Simultaneity Is Relative


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.

My Favorite Songs

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One of my projects over this last month has been to make a list of my favorite 250 songs. (This list is now available on youtube and can be yours for the low, low price of 48 minutes and 13 seconds of your precious time.) As you may be able to guess, this was a pretty time-consuming project. Why, you may ask, would I choose to commit my time and effort to such an utterly pointless endeavor? Well, I happen to have quite an affinity for utterly pointless endeavors if they involve carefully organizing things into lists that will continue to exist in a tangible form after the project is finished. Some people knit or sew or do woodwork because they like their hobbies to produce tangible results; I make lists.

Part One: #250- #201

For the record, only pop songs are eligible for this list. That means that oldies, songs from musicals, and folk songs are all valid possibilities, but hymns and classical music are not. Current hits are eligible if I happen to like them, but very few songs from my own lifetime make the list. There are some, but not many. (A significant portion of the list consists of songs from the 1960s, and I noticed that the year 1967 in particular showed up quite a lot.) In order to be an available option for the list, a song must also have words; instrumentals aren’t allowed. These rules exist because certain types of music can only be judged according to different criteria. (This is especially true for hymns. It wouldn’t be possible to compare a hymn to a pop song according to a standard that takes into account the different things that make them “good”.) Christmas music, songs in languages I don’t know, or especially goofy songs are eligible, but tend not to do particularly well.  That may be less true of my current list than in previous years; I can think of five songs offhand that are in different languages and there might be more I’m forgetting. At least a couple are actually pretty high. Also, a Christmas song was #1 in January 2012, (and #14 this year) but I didn’t really think of that specifically as a Christmas song because it happened to be from the Doctor Who soundtrack, which placed it into yet another genre, and these genres kind of cancelled each other out and led me to treat it as a run-of-the-mill pop song.

Part Two: #200- #151

It is worth noting that my methodology for favorite-song-lists is very specific. It is necessary that I follow the exact same procedure every time I make such a list. The first step is to look through all of the music I own and write down the title of every song that I like enough that I believe it deserves a place on the list. Normally, the final list has one hundred songs rather than two hundred fifty, but the preliminary list always has a large surplus. Usually, it has somewhere between six hundred and seven hundred songs. This implies what the next step is: I must cut songs off the list until I’m down to the predetermined number. In theory, this step could be done fairly quickly, but I spread it out over the course of several days in order to ensure that a temporary mood doesn’t play too large of a role in this selection. Once I have my 100 or 250 songs chosen, the next step is to record a clip from each song and to save it onto my computer. These clips can be anywhere from five to twenty seconds, although I aim to get them as close to ten seconds as possible. Generally, the average length ends up being a bit higher than ten seconds. These clips can come from my favorite part of the song, from the very beginning of the song, from the title line, or from a place that just happens to be convenient to edit. That detail isn’t particularly important. Collecting these clips is the most time-consuming and least fun step, but the next step is the funnest.

Part Three: #150- #101

That’s when I put them in order. First, I sort them into three folders: A is for the songs that I really love and wish I could put at #1, B is for the songs that I really like, but not quite that much, and C is for the songs that I also like, but it wouldn’t make me extremely sad if they didn’t make it very high. Each of the three folders is then subdivided into three more folders, so I end up with A1, A2, A3, B1, B2, B3, C1, C2, and C3. At that point, any folders with ten or fewer songs can remain as they are, but any folders with more than ten songs must be further split. If I recall correctly, this time I ended up with some folders that had names that were seven characters long. Once all of the folders are manageably small, I can start editing the clips together into a longer audio file. I don’t put them all into one file, because that would be too long to work with easily. This time, I used ten files, each of which were about 25 songs long. Finally, I use these audio files as the music for a video which gives the number, title, artist’s name, and release date of each song. (I don’t include the artist and date if the song has many different versions and the version is not significant to the placement on the list. Generally, this is true of the folk songs. I also occasionally am unable to find this information and have to leave it out. In some cases, this could conceivably be because I was wrong about the title of the song.)The video editing process is my second least favorite step. It gets slightly tedious and it takes longer than you’d think. This time, it’s taken me probably about six or seven hours spread out over five days. To answer the questions you might have, yes, I do have more important things to do, and no, I don’t sleep. Not very much, anyway.

