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Admiral Regulus

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  1. Admiral Regulus

    Why

    By Admiral Regulus,

    Why?
     
    It's a simple question. Often, I consider it the most important question. It's easy to make observations--this is happening, this causes this, this is like this, this is not like this, and so on. Understanding the fundamental reason, or underlying reasons why is something different altogether. But it's what I try to do in every possible context, even if I don't always understand.
     
    So, when I was in my early teen years and looking to study engineering, I was often asked why. I'd heard so many things. Things like... Engineering is hard. You'll graduate in six years rather than four. You have to be good at math. You have to get good grades now or you'll be lost in college. You won't have much of a social life because you'll be doing math at 3am. You'll be loaded down with student debt and never be able to pay it back. You won't be able to get a job anyway because you'll graduate with no experience.
     
    So why? Why go through all the blood, sweat, and tears to get an engineering degree in the six years after high school? So people asked me: Is it to please my parents? Do I really, really, really like math? Do I feel some need to be challenged? Is it what I really want to do, or am I just in it for the money?
     
    The only answer I could come up with was, "what else do I do?"
     
    I am good at math. It frustrates me just as much as anyone, but I can do it and I can do well if I apply myself. But make no mistake, I don't love it. The truth is, I'm motivated to stick with it because I have no desire to do anything else.
     
    I have no intention to work in the retail or service industry, nor will I ever acquire such a thing. I don't want to work fifty or sixty hours a week for the rest of my life, at less than $10 an hour, just to make enough money to pay for a single-bedroom studio apartment and whatever car repairs I need that month. I don't want to wake up early every morning and have to talk to people complaining that the pasta I served them is a little cold. I don't want to spend the rest of my life cleaning feces and vomit off the bathroom floor. I don't want to be a landscaper or work in the construction industry, where I have to be outside in hot or cold weather all day. I don't want to work in the medical field, where I may have to see blood and gore on a frequent basis. I don't want to be a police officer or fireman, where I could potentially be putting my life in danger every day.
     
    So when my parents told me they would make me go to college and they'd pay for every expense along the way, I had no reason to argue with that.
     
    But biology was boring in high school. Geology and archeology never caught my interest, either. Game design could be fun, but I don't want to be a part of an industry that I have a huge distaste for. What about computer science? Web design? Or something more technical like welding? Machining? Plumbing? Or... y'know, I could always just suffer a few years of intense math and do engineering.
     
    So here I am, at twenty months, two summers, two falls, and one more spring semester away from graduation with a bachelor's of science in mechanical engineering. Overall GPA is a little more than 3.6, and my major GPA is a little more than 3.0. No work experience, no internship, not much of a social life, but I'll graduate without any debt and with, hopefully, a few job prospects.
     
    But my experience is... I don't like it that much. I spend so much time studying, just barely trying to cram all the knowledge into my head. It's stressful, so very much. For a few weeks every semester, my mental health takes a plunge. I lose the ability to sleep well. Open-book pop quizzes happen and it turns out I didn't have my book. Tests happen and I never have the time to finish them. I get so worried I'm not doing well enough. I try everything I can to do my best, but my professors aren't clear with their expectations, they don't always speak English very well, they do little more than read off of PowerPoint slides. I show up to class most days and almost fall asleep. The next day I try the homework--I work and work and work, the day goes by and I still don't finish. I pull my hair out, I submit what I have, and then I wonder what I was doing wrong for the rest of the night.
     
    It's true, I've done math at 3am. I've had dreams of solving differential equations. I can't watch movies anymore without thinking about how physics would never happen the way they're portrayed. Over the years, I've been enlightened on so many different topics, and I can't remove them from my head no matter what. Bending moment and transverse shear stress are good subjects for dinnertime conversation. I live and breathe the Carnot cycle in thermodynamics. Under normal walking conditions, my Reynold's number is between 30 and 35 thousand.
     
    I'm so far into this, I can't back down now. I never would, no matter how difficult it gets. It's still just one more year, and if I don't keep going, then the past five years of my life would have been a waste. That's a good reason why I've kept grinding along, but at this point, I'm just barely explaining anything yet. I've still not touched on the reason why. Above all else, there actually is one.
     
    That's it. There's only one real reason. One reason and one reason alone why I've decided to study engineering, and why I've continued doing so when it's been so stressful and challenging.
     
    It's because I'm so bad at dealing with stress, and I want an easy life. I have no desire to be the president. I have no desire to be a CEO, or even a project manager. I honestly don't care about money--as long as I'm not broke there are so many other things that are more important to me, such as having friends and family and not being stressed at work. Maybe it seems counter-intuitive, but the simple fact is that once I finish school, if I can get a job as an engineer, it will be virtually stress-free compared to being an engineering student. I'm making myself suffer in the short term so that I can benefit in the long term.
     
    What I want, is to be able to go into work every morning at 9am, do my job, have lunch, do more of my job, and then go home at 5pm having earned enough money to support myself and hopefully someday a family. That's pretty much all there is to it. Maybe when I'm in my 30's and 40's and even 50's I might feel better equipped to handle more responsibility, and I might seek a position that's more involved. But that's not what I want right now.
     
    Someday, I'll be done. I'll graduate. I'll get a job. I won't be rich and I don't have any desire to be, but I'll be able to buy a new car and pay for my hobbies. In a few years after that, I'll be able to buy my own house. I'll live there, work a mildly-interesting, medium-pay, low-stress job, and hopefully be able to support a wife and a child sometime soon after that. I'll save money for my kid's education in the same way my parents did for me, and thus I will fulfill my place in the circle of life.
     
    So that's why. That's why I do what I do; that's why I suffer. It's so that I won't have to suffer in the future.
  2. Admiral Regulus
    A member of this forum once said...
     

    So, you know what? Challenge accepted.
     
    Let's start with the basics. We know that the speed of light, denoted c, is always constant. Whether you're walking at 5 mph, riding in a plane at 500 mph, or on a rocket going 5,000 mph, you're always going to see light travel at the same speed. Why is this? Let's take a closer look.
     
    Speed is defined by a distance covered over time. In the case of the speed of light, it's a distance of 299,792,458 meters covered over a time of one second. If this is always going to be constant, then either the distance has to change, or the time has to change. You guessed it, it's the time that changes.
     
    But let's look at this more analytically. Let's suppose the we're going to shoot a radio transmission to astronauts on the moon, and instantaneously, as soon as they get it, they'll send the signal back to us. Let's also say that the distance to the moon is exactly a distance of d in km. Since we know how fast the signal goes, c, we can expect the transmission to hit the moon at a time tone-way = d / c. Then, we can expect the time to get our signal back to be tround-trip = 2d / c, since it has to make a return trip, too. To make things simpler, let's just call tround-trip to be t0.
     
    But what if another group of astronauts are on a shuttle going some speed v? Let's look at that.
     

