Since then, things have been optimistic. As of now most of the larger fires seem to be at least 50% contained, which does not mean half way out. They just have preventative lines drawn around them using whatever techniques fire fighters use (or at least, that's how I am interpreting this). If the winds pick up strongly again the fires could get over the containment lines, but so far it doesn't look like those will come.
Though many people have been allowed to return to their homes, and some shelters have closed due to lack of necessity, no one is out of the woods yet. I don't know what the plan is to put out the fires, but it might be a while before they are 100% out. That said, the amount of help California is receiving is incredible. Apparently there are over 10,000 fire fighters working, and as of yesterday (I think) there were fire fighters from 17 additional states (Oregon, Washington, Idaho, Montana, Nevada, Utah, Colorado, Arizona, New Mexico, New York, Minnesota, Florida, South Caroline, Alaska, South Dakota, Wyoming and Indiana) and Australia helping out. Australia! Together they contributed 266 fire engines, 79 fire crews, and 56 other personnel. I am very grateful for the support that they have shown and for the work that they all are doing. If I weren't on the other side of the world I would sit outside the local fire station and cook pancakes all morning for them. My girlfriend works right next to it and will be dropping off a few batches of homemade brownies.
So while the battle is far from over, things are looking up, and I'm hoping they keep looking that way.
So: player characters in Pokémon. They aren’t characters, really. They’re consistently left totally and completely blank so that whoever’s playing the game can project themselves onto this avatar with as little friction as possible, taken to unnecessarily hilarious ends with Red’s silent reappearances in later games. Naturally, this approach has its fair share of pros and cons. On one hand, this aids immersion tremendously—you’re free to name this character whatever you want, command them to do whatever you want, interpret their behavior and thought processes however you want, and more recently even dress them however you want. Players turn that character into themselves, and are able to see themselves in the Pokémon world, albeit from a top-down perspective. It’s the ultimate extreme of role-playing, giving you a place in this world but then allowing you complete freedom to adjust to it however you like. But on the other hand, this might have some connection to the fact that Pokémon has never really been known for its story. It’s difficult to write a plot centered around an empty shell. The player does things to continue the story, but they’re very much watching it unfold before them, and only stepping in when given the opportunity as opposed to doing much to actively push it forward. Again, Pokémon’s pretty much always done it this way, and it seems to be working for them, so it may not be something you see a lot of people clambering for. But since there’s a boatload of Pokémon media that does feature main characters who are actually characters, I don’t know that we can say people are totally averse to the thought.
It seems to me that Lillie is GameFreak’s attempt to have it both ways. The player character of Sun and Moon remains a void who can be anyone the person holding the 3DS wants them to be, but they have a very close friend who has her own desires and faults, is heavily-entwined in the overarching plot, and develops greatly as a character. Granted, she doesn’t do very much herself in terms of actively driving the plot forward—she spends a lot of time reacting, and not as much time decision-making—but her character is written in a way that that’s actually part of her development. Which is…kind of ingenious, really. Is she meant to be a metaphor for the Pokémon main series games learning to be more active in their storytelling, as opposed to just being an observer? Well, maybe at that point I’m reading a bit too much into it.
For the sake of argument, let’s accept my premise as true: Lillie is an attempt to have a “main character” the plot centers on while still having a totally blank “player character” for absolute immersion. Then the only question becomes: Does it work?
I’d say yes.
People love Lillie. If you looked at a discussion of Sun and Moon prior to their release, you’d see people saying “This Lillie girl is off, we all agree she’s a Nihilego in disguise right?” Check them after its release, and you’ll see dozens of fans shouting about how wonderful she is. Like, I’m sure there are some people who don’t like her, no character can be universally-loved, but…I’m not sure I’ve seen anyone bashing her, and Sun and Moon have been out for close to a year now. When you have to go out of your way to find people who hate a character but get bombarded by people who like them without trying, it’s safe to say they’re pretty darn popular. Has the series had a breakout character like this before? Maybe with N? Certain Hoenn characters certainly had a resurgence when ORAS came out, but even then it seemed to typically be antagonists, plus Steven who just sort of pops in and out on occasion. Even when N does become an ally in B2W2, he’s only in, what…one scene that’s actually plot-relevant?