Part Four: #100- #51

If I knew more about music, it would be fascinating to analyze the patterns and similarities between my favorite songs. Since I don’t really know what I’m talking about, I probably shouldn’t say much about those observations. However, there is one simple pattern that’s very obvious. I apparently really, really like The Seekers, since they came in at #1, #2, #3, #4, #6, and ten other places farther down on the list,  plus two more songs that fall under the category of folk songs that I like regardless of the artist performing them. Lately, I have indeed become somewhat obsessed with The Seekers, as anyone who has seen my facebook profile or my tumblr page will tell you. (And this isn’t the first time I’ve mentioned them on my blog, either.) The Moody Blues made quite a few appearances in my top 50 as well, which is somewhat surprising since I don’t listen to The Moody Blues a whole lot. The Beatles didn’t do as well as usual if you judge based upon the top of the list, but in the entire list of 250, they certainly still had more songs than any other group. There also were a number of Monkees songs, which included #5, and this is noteworthy because The Monkees haven’t played a prominent role in my previous lists. To make a more general summary of the kinds of songs I like, I notice that the 1960s are disproportionately represented, and in particular, I saw the year 1967 quite a lot.

Part Five: #50- #1

I Don’t Like Aristotle

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AristotleI have this weird thing about Aristotle. I don’t like him. I know that his was one of the greatest minds of all time, I know that he made valuable contributions to just about every field of study in existence, and I know that his influence has played a large part in the course of human history, but something about Aristotle just annoys me. In theory, I ought to like Aristotle, because one of his defining characteristics was a tendency to classify everything, and that is a tendency which I share. (For example, I am in the process of posting my list of top 250 favorite songs on youtube after spending about a month carefully sorting and organizing them, and I am also currently trying to classify emotions into a small set of primary emotions, so that I can better categorize and document the entire range of emotions and collect data on a multi-daily basis in order to determine how various factors of everyday life affect emotion, as well as cognitive ability, which I have already developed a method for quantifying. This is just the kind of thing I do for fun in my spare time.) Some of Aristotle’s contributions to the world include taxonomy, various fields of theoretical science,  the foundations of all mathematics and physics for subsequent centuries, organization of rhetorical techniques, deductive logic, and various other systematic modes of thought that are either dear to my heart or at least appealing to the natural tendencies of my brain. Basically what I’m saying here is that Aristotle was brilliant and apparently obsessed with organized thought, which is reason for me to admire him. But instead, he annoys me like crazy.

Part of this is because there are a few specific things he said that I dislike. The most obvious and significant examples are theological, because Aristotle wasn’t exactly a Christian. (Despite what Plotinus said centuries later)To be honest, I’m not quite clear on what Aristotle did believe, although I’ve always gotten the impression that his beliefs more or less corresponded to what is now called Deism; that is to say, he believed in a God who created the world and invented moral rules, but hasn’t been particularly involved in the world since then. Although Aristotle definitely believed in “The First Cause” and “The First Mover”, he clearly didn’t believe in the triune God and he didn’t discuss sin and salvation in the Christian sense. Yet his philosophical ideas somehow still got tied up into Christianity in medieval times. For this reason, Martin Luther hated him and had some very choice words to say about him, which is enough to verify to me that Aristotle is not to be liked. Granted, Aristotle lived before Christ, but still, the point is that he didn’t believe in THE God; he believed in a god that he made up out of his own logical thought process, which, as brilliant as it was, was still human and thus not entirely reliable.

As long as we’re on the topic of unreliability, it is worth noting that Aristotelian physics turned out to be totally messed up and wrong. They held sway until Newton and Galileo came along, but then it was thoroughly demonstrated that Aristotle was mistaken, which isn’t really all that surprising since he was just making stuff up based upon his casual observations. Yes, I know that theoretical physics means that hypotheses are formed without the immediate verification of precise experimental data, but theoretical physics isn’t good for much unless its conclusions are justified by subsequent developments and experiments. (I feel a need to point out that the physics of the last century plus a few years, based upon Einstein’s postulates and theories, have disproved some of Newton and Galileo’s theories, so Aristotle’s physics is now at two degrees of proven-wrong-ness.)

