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Akano

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Blog Entries posted by Akano

  1. Akano

    Equation of the Day #1

    By Akano,

    So, I've decided to do one of those daily-like blog entries, though I can't guarantee that I'll be able to do this every day (being a busy grad student and all). I figured that, being a physics grad student, math might be one of my stronger suits (next to reviewing LEGO sets), so I'm going to try and share an equation with you and see if I can explain it well enough for people to understand. 8D
     
    Tonight's equation: The wave equation.
     




     
    This says that the sum of the change in the change in the function, ψ, with respect to the coordinates used to represent it is equal to the inverse square of the speed of the wave,c, modeled by ψ times the change in the change of ψ with respect to time.
     
    This equation is the governing equation for all wave phenomena in our world. Sound waves, light waves, water waves, earthquakes, etc. are governed by this mathematical equation. In one dimension, the wave equation simplifies to
     




    which has the lovely solutions
     




     
    where A and B are determined by appropriate boundary conditions, and ω/k = c. This equation governs things like vibrations of a string, sound made by an air column in a pipe (like that of an organ, trumpet, or didgeridoo), or even waves created by playing with a slinky. It also governs the resonances of certain optical cavities, such as a laser or Fabry-Perot cavity.
     
    Since waves are one of my favorite physical phenomena, I find it very appropriate to start with this one.
     

  4. Akano
    Or, so some of my students in my Intro Physics lab think. Hopefully when you read the title you were ready to get your typing fingers ready to disprove me. You probably would have made an argument akin to the following mini-lecture.
     
    Gravity is a force between objects/particles proportional to the objects' mass. Newton's universal gravitation looks like this:
     

    Fg = - G m1m2/r2


     
    where G is a proportionality constant, the m's are the masses of the two objects in question, and r is the distance between the two objects. This is why we feel the Earth's gravity affect us, but we don't feel the moon's or sun's gravity affect us. They most definitely influence the Earth (since the sun causes our orbit and the moon causes the tides), but we don't feel the effects of their presence.
     
    So, if we have an object with mass m on Earth in free fall, its equation of motion is determined by
     

    Fg = m a = - G m ME/r2


     
    where ME is the mass of the Earth and a is the acceleration of the object. Note that, if we divide both sides by m, we find that
     

    a = - G ME/r2


     
    which means that the acceleration of an object in free fall has nothing to do with the mass of the object. In fact, you can see a video of this on the moon at Wikipedia's Gravitation page that shows Apollo 15 astronaut David Scott dropping a feather and hammer simultaneously. Since there is no air on the moon, the feather is not afloat longer than the hammer, and they fall at the same rate and hit the ground at the same time.
     
    Also, while I said earlier that gravity affects things with mass, it also affects light, which does not have (rest) mass. However, light has energy, and as Einstein showed with his Special Theory of Relativity, energy and mass are equivalent:
     

    E = m c2


     
    So, you can construct the relativistic mass of light, thereby finding the equations that govern the changing of the straight path of light in a gravitational field. Using Einstein's General Theory of Relativity, you can also view the gravitational field as a curvature of spacetime, which influences straight lines to be curved in the space near the massive object, affecting the path of light.
     
    Another interesting thing about mass: objects actually have two different masses associated with them: gravitational mass and inertial mass. Gravitational mass tells you how much an object interacts gravitationally, while inertial mass tells you how much an object resists a change in motion. In other words, more massive objects take more force/energy to alter their paths than objects with less mass. Here's the interesting thing, though: both these masses are equal, even though there really is no physical law stating that they have to be. The only reason we know these masses are equal is because empirical evidence says they are; there is no indication that these two masses are different to an appreciable/statistical extent.
     
    So, if you think that there are no unanswered questions in the realm of physics, you are sorely mistaken.
     

  5. Akano

    Autumn is here...

    By Akano,

    I went for a couple walks yesterday and today, and everything feels perfect. The air is crisp, the hoodie/jeans combo is perfectly comfortable, and the smell of fallen leaves permeates everywhere.
     
    Now if only all the trees decided to finally change color to match the rest of the mood.
     

  8. Akano
    Science is awesome. I am currently reading a journal article about how people are making the acoustic version of iridescence. For those who don't know, iridescence is what certain insects, jewels, soap bubbles, and CDs exhibit as that rainbow effect that changes color depending on what angle it's viewed. The sonic or acoustic version of this is creating something that varies in pitch depending on the angle at which you stand relative to it.
     