What I’m getting at is that there’s a novelty to Lillie’s role in Sun and Moon’s story. How big a factor that novelty is in her appeal is something we can only know if this becomes more regular. I do hope to see this technique or something similar employed in future Pokémon games, because while I do like feeling like I’m my own trainer, I enjoy stories as well, and Lillie’s story is one I really enjoyed. I’ve gone on record as saying there are aspects of Alola and its cast I wish we’d seen more of, and perhaps the focus on Lillie has a hand in that, but still: she’s very unique in this franchise, and very interesting. Hopefully, she’s a good sign of what’s to come.
Say what you want about the movie, the sets have been pretty epic, and this one had me drooling from the get go. I won't be able to build it straight away (have a few things to clear out first) but it's going to get built sooooon. It was either get this set or collect all the other Ninja sets from the theme... so I chose this. It's only about half a month's rent, plus the largest Lego set I've ever purchased.
... and yes, I know it's probably the priciest way to get civilian Kai, but I have to complete my collection somehow.
When not raiding Soviet bases to 80s hits in Metal Gear Solid V, I've been playing Until Dawn with my roommate. Now, I don't really do horror, like, at all. But Until Dawn features a supposedly robust choices and consequences system, which I am, of course, a sucker for.
We’ve finished the game and there's been a good deal of payoff to some of the choices we've made. The big thing we're looking forward to, though, is playing it again and making different choices to see what would happen.
Because right now a lot of what happened feels like a direct result of the choices we've made and I wanna know how much of that is really because of what we did. Every little plot turn can’t be the result of our decisions, even though it can feel like it.
A lot of the time, when we play a game with multiple choices, we want everything we do to be impactful and for it to create a tailored set of consequence that are entirely dependent on what we did.
Doesn’t that sound cool? Every choice you make has consequences! Siding with Miranda or Jack when they argue aboard the Normandy in Mass Effect 2 could spell disaster down the line! If Walker doesn’t spare that guy in Spec Ops: The Line what will it mean for the future?
The problem is, games are a finite medium. What’s done, is done, and has to have been doable. There’s a limit to your free will, a limit set by the game developers and their bother and/or budget. It turns out that choosing Kaiden or Ashley has no real choice on the rest of Mass Effect, as the survivor fulfills basically the same role in the sequels. Picking Udina or Anderson doesn’t have much bearing on Citadel politics, because Mass Effect 2 doesn’t have much of it, and by the time 3 rolls around, Anderson (if you chose him) has stepped down so that Udina represents the humans and the intrigue on the Citadel proceeds accordingly.
Now, I am kinda picking and choosing some examples, Mass Effect does have some brilliant moments of consequence (whether or not you saved Mealon’s research in the second game has a massive impact on the third – it’s that it’s one of the few choices of that nature that make it stand out so), but a few different playthroughs, the cracks in the game’s design start to show. No matter what, Udina will end up on the council. The Rachni will return whether or not you kill their Queen. Whether or not you sacrifice the Council in the Battle of The Citadel doesn’t mean much ultimately. To quote Eloise Hawking in LOST: the universe has a way of course correcting.
Which is a bummer, because what if, to beat a dead horse, picking Anderson or Udina made for totally different plot lines in Mass Effect 3. Maybe Anderson as Councilor meant that Cerberus never managed to attack the Citadel, but in exchange made the mission to Earth that much harder without him in your corner. It does mean a lot of resources, but it also means a more personalized experience.
I think that might be why I’m hesitant to jump back into Until Dawn. Right now everything happened as a result of my choices. Little tweaks to the game’s horror were because of my answers to questions posed to me (Snake-Clowns with Needles, though the snakes never showed up). Playing the game again (which I absolutely want to do to, why else, see what would happen) will probably show where the seams are and reveal how little impact my decisions had. That it doesn’t on the first play through speaks to good writing.
Because choice in games are an illusion, and will continue to be until you have an infinite number of monkeys typing up an infinite number of outcomes to an infinite number of players’ decisions. But until then, players can be tricked into thinking we have a decision. If the game’s narrative makes the causality feel like it had to happen, like that your choice led you here no matter what, then the illusion isn’t broken. Just spackle those cracks with good writing and we’re onboard.
