and everyone would seriously run right over me if I tried to drive at a normal speed.) Earth’s average speed is about 0.0001 the speed of light, by the way, which is about 67,061.66 miles per hour.

4. This doesn’t exactly count as something new I learned, but in this class, we used a slightly different definition for inertia than what I’ve usually heard. We basically defined inertia as a force that resists change in velocity. (I wrote a bit more about that here.) In discussing special relativity, the terminology “inertial reference frame” shows up a lot. That basically means that you’re either motionless or moving at a constant velocity.

5. The Principle of Relativity (which, by the way, predates Einstein) says that, if one is in an inertial reference frame, the laws of physics work the same way regardless of whether or not the reference frame is moving. For example, if you’re flying in an airplane and you drop a bookmark or something, that bookmark will fall to the floor of the airplane, just as it would if the airplane was sitting motionless on the runway. However, if you’re in a vehicle that is accelerating, decelerating, changing direction, or bouncing because of a bumpy road or air turbulence, it’s not an inertial reference frame, which is why things slide around in a moving car. This is inherent in the definition of inertia, but the implication of the Principle of Relativity is that, if you are in a completely inertial reference frame, you can’t even tell whether or not you’re moving. Even if you are looking out a window and see the view changing, you can’t scientifically prove that it is you and not the scenery itself that is in motion. Technically, relativity says that it’s equally true and valid to interpret it either way; the significant point is not who is moving and who is stationary, but just that the reference frames are not stationary relative to each other.

6. Einstein’s big breakthrough (or, to be more precise, his first postulate in the Special Theory of Relativity) was that the principle of relativity applies not only to forces such as gravity, but also to things such as the way light behaves. It had recently been suggested by various physicists that the principle of relativity didn’t apply to light and to Maxwell’s equations regarding light, so Einstein was basically just disagreeing with that hypothesis. His second postulate, which was really just a necessary result of the first postulate, was that the speed of light is the same in any inertial reference frame. The weird thing, which leads to all of the weirdness inherent in relativity, is that this requires giving up on the assumption that time is a constant. Time has to go at a different speed depending upon how fast the clock is moving relative to the speed of light. (The faster the clock is going, the less time passes, so basically, time goes faster at higher speeds.) But this doesn’t have much of an effect on everyday life because the speed of light is so extraordinarily fast that people never travel at a significant fraction of the speed of light.

7. We defined an “event” as a single point in space and time. In most of our homework assignments, we labeled events that described the emission or reception of a light beam or the collision between two particles or spaceships, but technically, even a point where nothing of interest happened is an event. Unfortunately for my lovely time gravity theory, it turns out that all events are equal, and there’s apparently no such thing as time mass.

I posted this on tumblr a couple weeks ago.

I posted this on tumblr a couple weeks ago.

8. Simultaneity is relative. This is the title of this blog post because the professor emphasized this very strongly and used any relevant occasion to remind us of it. Because of the relativity of time, two events can happen at the exact same time in one inertial reference frame and at different times in another inertial reference frame. It’s weird, but it’s true, and we did a lot of homework problems with spacetime graphs to prove it. The coolest one involved a Klingon ship firing laser blasts at a Federation starship in neutral territory shortly before passing into Klingon territory. From the reference frame of the Federation starship, it was hit while the Klingon ship was still in the neutral zone, which meant that the Klingons committed a crime. But from the Klingons’ reference frame, they passed into Klingon territory before the laser blast actually hit the Federation starship, and thus, they didn’t do anything wrong. Except that they were definitely in the neutral zone when they fired the laser blast, and the Federation starship was definitely in the neutral zone both when the blast was fired and when the blast hit, but for the sake of that problem, we assumed that the law was so poorly written that the only thing that mattered was where the Klingons were when their laser blast hit the Federation starship.

This is what a spacetime graph looks like.

This is what a spacetime graph looks like.