    Awesome.
     

  10. Akano

    Neutrons Bouncing on Glass

    By Akano,

    Yes, you read that right.
     
    So, today our physics department had our Journal Club, where one of the professors/grad students get to share a journal article or two that they found in the vast amount of physics literature available to academia. Today our resident dark matter-seeking professor gave the talk, and boy was it awesome.
     
    The researchers whose papers he found were bouncing neutrons on glass and looking at their quantum states due solely to the potential energy caused by gravity. Quantum mechanics with gravity.
     
    For those of you who don't understand how ridiculously awesome this is, let me put it in terms of Classical Mechanics: when a classical object is under the influence of a uniform gravitational potential (like that near Earth's surface), it follows parabolic trajectories. Imagine a ball bouncing on a table; it forms a series of parabolic bounces, each one smaller than the last due to friction and lost energy due to sound and such. This is essentially what this group did, but with neutrons and glass.
     
    However, because neutrons are not classical particles and instead behave quantum mechanically, they don't bounce in parabolic trajectories. Instead, they abide by the laws of quantum mechanics, which means that there are only certain heights above the table at which they are likely to be found and certain heights that they cannot be found. So, a neutron in the ground (lowest) state of this system is most likely to be found at about 10 microns (thousandths of a millimeter) above the glass.
     
    Also, when this was published back in 2005, it was the first time quantized energy levels due to Earth's gravitational potential alone were ever observed experimentally; the theory has been known for a while, but this is the first time anyone has in any way verified it.
     
    Now, this group is attempting to test the properties of the force of gravity using this apparatus and their neutrons. HOW AWESOME IS THAT?!
     
    This blog entry brought to you by SCIENCE!
     

  11. Akano

    Back to School

    By Akano,

    So, today was the first official day of school at my grad school, but I didn't have any classes. Today was lab orientation for Monday and Tuesday lab sections (since we had yesterday off). Having nearly 50 students crammed into a room only able to seat 32 is rather entertaining.
     
    Also, I have a talk to give on Friday on my research I did over the summer. This wouldn't be so much of an issue if I knew which part of the research to discuss, as I worked with two undergrads, and we have to split the topics of our research between us. However, one of the students worked in another lab over the summer as well, so she's probably not going to present on what the three of us did at all. Now the talk has to be divided in half.
     
    Also, did I mention the talk was Friday? ._.
     

  13. Akano

    NYC and other Adventures

    By Akano,

    So, on Tuesday my roommate, one of the other physics grad students and her friend, and I all took a trip to the Big Apple. My roommate and I had never visited, and I have to say it was not a horrible city experience.
     
    Our first stop was lunch in Central Park, after which we headed to the American Museum of Natural History where we spent time exploring various exhibits including DINOSAURS(!!!), marine life, Egyptian stuffs, and the Rose Center. Unfortunately, we did not see Neil DeGrasse Tyson there, which makes the physicist in me slightly sad, but good times were had. We then headed over to the awesome Nintendo World, where there was more Pokémon merchandise than I could believe. I wish there had been more Legend of Zelda merch that wasn't baseball caps or overpriced T-shirts (I would love to own a pair of Triforce pajama pants). Then we headed to Rockefeller Center to visit the majestic NYC LEGO Store, where I bought a magnet of a LEGO minifigure with an I ♥ NY t-shirt (with the ♥ made of LEGO bricks). Then we visited McGee's Pub, famous for being the bar that MacLaren's Pub of How I Met Your Mother is based on. We then took a subway downtown to view Lady Liberty herself over the bay after sunset.
     
    It was fun times. 8D
     
    Also, today my grad school had an academic fair for the incoming freshman class. The physics department had LED magnet-badge type things to give away to students to suck them toward our table. Go physics!
     

  15. Akano
    Today, we take a journey to Middle Earth and take a look at the LEGO reimagining of the Mines of Moria.
     
    Presentation
    From the design of the box to the instruction manual, these are the first things you see before building the set.
     



     
    I really like the LEGO LOTR logo with the one ring on Sauron's finger in the upper right corner along with the map of Middle Earth in the background. The back highlights various parts of the set. I do like their cave-like choice of background for the front picture.
     