Categorical SyllogismsIn my logic notes from last semester, there’s a line that reads, “Yet another reason to be annoyed by Aristotle”. I didn’t even bother to write down what that reason was, because I knew I would remember. I was right; I remember both the note and the reason for the note even though I haven’t looked at those notes since the semester ended. This source of annoyance was the discrepancy between Boolean logic and Aristotelian logic in a case where Boolean logic is clearly better. Aristotle says that certain forms of categorical syllogisms are valid if the terms are existing things and invalid if the terms are non-existing things. That makes sense, except that the whole point of distinguishing between valid and invalid syllogism forms is that valid forms are valid regardless of what the terms are. According to the Boolean standpoint, if the truth of the syllogism relies upon whether or not the terms exist, then the form of the syllogism is valid. In other words, it is valid to say, “All unicorns are mammals and all mammals are animals; therefore, all unicorns are mammals” because, if both premises are true, then the conclusion is true. The fact that unicorns don’t exist (or so I’ve been told) is irrelevant because, if they did exist, they would clearly be animals if we can assume that they are mammals and that mammals are animals. But, according to Aristotle, the validity of the entire syllogism depends upon the existence of unicorns. For the sake of my logic class, we had to answer questions from both the Aristotelian standpoint and the Boolean standpoint, but I would like the record to show that I am totally on Boole’s side on this one.

Just look at his arrogant, self-satisfied smirk!

Just look at his arrogant, self-satisfied smirk!

But, despite his flaws in theology, physics, and (in my opinion) the rules of categorical syllogisms, the fact remains that Aristotle was a remarkably intelligent person and that he made remarkable contributions to every aspect of academia and human thought. I can fully justify my disdain of Aristotle only by acknowledging one other reason for it: I’m jealous of him. He is widely regarded as one of the greatest geniuses ever to live, and his thoughts have been among the most prominent thoughts ever thought for more than 2300 years now. My brain aspires to great genius and doesn’t like the fact that there have been minds so great that my mind will never achieve the success and accolade that they did. This may very well be the same reason that I find Einstein annoying and have tried so hard to deny the fact that nothing can travel faster than light. I now reluctantly agree that this is the case, because it has been mathematically demonstrated to me in various fascinating and undeniably clever ways. But I am so totally not happy about it.

Some Thoughts on Genesis 24

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Disclaimer: After I finish the long quotation from Genesis, the end of this blog post is just some things that have occurred to me regarding this particular Bible passage. I’m not trying to claim that what I’m saying here is official doctrine or that my thoughts constitute theological truths. In fact, since the notes in the Lutheran Study Bible (which are extensive and very awesome) don’t make these connections, I’m willing to accept the possibility that they aren’t valid. It is entirely possible that I’m really stretching things and that it’s just plain wrong to take these things from this text. If anyone reading this has anything to say, particularly if it involves quoting Bible verses or good biblical commentary, your comments are welcome and appreciated.

Rebekah at the wellGenesis 24 is the account of how Abraham sent his servant back to his native land to find a wife for his son Isaac. The chapter begins with the conversation between Abraham and the servant, and then the servant sets off on the journey. Starting at verse twelve, here is the text as quoted from the ESV (English Standard Version):

And he [Abraham’s servant] said, “O Lord, God of my master Abraham, please grant me success today and show steadfast love to my master Abraham. Behold, I am standing by the spring of water, and the daughters of the men of the city are coming out to draw water. Let the young woman to whom I shall say, ‘Please let down your jar that I may drink’, and who shall say, ‘Drink, and I will water your camels’ – let her be the one whom you have appointed for your servant Isaac. By this I shall know that you have shown steadfast love to my master.”

Before he had finished speaking, behold, Rebekah, who was born to Bethuel the son of Milcah, the wife of Nahor, Abraham’s brother, came out with her water jar on her shoulder. The young woman was very attractive in appearance, a maiden whom no man had known. She went down to the spring and filled her jar and came up. Then the servant ran to meet her and said, “Please give me a little water to drink from your jar.” She said, “Drink, my lord.” And she quickly let down her jar upon her hand and gave him a drink. When she had finished giving him a drink, she said, “I will draw water for your camels also, until they have finished drinking.” So she quickly emptied her jar into the trough and ran again to the well to draw water, and she drew for all his camels. The man gazed at her in silence to learn whether the Lord has prospered his journey or not.