     
    In this case, the people on the shuttle are going to cover a distance a = dt * v, where dt is the time that passes for them. We also know that the distance the light travels is going to be distance b + distance c, which, is going to be 2 * sqrt(d2 + (a/2)2). Using what we know for a, this becomes 2 * sqrt(d2 + (dt * v / 2)2).
     
    Since the speed of light is always going to be a constant c, this ultimately means that the light takes dt = 2 * sqrt(d2 + (dt * v / 2)2) / c seconds to reach the shuttle again. But for stationary observers, we can simply say that d = c * t0 / 2 as previously mentioned. Combining the two equations gives: dt = 2 * sqrt((c * t0 / 2)2 + (dt * v / 2)2) / c.
     
    This is a complex equation to solve, so I hope you remember your algebra. With a little bit of jiggery pokery we can move the terms around to find out what dt is. First, square both sides:
     
    dt2 = 4 * ((c * t0 / 2)2 + (dt * v / 2)2) / c2
     
    Then expand a little:
     
    dt2 = 4 * (c2 * t02 / 4 + dt2 * v2 / 4) / c2
     
    Then expand a little more to kill off some unnecessary terms:
     
    dt2 = t02 + dt2 * v2 / c2
     
    Then move both dt terms to the same side:
     
    dt2 v2 * c-2 * dt2 = t02
     
    Now, we can factor out dt:
     
    dt2 (1 - v2 * c-2) = t02
     
    From here, solving should be pretty easy. Let's just skip to the answer, which is:
     
    dt = (t02 * (1 - v2 * c-2)-1)1/2
     
    Or, alternatively:
     
    dt = t0 * (1 - v2 * c-2)-1/2
     
    So yes. That's the way this works. There, you have a mathematical expression for the way time changes relative to a difference in velocity between observers.
     
    We can plug in some numbers here and get a general idea of how this equation behaves. Going back to our example with things on the moon, a radio transmission from Earth to Moon takes 1.2822 seconds for observers on either body. But for observers moving on a rocket going 5,000 m/s, it's still 1.2822 seconds, because 5,000 m/s is such an insignificant speed. But what if the speed of the shuttle is 90% of the speed of light? In that case, it's 2.9416 seconds that pass on the moon, for those 1.2822 seconds on the shuttle.
     
    Another way to analyze this is to observe what happens at the extremes. If v is infinite, then dt becomes 0. If v is 0, then dt becomes t0. Larger v means a larger difference in time perception from stationary and non-stationary reference frames. This will be important later.
     
    What's interesting, is that just as time is not constant, neither is mass. A similar equation times an object's rest mass, m0, is the mass of an object traveling at that speed. So, in essence, we have:
     
    (1 - v2 * c-2)-1/2 * m0 = M
     
    Where M is the mass accounting for relativistic effects at high speeds.
     
    Now, let's look at what exactly energy is. Kinetic energy, at least, is defined by the integral of a force multiplied by a distance. Because of newton's laws, this force is d(M*v)/dt. So, the integral looks something like:
     
    d(M*v)/dt * ds, where the ds is the distance that the equation is being integrated over.
     
    Now, since ds/dt is just simply v, this means the form can be reduced to v * d(M*v). We know what M is based on the prior equation, and this becomes v * d((1 - v2 * c-2)-1/2 * m0*v). This is not an easy integral to evaluate, but it can be evaluated using integration by parts.
     
    The solution becomes:
     
    KE = M * c2 - m0 * c2
     
    Where KE is the kinetic energy. Rearranging this, we can write:
     
    KE + m0 * c2 = M * c2
     
    Or, in terms of energies:
     
    KE + E0 = E
     
    Here, we're basically saying the E0 term is the energy in which the reference frame is stationary, and E is the relative energy. Now, assume the mass is stationary in a certain frame, such that kinetic energy is zero. We still have that the energy is E0, and we know that E0is m0 * c2. So, in essence, this really just comes down to E = m * c2, which is the nice, cute and simple formula that everypony and their grandmother remembers.
     
    So, the answer is yes. I do believe the idiot that was Einstein. I believe this is completely true, and I do attempt to understand the mathematics behind it to the best of my abilities. My understanding leads me to believe that this is entirely correct.
  4. Admiral Regulus
    Dear Princess Trollestia,
     
    Today has been another eventful day, to say the least. Spring semester is over, and summer has started. I think the classes I'm taking won't be too bad. Today I stayed at school a little longer than usual. In that time, I bought my books and necessary software, and certified my hours so I get my money for all this. I got a spicy burrito, too. It was rather tasty.
     
    On the way back, the pegasi must have messed something up. Today was unusually hot for May, and the thunderstorm occurred thirty minutes before schedule. These complications meant that I was oven baked and then steam-cooked. This mistake nearly burnt my ass with five lightning strikes within a radius of ~400 meters as I was walking to my car. The rogue Pegasus causing this great dilemma must surely be found and held trial for this. Such atrocities must not be allowed to continue!
     
    In other news, I found not one, but two new bronies at school today. One was wearing a Doctor Whooves shirt, and the other had a mane six wallpaper on his laptop. Since we are in the same class, I expect to see him again. I need ideas on how to troll this guy. Please send me your advice. I await patiently.
     
    Your faithful admiral,
     
    Regulus
  6. Admiral Regulus
    This week's homework is mind-numbingly difficult. I started on Monday, and finished one problem. I finished five problems yesterday, working almost continuously from 3AM to 3PM. Today, I've been working on it for six hours, and I've finished only two problems.
     
    The first problem was just extremely complex, and it took me several hours to go through each step as I needed to do. The second was easy in comparison, and I did it correctly—it was only after a few hours that I figured out the solution was wrong. In the problem it stated R = 2m, but then in the solution it listed R = 3m. That one little thing changed everything. I had the right solution, but it was wrong because I used the right number. Makes sense, right?
     
    Today is also the day that my calculator has officially bit the dust. This morning was its final moment of life. It is now a brick. Hopefully the replacement I ordered will arrive before tomorrow morning, when I have my exam in another class.
     
    In the midst of this angst and frustration, I went for a short walk outside. It was really hot, so in doing so, my head immediately started to sweat and itch. I had too much hair for this kind of weather. So... I fixed that.
     
    When I went back inside, I grabbed the buzzer and immediately started cutting my hair. Yep, I needed to do that a month ago. It was long overdue. However... I didn't look at what size attachment I had on the buzzer before I started shaving my head. I thought it was the medium-sized one, but it was the really short one.
     
    So... y'know... in short, you can probably guess what happened. I'm now almost completely bald. Yes, I did want my hair shorter, but this is not what I had in mind. As if losing my wallet last month wasn't bad enough, I've now lost my hair and my calculator.
     
    Fantastic. I mean, it'll grow back in a week—a month at most—but for now, this is simply fantastic.
  7. Admiral Regulus
    My profile now has a background image! Hooray!
     