For the first playthrough or two, anyway. After that it boils down to just gaming the system as much as you can (how can I make sure everyone dies in the most gruesome way in Until Dawn?).
So, Made in Abyss ended and I didn't actually make an entry about the finale. It was...very good. Just like the entire series, really. Gonna spoil it a bit but...
All in all, it was a fantastic series. Some pacing felt off here and there, but it ended on a solid note. And now I'm sad, 'cause I don't have more to watch. Maybe we'll get a second season...
Oh well. There's always tomorrow. I still have Xenoblade 2 to look forwards to.
A wave, in general, is any function that obeys the wave equation. To simplify things, though, let’s look at repeating wave patterns.
The image above depicts a sine wave. This is the shape of string and air vibration at a pure frequency; as such, sinusoidal waveforms are also known as “pure tones.” If you want to hear what a pure tone sounds like, YouTube is happy to oblige. But sine waves are not the only shapes that a vibrating string could make. For instance, I could make a repeating pattern of triangles (a triangle wave),
or rectangles (a square wave),
Now, making a string take on these shapes may seem rather difficult, but synthesizing these shapes to be played on speakers is not. In fact, old computers and video game systems had synthesizers that could produce these waveforms, among others. But let’s say you only know how to produce pure tones. How would you go about making a square wave? It seems ridiculous; pure tones are curvy sine waves, and square waves are choppy with sharp corners. And yet a square wave does produce a tone when synthesized, and that tone has a pitch that corresponds to how tightly its pattern repeats — its frequency — just like sine waves.
As it turns out, you can produce a complex waveform by adding only pure tones. This was discovered by Jean-Baptiste Joseph Fourier, an 18th century scientist. What he discovered was that sine waves form a complete basis of functions, or a set of functions that can be used to construct other well-behaved, arbitrary functions. However, these sine waves are special. The frequencies of these sine waves must be harmonics of the lowest frequency sine wave.
The image above shows a harmonic series of a string with two ends fixed (like those of a guitar or violin). Each frequency is an integer multiple of the lowest frequency (that of the top string, which I will call ν1 = 1/T, where ν is the Greek letter "nu."), which means that the wavelength of each harmonic is an integer fraction of the longest wavelength. The lowest frequency sine wave, or the fundamental, is given by the frequency of the arbitrary wave that’s being synthesized, and all other sine waves that contribute to the model will have harmonic frequencies of the fundamental. So, the tone of a trumpet playing the note A4 (440 Hz frequency) will be composed of pure tones whose lowest frequency is 440 Hz, with all other pure tones being integer multiples of 440 Hz (880, 1320, 1760, 2200, etc.). As an example, here’s a cool animation showing the pure tones that make up a square wave:
As you can see in the animation, these sine waves will not add up equally; typically, instrument tones have louder low frequency contributions than high frequency ones, so the amplitude of each sine wave will be different. How do we determine the strengths of these individual frequencies? This is what Fourier was trying to determine, albeit for a slightly different problem. I mentioned earlier that sine waves form a complete basis of functions to describe any arbitrary function (in this case, periodic waveforms). This means that, when you integrate the product of two sine waves within a harmonic series over the period corresponding to the fundamental frequency (T = 1/ν1), the integral will be zero unless the two sine waves are the same. More specifically,
Because of this trick, we can extract the amplitudes of each sine wave contributing to an arbitrary waveform. Calling the arbitrary waveform f(t) and the fundamental frequency 1/T,
This is how we extract the amplitudes of each pure tone that makes up the tone we want to synthesize. The trick was subtle, so I’ll describe what happened there line by line. The first line shows that we’re breaking up the arbitrary periodic waveform f(t) into pure tones, a sum over sine waves with frequencies m/T, with m running over the natural numbers. The second line multiplies both sides of line one by a sine wave with frequency n/T, with n being a particular natural number, and integrating over one period of the fundamental frequency, T. It’s important to be clear that we’re only summing over m and not n; m is an index that takes on multiple values, but n is one specific value! The third line is just swapping the order of taking the sum vs. taking the integral, which is allowed since integration is a linear operator. The fourth line is where the magic happens; because we’ve integrated the product of two sine waves, we get a whole bunch of integrals on the right hand side of the equation that are zero, since m and n are different for all terms in the sum except when m = n. This integration trick has effectively selected out one term in the sum, in doing so giving us the formula to calculate the amplitude of a given harmonic in the pure tone sum resulting in f(t).