RebekahWhen the camels had finished drinking, the man took a gold ring weighing a half shekel, and two bracelets for her arms weighing ten gold shekels, and said, “Please tell me whose daughter you are. Is there room in your father’s house for us to spend the night?” She said to him, “I am the daughter of Bethuel the son of Milcah, whom she bore to Nahor.” She added, “We have plenty of both straw and fodder, and room to spend the night.” The man bowed his head and worshiped the Lord and said, “Blessed be the Lord, the God of my master Abraham, who has not forsaken his steadfast love and his faithfulness toward my master. As for me, the Lord has led me in the way to the house of my master’s kinsmen.” Then the young woman ran and told her mother’s household about these things.

Rebekah had a brother whose name was Laban. Laban ran out toward the man, to the spring. As soon as she saw the ring and the bracelets on his sister’s arms, and heard the words of Rebekah his sister, “Thus the man spoke to me,” he went to the man. And behold, he was standing by the camels at the spring. He said, “Come in, O blessed of the Lord. Why do you stand outside? For I have prepared the house and a place for the camels.” So the man came to the house and unharnessed the camels, and gave straw and fodder to the camels, and there was water to wash his feet and the feet of the men who were with him. Then food was set before him to eat. But he said, “I will not eat until I have said what I have to say.” He said, “Speak on.”

[Verses 34- 49 are spoken by Abraham’s servant and repeat everything from the previous 33 verses. Then Rebekah’s father and brother agree to send Rebekah back with Abraham’s servant, and they all eat together. The next day, Rebekah and the servant depart, and Rebekah marries Isaac at the end of the chapter.]

This is what I find really interesting about this passage: Abraham’s servant recognizes Rebekah as Isaac’s bride because of the words she speaks (“Drink” and “I will water your camels”) and the water she gives, in the same way that Christians can recognize the true church by the words it speaks (the Bible) and the water it gives (Baptism). In fact, the reason that Abraham’s servant has to take this trip in the first place is because any potential brides in Isaac’s current homeland belong to pagan religions, which is to say that they’re associated with false churches.

I'm reusing this picture of a sign I stuck on my dorm room wall, because it's a cool sign.

I’m reusing this picture of a sign I stuck on my dorm room wall, because it’s a cool sign.

That’s something I noticed while ago that I thought was cool, but this morning it occurred to me that the order of events in this account could be significant, too. First comes the part about the water, then Rebekah and her brother invite the servant into their home, then they talk things over and agree that Rebekah will marry Isaac, and then Abraham’s servant eats the food that Rebekah’s family provides. (The Lutheran Study Bible does have a note that points out that it would have been customary for the guest to eat before such a discussion, but in this case, it was important to the servant to get that matter taken care of first.) Likewise, Christians enter the church through baptism; baptism can occur even before a person makes a conscious decision to enter the church. (In this case, my opening disclaimer doesn’t apply. It is official doctrine in the Lutheran Church that infant baptism is valid because baptism is a gift from God that does not require a deliberate decision to accept Jesus. It is something that the church can give to us even before we have the knowledge to recognize what we are receiving in baptism.) However, when the church offers us food, (Holy Communion, aka The Lord’s Supper, aka the Eucharist, etc.) before we partake in this meal, we should be sure that we’re in the right place and that we are in agreement with the congregation with whom we’re eating. In the case of Abraham’s servant, that means negotiating the betrothal before accepting dinner. In the case of communion, that means two things. First, unlike baptism, communion isn’t something that should be offered to babies or to people who have not yet been instructed in the church’s teachings. Second, it’s an argument for close communion (aka closed communion), which is the practice by which a congregation only offers communion to members or to visitors who believe the same thing. (Basically, that means members of another congregation of the same denomination.)