     
    I'm trying my best to make it blend well with the typical background of the site, and scale across various resolutions. It's harder to do than I initially would have thought.
  8. Admiral Regulus
    This is the crash I'm referring to:
     
    https://www.youtube.com/watch?v=J9eUwJ79fvo
     
    And the same crash from a second point of view:
     
    https://www.youtube.com/watch?v=5quxhNEio_g
     
    This doesn't even look real, but I can assure you it is. So, what happened here? Why is it that a car—especially one with such tremendous downforce—could do something so crazy as this? Well, first, I think it's important to take a closer look at how these aerodynamic systems work.
     
    Think of what happens when you're skating on ice. You slide. You have less friction with the ground, so you can't grip it to walk like you normally would. Now, imagine that you're carrying a heavy weight over your head, and this weight pushes your shoes into the ice (without breaking it). The force of the weight would give you better grip and allow you to walk on the ice, right? Sure, that makes sense.
     
    So, obviously, the better you can grip the ground, the faster and easier it is for you to walk. Race cars work by this same principle—the more weight there is pushing down against the ground, the more power can be applied without the wheels slipping.
     

     
    Notice there how at around 35 seconds in, the wheels start to spin, but they slip on the ground. Now imagine that if there was a force pushing the car to the ground, the wheels wouldn't slip, and the motion would be transferred entirely to the car. Thus, the car would be faster.
     
    This is where downforce comes in. Using wings, race cars generate a literal force pushing downward, and this helps the car stick to the ground. It does so without adding mass to the vehicle, so acceleration is largely unimpeded. This is why more downforce is generally better.
     
    The rear wing of the car is what generates downforce. It works in the same way a plane's wing generates lift, just in reverse. The wing creates a pressure difference in the air around it, so that a force is generated on the wing itself. This force pushes the rear of the car downward. This force allows the tires to grip the road better, which, as I mentioned, allows for better cornering and more stability.
     
    So, why is it that this one time, the downforce didn't work? You saw that car—it was literally flying. Something must have gone horribly wrong here, but what?
     
    The answer is actually not that complicated. Notice that before the car takes off, it is coming up on a hill. Due to the car's speed, the front of the car comes off the ground a little at the top of the hill. When this happened, it reached a critical angle. It reached the angle at which the air flowing under the front of the car starts to push the front upward.
     
    So, what we have is a car with a front end going upward, and a rear end going downward. This creates a moment, or a torque, or a spin, most informally. The back goes down, the front goes up, and voila! You're airborne. The car still has downforce, but it's all in the back of the car. The front of the car loses its downforce, and instead creates lift. Effectively, the whole thing acts like a wing, and up it goes.
     
    Still don't believe me on this? Consider what would happen if you have a sheet of paper sitting on a desk. If there's no wind, the paper won't move. If there's a little wind, the paper still may not move. But if you lift the edge of the paper up slightly and into the wind, air will flow between the paper and the desk, and this will push the paper up, up, and away.
     
    These cars work in a similar way; they're just heavier and we're talking about much stronger winds. Once that front end goes up, it's like that sheet of paper in the wind.
     
    As crazy as it looks, the phenomenon is hardly as uncommon as you'd think. This isn't the only time race cars do this. This happened once to a Mercedes prototype in 1999, and again to a Porsche in 2008...
     

     

     
    Notice how it always starts as the car rounds the peak of a hill. Notice how the back end still keeps pushing downward, even when the front of the car is high in the air. That's the combination of downforce and lift at work, simultaneously.
     
    There is one crash that doesn't involve the car first going over a hill, though. It's this one.
     

     
    So what happened in this case? When the Ferrari hit the prototype, the left rear wheel came off. You can see it rolling along the track. This impact made the left rear corner of the car go down, and by extension, the right front corner of the car came up. It's the same problem, just a different cause. The motion, in principle, allowed too much air to flow under the car, and again, the whole thing acted like a wing. Up, up, and away!
     
    And to think some people say flying cars are infeasible. Nonsense!
  9. Admiral Regulus
    Let's start with the basics. Force, measured in Newtons, can be broken down further into units of mass * acceleration. So...
     

    1 N = 1 kg * 1 m/s2


     
    As far as physics goes, this is pretty simple so far. So, what happens if you apply a force for a period of time, say, one newton for one second?
     

    1 N * 1 s = (1 kg * 1 m/s2) * s = (1 kg * 1 m/s)


     
    We end up with units of mass and velocity, in kg and m/s. This means that a force multiplied by a time is identical to a mass multiplied by a velocity. If you know any of the three, you can use algebra to solve for the fourth. In other words,
     

    F * t = m * v


     
    Instead, though, we'll call the velocity "Δv," with the Greek character delta representing change. This is because a force doesn't set the velocity, it changes the velocity based on what the initial velocity was. So,
     

    F * t = m * Δv


     
    Next, we'll move the mass over to the left side, so that we have isolated Δv. The Δv is what we're looking for, because that's how fast a rocket can go. Generally speaking, faster is better... yes? Right! Of course.
     

    F * t / m = Δv


     
    But, with rockets, the mass can change by a significant amount. Most of a rocket's mass comes from its fuel supply, so it isn't constant. It changes. Considering, we're going to need to edit this equation a little to make it more useful.
     
    We can say that's the instantaneous delta v, but what we're really looking for is the total delta v. So, let's break this up into small pieces of time, and sum that up over a variable range of m.
     

    Δv = ∫ F / m dt


     
    Now we just need an equation for m. Let's say that the starting mass is m0, and the mass decreases at a rate of ṁ. So, this leads to:
     

    m(t) = m0 - ṁ * t


     
    Note that we could also consider ṁ the rate of fuel consumption by mass. Substituting this back into the last equation, we get:
     

    Δv = ∫ F / (m0 - ṁ * t) dt


     
    The evaluation of this integral from t = 0 to t = t results with:
     

    Δv = (-F / ṁ) * ln ( | ṁ * t - m0 | / | m0 | )


     
    Since ṁ is the rate of fuel consumption and t is the time of the burn, ṁ * t is the total amount of fuel burned. Since mass can never be negative, we can also eliminate the absolute value signs. Considering, we can rewrite this as:
     

    Δv = (-F / ṁ) * ln ( mf / m0 )


     
    Where mf is the final mass, dry mass, or the mass of the rocket after the burn. This can be further simplified using properties of logarithms.
     

    Δv = (F / ṁ) * ln ( m0 / mf )


     
    And this is identical to the "delta v" equation on the KSP wiki. Hooray! I did something today!
  11. Admiral Regulus
    Disclaimer: rocket science isn't exactly the easiest thing to understand, but I'm going to try to make this as simple as I possibly can without dumbing things down. This *will* still contain math. Considering, proceed at your own risk. I am not responsible for any exploding minds caused by advanced mathematics.
     
    The acceleration due to gravity is typically treated as a constant number, 9.81 m/s2. This is really just an approximation, though—the Earth's gravitational pull is going to be less farther away from Earth, and more closer to the center.
     