This formula that I’ve shown here is how synthesizers reproduce instrument sounds without having to record the instrument first. If you know all the amplitudes bn for a given instrument, you can store that information on the synthesizer and produce pure tones that, when combined, sound like that instrument. To be completely general, though, this sequence of pure tones, also known as a Fourier series, also includes cosine waves as well. This allows the function to be displaced by any arbitrary amount, or, to put it another way, accounts for phase shifts in the waveform. In general,
or, using Euler’s identity,
The collection of these coefficients is known as the waveform’s frequency spectrum. To show this in practice, here’s a waveform I recorded of me playing an A (440 Hz) on my trumpet and its Fourier series amplitudes,
Each bar in the cn graph is a harmonic of 440 Hz, and the amplitudes are on the same scale for the waveform and its frequency spectrum. For a trumpet, all harmonics are present (even if they’re really weak). I admittedly did clean up the Fourier spectrum to get rid of noise around the main peaks to simplify the image a little bit, but know that for real waveforms the Fourier spectrum does have “leakage” outside of the harmonics (though the contribution is much smaller than the main peaks). The first peak is the fundamental, or 440 Hz, followed by an 880 Hz peak, then a 1320 Hz peak, a 1760 Hz peak, and so on. The majority of the spectrum is concentrated in these four harmonics, with the higher harmonics barely contributing. I also made images of the Fourier series of a square wave and a triangle wave for the curious. Note the difference in these spectra from each other and from the trumpet series. The square wave and triangle wave only possess odd harmonics, which is why their spectra look more sparse.
One of the best analogies I’ve seen for the Fourier series is that it is a recipe, and the "meal" that it helps you cook up is the waveform you want to produce. The ingredients are pure tones — sine waves — and the instructions are to do the integrals shown above. More importantly, the Fourier coefficients give us a means to extract the recipe from the meal, something that, in the realm of food, is rather difficult to do, but in signal processing is quite elegant. This is one of the coolest mathematical operations I’ve ever learned about, and I keep revisiting it over and over again because it’s so enticing!
Now, this is all awesome math that has wide applications to many areas of physics and engineering, but it has all been a setup for what I really wanted to showcase. Suppose I have a function that isn’t periodic. I want to produce that function, but I still can only produce pure tones. How do we achieve that goal?
Let’s say we’re trying to produce a square pulse.
One thing we could do is start with a square wave, but make the valleys larger to space out the peaks.
As we do this, the peaks become more isolated, but we still have a repeating waveform, so our Fourier series trick still works. Effectively, we’re lengthening the period T of the waveform without stretching it. Lengthening T causes the fundamental frequency ν1 to approach 0, which adds more harmonics to the Fourier series. We don’t want ν1 to be zero, though, because then nν1 will always be zero, and our Fourier series will no longer work. What we want is to take the limit as T approaches infinity and look at what happens to our Fourier series equations. To make things a bit less complicated, let’s look at what happens to the cn treatment. Let’s reassign some values,
Here, νn are the harmonic frequencies in our Fourier series, and Δν is the spacing between harmonics, which is equal for the whole series. Substituting the integral definition of cn into the sum for f(t) yields
The reason for the t' variable is to distinguish the dummy integration variable from the time variable in f(t). Now all that’s left to do is take the limit of the two expressions as T goes to infinity. In this limit, the νn smear into a continuum of frequencies rather than a discrete set of harmonics, the sum over frequencies becomes an integral, and Δν becomes an infinitesimal, dν . Putting this together, we arrive at the equations
These equations are the Fourier transform and its inverse. The first takes a waveform in the time domain and breaks it down into a continuum of frequencies, and the second returns us to the time domain from the frequency spectrum. Giving the square pulse a width equal to a, a height of unity, and plugging it into the Fourier transform, we find that
This is one of the first Fourier transform pairs that students encounter, since the integral is both doable and relatively straightforward (if you’re comfortable with complex functions). This pair is quite important in signal processing since, if you reverse the domains of each function, the square pulse represents a low pass frequency filter. Thus, you want an electrical component whose output voltage reflects the sinc function on the right. (I swapped them here for the purposes of doing the easier transform first, but the process is perfectly reversible).