Matthew 6The English major part of my brain is wondering if there’s something metaphorical to say about the camels. It seems important that Rebekah is so attentive to them, offering them water and then assuring Abraham’s servant that her family has plenty of straw and fodder for the camels, even though he hasn’t specifically asked about that. Obviously, Rebekah was a generous and caring hostess, but if there’s a parallel to be drawn here, I’m going to guess that it’s along the same lines as what Jesus says in Matthew 6: 25-34. (See accompanying picture) If the camels stand for something, they stand for Abraham’s worldly possessions, and the fact that they are well provided for stands for the fact that, by God’s grace and love, our worldly needs are met, in addition to the forgiveness, salvation, and eternal life that God has already given us.

The end. I reiterate that comments, corrections, and additional remarks are welcome and requested.

An Unforgetable Moment In My Life

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This comparitively recent picture in the kitchen is included for context, and as an extra bonus, it also happens to be a cute cat picture.

This comparitively recent picture in the kitchen is included for context, and as an extra bonus, it also happens to be a cute cat picture.

‘Twas a moment I shall always remember. It took place in the kitchen on a relatively ordinary summer morning when I was thirteen years old, soon to be fourteen, for my birthday was in early September. (As a matter of fact, it still is.) It was fairly early, probably about eight O’clock, and my sister and I were doing the dishes. Normally, this was a chore that was executed later in the day, but on this particular day, we were doing it earlier because we were about to leave for a multi-day trip, and the dishes must be done before then. My sister and I both greatly hated this chore, but I don’t recall that fact having much bearing on the story that I am currently telling. In fact, I seem to remember being pretty happy at the time because I was excited about the aforementioned trip. On this particular day, my sister was doing the washing and I was doing the drying, a task which also included putting away the clean and dry dishes.

The pan of which I speak looks very much like this.

The pan of which I speak looks very much like this.

This was the scenario when the moment that I will always remember occurred. I was standing on a wooden stepping stool in order to reach the top shelf of the cabinet where we keep casserole dishes and baking pans, and I was lifting a fairly heavy brown-tinted glass pan onto that shelf. I don’t remember what that pan had been used for most recently, but we often make things like corn bread in it. As far as I know, my family still has that pan and still uses it frequently, although I don’t specifically recall seeing it anytime recently. Since I don’t go to my house very often, it isn’t surprising that I don’t have a very complete and up-to-date knowledge of my family’s culinary tools and devices. But, whether my family still uses that pan or not, the fact remains that at that particular moment, I had it in my hands and was putting it on the shelf where it belonged. That objective was a little more complex than it sounds, because the cabinet was pretty full. To put one dish away required removing a stack of dishes and restacking them to make room for the new arrival. I had just done that, and was sliding the stack of rectangular pans back onto the shelf. I had to be very careful, because they were heavy and many of them were breakable, and I had to reach above eye-level, even with the added height of the stepping stool. For the record, I succeeded in doing this without breaking anything, which wasn’t surprising considering that I was accustomed to doing this every single day.

At that precise point in time, I promised myself that I would never forget that moment. It wasn’t because there was anything significant or memorable about it. It was just that I was fascinated by the idea that I could permanently preserve a certain moment in my mind just by deciding to remember it, even a perfectly ordinary moment like that. It worked. I have never forgotten that incident, and I’m pretty sure I never will.

Slightly Politically Incorrect Thoughts on Beauty

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I don't know where this picture came from originally, but it is a computer-generated image that has been posted in many places online as an example of a fairly normal but objectively beautiful female face.

I don’t know where this picture came from originally, but it is a computer-generated image that has been posted in many places online as an example of a fairly normal but objectively beautiful female face.

Society and the mass media promote two different ways of defining and thinking about beauty. The first tells us that beauty is objective and can be judged according to a standard set of ideals, that some people are much better-looking than others, and that it’s important for every individual to do whatever they can to make themselves as attractive as possible, especially in cases where this individual is female. The other perspective says that beauty is only skin deep and that true beauty comes from within. According to this definition, there’s no such thing as objective beauty and it is unethical and hurtful to say that one person looks better than another. One of these views is considered to be superficial and the other is considered to be politically correct, but they’re both commonly held ideas and they’re both deeply ingrained into people’s minds. I would like to offer the opinion that actually, both of these ways of thinking of beauty are incorrect and potentially harmful. Even though one is always critical and the other is always complimentary, they’re both too extreme and just plain wrong.