    More specifically, the formula for universal gravitational attraction is:
     

    a = - G M / r2


     
    Where a is the acceleration, G is the universal gravitational constant, M is the mass of the object, and r is the distance from the object. G, the constant, is always 6.67384 × 10-11 m3 kg-1 s-2.
     
    If we model an object that has a constant speed, guessing how far it'll go in any period of time is pretty easy. If we have an object that has a changing speed, we can still guess how far it'll go based on the rate at which it's changing... but this is much more difficult. The problem here is that we don't just have a changing speed, but a changing speed that changes.
     
    So, let's say that we have a spaceship above Earth. Using the formula and the known mass of Earth, we can know the acceleration (a) if we know the distance ® from Earth. If we're farther away from Earth, the pull is less, and so we accelerate less. If we're closer to Earth, the pull is greater, and so we accelerate more.
     
    As our object gets closer to the other object it will be pulled more, so the acceleration changes. The acceleration is the change in speed, and the speed is the change in position. So, here's the thing: can we model the change in position based off of a speed that changes with a variable rate of change?
     
    Yes, we can. It's just a little difficult.
     
    We know that acceleration is the rate of change of velocity, and velocity is the rate of change of position, so we can write this as:
     

    a = - G M / r2


     

    dv/dt = - G M / r2


     

    d2r/dt2 = - G M / r2


     
    Where dv/dt means change in velocity per change in unit of time, and d2r/dt2 refers to the change in the rate of change of the position, per unit of time. Rearranging this, we have:
     

    r2 d2r/dt2 = - G M


     
    It looks more complicated than it really is. What this means is that the acceleration towards earth multiplied by the distance from earth squared is always going to be equal to the gravitational constant times Earth's mass. This is a differential equation, but unfortunately, it is not one that I know how to solve. Even using a computer algebra system (Maple 13 for anyone curious), I wasn't able to find the equation for the distance from Earth as a function of time.
     
    However, computers are really good at doing a lot of simple calculations very quickly. So, the next best thing is to use computer software to approximate any solution to this equation. So, we can plug in some numbers and see if we can find some solutions.
     
    Let's pretend we have a spaceship in orbit around Earth. Our orbit is at the same distance from Earth as the moon—384,400 km. We fire our engines to kill our velocity, so that we're not moving at all. Relative to Earth, we're now a static object. Our initial distance from Earth is 363,295 km, and now it's pulling us in.
     
    Since we know the Earth's mass is 5.972e24 kg, we can plug this in and see where the computer takes us.
     



     
    r(0) = d means that the initial starting distance at t = 0 is d, which is the value set in the parameter box. r'(0) = v means the initial speed is v, which is also the value given in the parameter window.
     
     
     
     



     
    Now, I can give any value of t, and find the corresponding values of r (distance) and r' (change in distance) through numerical approximation. So at t = 86400 seconds, or 1 day, the distance away from Earth is r = 374,243 km. We're moving toward Earth at a speed of 237 meters per second.
     
    After 2 days:

    r = 342,603 km



    r' = 503 m/s


     
    After 3 days:

    r = 285,069 km



    r' = 850 m/s


     
    After 4 days:

    r = 188,600 km



    r' = 1,467 m/s


     
    After 5 days:



     
     
    Hmm...
     



     
    So, let's look at what happened here. After t = 419307.05 seconds, the computer can no longer solve the equation due to a "singularity"... whatever the heck that is. That's roughly 4.85 days, so something must have happened at that point.
     
    We were getting closer and closer to Earth, and as we were getting closer, our speed was increasing. We inevitably got so close to Earth that our distance reached zero, and our acceleration reached infinity. We got so close to the Earth, that the gravitational pull was too strong to escape. In essence, we crashed into the Earth.
     
    See, at exactly 419,307 seconds, our distance was 16.793 km from the center of Earth. At that time, our velocity was 217.860 kilometers per second.
     
    At 419,306 seconds, just one second prior to that, our distance was 125.617 km from Earth's center.
     
    At 116 hours, the distance is 17,197 km from the center of the Earth and the velocity is 6.654 km/s. In the next hour it goes over the point of singularity, so we can guesstimate that we'll be hitting the Earth's atmosphere between hour 116 and hour 117.
     
    At that point, we'll need a completely different set of equations to model the trajectory. I'm getting lazy and my eyes are starting to hurt, so that's a subject for some other time.
     

    ---


     
    Before I'm totally done yet, we need some way to check and make sure these numbers are correct. There is another way to look at this same problem—using the law of conservation of energy.
     
    The law states that the total energy in any given system doesn't change. Normally we could model kinetic energy as:
     

    KE = 1/2 m v2


     
    and potential energy as:
     

    PE = m g h


     
    Where g is the acceleration due to gravity. But that's not going to work in this case, because as previously stated, the acceleration changes. So, we're going to need a different equation for that one.
     
    Work is a form of energy. For a variable force, work is computed as the integral of the force times the change in position. By evaluating the integral, we have:
     

    W = m M G (1/r - 1/d)


     
    Where d is the starting distance before the descent, and m is the mass of the spaceship.
     
    Since the total energy is just the sum of the work and kinetic energy, we can just add the two. And since there can be no increase or decrease in energy, the sum should be equal to zero.
     
    So, all the work done should be converted into kinetic energy for every frame of time. So, this means:
     

    m M G (1/r - 1/d) = 1/2 m v2


     
    Since m appears on both sides of the equation, we can cross that out. As such, the mass of the ship is unimportant, and has no effect on the calculation. This leaves us with:
     

    M G (1/r - 1/d) = 1/2 v2


     
    Using the same numbers calculated previously, we can say that the position at 116 hours is 17,197 km from Earth's center. So, we can plug all these numbers into the equation and solve for v to get 6.654 km/s. Everything checks out, and it's all good. These numbers make sense, so the calculations are correct.
     
    Perhaps some other time I'll also look at modeling orbits in two dimensions, but that gets even more complicated. I need to figure that one out first. You see, this is what I do when I don't have homework...
  13. Admiral Regulus
    The problem with space is that there's nothing up there. A normal car engine, diesel engine, or even jet engine mixes a small amount of fuel with the outside air to burn it. You need that air in order to be able to burn the fuel—and as such, normal engines don't quite work in space.
     
    The way we work around this problem is by using rockets. Rockets, unlike normal engines, take the "air" with them to space. In order to burn fuel with air we have to bring concentrations of the chemicals in air with us to space. While this works, it's inefficient because it makes our spacecraft very, very heavy. Whereas a plane's fuel may only be 10-30% of its total weight, a rocket's fuel is upwards of 90% of its total weight.
     

     
    Just look at it all. The amount of fuel attached to that thing is ridiculous!
     
    Since it's so ridiculous, this makes rocket launches very expensive and inefficient. If you want to go to space, you're going to need a lot of fuel. A lot of fuel costs a lot of money. This is why we've been trying to develop alternative methods of getting to space.
     