    Building
    Half the fun is had building the set. How fun is it to build and how easy or challenging is it?
     



     
    This set comes with four bags of pieces which build the well & Balin's tomb, the wooden doors, the center of the wall, and the outsides of the wall. The build took me about 2-3 hours or so (not counting distractions). I must admit that at times I jumped the gun with some of the smaller pieces and thought I had run out of pieces, meaning that I was frantically searching my pile of pieces for I piece I simply misplaced during the build, so follow instructions carefully.
     



     
    Again, this set does come with stickers (grr!) for some of the detail, such as the dwarves' record and Balin's tomb.
     
    Set Design
    Now that the set is complete, we can critique how it looks from every angle. New or interesting pieces can also be examined here.
     

    I totally forgot the cave troll in this pic, sorry.


     
    The set consists of three main parts: the wall, the door, and the tomb and well.
     



     
    The door has some pretty good detail, but some of that is provided by stickers with the wood plank patterns. They also included the axe that locks the doors shut for about 10 seconds from the movie, and this axe has a metallic copper blade, which I thought was cool. I also like the use of spyglass pieces as torches. Looking from the back, the wall on the right has a lever that makes it fall.
     



     
    I like the detail of the cave troll; however, he has absolutely awful balance while holding his hammer, so the number of poses he can have while wielding it are limited. He has a tendency of falling forward, since his mold is rather forward-heavy, even when not wielding the hammer. If you have studs beneath his feet, then he should be fine, but he's rather unstable just standing on a table.
     



     
    The wall consists of bookshelves with some of the oldest books stickers can convey. There is also some of the dwarves' treasure underneath the floor in its own little nook. For some reason the treasure chest moves in and out.
     



     
    The sides of the wall have towers that can be toppled using levers underneath them. The box shows one of these landing on the troll.
     



     
    These are my favorite parts of this set. I don't know if it's the fact that they're small and simple or if it's because these are the parts most focused on in the movie, but I love the well and the tomb. The tomb actually opens to reveal Balin's skeletal remains.
     

    Shouldn't Balin's skeleton be dwarf-sized?


     
    My only qualm with the well would be that the skeleton does not have any armor/helmet on it unlike the movie. Otherwise, I love this part of the set.
     
    Now, onto the minifigures:
     



     
    The heroes are very true to their movie selves save probably for Pippin; I don't really see Billy Boyd when I look at him; in fact, Pippin's face isn't too different from Shire Frodo's face. My favorite is probably Gimli,since the detail in his face, beard, and helmet are amazing. Boromir's appearance is probably second in terms of movie accuracy.
     



     
    the goblins are pretty creepy looking, and while I'd say their faces are pretty good, they seem to have too much hair (but maybe I'm remembering the movie wrong). I do like the shield that the one carries, as it's very jagged and looks goblin-made.
     

     



     
    All the characters have back printing on their torsos, which is more impressive on some than others. They also all have flip faces, which is amusing for Gimli, since all that changes when his beard is on is that his eyebrows go from neutral to angry. Also, they tried to make Legolas look intimidating, which just never happens in the movies.
     



     
    The hair/helmets of the characters all seem to be new molds to match the movies. I particularly like Gimli's helmet, which again has a lot of detail put into it (including printing).
     



     
    As far as interesting pieces go, there are quite a few jewels in this set. You also get a set of weapons that came originally in the Heroica games which I found interesting. They're mainly there to litter the ground of the tomb, probably to serve as the weapons of the dwarves who once populated the halls. You also get a bone and a rum bottle that originated the Pirates of the Carribean sets.
     
    Playability
    The other half of the fun is in playing with the set. How well does the set function and is it enjoyable to play with?
     

    For the Shire!


     
    This set has quite a bit of play to get out of it, since you can basically reenact the battle in the tomb with it. It's also makes for good scenery for any type of underground adventure you'd like your characters to embark on, so there's a good deal of potential. Any Lord of the Rings fan, of course, will just want to spend hours having our heroes take out that cave troll.
     
    Final Thoughts
    Once it's all said and done, how does the set stack up? Should I get it?
     



     
    For any fan of the movies this set is a good pick, since it is, I think, one of the more accurate depictions of one of the movie scenes. All the minifigures in this set, save for the skeletons and Gimli, are exclusives, so it's a must-have for those who want, well, at least half of the Fellowship.
     