9. On a spacetime graph, if two events are farther apart in space than time, then they are spacelike separated, which means that the order of the events is relative. Depending upon how fast an observer is moving, either one of them could have happened first, or they could have happened simultaneously. It is impossible for one to have been the cause of the other, because they are too far away in space for the effects of one to reach the other in time to have caused it. If two events are farther apart in time than space, they are timelike separated, which means that the first one happened before the second one from the perspective of any inertial reference frame. Therefore, it is possible (but not necessarily true) that the first event caused the second event. However, depending upon the speed of the observer, the events may or may not have happened in the same place. If two events are separated by an equal amount of time and space, they are lightlike separated, and this will be true from the perspective of any inertial observer, regardless of his or her speed.  Incidentally, there is one way of measuring the distance between two events that does not vary between observers. This measurement is written as delta S, and the equation is delta S squared equals delta T squared minus delta X squared where T is time and X is space. Even though delta T and delta X will be different for different observers, delta T squared minus delta X squared will yield the same result for every observer. (You can read more here about the stuff that passed through my brain on the day that we discussed these things.)

10. In addition to affecting the passage of time, high speeds also affect length. For example, in a video we watched, a couple scientists measured time dilation by tracking particles descending rapidly through the atmosphere past a mountain. It would take too long for me to explain exactly how that worked, and that isn’t the point of this paragraph anyway, so I’ll just say that they did in fact demonstrate that less time passed for those particles than for the mountain that was stationary relative to the Earth. But, according to special relativity, the particles may as well have been stationary and the mountain may as well have been traveling upwards. The result is the same, and the result is that the time interval between the particles’ presence at the top of the mountain and their presence at the bottom of the mountain was a shorter time interval for the particles than for the mountain. So, from the particles’ point of view, the mountain is actually shorter than it is from its own perspective. To put this in general terms, the length of a very quickly moving object is contracted. Yes, in this particular case, it was the particles that were moving quickly and the length-contracted mountain wasn’t, but that’s only from the perspective of the scientists observing this incident. (And anyone or anything else that is stationary relative to the planet’s surface) Relativity says that it’s just as true and valid to say that the particles are stationary and the mountain is moving. The question of which object’s length is contracted is a matter of perspective.

11. The Doppler Effect applies to light as well as sound. As explained in high school physics books, the Doppler Effect is when sound waves are perceived as being grouped closer together (and therefore, higher pitched) when the thing emitting the sound is travelling towards the observer, and they are perceived as being spread farther apart (and therefore, lower pitched) when the thing emitting the sound is travelling away from the observer. According to most textbooks, one should learn about this phenomenon by getting someone to drive their car past you while honking their horn continuously, but my parents didn’t do this for me and I somehow still managed to understand the concept of the Doppler Effect. Anyway, it turns out that a moving light source will produce the same effect, except that the perceived pitch of light can’t change, for the simple reason that light doesn’t have a pitch. But the frequency still changes, just as it does for the sound. In the visible range of light, this is perceived as a change in color. The other thing worth noting (in order to avoid disagreeing with the principle of relativity) is that the Doppler Effect works the same way if it’s the receiver rather than the emitter that’s moving. It also works if the receiver and emitter are both moving, but in that case, you have to do actual math to figure out what exactly happens. (But it’s actually pretty simple math.)

