Akano

HI, BZPOWER! So, in the last few weeks, my family came to visit (including Tekulo and KK) and we spent the latter half of the week seeing sights and enjoying each other's company. My mom won a game of Trivial Pursuit on a category that was supposed to stump her. Story of my Trivial Pursuit life. When they left, they abandoned KK with me, which has led to me stepping into the nerd realm of playing Dungeons & Dragons. We're doing a campaign in the land of Hyrule with the races of Hyrule being used as analogs of D&D races. We're currently in the Forest Temple seeking an herb to cure the Great Deku Tree's muteness. I'm also working in a new physics lab where I'm studying the energy states of the hydrogen molecule (H2). I'm thoroughly enjoying it, since I'm learning computational stuffs and learning my way around Linux. (Emacs rules the school.) The program I'm working with is in Fortran, which is my native programming language but was written by someone else with a lot more skill than I possess. And now I'm shoveling through a LOT of data.

Taka: Thankee! I found how to make it from one of Dr. James Grime's videos online. I am now looking for various other origami Platonic shape stuffs. Tekulo: AND WHY DIDN'T SOMEONE GIVE ME SOMETHING TO YELL ABOUT?!

Your parents aren't dead; you're not a billionaire businessman mechanical wizard; and you don't protect Gotham City from dangerous criminals. I fail to see how you relate to Batman. Also, DJ Pirate Fez Crab FTW. Tis a shame to see him go, but I think he'll fit in well. He is a DJ Pirate Fez Crab, after all.

I made a Post-It note dodecahedron: It was fun. 8D For the record: each face is made up of five Post-It notes, each a different color, so that, per face, no color is repeated.

Our state does a "maneuverability" test, which is essentially parallel parking, but with cones in the middle of a lane instead of cars on the side of the road. That's totally what parallel parking is like, right?

Don't worry, good sir. Said party's dweebness shall be made aware. Also, feel better soon. May your presentations and projects and other such things go smoothly.

I didn't know you had a second interview. That's pretty awesome. Also, temps. That's pretty sweet as well.

*facepalm* The 3DS is a nice portable gaming device, even if you don't include the 3D gimmick.

I have finished my last Jackson E&M homework ever. Of all time. *insert angelic choir here* Also, NEW ZELDA 3DS GAME HOLY MUKAU I CAN'T WAIT! [/slowpoke]

You may have learned once that classical mechanics all stems from Newton's laws of motion, and while that is true, it is not necessarily the best way to solve a given physical problem. Often when we look at a physical system, we take note of certain physical parameters: energy, momentum, and position. However, these can be more generalized to fit the physical situation in question better. This is where Lagrange comes in; he thought of a new way to formulate mechanics. Instead of looking at the total energy of a system, which is the potential energy plus the kinetic energy, he instead investigated the difference in those two quantities, where T is the kinetic energy and V is the potential energy. Since the kinetic and potential energy, in general, depend on the coordinate position and velocity of the particle in question, as well as time, so too does the Lagrangian. You're probably thinking, "okay, what makes that so great?" Well, if we were to plot the Lagrangian and calculate the area under the curve with respect to time, we get a quantity known as the action of the particle. where t1 and t2 are the starting and ending times of interest. Usually if the motion is periodic, the difference between these times is one period. Now, it turns out that for classical motion, the action is minimized with respect to a change in the path along which the particle moves for the physical path along which the particle actually moves. This sounds bizarre, but what it means is that there is only one path along which the particle can move while keeping the action minimized. Physicists call this the Principle of Least Action; I like to call it "the universe is inherently lazy" rule. When you do the math out, you can calculate an equation related to the Lagrangian for which the action is minimized. We call these the Euler-Lagrange Equations. These are the equations of motion a particle with Lagrangian L in generalized coordinates qi with velocity components denoted by qi with a dot above the q (the dot denotes taking a time derivative, and the time derivative of a coordinate is the velocity in that coordinate's direction). This is one of the advantages of the Lagrangian formulation of mechanics; you can pick any coordinate system that is best-suited for the physical situation. If you have a spherically symmetric problem, you can use spherical coordinates (altitude, longitude, colatitude). If your problem works best on a rectangular grid, use Cartesian coordinates. You don't have to worry about sticking only with Cartesian (rectilinear) coordinates and then converting to something that makes more sense; you can just start out in the right coordinate system from the get go! Now, there are a couple of special attributes to point out here. First, the quantity within the time derivative is a familiar physical quantity, known as the conjugate momenta. Note that these do not have to have units of linear momentum of [Force × time]. For instance, in spherical coordinates, the conjugate momentum of longitude is the angular momentum in the vertical direction, which has units of action, [Energy × time]. The Euler-Lagrange equations tell us to take the total time derivative of these momenta, i.e. figure out how they change in time. This gives us a sort of conjugate force, since Newton's second law reads that the change in momentum over time is force. The other quantity gives special significance when it equals zero, This is just fancy math language for saying that if one of our generalized coordinates, qi, doesn't appear at all in our Lagrangian, then that quantity's conjugate momentum is conserved, and the coordinate is called "cyclic." In calculating the Kepler problem – the physical situation of two particles orbiting each other (like the Earth around the Sun) – the Lagrangian is Note that the only coordinate that doesn't appear in the Lagrangian is ϕ, the longitude in spherical coordinates. Thus, the conjugate momentum of ϕ, which is the angular momentum pointing from the North pole vertically upwards, is a conserved quantity. This reveals a symmetry in the problem that would not be seen if we used the Lagrangian for the same problem in Cartesian coordinates: That just looks ugly. Note that all three coordinates are present, so there are no cyclic coordinates in this system. In spherical coordinates, however, we see that there is a symmetry to the problem; the symmetry is that the situation is rotationally invariant under rotations about an axis perpendicular to the plane of orbit. No matter what angle you rotate the physical situation by about that axis, the physical situation remains unchanged.