    One such alternative is a SSTO, or single stage to orbit craft. It's a space plane—you could think of it as a plane that can fly high enough and fast enough to go to space. This is a dream that has existed in people's minds since the whole space race started, but only now is it coming close to reality.
     

     
    Meet the Skylon, by Reaction Engines Ltd.
     
    It can take off and land like a plane, and it has air-breathing jet engines like a plane does. This means its first and only stage is lightweight—like a normal airliner, it doesn't carry too much fuel because it uses the fuel that's already in the air.
     

     
    Unlike a normal airliner, the Skylon's jet engines are a little different. The Skylon is the first plane to be designed with the SABRE (Synergistic Air-Breathing Rocket Engine). This means the engines function as jet engines would in the atmosphere, but they also have the ability to switch to a closed-cycle mode. When the plane is high enough and the air in the atmosphere is too thin to sustain a burn, the engine can switch to its internal fuel source and burn that.
     

     
    Unlike normal jet engines, the SABRE functions a little differently. It doesn't burn the air at as high of a temperature, so it can be made with lighter, less heat-resistant materials. As a result, it also has a thrust-to-weight ratio much higher. Unlike ramjets or scram jets, which operate at high speeds, the SABRE runs at lower speeds in the atmosphere, and thus needs less heat shielding. Again, this means less weight, and better efficiency.
     
    Just how much better are these engines, you ask? The peak thrust is at 1,350 kN for each engine in air-breathing mode. The F-22 Raptor, a modern American jet fighter, has a thrust of 116 kN for each engine without afterburner. Skylon is serious business.
     
    The engine has already been tested on the ground, and Skylon's first launch is expected to occur in 2019.
     
    All I can think is, "this probably wouldn't work in Kerbal Space Program," though.
  14. Admiral Regulus
    WHY DO WE NOT HAVE THEM ANYMORE!
     

     
    I swear, this happens to me at least once every fucking week. I'm working on something for two hours, and then something goes wrong and I lose it all. No problem, right? This is 2015, right? We have autosave features built into almost any software, right?
     
    No. For some reason, no. Loading unsaved documents only worked from 2007-2013. It stopped working in 2014, but I've yet to learn my lesson. I just don't get it.
     
    WHYYYYYYYYYYYYY? Why is it that the feature never works anymore? Why is it that every time I lose something I was working on, it has to be after exactly two hours of work, every time?
     

  15. Admiral Regulus
    Do you ever have one of those days when you're really tired, but have some ridiculous amount of energy to burn? Yeah... today is like that.
     
    I kinda want to go back to sleep, but for some reason I'm feeling so energetic that I can't even sit still. I had three hours of classes this morning, but even then I couldn't concentrate for more than thirty seconds. Just. Can't. Do it.
     
    Today is an exceptionally nice day. The weather is absolutely perfect right now. I might have spring fever or something. Is that what this is? Maybe I should just go for a walk in the park or something...
  16. Admiral Regulus
    I've had this idea for a fanfic for quite some time, but I haven't yet got around to writing it. Before I do, though, I'd like to be able to gauge the level of interest here. So, what do you think of this premise?
     
    Alien Infestation
     
    An influx of exotic ponies strikes up an unforeseen dilemma. They call themselves Bronies, and they're migrating to Ponyville in alarming numbers. Celestia incarnates the Ministry of Homeland Security in response, but cleaning up Equestria proves to be no easy task.
  17. Admiral Regulus
    “So — what is the meaning of life? I think people ask that question on the assumption that ‘meaning’ is something you can look for and go, ‘Here it is, I found it. Here’s the meaning. I’ve been looking for.’ That scenario, however, doesn’t consider the possibility that ‘meaning’ is something you create. You manufacture it for yourself and for others.
     
    “So when I think of ‘meaning’ in life, I ask, ‘Did I learn something today that I didn’t know yesterday, bringing me a little closer to knowing all that can be known in the universe?’ If I live a day and I don’t know a little more than I did the day before, I think I wasted that day. So the people who, at the end of the school year, say ‘The summer! I don’t have to think anymore!’ — I just don’t know. To think brings you closer to nature. To learn how things work gives you power to influence events. Gives you power to help people who may need it — to help yourself and your trajectory.
     
    “So when I think of the meaning of life, that’s not an eternal and unanswerable question — to me, that’s in arm’s reach of me everyday. So to you, at age six-and-three-quarters, may I suggest that you explore nature as much as you possibly can. And occasionally that means getting your clothes dirty because you might want to jump into puddles and your parents don’t want you to do that. You tell them that I gave you permission.”
     
    —Neil deGrasse Tyson (
    ) 
    This guy is the greatest guy to ever exist. 'Nuff said.
  18. Admiral Regulus
    If you go to your profile, you can view the amount of posts you have at different times of day. It's kinda cool, but I never thought I'd find a use for it.
     
    Until now, that is. As it so happens, I've been able to match up my posting frequency directly with my typical schedule. Take a look:
     

  19. Admiral Regulus
    This blog is an extended response to this thread: http://mlpforums.com/topic/118166-you-have-been-granted-3-wishes/
     
    I wrote that I would decline all three wishes, and I really do feel that way. I know, it makes no sense... it defies everything most people would probably think, but I am very firm in this decision. There are a few reasons why, but I'll get to that in a bit.
     
    This seems especially weird, considering that this time last year I was severely depressed. I saw tremendous issues with my life, and I was worried that I would not be able to overcome them. Of course I would have had many wishes. I did have many wishes.
     
    It is true that my state of mind has increased dramatically since this summer, but there are some other things going on at work here. This time last year, I would have wished for the following things:
    Someone I love to be my girlfriend
    Someone else to talk to and keep me company when she's gone
    Increased attractiveness/charisma so that more people like me

    Look, I'm not the guy to want a whole bunch of things. I often make jokes about wanting a hundred cars to drive, or a computer so powerful that it needs to be near a hydroelectric power plant... but that's all a jest. I really don't want much in life.
     
    I have most of everything that I need; money isn't an issue for me. I grew up poor, so I'm used to living an easy, simple life without unnecessary spending. When I was a baby, my family was on food stamps. I grew up being told that I couldn't have any toys because they wouldn't fit in the budget. But when I was a sophomore in high school, my father graduated with a master's degree—his income went up by a factor of 3x and off into the triple digits. Since then, we've all had more spending money than any of us know what to do with.
     
    I have a plan to go to school, get a good paying job, and buy a house. That's all stuff I can do on my own, and that's my goal for the next 5 years or so. If I wish that I suddenly have all of that, I'll be wishing those five years away from my life. I'll miss out on a whole breadth of life experiences.
     
    So, based on this line of thinking, nothing of physical or monetary value is of much interest to me. I have a car of my own, an apartment of my own, a decent computer, and I'm getting a good education without having to work a retail job or pay off any loans. What more could I really ask for, really? It's not that I hate my life... in fact, I actually love it.
     