Some more stuff from my tumblr page

Some more stuff from my tumblr page

12. Even though we actually spent several days of class time talking about “E equals M C squared” and radiation and subatomic stuff, I’m not going to say too much about that because, to be honest, I find that kind of thing a lot harder to understand than special relativity and its effects on space and time. But I will say this much: I know how nuclear bombs work. Some types of atoms are more stable than others, depending upon the number of electrons, neutrons, and protons. One factor is simply the size of the atom. The most stable kinds of atoms are iron atoms and atoms of similar masses. Smaller atoms are more likely than medium atoms to join together (nuclear fusion) and heavier atoms are more likely to split apart (nuclear fission). Fusion and fission both give off energy, which can be proven by adding up the energy and mass in the ingredients and the products of the event and taking into account that “E equals M C squared”. Uranium 235 (an atom that has 92 protons, 92 electrons, and 143 neutrons) is very radioactive. If you smash a neutron into a Uranium 235 atom, it’ll probably decay into Barium 144, Krypton 89, and three more neutrons which can go on to smash into more Uranium 235 atoms. If you have a critical mass of Uranium 235 and bombard it with a bunch of neutrons, you get a chain reaction that leads to a massive explosion and kills Hiroshima. (Unless, of course, you drop it on someplace other than Hiroshima, but I wouldn’t recommend that. In fact, I wouldn’t recommend dropping it on Hiroshima, either. Nuclear bombs are nasty things.) Incidentally, Uranium 238, which is more common than Uranium 235, is much less reactive, and unless I’ve misunderstood some things, it’s because of those extra neutrons. In really big atoms, larger amounts of neutrons make the atom more stable because the protons are trying to repel each other, and the neutrons are necessary to hold the atom together. Okay, that’s it; that’s the extent of my knowledge of nuclear stuff.

Ooh, here's something else I learned in this class which isn't quite worthy of a place on this list.

Ooh, here’s something else I learned in this class which isn’t quite worthy of a place on this list.

13. Even after finishing this class, I don’t quite get the concept of General Relativity, but we didn’t go into it in great detail because apparently the mathematics is well beyond the scope of this course. (I think that the real reason I decided to be a math minor is because I’m sick of hearing professors end sentences with the phrase “But we’re not going to go into that because the mathematics is beyond the scope of this course.”) But I do have a better grasp of it than I did before. The explanation of general relativity that I have heard many times before is that space is like a cushion. If you put a bowling ball in the middle of it, it will bend under the weight of the bowling ball, and if you put a marble near the bowling ball, it’ll roll down the cushion towards the bowling ball. This, I have been told, explains gravity according to Einstein’s Theory of General Relativity. When I questioned this, adults would explain to me that this was just the way it was and would give me looks that said, “It’s relativity, Small Child. Don’t expect it to make sense. Don’t be presumptuous and assume that you can understand the thoughts of The Great Albert Einstein.” Okay, it’s just one person in particular who seemed to be telling me this, and I am willing to accept the possibility that I was grossly misinterpreting this person’s lack of inclination to answer my question. My question wasn’t exactly a question anyway; it was more of a complaint. I felt that using this explanation was like using a word in its own definition. The reason that a bowling ball will bend a cushion is that it is heavy and is being pulled towards the Earth below the cushion, and the reason that the marble will roll down this bend is that it is likewise being pulled towards the Earth. And gravity is the thing doing the pulling. I guess I was being a bit too literal and failing to understand that the cushion explanation was merely an analogy. But my professor gave the class a similar analogy that I like better. This analogy involves an ant walking around the inside of a bowl that is empty except for a sugar cube at the bottom. Now, the ant doesn’t realize that it’s inside a bowl; it thinks that it’s walking in a straight line on a flat surface, and that there’s a sugar cube off to one side. As the ant keeps walking, it realizes that no matter how far it goes, the sugar cube stays in the same place relative to it. The ant is kind of clever for an ant, and quickly determines from this that it is in fact circling around the sugar cube. However, it still has no idea that it’s inside a curved bowl, so it can only conclude that there is some force, like gravity, attracting it to the sugar cube and causing it to orbit. In fact, there is no force; the ant is simply following a curved path because it’s walking on a curved surface. This analogy still isn’t perfect because General Relativity does say that mass (the sugar cube) causes space (the bowl) to curve, and the analogy doesn’t explain how that could happen. But it’s still a better illustration than the cushion one because it makes the point that Einstein was making with General Relativity. According to Einstein, gravity isn’t a real force. He came up with the Equivalence Principle, which says that the effect of perceived gravity is the same as the effect of being in a non-inertial reference frame that is accelerating upwards. (The acceleration is why it isn’t inertial) I’m not sure if Einstein literally meant that what we perceive as gravity is caused by acceleration of the Earth; I had thought we were considering the Earth to be an inertial reference frame. And I also don’t quite understand how curved spacetime relates to the Equivalence Principle. Like I said, General Relativity still doesn’t quite make sense to me, but at least now I’ve got analogies that make sense, and that’s progress.