Let’s look at the triangular pulse and its Fourier transform,
If you think the frequency domain looks similar to that of the square pulse, you’re on the right track! The frequency spectrum of the triangular pulse is actually the sinc function squared, but the integral is not so straightforward to do.
And now, for probably the most enlightening example, the Gaussian bell-shaped curve,
The Fourier transform of a Gaussian function is itself, albeit with a different width and height. In fact, the Gaussian function is part of a family of functions which have themselves as their Fourier transform. But that’s not the coolest thing here. What is shown above is that a broad Gaussian function has a narrow range of frequencies composing it. The inverse is also true; a narrow Gaussian peak is made up of a broad range of frequencies. This has applications to laser operation, the limit of Internet download speeds, and even instrument tuning, and is also true of the other Fourier transform pairs I’ve shown here. More importantly, though, this relationship is connected to a much deeper aspect of physics. That a localized signal has a broad frequency makeup and vice versa is at the heart of the Uncertainty Principle, which I’ve discussed previously. As I mentioned before, the Uncertainty Principle is, at its core, a consequence of wave physics, so it should be no surprise that it shows up here as well. However, this made the Uncertainty Principle visceral for me; it’s built into the Fourier transform relations! It also turns out that, in the same way that time and frequency are domains related by the Fourier transform, so too are position and momentum:
Here, ψ(x) is the spatial wavefunction, and ϕ(p) is the momentum-domain wavefunction.
Whew! That was a long one, but I hope I’ve done justice to one of the coolest — and my personal favorite — equations in mathematics.
P.S. I wanted to announce that Equation of the Day has its own website! Hop on over to eqnoftheday.com and check it out! All the entries over there are also over here on BZPower, but I figured I'd make a site where non-LEGO fans might more likely frequent. Let me know what you think of the layout/formatting/whatever!
I was just informed that two of my RA's had made it their personal challenge to figure out what the weird circles on my door mean. They have apparently spent the last three weeks trying to crack what it says letter by letter.
They managed to do it. They still don't know what alphabet that was.
I'm amazed and stunned.
I GOT A JOB IN WASHINGTON AS A PASTRY CHEF AND I ACCEPTED IT AND NOW I HAVE TO APARTMENT HUNT AND FIND A PLACE TO LIVE WITHIN A MONTH AND THIS IS REAL ACTUAL ADULT STUFF THAT MY EDUCATION AND LIFE EXPERIENCES DID NOT PREPARE ME FOR.
WHAT IS? HOW DO?
But, like, everyone at work keeps telling me finding a place is the easy part and that I'll be fine and that is reassuring.
This is gonna be fuuuuuuuuuuuuuun.
So let's see:
I'm cute, so bi, so trans, still part of Thunderfury, all that.
Dang, I can't believe it will have been two years since I started HRT in November.
Now the bit that I wasn't prepared for was the fact that Lhikan's Greatswords apparently have very fragile and breakable axles. Upon close inspection of the pieces, I realized one of the axles was glued to the actual sword and when I poked at it it came off with barely any effort; needless to say I'm rather disappointed with the seller, but I've decided to let it go. Here's the issue: Lhikan Greatswords cost a lot on BrickLink, precisely because of their breakability. So I've decided that I'll go ahead and try to mend broken fences, i.e. axles.
My idea right now is to basically even the surface out of both the sword and the axle and then glue them together at as perfect an angle as I can manage. First I'll need to fill in the small crater on the sword with glue or plastic, then file it to produce an even surface. Then I'll file the broken surface of the axle. Then I'll glue the two.
What do you guys think? Yea or nay? Any better ideas? Have any of you gotten a broken piece like that and how did you deal with it?
Perhaps I should get a cheap piece in the same pearl light gray (I think?) color, melt it somehow and use that instead of glue?
- 1,896 Total Blogs
- 111,934 Total Entries
- 550,943 Total Comments
- ToaKumo's Blog Latest Blog
- CommanderKumo Latest Blogger
63 user(s) are online (in the past 20 minutes)
2 members, 60 guests, 0 anonymous users
~Shockwave~, Google (1), Toa Smoke Monster