Of course, everyone knows what’s wrong with the idea of objective beauty that is promoted by movies, the fashion industry, and advertisements in general. It’s unrealistic and artificial, and it promotes the idea that a person’s self-worth is based primarily upon their physical appearance. It makes people, especially women, feel inadequate, and it opens opportunities for marketing strategies that prey upon people’s insecurities. Women are told that they are supposed to strive for a certain ideal, and if that means spending ridiculous amounts of money and time on nice clothes and makeup and hair care products and skin care products, then that’s what you have to do. If you don’t, you’re ugly, no one likes you, and your opportunities in life will be very limited. Those ideas are obviously neither correct nor pleasant.

The other definition of beauty sounds better, though. It’s nice to be able to say that everyone’s beautiful just the way they are and that a person’s facial features have no impact whatsoever either on their potential in life or their overall degree of attractiveness. The problem is that, strictly speaking, that isn’t true in every context, and anyone who really believes it is going to have a hard time dealing with a world in which looks really do matter sometimes. Personally, I feel that there’s a bit of a contradiction in a philosophy that states that everyone is beautiful and that beauty doesn’t really matter. The only way in which that conflict is resolved is to make “beauty” an extremely vague term, which is easy to do when you’re already operating according to the idea that beauty is unimportant. But then you’re basically denying the existence of any such thing as objective physical beauty, and that’s kind of sad because beauty is, by definition, a good thing.

To be honest, I have never understood why people say that the Mona Lisa is pretty.

To be honest, I have never understood why people say that the Mona Lisa is pretty.

I think it makes the most sense to think of beauty in the same way as you’d think of a skill in a certain area. For example, some people are born with a mathematical mind and are guaranteed to be good at math as they grow and learn. If that is something that really matters to them, they will put effort into mathematics and will end up being excellent; otherwise, they’ll just be a little bit good at math and they’ll be better at something else that matters a little more to them. In other words, a person’s mathematical ability comes from a combination of natural ability and deliberate effort. It would be silly for another person to tell a mathematical genius that being good at math is not something they should be proud of because they were born with it, but it would also be silly for others to put that mathematical genius on a pedestal as a model of human perfection just because he or she is extremely good at one certain thing. Other people are born without that degree of mathematical talent. If they work really hard, they can still become somewhat good at math, but certainly not to the degree of being a genius. It would be incorrect and hurtful for other people to claim that this non-genius is an inadequate human being just because of a lower level of innate proficiency in one area.

Likewise, some people are born being naturally good-looking and others aren’t. Regardless of how naturally attractive someone is, there are things he or she can do to look better. The question of whether or not it’s worth it is really a matter of opinion. For example, I personally think that plastic surgery, except when it’s reconstructive in nature, is not worth the money and the recovery time. I don’t, however, think that it’s silly or wasteful for me to use makeup or to occasionally spend some time doing something cool with my hair or to prefer wearing clothing of certain colors simply because I think I look better in those colors. But I do know a lot of girls who wear an awful lot more makeup than I do and who care more about their hair than I do and who buy a lot of clothes because they find it necessary to have as many flattering or “cute” outfits as possible. Some of them are naturally beautiful people who do their best to enhance their good looks because it’s something that they value in themselves. Others are less good-looking to begin with, but they are dedicated to making themselves look as good as they can, and usually, the result is that they succeed in being pretty.

I don't often spend any more time on my hair than absolutely necessary, but I do admit to having wasted some time recently trying to imitate this hairstyle. This is Clara Oswin, from the latest Doctor Who episode.

I don’t often spend any more time on my hair than absolutely necessary, but I do admit to having wasted some time recently trying to imitate this hairstyle. This is Clara Oswin, from the latest Doctor Who episode.

To be honest, I am a little biased against people who think that their appearance is a high priority in their life, and I am very baffled by some girls’ willingness to spend so much time and money on the way they look. Really, though, it’s a lifestyle choice. To me, my appearance is slightly important, but there are a number of things that are much more important. I’d rather put my time and efforts into the pursuit of intellectual achievements, partly because that seems much more important to me and partly because I’m aware that any natural assets I have are intellectual rather than aesthetic. I’m not saying I’m a genius, either, but I do go to a fairly prestigious college and make fairly decent grades, which is worth something.  I’m not sure what an equivalent achievement in prettiness would be, but it’s certainly something well beyond my potential.

