jelliott

My fellow AP-C students and I are working on the Work-Energy unit right now, and in the Webassign there are some questions involving the dot product of vectors. The maximum amount of elements these vectors have is 3, though: <x,y,z> or <i,j,k>. Well, this makes sense, since we live in a 3-dimensional world, of length, width, and depth. Or do we? Obviously, the concept of 3 dimensions has been around as long as mathematics (even in its most rudimentary of forms) has been around. It's obvious because it's what we see, and touch, and live. Trying to imagine a 4th dimension is like trying to imagine a color we've never seen before - it's impossible for our brains to comprehend. Mystics used to describe the 4th dimension as a sort of "spirit realm" - a place free of Earth's bounds and restrictions. With the advancement of science and mathematics, many began to view time as the 4th dimension. It makes some sense - just like we humans are constrained to length, width, and depth, we're constrained to constant increments of time (well, some believe it's not constant...but I'll get to that some other time). (May or may not be inspired by the theory of relativity) In the theory of relativity, Einstein describes time as a fourth dimension. Space being inseparable from time, spacetime became known as its own continuum, but time is mathematically treated differently from the other spatial dimensions. After all, we can move in all directions 3-dimensionally, but only forward in time. For now. However, some more modern scientists such as H. S. M. Coxeter state that using time as a 4th dimension is a cop-out. (Paraphrasing) In this regard, there is a spatial/Euclidean description of the fourth dimension: the vector <x,y,z,w>. Try to imagine this: you know that x, y, and z are all perpendicular to each other. Well, w, the fourth dimension, is perpendicular to all of these. It's pretty much impossible to comprehend, since we live in a 3-D world, but its properties can be inferred. Using dimensional analogies, we can see how 3 dimensions relates to 2, or 2 to 1, and infer how 4 would relate to 3. This can be used for even more dimensions - string theory, for example, relies on the existence of 10. There are mathematical limitations to these inferences. Here's one example: Circumference of a circle = 2Ï€r Surface area of a sphere = 4Ï€r^2 So what's the surface volume of a hypersphere, a fourth dimensional figure? Using dimensional analogies, we might be tempted to say 8Ï€r^3, assuming it's multiplied by 2r each time. However, the real answer is apparently 2Ï€^2*r^3. Don't ask me why, I didn't derive the equation. I can't do this subject justice in a concise blog post, or probably with any. It's incredibly complicated and I don't wish to oversimplify - so research further if you're interested!

Don't be too jealous, BC Calc makes sure that I have very little time for this stuff

"Video gamers" is derogatory, please refer to me as a "digital warrior" from now on. Thanks.

It's no "Big Rigs: Over the Road Racing", but it looks okay.

To start, I apologize for a fourth consecutive video game physics blog. But I somewhat recently splurged on a new game that I think demonstrates a point I touched on earlier - video game physics are becoming more and more visually impressive. Destiny is developed by Bungie, a well-loved company that brought the masterful Halo franchise into the gaming world. It's a quite repetitive adventure, and flawed in several ways - but gameplay aside, both fans and detractors agree that the game looks incredible, depicting the solar system (well, parts of it) beautifully. (The game's dancing physics were actually perfected by Paula Abdul herself. Not really though) Destiny uses a physics system developed by the company Havok, who are well-renowned in the world of gaming physics. It relies heavily on physical simulations and collision physics, both of which are prevalent here. Things like a character's hair or cape will actually show realistic signs of movement while running, etc. By blending vibrant artistry with actual soft body simulations, they believe they have the cutting edge technology to bring to life the exciting world of computer-generated foliage. In all seriousness though, these superficial little details truly show how much gamers care about graphics, and how fluently the game moves. And, I'll be the first to admit, these details do significantly increase the immersion factor while playing. It's one of those games where you just have to stop every once in a while and look around. My favorite use of this physics system though is without a doubt the Sparrow mechanics - a Sparrow being, of course, an all-terrain space hover bike. It's unrealistic...for now. For an added bonus, we note how the thrust of the engine in the back of the bike propels the bike forward, due to Newton's 3rd Law, which not-so-surprisingly, holds up pretty well in space. But also note how the bike seems to instantly lock on to the gradient slope of the terrain it hovers over, a pretty interesting physical phenomenon that permeates the whole game. All of these crazy, futuristic weapons and gadgets seem far off, but we never know if something like this could end up coming into fruition. Check out, for instance, a "fusion rifle". Could we ever harness the energy to create something like this? I mean, if its name is accurate, I assume it generates energy through the process of fusion - yes, not fission, FUSION - going on INSIDE some kind of fusion chamber in the rifle. In like a split second. (And we don't even know how to do fusion yet, so we better get on it if we want to stand any chance against the aliens.) To conclude, though, I'll quote the ever-popular video game aphorism: "Graphics aren't everything." And that's certainly accurate. You can create a beautiful game with inspiring physics engines that still manage to disappoint thousands and thousands of gamers - that's what happened here. This game is now the most popular new game franchise of all time, and its budget was a whopping half billion dollars. Yeah, with a 'b'. However, it gives us gamers a friendly reminder that if the game doesn't play well, all of this money is for naught. Destiny's story doesn't hold up at all, especially looking at Bungie's Halo series, which had beautifully done storylines. This isn't to say Destiny's bad, I personally enjoy this game - but it certainly won't satisfy anyone looking for a storyline that's followable - or even coherent. So here ends my rambling Destiny physics-discussion-review-hybrid blog post. Hopefully it helped anyone on the fence make a decision to purchase it or not - and if not, tune in for my next post. Which is hopefully about something other than video games.

