Computers are good at math, right? So it follows that video games should be able to do plenty of physics calculations while you run around shooting zombies and stuff, right? Well, the thing is, they have to do a lot of calculations - and they have to do them really, really fast. Take, for example, some game based on a large map, with somewhere around a hundred players, all trying to shoot each other to death. Handled naively, every time a player shoots, the game would have to continuously test if the bullet is intersecting any player on the whole map at any given point along its path. And even handling one single player isn't easy! It's gotta check if it hit the player's foot, leg, other leg, hip, abdomen, shoulder, arm, other shoulder, other arm, neck, head... And then it gets even more confusing when you suddenly have an impenetrable pan on your back blocking some bullets. Now, check for all of these intersections somewhere between twenty and a hundred and twenty times per second, for every single bullet, for every single player. Basically, it's kinda hard for even fast computers to keep up, while remaining accurate.
But that's where humans and their fandangled logic comes in! Now, how could a bullet possibly hit someone, if it's practically in a different time zone from them? Short answer: it can't! (Unless you have teleporting bullets, in which case you should be selling the technology for billions, not shooting people with it). So, take this giant map, and split it up into anywhere from a few to a bunch (so specific, I know) of little bitty squares. Now, as players move around, you've gotta keep track of which square they're in, which takes a bit more work. But now, when you have a bullet (or a few thousand) flying through the air, there's no way it's going to hit someone that's not within either its own zone, or maybe one of the adjacent zones. Now you've gone from checking every player in the game, to between zero and a handful! Much easier!
These same sorts of logical assumptions can be made for all sorts of locality-based applications, like virtual lighting (really, do you want to simulate a billion photons shooting around a room?), more advanced collision detection (we've done point-like bullets hitting round-ish parts of bodies, but what about really complex, non-convex things hitting each other?), as well as odd things like splitting up a group of points into non-spiky triangles (or tetrahedra). That actually has applications in fluid dynamics, modelling the density of stars in galaxies, and a bunch of other things way over my head.
Electricity is cool. Electricity travelling through air is cooler. Well, it looks cooler at least. It's actually really hot.
Jacob's Ladders are neat little devices that send a roughly-horizontal electrical arc travelling upward between two electrodes.
This is a long exposure picture of a Jacob's Ladder - there's actually only one arc at any given time.
The mechanism behind the ladder effect is actually pretty simple. When the arc initially forms, it heats the air up quite a bit, as is evident from the glow it produces. This hot air has more energy, so it expands, which decreases its density relative to the air around it. Since it's less dense, it experiences a buoyant force upward, and since the electrons can more freely travel through already-ionized air, the arc follows the hot air upwards. Once the arc reaches a length at which it can't keep the air hot enough to remain ionized, the arc breaks apart and the path of least resistance returns to being the very base of the ladder, so the process repeats.
Pendulums seem fairly simple, right? You take some mass, you take some string, throw them in a gravitational field, and bam! It goes back an forth, back and forth, back and forth. Without any kinds of friction, this will continue forever!
But, what if you take a pendulum, and then stick a pendulum on the end of that pendulum? Well basically, things get incredibly more complicated. For a single pendulum, especially one that has a small angle of oscillation, you can predict exactly where it will be in its cycle virtually infinitely far into the future. However for even a double pendulum, this becomes impossible, without calculating every single intermediate state of the pendulum. And the motion of multi-pendulum systems is incredibly complicated in and of itself - for an n-pendulum system, one must solve an n-dimensional system of equations do calculate the motion of each pendulum, involving the momenta, kinetic energy, and potential energy of each of the individual components of the system. Basically, multi-pendulums are hard.
Another property of these systems is that they are so-called "chaotic," meaning that a small change in the initial conditions can lead to large changes in the end result of the system, especially as time goes on. For instance, say you have two double pendulums set up. You start them both at just about the same place, but offset the second one by a single degree from the first one. Initially they may follow very similar paths, but as time goes on, it will seem as if they could have started from completely different initial conditions. Chaos appears all over nature and mathematics.
Cheetahs. They're pretty fast, right? There's no way a human could ever catch one, right? Wrong.
Humans are evidently not the fastest creatures to roam this planet, but we are pretty good at getting anywhere we want to be, no matter how long it takes us to get there. Many creatures rely on hind legs to thrust them forward - have you ever noticed how a cat's or a dog's back legs are practically springs? They push themselves forward, accelerating incredibly rapidly, but at the expense of quite a bit of energy - and all that muscle movement in the abdomen can make it difficult to breathe effectively in the midst of a sprint. Humans, though? We just fall over. Seriously. Try to start walking forward, but then don't put your foot down - actually, don't, I don't want to be liable for any injuries. But the thing is, humans walk by simply falling forward, and then relying on that forward momentum to help lift us back up again. Talk about efficiency! You might not be able to run a mile in a minute, but you could certainly walk several before you run out of breath.