black hole14. In class today, we were talking about black holes, and the professor was explaining why it is that nothing can escape from a black hole once it’s within a certain distance from the black hole, known as the event horizon. (Note to self: remember to use the phrase “The Event Horizon” as a title for something awesome someday.) The common explanation is that the gravitational pull is acting so quickly that you’d have to travel faster than the speed of light to get farther away from the black hole. Unfortunately, travelling faster than the speed of light is impossible. (Yes, I have grumpily accepted this fact, despite having spent years trying very hard to deny it.) There’s another way of explaining this that is both weirder and cooler. If you will remember, one can find delta S, a non-relative measure of spacetime separation between two events, with the equation delta S squared equals delta T squared minus delta X squared. The result of this equation is the fact that, no matter how we move in space, we are unavoidably drawn forward in time at the speed of one second per second. (According to our own perspective, that is. If we are moving at relativistic speeds, of course, our speed through time will be different from the perspective of an observer who is not moving likewise. But even then, we’ll still be moving forward in time from any perspective.) Now, here comes the awesome bit. For some reason that I don’t actually understand, apparently inside the event horizon of a black hole, this equation changes to delta S squared equals delta X squared minus delta T squared. In other words, time and space change places. The implication is that, in this situation, you are drawn into the black hole in the same way that, in a more typical scenario, you are drawn towards the future. The other implication (which is the really, really awesome bit) is that I was right when I wrote a certain passage in a certain science fiction story a long time ago. I didn’t even have any idea what I was talking about; I was just writing random science-fiction-sounding stuff about gravity and time, and I threw the phrase “time gravity” and “black time hole” in there for the sake of awesomeness. But, from what I learned today, it would appear that there was some validity to that stuff. Clearly, I am a genius. Or something like that.

15. I don’t understand quantum physics at all. In fact, I’m not even quite clear on what the word “quantum” means. This is clearly something that I need to learn. You know, now that I understand relativity.

Help! My Brain’s Being Weird Again!

2 Comments

From my tumblr page

From my tumblr page

This morning, I had something else in mind to write about today; in fact, I had started it and already had almost six hundred words written and the rest planned out in my head. But then I had to leave it behind and go to class, and while I was in class, I changed my mind about what I wanted to say to the internet today. When I say that I changed my mind, I don’t just mean that I altered my plans; I mean that my mind literally started behaving in a different way. That different way was quite odd.

Me doing my homework this morning

Me doing my homework this morning

For example,  when the professor introduced the terminology of “spacelike”, “timelike”, and “lightlike” intervals, I almost started laughing because that sounded so much to me like the modified language known as Newspeak from the novel 1984 by George Orwell, which I am currently reading. It occurred to me that, even if I were to point out this hilarious connection that my brain had made, nobody else would have understood why I was greatly amused. I can’t even explain now in writing what it was that was so funny, because the humor of the situation depended upon a unique combination of facts: A) the observer, me, was taking a course in relativity in time and space, B) the observer, me, was currently in the middle of the said novel 1984, C) the observer, me, was particularly interested in Orwell’s predictions of the linguistic future of dystopian humanity because that is the kind of thing that interests said observer, D) the observer, me, already had enough of an understanding of the concept being discussed in class to be able to pay attention while simultaneously making random and irrelevant mental connections,  E) the observer, me, had a sense of humor of just the right type to be entertained by that particular kind of thought, and F) the observer, me, was in a kind of strange mood that involved thinking very random thoughts and finding them very hilarious.