Yet another video game physics blog: As video games become more and more advanced, naturally, their physics improve as well. Advancements in computing technology allow for more realistic movements in player models - and this leads us into a discussion in something known in the computer physics world as "ragdoll physics". Anyone who has played a video game involving the death of a character (which is, well, most of them) knows that death animations are anything but static. This is to make them appear more human, by simulating human joint/muscle/bone movements during a fall or collapse of some sort. (A real-life example of "ragdoll physics" - ouch.) In the beginning, when video games lacked the processing power to compute accurate "death sequences", manually created animations were used. Basically, the animations would come from one of several sequences of pre-drawn frames. By today's standards, it's primitive, but it was a clever solution. As computing power increased, though, it was possible to simulate real-time physical simulations. Video games could now include these ragdoll simulations by constraining rigid bodies such that their bones and joints react realistically to their circumstances. These constraints usually cause a lack of muscle stiffness at the moment of death or collapse, so that the model can collapse authentically, hence the term "ragdoll". This can lead to some interesting (and often humorous) results. (From the ever-popular Grand Theft Auto - this franchise is well-known for its ragdoll physics.) Finally, some examples of different ragdoll physics: Inverse kinematics: This involved using a preset animation, but by using kinematics to provide a physical constraint, the character was forced into a possible position after death. Used in the first Halo game. "Blended" technique: Provided realistic effects by using a preset animation, where the animation was constrained to what that physical system would allow. Used in Halo 2 and 3, Call of Duty 4, Left 4 Dead, and Uncharted. Video game physics have come a long way. Jurassic Park: Trespasser, while a faulty and buggy game, was a pioneer in the use of ragdoll physics. Just looking at these huge advancements within the course of a couple decades, we can assume that character models in video games will continue to become more and more humanlike.

FIFA 15 has recently been released, and it claims to have pretty good physics. For that, they can thank last year's edition, FIFA 14. Now, I (and another user on this site, whose name I will refrain from mentioning - you know who you are, Dan) have played a good amount of FIFA 14. For some reason or another, though, we haven't really delved into the physics of its engine, the "next-generation" EA Sports Ignite Engine. Whether or not the recent engine is a marketing ploy is irrelevant in this discussion (though it probably is) - here, we're just going to talk about how, according to gaming and scientific blogs alike, FIFA 14 got their physics right. My AP-C pals and I are doing dynamics right now, and for those of you who have taken a look at the retarding/drag forces stuff, you'll probably feel a little nauseated when I mention...well, drag forces. Don't worry, don't worry, I'm not going to pull any derivatives out on you or anything like that. But I will mention drag coefficients, because they're vital in FIFA 14's gameplay mechanics. Before this game, balls kicked would travel in a strangely floaty type of way, like they were balloons. They would basically travel in near-perfect parabolas, with no wind or air resistance affecting its path of motion in the slightest. Basically, the ball accelerated at a set rate regardless of its initial velocity. So according to EA (voted the worst company in America until Time Warner Cable overshadowed it), some "intense research and auditing" of game mechanics came into play. And guess what? They got the drag forces wrong! Yeah, the drag coefficient of a spherical soccer ball was miscalculated in the engine. Or maybe it was just a typo. Either way, how it slipped testing for over a decade is pretty impressive, especially considering one of these games gets made every year. When a soccer player (or footballer, depending on your location) kicks the ball, it often dips and swerves in various directions. Due to this faulty coefficient, though, the ball would swerve inaccurately. By miscalculating the force of air resistance on a swerving ball, the Magnus force (Newton's 3rd Law) was also miscalculated. I say Newton's 3rd Law because the Magnus force, the force of air on the ball, is equal to the force of the ball on the air. Anyway, here's hoping that game physics improve with each new edition of FIFA. And maybe we can stop stuff like this from happening.