    The reason why I was depressed can be answered by the things I would have wished for. This time last year, I was going through the most painful thing I've ever been through—heartbreak. It didn't just smack me around; it had me crippled. I went through the entire grieving process for about two years before I started to make a recovery.
     
    I had no friends I was comfortable talking to, and because of the nature of the situation, I was convinced that I was completely unlikable and worthless. Of course it's ridiculous to think those things, but I did think them. I had empirical evidence to believe it. I saw that no one appreciated me, no one cared about me, and, at times, no one would even talk to me.
     
    Any wishes I made would have been to alleviate the pain that I felt. I would have changed things around, so that I was a likable person with a working social life. I would have made sure that she liked me, and if not her, then at least someone did.
     
    Crazy? Yes! Of course! That's the point! That's why I would decline my wishes, if I were given them today.
     
    In this past year, I've come to realize that I am a likable person. I've realized that I'm not worthless. I've realized that I do have friends, and there are people I can talk to. A large part of that is because of this site, and an even larger part of that is because of MLP: FiM and the brony fandom as a whole. The largest part of that was removing a certain crappy person from my life.
     
    Since then, I've just come to accept that whatever happens, happens. I've gone through a lot of pain from that bout of depression, but it's made me a wiser, stronger person. It's produced a lot of good things, including a 250k+ word long fanfic. It's allowed me to reflect on so many of my own beliefs and desires, and develop a greater understanding of so many fuzzy concepts.
     
    There was a time when all I wanted was someone to love me, and I do still want that... but since I see that I am worthy of love, I know it can wait. It may not happen this year, next year, or even the year after that. Still, I can be patient. Thanks to all the positive support I've received from all the new and old friends I've talked to this past year, I am confident that it will happen eventually.
     
    And as long as I know that, I can be happy.
     
    I have a good life. Aside from that one hump, things have gone well for me in the past, and I predict things will go well for me in the future. I really don't feel the need to make any wishes, because I'd actually rather not mess anything up.
     
    In a way, living the life I have—especially after overcoming this depression—is already like a wish come true.
  20. Admiral Regulus
    Dear Princess Luna,
     
    What was it like being banished to the moon? It seems like a pretty nice place to be, actually. Being banished there doesn't seem like such a bad thing. I managed to capture an image of the lunar surface through my telescope tonight, and I think it looks beautiful. I would really like it if you could take me there someday.
     

     
    See? Doesn't it look nice? It's an even better sight in reality, without my cheap camera's grainy blur.
     
    Your faithful student,
     
    Regulus
  21. Admiral Regulus

    The Last of Us

    By Admiral Regulus,

    With midterms long gone and finals soon approaching, mid-November typically marks the pinnacle of procrastination in the life of Regulus. This year is no different—this time around, I started playing The Last of Us on PS3. I had heard many good things about the game, and after waiting for well over a year, I figured it was time to give it a try. I will admit that it's not a game that would normally pique my interest, but I heard the story is "soooooooooooo goooooooood", so... y'know... I had to give it a go.
     
    So, what do I think of it, you ask? I'm not typically one to review games, and I'm not typically one to even form opinions worth sharing. Something about this game is different, though. There is something about this game that I just... really found unsettling.
     
    First of all, this is not a review. That's not what this is. I'm not going to say the game is good, and I'm not going to say the game is bad. I'm not going to tell you whether or not to buy it. What I will do is describe my reaction to it, which means, you know, spoilers and all that good stuff. There's also going to be some vulgar language and descriptions of violent content here, so you've been warned.
     
    The game opens with you playing as a young girl, who happens to be the daughter of an older man. It's the typical horror story: it's late at night, sirens and gunshots are going off, and people are yelling and screaming. The doors are locked, but zombies are bursting through anyway. You know the drill. It's an attack. Run! Escape! Grab your gun and shoot anything that moves!
     
    The beginning of the game is very fast paced, but you don't encounter many, if any, enemies. It's just chaos, and you're just running. Eventually, you think you make it to safety, but... a soldier stops you. He points his gun at you, shoots you, and kills the little girl, your daughter.
     
    Immediately, I had a love-hate relationship with this game. The scene was intense, and I would be lying if I said I wasn't near the point of tearing up when the girl was shot. But immediately, this game makes a very blunt impression: no one is friendly in this world. I was baffled when the armed man started shooting at an unarmed, injured civilian and his daughter. Why? What is the—
     
    I'm sorry, I just don't get it. I don't understand. Soldiers are supposed to be protectors, not murderers. There was absolutely no reason for him to open fire. It was completely unnecessary, out of place, and just, in general, a terrible thing to do. It's against the Geneva convention. No civilized man would... it's just...
     
    Anyway, that was my first impression. From there, the game quickly jumps forward 20 years in time. You're working with an older girl named Tess, who's your partner in crime. Together, you're going after this guy named Robert, who is presumably some sort of crime lord. All you know is that he stole your guns, and you want them back. So, without much thought, I followed through the game's quests and got to the point where I found and interrogated Robert.
     
    Already, I was starting to have a bad feeling about this game. Even though Robert tells you what you want to know, you and Tess still end up killing him in the cutscene. At that point, I wasn't too pleased with what my character was doing, but I went along it. Robert stole my guns, therefore Robert is an asshole. Therefore, Robert should have died. Got it.
     
    It is at that point when you meet a younger girl named Ellie. You're asked to smuggle her, without much a reason as to why. Initially, I was expecting to go on some quest to reunite her with her family or something, but as it turns out, Ellie's family is long gone. The reason why you're supposed to smuggle Ellie is because she is infected, but not turning into a "clicker." There are people working on a cure for the fungus, and Ellie's immunity is the key to finding it.
     
    Okay. I liked that. Sounds good, right? I can help Ellie get to the people working on a cure, save humanity, and help overcome mankind's greatest challenges. Out of all the chaos I've seen, I can bring some good out of it. Right...?
     
    Wrong.
     
    Apparently, my character is a complete asshole. Oh, no. He doesn't want to do it. Tess wants him to do it, but he refuses. He's only looking after his own skin. My character beats the shit out of a guy and his hundred minions to recover a few stolen guns, but when it comes to saving the future of humanity... oh no, to hell with that. Let's let humanity die, shall we?
     
    So, moving forward, he does agree to smuggle the girl, against his will. Tess dies, and Ellie becomes your new companion. That's when the adventure begins.
     
    Nothing interesting happens between the two main characters until they get to a character named Bill. Bill is another survivor, who has an entire town to himself. The whole area is lined with booby traps and other point defenses. Again, we meet a character who is an asshole. He nearly kills you and the girl on sight, and then goes on to talk about how he refuses to look after anyone but himself.
     
    If you haven't noticed it yet, everyone in this game (except Ellie) is inherently cynical. The characters are all as dull and lifeless as the world around them. They don't have any compassion; they're just cold and stoic reflections of the world they live in. They shoot, and then ask questions later... if at all.
     