There are some people out there who are very good-looking and very smart and very talented in other areas as well.  I guess that must come from a combination of being very naturally gifted and being extremely non-lazy. In that case, those all-around awesome people deserve admiration and respect, even from those of us who just can’t understand how an intelligent and motivated person can find the time to make their hair look that nice or put that much effort into putting together a really great outfit.

It’s true that there are a lot of people out there who are superficially obsessed with their appearance or who are misguided enough to judge other people based upon their looks. And it’s true that it’s bad to be entirely focused on physical beauty and that our society shows many of the negative results of that mindset. But that doesn’t mean that it’s wrong to acknowledge that there is such a thing as objective beauty and that some individuals do have quite a bit of it.

Here is a picture of Grace Kelly, because I once had a paper doll of her that I deemed to be the prettiest of all my paper dolls.

Here is a picture of Grace Kelly, because I once had a paper doll of her that I deemed to be the prettiest of all my paper dolls.

For the record, this blog post was in part inspired by a website I found (and unfortunately lost again, so I can’t share the link) which lets you upload a picture of a person’s face and then uses objective details to calculate how good-looking  that person is. This strongly appealed to the part of my brain that is fascinated with quantifying everything. Unfortunately, I couldn’t do a lot with it because it requires pictures that are completely straight-on; the slightest angle or the tiniest incline of the head confuses it. I therefore only had a couple pictures available to feed into the program, but I was interested to note that the analysis of one particular picture of one particular sister indicated that she was more than 95% pretty. Given the fact that I have myself beheld the face of this sister of whom I speak, I am not at all surprised, and I expect that pictures of some of my other sisters would have gotten similar scores if I had been able to find correctly angled pictures to use. My point here is to justify the coolness of such a computer program (and the amount of time I wasted playing with it) and to explain why it is both awesome and unfair that my sisters are pretty people. The additional point of this particular paragraph is to subtly point out that my sisters are pretty people without actually complimenting them, because, you know, that would go against all the principles of sibling rivalry.

Note: Those of you reading this who know me and/or my family in real life may be curious about which sister’s picture I used. If you want to know, you can see it for yourself, because it’s my current cover picture on facebook. It is pretty obvious which sister’s face I was able to use because she’s the only one who isn’t leaning and doesn’t have her head turned or someone else’s hair obscuring her face.

Other note: I notice that all of the pictures I have used here happen to be of Caucasian women, and I would like to note that 1) This is a coincidence where my choices were concerned and I hope that isn’t offensive, and 2) It is interesting and strange, though, that Google images don’t give you racial diversity unless you specifically ask for it.

Things I’ve Learned From Watching The Big Bang Theory

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The Big Bang Theory 1I can’t remember exactly when I first became aware of the TV show The Big Bang Theory, except that it was at some point during spring semester my junior year. (That is to say, last year) I also don’t remember exactly what I saw first, except that I know I saw a lot of short clips on youtube long before I ever saw a full episode. In fact, I still haven’t seen many full episodes beyond the first season. I enjoy The Big Bang Theory for two reasons: the characters and the nerdiness. The main characters are all unrealistic enough to be ridiculous while still being realistic enough to be relatable, which is a combination that maximizes the humor. Sheldon Cooper, for example, is more socially inept and more obsessive than anyone in real life could possibly be, but there are at least a couple moments in nearly every episode where he says or does something that is exactly the kind of thing that I would say or do, or where he seems exactly like certain people I know. That fact actually has to do with both of my reasons for liking The Big Bang Theory; the fact that I find Sheldon relatable just goes to show that I’m a nerd and that the nerdiness is the real reason that I like the show.

The Big Bang Theory 3The problem with The Big Bang Theory, though, is that it’s kind of inappropriate. Not only is there often some obscene humor, but the plotlines themselves are often pretty raunchy. It’s annoying enough when you’re watching something that contains a lot of sexual innuendos, but it’s pretty hard to ignore when the story itself revolves around the characters’ promiscuity. I know that The Big Bang Theory isn’t exactly X-rated and that it might sound a bit prudish to find it offensive, but I think it’s pretty sad that our culture is so accepting of obscenity that it can be considered prudish to be disturbed by it.