    Pros
    What's to like?

    Great detail
    Very true to the film
    The minifigures
    Cool pieces

    Cons
    What's not to like?

    The price tag
    Cave troll is a bit unbalanced

    I hope all the LOTR fans who are reading enjoy this review. For the gallery, go here when it becomes public.
     

  16. Akano

    Family vacation

    By Akano,

    Going to spend some time with KK, Tekulo, my mom and my roommate for the next week. I'll have BZP access, but I'm not sure if I'll actually be on during that time, so if I'm quiet for the next week, you now know why.
     

  18. Akano

    New Skin is New

    By Akano,

    And I likes it! Thankee to Than and Watashi Wa.
     
    Also, an awesomely amazing photo autographed by Yakko Warner/Pinky himself, Rob Paulsen, came in the mail today. I am quite happy.
     

  19. Akano
    In continuing my trend of reviewing 90s LEGO System sets, I'm turning my criticism to one of the most beloved, nostalgic LEGO sets arguably of all of LEGO's existence.
     
    Presentation
    From the design of the box to the instruction manual, these are the first things you see before building the set.
     




     
    Ah, the desert. Something about it inspires adventure. Perhaps it's the survival aspect of it. Anyway, the box pulls off the desert background very nicely, and the action of a bunch of cavalry men attempting to catch bandits gives off the Wild West feel. Also, the back of the box has alternate models, which LEGO doesn't do anymore and is something that I personally miss a lot from the newer sets. The large set also has the flap on top which opens to reveal the interior of the box. The plastic/cardboard sheet inside was used to preview minifigs and/or exclusive/unique pieces, but seeing as mine was used, this is not the case here.
     
    Building
    Half the fun is had building the set. How fun is it to build and how easy or challenging is it?
     




     
    This set is rather ridiculous with the space its pieces take up, so I couldn't organize them completely. There are 668 pieces total, which makes for a mild build. I think I built it up within an hour, since the build isn't terribly difficult. Also, I couldn't help but hear Gerudo Valley in my head as I was building. I can't imagine why.
     


    These pieces and the 1×2 and 1×4 log pieces are extremely prominent, in case you couldn't tell.


     
    Set Design
    Now that the set is complete, we can critique how it looks from every angle. New or interesting pieces can also be examined here.
     
    There are four 16×32 baseplates in this set (no, I'm not kidding), so the build is split up into four parts. First, let's look at the entrance. the entrance:
     


     

    A fort? That's easy! Feel free to follow along with my simple step-by-step instructions. I make building FUN!!


     
    The entrance is pretty...entrancey. The watchtowers are cool, even though (as seen from the back) they have no ladders to lead up to them, so one must wonder how a guard could get up there to look out from there. The doors are barricaded from the inside with a bar made from a 1×10 plate and two 1×2 hinge pieces, as are the other doors on this set. It's pretty cool how they designed that (it is a fort, after all).
     
    Now, the walls:
     




     
    The first wall is rather nondescript. Just a guard wall with a ladder leading up to the top.
     




     
    The second wall has a little more going on. There's a side entrance and a rock wall made with, which I recently found out is called, a Big Ugly Rock Piece (BURP). The cactus at the bottom of the wall hides a cache of coins. This wall also has an actual tower on it to place a sentry in, which is cool. We also have a flag like the one at the entrance adorning the tower.
     
    The final part of the set is headquarters:
     




     
    This is my favorite part of the set, as it actually has something going on other than being a wall. The headquarters reminds me of the Hydeout in the Borscht Bowl Club from the first case of Apollo Justice: Ace Attorney. It has its secrets, like the hiding place in the chimney behind the fireplace.
     


    I don't know what you're talking about; I'm not hiding anything.


     
    Or the spinning table that sends the bandit or cavalry member to the prison/floor below.
     


    You have a full house? I only have a two pair: a pair of ones, and another pair of ones.


     
     
     
    Here, you can see the Colonel and Dewey Cheatum (no, I did not make that name up) playing at the aforementioned table. Rotate the table counter-clockwise, and Dewey ends up doing time for the vast number of card-based crimes he's committed.
     


    Not pictured: The incarceration of whoever came up with the name "Dewey Cheatum."