The new and revolutionary kind of graphing paper that my professor had us use in class today

The new and revolutionary kind of graphing paper that my professor had us use in class today

Another one of these random thoughts that had occurred to me only moments before was inspired by a new kind of graph paper that the professor had just shown us how to use. One benefit of this kind of graph paper is that it makes it significantly simpler to draw a two-observer space-time diagram, which is what we’ve been doing in class for the last few days. The other benefit is that this kind of graph paper just looks awesome, and it makes me feel very clever. Apparently, on a subconscious level, I believe that knowing how to use fancy graph paper is proof of extreme cleverness. As the logical and intellectual part of my brain did math and stuff and used the graph paper to draw graphs, the part of my brain that detects awesomeness came up with an awesome idea. You see, the point of two-observer space-time diagrams is that an observer who is moving relative to the coordinate framework has a different set of coordinates because this observer sees space and time differently. As it so happens, because space and time are weird, this coordinate system is shaped differently. The faster the second observer is moving, the closer the x-axis and time-axis will be to each other. I understand the relativistic principals behind that, and I agree that the physics and math are interesting, but, to me, the sight of a graph distorted by the principle of relativity has implications that go beyond physics and beyond the nature of the universe itself. The question that was implied to me was this: could you play scrabble and chess on a two-observer relativistic board?

This is a normal chess board, so this picture isn't particularly relevant here.

This is a normal chess board, so this picture isn’t particularly relevant here.

Needless to say, this idea revolutionized the way I thought of time, space, physics, math, relativity, and life as I know it. While everyone around me marveled at the usefulness of this type of graph paper and the interestingness of relativity, I pondered the ways in which board games could be changed to use such a board. I immediately gave up on the idea of playing scrabble that way; scrabble isn’t a relativistic game. I could explain what I mean, but it would take a lot of words and require a very detailed analysis of the differences and similarities between chess and scrabble and how this relates to Einstein and physics. So I won’t explain what I mean right now, but maybe that would make a good blog post for another day. For now, it suffices to say that scrabble cannot be played relativistically, but chess presumably could. The board would be more complex and would resemble the new kind of graph paper pictured above. From each player’s perspective, the other player’s pieces would move differently. For example, to me, my pawns would be moving forward, but to my brother, they would be moving diagonally. (I say “my brother” rather than “my opponent” because I am fairly certain that my brother is the only person I know who would be interested in playing Two-Observer Relativistic Space-Time Chess with me.)I didn’t work out all of the details and rules of this variant of chess, but I’m pretty sure it could be done. It would just take a good deal of math and even more nerdiness.

This is the kind of space-time graphing we've been doing.

This is the kind of space-time graphing we’ve been doing.

As all of these thoughts rushed through my brain faster than the speed of light, my professor was using two-observer space-time graphs to show why nothing can travel faster than the speed of light. You see, the faster something is moving relative to the perpendicular coordinate system,  the closer together the x-axis and time-axis of its own coordinate system are. (I am tempted to go off on a lengthy tangent explaining why this is and what this means in terms of relativity, but again, I must refrain from doing so if I want to finish this blog post at some point today. If I could post my entire brain onto the internet, I probably would, but I can’t.) If something travels at the speed of light, its x-axis and time-axis are actually the same line, which is the 45 degree angle bisecting the 90 degree angle formed by the x-axis and the time-axis in a regular perpendicular coordinate system. The point of all of the above is this: if you were to go faster than the speed of light, time would go backwards and causality would be reversed. Of course, I already knew that; that’s what everyone tells you on a regular basis if you’re like me and have a habit of repeatedly asking physics professors why nothing can travel faster than the speed of light. (This is, in fact, why certain professors told me to take this class.) But still, it’s cool to see it proved on a graph.

Here's a somewhat simpler and easier-to-read space-time graph.

Here’s a somewhat simpler and easier-to-read space-time graph.