Because everyone else was doing video game physics, so why not? First off, let's address something. What does Super Mario World for the Super Nintendo have to do with quantum/theoretical physics? Not much, right? Well, I stumbled across an article on mentalfloss.com, which I'd recommend looking at if you're at all interested. http://mentalfloss.com/article/17994/super-mario-world-quantum-physics-lots-fun It describes how some anonymous gamer (with a lot of time on his/her hands) programmed a playthrough of a Mario level where all previous attempts were superimposed upon each other. This level is gruelingly difficult, so the player dies a lot, but eventually one of the Marios survives the level, one out of...a lot. Here's the clip. So, it's just a bunch of Marios who die, and one of them survives at the end. What does this have to do with theoretical physics? Let me just define some stuff briefly, and I'll get to the point soon enough. The Schrodinger's cat paradox is a theoretical experiment where a cat is locked in a sealed box with a radioactive source, a cat, and some poison. If a monitor in the box detects radioactivity, the bottle of poison breaks, and the cat dies. But, a certain interpretation of quantum mechanics (named the Copenhagen interpretation) would state that in this scenario, the cat could be simultaneously dead AND alive. But obviously, if you looked into the box, you wouldn't see some zombie-cat-hybrid thing; you'd see a cat that was either alive or dead. This moment demonstrates the point where quantum superposition (scenarios "stacked" on top of each other) collapses, and one of two courses of reality takes place. Either the cat's alive, or it's dead. It can't be both. BUT WAIT...THERE'S MORE The many-worlds interpretation of quantum mechanics says, yeah...the cat is alive. It's also dead. But it's alive in one universe, and dead in another, and these two universes have nothing to do with each other. So is it true, then, that there can exist infinite universes, one for each possible scenario of every decision or event ever? That's where Mario comes into play. The death of all those Marios represent a bunch of universes where he failed to complete the level. But, if there can be universes for every scenario, he has to survive at least one...right? Well yeah, he does! That universe, where he survives, is represented by the final Mario left at the level's end. The programmer stated that this entire program demonstrates the MWI (many-worlds interpretation). And it does, to some extent, even though obviously not every possible outcome of Mario was shown here. But it's enough to prove a point. So the next time you get really ticked off when you die in a video game, just remember...somewhere, there's a universe where you succeeded.

One of the most interesting (and most challenging) techniques of playing a guitar is effectively utilizing a pinch harmonic (the aptly named "squeal"). It is typically used in metal music, as the heavy distortion used in amplifiers can greatly increase the sound of the otherwise subtle harmonic. Eddie Van Halen, for example, used this technique often, and well; an overwhelming number of his solos feature it. Take, for example, his iconic solo in Michael Jackson's "Beat It" (this obviously is a cover, but is nearly identical to the original): At around 0:24 is that awesome, squealy pinch harmonic that metal guitarists and enthusiasts love. I think it's pretty awesome myself. So what's "physics" about it? More than you'd think, and more than I'd thought. Obviously, guitar strings have a fundamental frequency when they are being played open (no fingers on any frets). They also have overtones when frets are being played (the harmonics higher than the fundamental). The strings even have those fun little nodes, points in the standing wave of the string that have the minimum amplitude. All of these are vital to the pinch harmonic. The technique involves lightly touching the thumb to the vibrating string, immediately after the string is picked. By doing this, and essentially "interfering" with the string's vibration, all fundamental frequencies and overtones are muted - unless the frequencies happen to have a node on that particular fret. Something interesting to note is that to make a pinch harmonic exactly an octave higher than the fret you are playing, you must pluck the string directly between that fret, and the bridge of the guitar. Doing it somewhere else will yield a different, yet equally cool, squealing sound. Guitarists like Eddie Van Halen and Joe Satriani use the "divebomb" - using a whammy bar to alter the bridge during a pinch harmonic, thus drastically changing the frequency of the harmonic. This can only be done with very heavy distortion. For a textbook example, I'll use Joe Satriani's "Satch Boogie" - check out 0:32 to see what I mean. Pretty cool, huh? So next time you listen to a Van Halen solo, or your favorite metal shredder, or even good ol' ZZ Top, keep this in mind - I'm sure you'll notice this technique!

I make math romantic with my TI-83 Plus calculator.

I really like the application of physics to video games. That's a pretty cool idea, especially considering a good amount of video games neglect physics. Come to think of it, the physics of Super Mario sounds like an interesting investigation...I might have to look into that.

The workload is definitely going to be a struggle, but as the adage goes, "The pine stays green in winter...wisdom in hardship". Just be sure to take root.

They said senior year would be a breeze. To avoid such a horrifying prospect, I decided to indulge in AP-C Physics, which, as they say, is one of the most challenging classes the school has to offer. But, as the Chinese proverb goes, "The gem cannot be polished without friction, nor man perfected without trials". I am not taking AP-C Physics simply because I enjoy torturing myself with hard problems. In actuality, I hope to be able to tackle hard problems step-by-step. There is always a logical process to everything, and that idea alone is why science exists. So, knowing this, I hope to increase my arsenal of processes this year. AP-B Physics was my most challenging class thus far, but also my most interesting one. The idea that this sometimes chaotic world can operate in such mathematical order is still pretty incredible to me, and I took this class to further understand the relationships that exist in the world around us. It's quite nifty. I'm definitely nervous to solve more complex problems than I ever have before, using calculus. Calculus is still some obscure, evil concept to me. And on that note, I'm excited to be able to utilize it and learn something that I will hopefully use throughout college and beyond. To quote another proverb here: "Just when the caterpillar thought the world was over...it became a butterfly", and I look forward to becoming a beautiful physics butterfly this year.