So, about that cheetah. How could you ever catch it, you might ask? Well that's simple! Just keep walking (or, in Dory's case, swimming)! Eventually, the cheetah will tire out, and be forced to rest. When you catch up to it, it won't be able to run any more!
Now, this is all relatively related to something that's more of an engineering term - mechanical advantage. In the simplest of terms, you can use the same amount of energy to do two things: go really far, or go really fast. The more Physics-y relationship is Work = Force * Distance. For the same amount of work, you can either maintain a large force over a short distance, or maintain minimal force over a large distance. Humans have opted for the minimal force over a large distance - most of the work we do is actually just to keep us from falling to the ground. Gravity basically just uses our legs as a lever to do the rest.
Magnets. They're pretty cool. If you connect a magnet to some thin cone, and run just the right currents through a wire somewhere in the mix, you can even get them to make weird noises. And that's what we call a speaker! But, for an class of Physics C students, that's probably fairly common knowledge, right? After all, I'm sure we've all seen the speaker contraption floating somewhere around the room. But wait - there's more!
As a matter of fact, some speakers and headphones (and microphones for that matter) don't actually use magnets to make their funny sounds! "What?! How can you make something move with electricity without magnets?", you may ask. Well, I'll answer your question with a question: do you remember that whole unit we did about charges that don't move? The whole one that makes your hair stand up and lets you shock your little sibling when you're wearing slippers? Well, that's just about all you need to know, really. It's only a few steps:
Take a stupidly thin film of something flexible, and make it nice and charged
Place that thin sheet between two more thin, conducting sheets
Use your audio signal to change the voltage between the two sheets
Bam! The thin film moves with the sick beat from your mixtape!
"But wait a second, I can't hear a thing! What gives?" Well, things get a bit complicated with that third step. You see, headphones have a little number called impedance attached to them. For the simplicity of this post, and so I don't have to actually do extensive research into it myself, we'll just say that higher impedance speakers/headphones are more difficult to adequately provide clean, powerful audio signals to than lower impedance ones. So anyway. Those little white earbuds you have in your pocket? Those probably have an impedance around 50 Ohms, depending on which brand they are, etc. Headphones driven by the method given above? Those have an impedance upwards of 150000 Ohms! That's quite a bit higher! So, in order to properly use these headphones and speakers, you'll also need to get a hold of a really powerful amplifier. Then, you'll be able to hear the sweet sound of electrons being lazy and not liking one-another.
So, that's about it. Magnets: they're pretty cool, but they're not the only cool kid in town.
So, in economics, we read this thing about someone who took all the mints from a restaurant cashier. He was subtle at first, but eventually he just shoved them all in his pocket and left. So that was pretty funny, I'd like to dare one of my friends to try it some time.
So I just finished that, and then I remembered I had to do a blog post (whoa, bye fourth wall), and it got me thinking about something I learned not to long ago. It's about napkin rings - more technically, spherical rings. I thought about them because, well, mints are toruses, as are napkin rings. That's about it.
A napkin ring is an object that's the result of taking a solid sphere, and cutting out a cylinder from the center of it, all the way through the sphere. They look like, well, napkin rings. Now, there's a pretty interesting property of napkin rings, that is kinda physics-y, but it's more just mathematical. Although I'm sure there's some interesting physics going along with these, maybe some cool rotational inertia properties. Anyway, the property I'm talking about has to do with the volume of the ring. You see, if you have two napkin rings that are the same height - that being measure one the same axis along which the cylindrical hole was cut - they will always have the exact same volume. Isn't that kinda cool? You could take an orange (well, a spherically perfect orange, in the shape of a perfect sphere), and the Earth (again, a spherically perfect Earth - ours is actually fairly eccentric) and you cut them into napkin rings of the same exact height, they will have the same exact volume.
Here's a video Vsauce made on the topic (I'll admit, it's not a very exciting video, it's just him going through some basic algebra, and proving this equal-volume property):
So yeah, there. Something kinda (probably not really for most people, but whatever, I think it's cool) cool about a physical object. See what I did there? It's totally physics related.
Hey! The first legitimate post, on what's sure to become a pretty cringey blog. See you next week!
Learning is fast
Knowledge is composed of isolated facts
Being good at a subject is a matter of inborn talent
I'm really good at multi-tasking (I, personally, suck at multitasking)
The one that resonates the most with me, is that I do often think learning is fast. Although, I have come to terms with the fact that it's not as fast as I think it is. In reality, it's more that I wish learning was fast, but I know it really isn't. As for the other three, I know knowledge is an interconnected web of ideas and understanding, I know that strength in a subject can be learned, and I know (very well) that I am quite bad at multi-tasking.
Meta-cognition is one's own measure of how much they think they understand a subject. The accuracy of one's meta-cognition goes hand in hand with how well they truly understand a subject.
The most important thing when studying is what you think about while doing it.
Deep processing and shallow processing are two ways someone can process information. On the shallow side, the person only thinks about / focuses on shallow details and facts - things that pop right out without much actual thinking involved. Meanwhile, during deep processing, the person thinks about / focuses on the meaning behind the information, especially something personal attached to the information.