    After several hours of wishing I had Ezio's hidden blades instead of cheap, flimsy box cutters from Sam's Club, I finally reached my destination: my brother's place. Apparently, he's the guy who can take Ellie to the Fireflies, the group of people who can find a cure and save the human race.
     
    At this point, my character wants to leave Ellie with brother Tommy, and leave that at that. It's over. He's done.
     
    ...Until, of course, Ellie goes on her little tirade about being alone. This is where the game starts making a turn. Instead of my character being this heartless bastard, he starts to lighten up a little. He actually starts to care about Ellie, but there is a reason for this. Ellie reminds him of the daughter he lost. Ellie is the replacement.
     
    So, what happens? My character decides to go with Ellie to the Fireflies' headquarters. This is a genuinely good moment in the story. Finally, I get the impression that this asshole of a character I'm playing is finally starting to lighten up. Ellie is a breath of fresh air and a beacon of hope in this world; it's good to see that my character thinks so, too.
     
    All is well until the very end of the story. The bond between the main character and Ellie strengthens, and it's clear that a father/daughter relationship is forming. But the endgoal—getting Ellie to the Fireflies—turns out to be a big disaster.
     
    You see, Ellie wants to save humanity. She knows she's infected, and she knows she holds the cure. She's willing to embark on this mission, and she fights harder than anyone else. She's strong, fiery, and feisty. She's a badass, but she doesn't have the same "I don't care" attitude as everyone else. She does care. She knows what she has to do, and she's willing to do it.
     
    On the other hand, when the operation to extract her brain and examine the fungus begins, my character flips out. My character knows this means Ellie is going to die, but he can't have that. Oh, no. You know what he does? He goes around and starts killing everyone!
     
    No, no, no! Stop. These are the good guys! They're working to develop a cure, and you're having me shoot them all? Why? I'm the player. Why can't I decide what to do, here?
     
    I don't know. But, the point is, I can't. My character is insane, and there's nothing I can do to stop it. I'm forced to kill everyone, even the unarmed civilians. These are some of the last decent human beings on the face of the Earth, and I'm stabbing them in the throat for no good reason.
     
    Oh, but it gets better. Eventually, I do end up saving Ellie before her operation begins. My character brutally kills everyone in the entire facility, even when they try to talk sense into him. Then, he takes Ellie back "home."
     
    In the end, Ellie wakes up. She asks what happens. The answer? My character lies and says the Fireflies stopped looking for a cure. He says lots of people are immune, and they just don't care.
     
    WHAAAAAAAAAAAAAAAAAAAAT?
     
    No. Goddammit, no! That is not true. I care. Ellie cares. The Fireflies cared before you shot them all to pieces. There was hope for humanity, and it was you who ruined it. You wanted your daughter back, and you were too selfish to let Ellie make her sacrifice. You'd rather live your boring life out in the woods with your daughter than save the future of humanity. You'd rather forget about the past than face it and overcome it.
     
    Ellie asks if it's really the truth. The character says yes, to which Ellie pauses. "Okay."
     
    The end.
     
    Okay? How is this okay?
     
    I have never had such a bitter taste in my mouth after playing a game. I feel like I need to unwind the last few hours of my brain. The whole game is nothing but people cheating, lying, backstabbing, and killing with brutal hatred. I can't stand it. I know the game is supposed to have a good story, but it doesn't.
     
    The characters aren't relatable except Ellie, Sam, and Henry. Everyone else is just a sick person who would rather put a bullet in your head. At no point are there ever any negotiations. At no point is there ever an act of kindness. At no point does a character do something that I myself would do. The story goes out of its way to kill as many people and be as heartless and depressing as possible.
     
    In fact, the character I was playing as was basically an anti-me. He makes one choice I disagree with after another. I never would have killed Robert. I would have been more than happy to smuggle Ellie. I would gladly have accepted the mission. I wouldn't have been so harsh toward Ellie in the beginning, but I wouldn't have grown so attached to her later on.
     
    I wouldn't deny Ellie the right to make her sacrifice. I would have encouraged her to do it. I would have wanted to find a cure for humanity more than anything. I don't believe humans are such vile creatures as they are portrayed to be in the game, and I would fight tooth an nail for humanity's survival, if I had to. I would be willing to work as a team more so than ever in any sort of apocalyptic event. I wouldn't backstab anyone, and I wouldn't kill anyone unless I absolutely had to.
     
    The reason why I felt it necessary to discuss this game is because it conflicts with my core beliefs so strongly. I didn't expect to think it would be the greatest game ever, but I expected to at least enjoy it. I did not expect to finish it and feel like I had done something horribly wrong and completely against my principles.
     
    No matter what, I'm really not that misanthropic of a person. Although it may not seem like it, I'm not that cynical. This game really struck a chord with me, but not in a good way. It went against everything I know and fundamentally believe in. I couldn't relate to the main character at all, and at many points in the story, I wished I had the freedom to make my own choices.
     
    The game tries to present all these events as being morally ambiguous, but I just don't see it that way. I wouldn't have made the same choices my character did, and the story told here isn't one that resonates with me. It's too dark. It's too bloody. It's too hopeless.
     
    I don't believe in killing unless it's necessary. I don't believe in saving one person at the demise of millions. I don't believe in the "every man for himself" ideology.
     
    I believe every human life is valuable, and I will do whatever I can to ensure the survival not of myself, but of the human race. I believe humanity has a future. I believe humans can genuinely be good, even in dark times. I believe anything is possible—I don't believe in no-win scenarios. I kill all I want, I steal all I want, and I rape all I want. That amount is zero, because I don't want to do any of those things. A few people growing fungi in their brains isn't going to change that.
     
    If anything, in an apocalyptic world like that, I'd be one of the characters working on a cure. I'd do anything I could to make sure I can help as many survivors as possible. It doesn't matter if everyone I know and love dies. That isn't going to change. That would only make me more dependent on my local community.
  22. Admiral Regulus
    I do sincerely apologize for the long interval since my last letter. It has been a while, yes? Perhaps I should give you an update of the recent happenings.
     
    I am beginning to suspect a magical curse was brought upon this dwelling many aeons ago. Not only has the washing machine ceased to function, but the plumbing has also started to become problematic. As a result, I have been unable to sanitize kitchen utensils for the greater half of this week. Thankfully Rarity is not here to see the mess the kitchen is in—if she was, I do believe she would faint. The mere smell of all the putridity is enough to initiate the blowing of chunks.
     
    Similarly, the shower has turned into a filly pool. I've tried even the strongest industrial-grade drain clog remover, with no results. This problem will not be solved without alicorn magic, I'm afraid. At best, perhaps I could turn the filly pool into an elegant reflecting pond in your honor, the next time you visit.That is, of course, if you still remain open to the idea. Hopefully the incinerating burrito incident is a thing of the past. My magic discombobulator was just out of calibration, that was all. I promise, it won't happen again.
     