But here’s the thing. I still don’t fully accept the idea that it’s definitely impossible for time to go backwards and for causality to be reversed. I can see on the graph what that would entail. It would mean that time and space would be reversed. Apparently, that idea is supposed to be utter nonsense, but I see some sense in it. I once wanted to write a science fiction story in which there was an alien species who experienced time and space as being reversed. These aliens would be able to travel through time in any direction and would be able to change direction and speed through time at will, but in space, they would only be able to move in one direction at a constant speed. After thinking it through, I came to the conclusion that, to us, these aliens would seem to suddenly appear and disappear as their paths in space and time meet and depart from ours. I hadn’t quite figured out what the plot of this story would be, but it would definitely be awesome. I basically abandoned this idea when my father informed me that Kurt Vonnegut had done something very similar in Slaughterhouse Five. I then became angry at Kurt Vonnegut for traveling in time to steal my idea, and I proceeded to add a section in a story I was writing which claimed that time and space are reversed in the set of dimensions that we know as hyperspace.  The point is that it isn’t necessarily total nonsense to image a situation in which time and space would be reversed. It’s just very, very weird and very, very awesome.

All of the ideas listed in the last five paragraphs actually occurred within the space of just a couple minutes, and in the meantime, I was listening to my professor, doing math, learning about relativity, making profound psychological observations about the connection between my handwriting and my current state of mind, and mentally sorting through all of these thoughts and trying to arrange them into greater and awesomer observations about life, the universe, and everything.

I did not interrupt the class to share these thoughts, because I wasn’t sure which of them, if any, made sense, and because I would have had to say them all at the same time, which would have been impossible. Even now as I type this out, I’m on the third page, although I’m single-spacing and using a somewhat small font. And I left out all the bits about the math and the non-relativity of scrabble and the rules of my new kind of chess and the exact details of my psychological analysis of my own handwriting. If I had included all of those things, plus all of the information from this class which is necessarily involved in this stream of consciousness, who knows how long this blog post would be. It certainly would be too long for me to say all that stuff in the middle of class. Besides, my brain works better when my mouth is idle and my hands are busy than when my mouth is at work. So I kept my mouth shut and thought stuff instead. In fact, when the professor asked me a rhetorical question moments later, the only word that managed to escape from the web of thoughts in my head and find its way to my mouth was the word, “What?” Such is the extent of my articulateness when I’m thinking stuff.

And my professors wonder why I don’t talk more in class.

Time Gravity

Leave a comment

I admit that when I start talking about the space-time continuum, most of the time, I’m just randomly inventing stuff. My science-fiction imagination has a much greater scope than my scientific knowledge, and my explanations of hyperspace, perpendicular universes, multi-dimensional time, temporal disequilibrium, and time gravity are very contrived and completely fictitious. That’s not to say that these ideas aren’t fairly developed; these are all concepts that I can and do use in science fiction with consistency and at least the semblance of sense. Science fiction is more like fantasy than science; it works as long as you can make it sound like your invented rules of the universe can be explained scientifically. For the sake of my own writing, therefore, I can claim that time gravity is real. Personally, I think it makes a lot of sense.

There’s one particular story in which time gravity is a very important plot point. It is a story that my sisters and I started years ago, but I still am adding to it and rewriting it. I don’t think it’ll ever be officially finished because that would end the fun. This is not a work that is meant to be finished. In the story, time has been acting in increasingly odd ways, sometimes skipping over days or months at a time, and at other times failing to move forward in a regular and predictable way. Officer Graxy of the Intergalactic Police of the Space Time Continuum is conducting an investigation, but he only discovers minor disturbances, such as irresponsible use of microwave timers. The strange phenomena occurring are clearly related to a much greater disturbance. Professor Johnson and his assistant Richard of the organization known as Scientific Explanations Inc. join forces with Darth Vader, who is searching for his stolen Death Star, and they realize the true cause of the disturbance: the Death Star has been concealed in hyperspace, an alternate set of dimensions in which the roles of time and space are reversed. Hyperspace is relatively empty, and therefore the presence of an object as massive as the Death Star introduces an astronomical source of gravity. (Notice the pun. Astronomical, Death Star. Get it?) This gravity manifests itself in regular space in the form of time gravity. All of the space-time anomalies are solved when the Death Star is returned to regular space.