My point here is that, even though I enjoy The Big Bang Theory, I wouldn’t necessarily recommend it.  However, I don’t regret the fact that I’ve watched a good deal of it. I would here like to offer a list of random nerdy trivia that I have picked up from The Big Bang Theory. This list comes entirely from season one and only contains facts that I didn’t already know. (For example, I felt no need to include the fact that tomatoes are technically a fruit.) It also omits all of the physics stuff that admittedly went over my head. Most of the items on this list are direct quotations; those that are paraphrased are the ones that I didn’t put in quotation marks. Also, it is worth noting that I was too lazy to look up any of these facts yet (even though that had been my intention when I started making this list) so it’s possible that some of them were fabricated by the scriptwriters.

1. “If the height of a single step is off by as little as two millimeters, most people will trip.”- Sheldon

2. “Curry is a natural laxative.” –Leonard

3. “Thailand has had the fork since the latter half of the 19th century. Interestingly, they don’t actually put the fork in their mouths; they use it to put the food on a spoon, which then goes into their mouth.” –Sheldon

4. “Evolution has made women sensitive to high-pitched noises as they sleep so that they’ll be roused by a crying baby. If you want to avoid waking her, speak in a lower register.” (Note: I kind of cheated by putting this one on the list, because I’d actually heard it before)

5. The development of the atomic bomb was in part due to someone named Oppenheimer, who regretted his involvement in the creation of such a weapon.  –Leonard

6. “You can’t prove string theory. At best, you can say, ‘Hey look! My idea has an inherent logical consistency!’ “- Leonard (Note: I kind of cheated on this one, too, because technically it’s not really a fact. It’s just a quotation I like that happens to be about a specific scientific theory.)

7. There are only eight consonants in the Hawaiian language. –Sheldon

8. “A serape is open at the sides; a poncho is closed.” –Sheldon (Note: Actually, I knew this one, too.)

9. “When you start a party at seven, no one actually shows up at seven.” –Penny (Note: It’s really sad that I picked up a fact of commonly accepted social conventions from a TV show that is largely defined by the fact that the characters have a poor understanding of commonly accepted social conventions.)

10. “A bed is oriented with the headboard away from the door. It serves the ancient imperative of protecting oneself against marauders.”- Sheldon (Note: I have always instinctively followed this rule whenever possible, and now, thanks to TV, I know why.)

11. The phrase sleep tight “refers to the early construction of beds, which featured a mattress suspended on interlocking ropes which would occasionally…” –Leonard (Note: It disappoints me that Leonard doesn’t actually finish the sentence, because I was genuinely curious. I presume that the following words would have something to do with the ropes either breaking or stretching.)

12. “Indian parents continue to have a greater than average involvement in their children’s love lives.” –Sheldon

13. The brain chemistry of white mice is actually more similar to that of humans than is the brain chemistry of guinea pigs. –Sheldon

14. Dentists have an extremely high suicide rate. –Raj

15. “Gram for gram, no animal exceeds the relative fighting strength of the army ant.” –Shldon

16. “In a proper sandwich, the cheese is adjacent to the bread in order to create a moisture barrier against the lettuce.” –Sheldon

17. Bertram Forer, in 1948, conducted research to debunk astrology. –Sheldon

18. “Starch absorbs fluid, which reduces the amount of vomit available for violent expulsion.” -Sheldon

The Big Bang Theory 2

Bonus Interesting Metaphors:

1.When Penny said that she both hated and loved her ex-boyfriend, Leonard equated this with the paradox that light acts both as a wave and a particle.

2. When both Penny and Leonard ask Sheldon for advice about whether or not they should go through with their date, Sheldon compares their uncertainty about the future of their relationship with the uncertainty described in the Schrodinger’s Cat thought experiment. (Here is a link to a blog post I wrote a few months ago that described Schrodinger’s Cat)

This concludes my list. Just for the fun of it, I might make similar lists for later seasons, if I find the time to watch them.

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