     
    The room is accessed by its minifig regulars by a set of stairs that can also be found in the LEGO Studios Vampire Crypt, along with others.
     




     
    Now that we've covered the set itself, let's go over the minifigures:
     




     
    There are two factions. Let's first go over the bandits.
     




     
    From left to right, we have Black Bart, Flatfoot Thompson, and (*sigh*) Dewey Cheatum. Of all the figs, I think Dewey's is the coolest. His playing cards style vest and top hat clash a lot with his nasty gold-toothed scowl. It's as though class and hillbilly merged. Flatfoot Tom has a great western villain face, and Black Bart always struck me as the muscle of the gang.
     




     
    The cavalry contains three soldiers, two lieutenants, and the colonel (whose face somewhat resembles that of the LEGO Chess king). Since this set is the headquarters of the cavalry, it contains the largest number of their figures, which is definitely a plus for this set.
     


    I may have shot the sheriff, but I did not shoot this guy.


     
    This set does not contain the sheriff (but Sheriff's Lock-Up does, and I hope to find a good one soon...), but it does contain his deputy. He has a white hat and hair and a sweet cowboy vest. Not much else to say about him; however, he looks to me like he's always chill about everything, even if a gunfight were to start.
     
    Playability
    The other half of the fun is in playing with the set. How well does the set function and is it enjoyable to play with?
     




     
    Other than the doors opening and closing and the table trap that leads to the prison, there isn't really that much functionality with this set, which disappoints me a little bit. However, this set is a great setting for a western adventure, so while there isn't much to do with the set, there is a lot that someone could come up with at the set.
     
    Final Thoughts
    Once it's all said and done, how does the set stack up? Should I get it?
     


    Who shot first, Dewey or the Colonel?


     
    This set, being a very nostalgic set, is quite pricey. If you can find this set for less than $100 and you want this set, grab it. I understand why it's so loved, but I personally wouldn't place it as more important than, say, Pharaoh's Forbidden Ruins or Night Lord's Castle.
     
    Pros
    What's to like?
    Big
    Many minifigs
    Classic theme

    Cons
    What's not to like?
    Price
    Not much functionality

    I hope you enjoyed this one. For the gallery, go here when it becomes public.
     

  20. Akano
    I got another 90s LEGO System set this week, and am currently writing up the review. I won't tell you what it is just yet, but I'll give you a hint: it was immensely popular, and I don't think it was one that I've talked about wanting to get. It was also featured in the PC LEGOLAND game.
     
    So there are three-ish hints.
     

  23. Akano

    Complex Numbers

    By Akano,

    Math is a truly wonderful topic, and since I'm procrastinating a little on my physics homework, I'm going to spend some time talking about the complex numbers.
     
    Most of us are used to the real numbers. Real numbers consist of the whole numbers (0, 1, 2, 3, 4, ...), the negative numbers (-1, -2, -3, ...), the rational numbers (1/2, 2/3, 3/4, 22/7, ...), and the irrational numbers (numbers that cannot be represented by fractions of integers, such as the golden ratio, the square root of 2, or π). All of these can be written in decimal format, even though they may have infinite decimal places. But, when we use this number system, there are some numbers we can't write. For instance, what is the square root of -1? In math class, you may have been told that you can't take the square root of a negative number. That's only half true, as you can't take the square root of a negative number and write it as a real number. This is because the square root is not part of the set of real numbers.
     
    This is where the complex numbers come in. Suppose I define a new number, let's call it i, where i2 = -1. We've now "invented" a value for the square root of -1. Now, what are its properties? If I take i3, I get -i, since i3 = i*i2. If I take i4, then I get i2*i2 = +1. If I multiply this by i again, I get i. So the powers of i are cyclic through i, -1, -i, and 1.
     
    This is interesting, but what is the magnitude of i, i.e. how far is i from zero? Well, the way we take the absolute value in the real number system is by squaring the number and taking the positive square root. This won't work for i, though, because we just get back i. Let's redefine the absolute value by taking what's called the complex conjugate of i and multiplying the two together, then taking the positive square root. The complex conjugate of i is obtained by taking the imaginary part of i and throwing a negative sign in front. Since i is purely imaginary (there are no real numbers that make up i), the complex conjugate is -i. Multiply them together, and you get that -i*i = -1*i2 = 1, and the positive square root of 1 is simply 1. Therefore, the number i has a magnitude of 1. It is for this reason that i is known as the imaginary unit!
     