Why Time Speeds UpAnother use of the idea of time gravity is more relevant to real life. (Or at least, it would be if I could demonstrate that it existed in real life.) I use it to explain why time seems to speed up as you get older. You see, major events in one’s life are sources of time gravity, and the greatest amount of time gravity comes from death or the apocalypse, whichever comes first. Because of this, everyone is pulled towards the future, a phenomenon which we observe as the passing of time. However, the second greatest amount of time gravity is exerted from the event of birth, and for a small child, birth will be a good deal closer than death. Therefore, the time gravity of birth exerts a significant pull also, which decreases as one gets farther and farther away from birth.

Why Christmas Takes So Long to ComeThe following example comes from a conversation that occurred at my house over Christmas break. We were discussing the fact that Christmas seems to come slowly when you’re a little kid, but it comes all too quickly when you’re older. I insisted that this is because little kids are less busy, a fact that is fairly obvious and straightforward, but I couldn’t resist complicating it by drawing a diagram to illustrate my opinion that this is an example of time gravity. The accompanying diagram is not the one that I drew at the time, but it is, to the best of my memory, pretty much the same. As you can see, a little kid only has a few major events occurring in the weeks before Christmas, but an adult is incredibly busy. (These are examples; I do not mean to imply that people’s ages are the only factor determining their pre-Christmas schedule and timeline.) The diagram clearly shows that there is a greater amount of time mass on the adult’s timeline than on the child’s. This obviously draws the adult towards Christmas quickly. The child is also pulled forward towards Christmas, of course, but because of the lesser degree of time gravity, as well as the aforementioned time gravity from birth, the speed is much slower.

It greatly baffled me that my family did not accept this diagram and explanation as a logical and likely explanation of why time works the way it does.

 

My life has taken a sudden turn for the randomer

2 Comments

The conditions of my life have entered a state in which a regular schedule is impossible, sleep is unusual, and time of day is irrelevant. I concluded this when I woke up to discover that 1) it was 3:00 in the morning, 2) I was still dressed for church even though I had left church many hours previously, 3) I had unexpectedly fallen asleep at about 9:00 the previous night, 4) The alarm I had set to keep such a thing from happening had failed to wake me up at 10:00 as I had intended, and 5) I had consequently failed to accomplish the homework that I had been aware I would need to stay up all night to do. Additionally, I realized that I had a fever and a headache and my nose was running. Taking all of this into consideration, I acted in the only possible logical manner, which was to get up and get the coffee machine going.

Here is a picture of Mariah Carey that Google gave me when I searched for pictures of 80s hair. I selected this picture because this is more or less what my hair looked like. Except it was even curlier, and less symmetrical, and much less neat. So basically, it didn’t really look like this at all.

Another thing that I noticed upon waking up was that my hair had decided that it was ‘80s hair day. It had already been unusually curly the day before, but while I was asleep, it had rearranged itself into an array of disorderly curls with a big asymmetrical poof that didn’t seem like it should have possibly been able to form without a deliberate effort on my part. This amused me so greatly that it temporarily distracted me from my homework. Shortly thereafter, my hair changed its mind about ‘80s hair day and decided instead to go for a Medusa look, as various sections of my hair decided independently which direction they wanted to point and how tightly or loosely they wanted to curl. I was greatly tempted not to do my homework and instead to laugh at my hair while pacing around in my darkened dorm room and pondering the question of which decade I ought to live in, taking into consideration my taste in music and fashion, my thoughts on matters of feminism or its absence, and the tendencies of my hair. It is worth noting that I never determined a conclusive answer to this question.

A surprisingly accurate picture of what my hair often looks like when I wake up

These events happened over twenty-one hours ago, and in that time, I have read a couple hundred pages, written a few thousand words, gone to a few classes and work, taken care of some paperwork, eaten a couple times, wasted some time lamenting the tragic fact that my life isn’t entirely as joyous as I could imagine it being, and used the internet to send my mother some squirrel emoticons. Throughout the day, there has not been a single moment at which my perception of the time of day has been accurate. Also, my hair has suddenly and spontaneously changed its appearance several more times.