    In other news, I have been nearly as busy as Twilight studying the magic of friendship and differential equations. Do believe me when I say that series solutions to differential equations are seriesly terrible. In fact, I am almost certain that my homework is getting sequentially worse. Fortunately, however, my hard work has paid off. The differential equations princess has recognized my improvement, and I am proud to report that I will not be going back to differential equation kindergarten.
     
    I also have several friendship lessons to announce, should you be interested. This week, I learned that I should be careful with what I say, because what may seem like a simple comment, statement, or joke may actually be interpreted differently. Someponies feel as though they are being judged, and may perceive a harmless remark as something worse. Sometimes, it actually is better not to say anything.
     
    My next friendship lesson is that not everyone will be your friend. Not all ponies seek friendship, and not all ponies are willing to be friendly. Sometimes, it is best to let it be. Let bygones be bygones—the future always holds something new, and there will always be plenty of other opportunities to meet new ponies. True friendship is reciprocal; if this is not the case, there will be better friends.
     
    Often, the best friends come from places you would not expect. Only when disaster strikes do you know who is truly on your side and who is worth sticking to. Sometimes, even the best of friends can abandon you, but those you would not normally associate with may help you through the toughest of times. It is good to keep an open mind, and consider that those you may not normally talk to much or know very well—they may actually happen to be the best friends you'll have.
     
    And, lastly, I believe this one is most important. All that is necessary is an explanation. No problem is too complex that it cannot be understood by some other pony. Often, ponies keep their problems to themselves, fearing that no one would understand. This is understandable, pun not intended, but incredibly fallacious. Of course other ponies are going to understand. A failure to understand is often the cause of a failure to explain. Start explaining every step from the beginning, and even the most absurd scenarios will make sense to most ponies.
     
    This concludes my report for now. The upcoming weeks will be treacherous, with family holidays, upcoming exams, and projectile vomiting in the kitchen, but nothing is unmanageable. I will keep you updated on future matters—to the best of my magically-inept Earth-feline abilities, at least.
     
    Your faithful student,
     
    Regulus
  24. Admiral Regulus
    I've always found it odd that when most people look back on their years of elementary school, they remember having mostly positive experiences. Those years weren't particularly bad for me, not for any specific reason. However, after a little bit of thinking, recently, I think I've figured out why I hated that time in my life so much.
     
    The typical day of school consisted of a lot of work. To start the day off, there would be several activities that I'd have to do. That included putting words in alphabetical order, writing out vocabulary words 5 times each, doing simple math problems, or other things of the like. I dreaded every last moment of it. Every day, I couldn't wait for it to be over with.
     
    It's like this. Here, solve this subtraction problem. Show all your work. Then do addition to check your work. Then, if it's wrong, fix it. Sound fun? Oh, I bet you wanted to do this forty times tonight for homework!
     
    Y'know, there's something about that just never settled well with me.
     
    It's not just math, though. During that same time, I was also reading on a high enough level that most of the books recommended for me were chapter books—long, thick, and in the hundreds of pages. When I was in the second grade, I was reading on a fifth grade level. However, I didn't have the attention span of a fifth grader. When I was forced to check out those higher level books, I couldn't bring myself to read them. Reading so many pages just seemed tedious to me, and it made me dread reading... even though it was something I was supposedly good at.
     
    In the second grade, I was also given a placement test at the end of the year. My teacher told me that it didn't matter how I scored, I would still move on to the third grade. With that in mind, I did not take the test too seriously. On the reading portion, I just wouldn't read. I answered what I knew without reading, and left the rest open to my most educated guesses. On the math portion, I did a similar thing. I answered the questions that had obvious answers, and if I was required to solve something, I just wouldn't do it.
     
    It wasn't that I just couldn't do it, mind you. I just couldn't make myself do it.
     
    As it turned out, my scores on that test were very poor. However, my score for "critical thinking" or something similar to that still ranked high. This confused the hell out of my teachers, parents, and principal... but that's not the point here.
     
    The point is, there's a pattern. It wasn't just the second grade. In the fourth grade, I learned that I didn't always have to do my work. I basically christmas-treed everything that I did, and then I would lie to my parents and say that I didn't have homework.
     
    My thought process was something similar to this. Show my work? Pfft! I know how to do this, but it's too much work. I have to add like 30 numbers and then divide that by 30... all by hand? No way. Forget that! The answer is probably somewhere between 40 and 50, so I'm gonna guess the answer is 42. That's probably it. Woo! I'm done!
     
    In fifth grade, I got even worse. I became so lazy that I wouldn't do my math homework without a simple 4 function calculator. If my homework asked me to answer a question, I would never write it out in complete sentences, and use abbreviations wherever possible. For example, if the answer was "hinge joint and ball and socket joint," I would instead write "h, b." I remember that one in particular.
     
    I wasn't lazy enough to forgo doing the homework completely. I would still think about the question, and provide the right answer. But when it came to the tedious part—running a calculation or writing a sentence—I would take shortcuts.
     
    In my later years of school, I continued that same pattern. As soon as it became acceptable for me to use a graphing calculator on assignments and tests, I went from the bottom to the top of my class in math. As soon as I was required to read long books in school, I developed an even greater hatred of literature.
     
    Oddly, though, once I started learning a little bit of computer programing, I found that I really liked it. Whereas most people would only write the most basic code to do the process required, I would dedicate all my time to going above and beyond the requirements, so that my code is organized, clean, and has additional, unrequested functions. In all honesty, I did it because I thought it was fun. That was like my forte.
     
    So, this all brings me to a question. Why is it that I was more than willing to create an algorithm to complete a simple task, but when I am asked to do a simple task, I just can't make myself do it?
     
    What prompted me to think of this is what I'm doing today. You see, I have a differential equations test tomorrow. I can't use a calculator on the test. When I do the homework, which doesn't need to be turned in, all I do is check to make sure I understand the process. All the numerical computations and algebra... well, I kinda skip that part.
     
    And I noticed something. Of all the homework problems that I've done... of all the hours I've spent studying, not once did I ever fully solve any of the equations. Without even realizing it, once I get that far into the problem I stop and say "that's good enough, the rest I can just put into the calculator."
     
    Now, most people would probably look at this and say I'm lazy—especially my parents, teachers, and that generation. But is that really the case? Is this laziness, or something else entirely?
     
    I think I just have this aversion to doing tedious things. If something can be done by a computer, like copying a paragraph, putting a list in alphabetical order, citing a book, solving an equation, or anything of the like... I don't understand why I have to do it.
     
    And so I don't do it. Not unless I can make a computer do it, or not unless you're holding a knife to my throat.
     
    Am I the only one? It sure seems like it, because most people don't complain about having to do tedious things anywhere near as much as I do. In fact, I've never met anyone who would go as far as to lie and cheat as much as I did, just to keep from doing something that's actually simple and easy.
     
    I know I kinda think differently from most people, but could this be it? Is it that what's easy for me (critical thinking) is hard for most people, and what's hard for me (working out simple, algorithmic processes) is easy for most people?
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