    Now that we have defined this new unit, i, we can now create a new set of numbers called the complex numbers, which take the form z = a + bi, where a and b are real numbers. We can now take the square root of any real number, e.g. the square root of -4 can be written as ±2i, and we can make complex numbers with real and imaginary parts, like 3 + 4i.
     
    How do we plot complex numbers? Well, complex numbers have a real part and an imaginary part, so the best way to do this is to create a graph where the abscissa (x-value) is the real part of the number and the ordinate (y-axis) is the imaginary part. This is known as the complex plane. For instance, 3 + 4i would have its coordinate be (3,4) in this coordinate system.
     
    What is the magnitude of this complex number? Well, it would be the square root of itself multiplied by its complex conjugate, or the square root of (3 + 4i)(3 - 4i) = 9 + 12i - 12i +16 = 25. The positive square root of 25 is 5, so the magnitude of 3 + 4i is 5.
     
    We can think of points on the complex plane being represented by a vector which points from the origin to the point in question. The magnitude of this vector is given by the absolute value of the point, which we can denote as r. The x-value of this vector is given by the magnitude multiplied by the cosine of the angle made by the vector with the positive part of the real axis. This angle we can denote as ϕ. The y-value of the vector is going to be the imaginary unit, i, multiplied by the magnitude of the vector times the sine of the angle ϕ. So, we get that our complex number, z, can be written as z = r*(cosϕ + isinϕ). The Swiss mathematician Leonhard Euler discovered a special identity relating to this equation, known now as Euler's Formula, that reads as follows:
     

    eiϕ = cosϕ + isinϕ


     
     
     
    Where e is the base of the natural logarithm. So, we can then write our complex number as z = reiϕ. What is the significance of this? Well, for one, you can derive one of the most beautiful equations in mathematics, known as Euler's Identity:
     

    eiπ + 1 = 0


     
    This equation contains the most important constants in mathematics: e, Euler's number, the base of the natural logarithm; i, the imaginary unit which I've spent this whole time blabbing about; π, the irrational ratio of a circle's circumference to its diameter which appears all over the place in trigonometry; 1, the real unit and multiplicative identity; and 0, the additive identity.
     
    So, what bearing does this have in real life? A lot. Imaginary and complex numbers are used in solving many differential equations that model real physical situations, such as waves propagating through a medium, wave functions in quantum mechanics, and fractals, which in and of themselves have a wide range of real life application, along with others that I haven't thought of.
     
    Long and short of it: math is awesome.
     

  24. Akano

    Reflection

    By Akano,

    The other day I decided to look at my comics from start to finish to remind myself of where I started and how far I've come to get to the comics I have today, and I have determined the following.
     
    I sucked in the beginning. I mean, I was awful! Did I really actually think some of those comics were post-worthy? Holy Mukau!
     
    Seriously, go over to my topic and read the first couple comics. Then, cry in a corner. For several hours. That's what I did.
     
    In unrelated news, I've been toying with the idea of voicing some of my comics in a sort of strange animated-comic sort of way. Would anyone anywhere think this would be entertaining? KK may even have a role.
     

  25. Akano

    Comic And Question

    By Akano,

    New comic is up! It covers the subject of learning new things.
     
    Now, I have a question to pose to you. My friends were talking about being productive with their evenings (both are fellow physics grad students), and I had mentioned that I had felt really productive lately due to the fact that I made two reviews (one of which no one has commented in yet. show it some love!) and finished my latest comic. Then they replied, "I wouldn't really call that productive; you just do that for fun."
     
    To be fair, my one friend was working on a paper she's trying to get published, but I feel I have to defend myself. While I do enjoy writing these set reviews and my comics (which I'm sure you all would love me to update more often), they do take honest work to produce since no one would want to read a review written by a twenty-three-year-old that looks like it was written by a four-year-old. I tried to convince them otherwise, but they kind of shrugged it off.
     
    So, my question to you is this: do you think that working on these "hobbies" is not productive? Just curious on your opinion.
     
    P.S. Please do not say anything hurtful about my friends, as they are my friends, and I do love them very much.
     

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