I have to say that I wasn't that big a fan of Apollo as a character, actually, and I am glad we get to have Phoenix as the main character again. I love the new look Phoenix has for this game, what with his awesome vest and pocket watch chain. Now if only the Layton/Ace Attorney crossover were localized...

Don't worry, everyone; I plan to immediately tend to this problem when the open schedule that is summer comes to town. (I have the GBA version for play, FYI)

Pretty much this.

Mask of Light is the one Bionicle movie I never tire of watching. The journey across Mata Nui and the bond between Takua and Jaller (and Pohatu and Onua) makes it a great experience for me.

I am very much looking forward to adding this new Zelda to my game library. Side note: I now need to play A Link to the Past.

I think that Takua is the most brilliant pick for this idea. He's the character through whose eyes I (and many others) first saw the BIONICLE universe; I think he deserves the glory of being illustrated like the original comics.

"My milk has a complete daily value of chlorophyll. It's also green." This is a fantastic photo.

Are you going to evolve it with a Dubious Disc? (Sorry, I couldn't resist.)

I heard he rocks.

So, in an earlier blog entry I talked about a journal article one of our professors presented at our department's journal club discussing neutrons in a purely gravitational potential well. Well, I decided to read it and am going to present it to the math and science grad students on Friday because I think it's pretty dang awesome. Related: Airy functions are weird. And cool. Perhaps I'll discuss them later... Also, tomorrow spring is here! (If it weren't for ponies, I would not say that with so much excitement.) `

Alas, my Spring Break has come to a close. I did have fun, though. I got Sonic & Knuckles for the SEGA Genesis and enjoyed time with friends and family. This week I get a midterm for my grad level E&M class. We have over two weeks to do it, though, which is quite nice. Also, Happy St. Patrick's Day, all! If you are old enough to drink, please do so responsibly.

Hecks yes! I'm glad this is happening, since Sherlock is one of the best Sherlock Holmes adaptations ever to be made.

Plato IDE Silverfrost is a free compiler for FORTRAN. Fun stuff.

It's more that, in the relativistic treatment of space and time, you can describe a particle's motion through spacetime with a four-dimensional quantity called the four-vector. When you take the magnitude of this four-vector, the magnitude is a constant — the speed of light. This means that your total speed through the three spatial dimensions plus one time dimension of spacetime must sum to the speed of light. Thus, any particle moving at light speed does not experience time progressing, and anything at rest in space must be moving through the time dimension at the speed of light. It also means that, if there are any particles moving faster than light, they would experience time backwards (like Merlin in The Once and Future King).