Minimizing distractions and maximizing focus: I'll make sure I'm in a quite environment with my phone far out of reach.
Developing accurate metacognition: I'll routinely reevaluate how well I know the subject material through the use of things like the assignments in class and the web assigns at home.
Deep, appropriate processing of critical concepts: I'll focus on how each topic is related to my everyday life - it is physics, after all, it's happening all around us.
Practicing retrieval and application: I'll practice the material we're working on, rather than reading through notes.
Elaboration: I'll make sure I relate the topics we study to each other, using notes and worksheets to spot the similarities and relations between the different topics.
Distinctiveness: I'll make sure I still understand the distinct nature of each topic. I'll continue to test my recall of old topics so I know I'm not confusing similar topics, and really do understand the differences.
Personal: The blog posts will really help with this. I'll make sure I make legitimate blog posts that I really do feel a connection to my personal life with.
Appropriate to retrieval and application: I'll practice each individual part of the topics we learn, until I understand how each is connected to the others, and how they're all applied mathematically, and in practice.
Automaticity: I'll continue doing practice on the topic we learn until I'm certain I don't need any notes or help to complete problems.
Overlearning: I'll challenge myself with harder, more in-depth problems, until I can quickly and easily work through the problems without notes or help. At least, as quick and as easy as I can.
What are good strategies for learning?
What types of questions should I ask?
How do questions impact the retention of knowledge?
Why should I come up with my own questions?
What makes a good question good?
What questions have I already asked without thinking about it?
Video lessons are a lot like lectures, the only difference being the ability to rewind, fast-forward, and skip whole parts. These abilities, though, make shallow-learning even easier and more dangerous. Videos should be watched carefully, while you take notes as described in the video. It will probably be better to take notes on paper, as it will make it less convenient to pause, rewind, fast-forward, or leave the video entirely. Notes that promote deep processing will help to prevent the need to re-watch parts of, or whole, videos. Whatever work is to be done concerning the video, i.e. this blog post, should be done only after fully watching, and taking notes on all parts of the video. This way, the knowledge and understanding is not only in short-term memory, but has been processed deeper.
I will definitely participate in study groups, though I might not stick to a single one (unless we just end up having a 15-person study group, that might be cool). I know my strengths relatively well, and I'm certain I can help to lead my classmates through the work load of this class. I don't want to stick to a single group, because I think I could both help more people if I jump around, and it would give me more experience with helping many different (although all nerdy) people. I also think that participating in different groups can help anyone, since different groups may often have different approaches to the same problem, each of which may be an entirely valid solution. It would be very helpful to experience all those different ways of thinking, for anyone.
Disclaimer: There's entirely a possibility that, if the workload of all of my classes combined pushes me too close to - or beyond - my limit, I become almost completely independent, probably for just a short while. I'll do my best to manage my time wisely, though, so that doesn't happen, and I don't send myself into a spiraling, endless pit of stress and lack of time.
Go into denial
Wait until the end of the semester to get help
Skip class to focus on others
Fall further behind while looking for ways to catch up
Ignore small assignments
Examine how you prepared, and be honest with yourself.
Review the exam, and focus on what you got wrong. Make sure you understand any problems you didn't during the test. Check if you had the necessary information to complete the problems you missed in your notes. If not, reexamine your note-taking.
Talk with your professor. Take steps early to make sure you know what path you need to take in order to improve your learning.
Examine your study habits. Make sure your strategies take effort to do.
Based on all of this, create a plan on how you're going to do better.
Commit time and effort (is anyone who's taking this class actually expecting to not put in time and effort?)
Minimize distractions (no cell phones during study time)
Attend class (except on senior skip day)
Set realistic goals (you're not gonna go from a 9% to a 90% in one week)
Don't begin to slide (if you do, seek help)
Don't give away points (unless you're the teacher, I'll take some free points)
That was a long post. Jeez Louise. Time for a nap. Probably, like, an 8 hour nap.
I'd like to think I'm a pretty cool dude. Okay, maybe not. I'm maybe, like, slightly below-average coolness. That's okay though. I am a nerd, after all: I like math and science (why else would I be in Physics C?), and I'm really good at both of them too. Most of the time. I also really like video games. I'm about average at those. Maybe a tad bit better than average.
I'm taking Physics because, well, I like math and science, and I'd like a challenge this year. I also really like the discover and learn about things that I've never seen, and might never see, like galaxies billions of light years from ours, or quarks so small that they don't even know where they are exactly. I really hope to just have fun this year, and learn all I can.
I'm most excited to learn the more in-depth math and theory behind many of the topics we touched on last year, but didn't go into in detail. I really enjoy beautiful math, and I can't wait to see all of it behind Physics. As for what I'm anxious about, well, I don't really like writing. I'm not exactly looking forward to writing blog posts, but I guess I'll make do. It can't be that hard, can it?
Note: "Qwayway" comes from what, in my opinion, should be the phonetic spelling of the word "Queue." Isn't it just more fun to say?
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