- The humor - By and far an important aspect of any comedy, the humor of Gravity Falls resonates very well, from the lamest pun to the brilliant stuff they get past the censors (and, wow, do they get a lot past the censors. This is a Disney show, right?). Expertly crafted and leaving me wanting more in the best way possible.
- The story - while not the most story-heavy series (a lot of the episodes are very standalone and can be watched without missing much of previous episodes), the story that is ongoing is very engaging. Gravity Falls, OR, is a place where weird, paranormal stuff happens. Our main characters want to know why, thus we want to know why, and their curiosity becomes ours in a genuine, unforced way.
- The relationships are believable - Dipper and Mabel, the two main protagonists, are twin siblings who are sent to their great uncle (or, you guessed it, Grunkle) Stan's tourist trap, the Mystery Shack, for the summer. And they have a relationship that is completely believable (and as a twin, I can fully attest to it). Even when they have a scuffle or conflict, at the end of they day they can hug it out and not hate each other, which is very refreshing in a kids show. Also, the characters are not just defined by single character traits; for instance, Mabel has a fantastically overactive imagination and looks at the world from a very different angle than most of the other characters, but she's never called stupid or foolish by the others. Soos, the Mystery Shack's general repair and groundskeeper guy, who is overweight and sometimes dull-witted, is not defined by these traits, nor is he mocked for them; everyone treats him as they do everyone else, which is also really refreshing to see in a kids show. As for romantic relationships,
First off, I played Mega Man X for the first time courtesy of the Wii U Virtual Console (prompted by a fantastic video by Egoraptor). Fantastic game; the more I play SNES games, the more I regret not owning a SNES in childhood.
After playing Fire Emblem (Rekka no Ken) and Sacred Stones, I finally caved into my roommate's demands that I play Awakening; OMG SO MUCH AWESOME! Probably one of my favorite games of all time, and definitely looking forward to playing it again.
Right after completing Awakening, I received Professor Layton vs. Phoenix Wright: Ace Attorney in the mail. Another fantastic game; Layton puzzles and story combined with Phoenix Wright courtroom shenanigans made for an awesome crossover. I just wish Maya hadn't been given a valley girl accent. :/
And, finally, my roommate got some 3DS Smash Bros codes, one of which he shared with me. I'm loving Mega Man so far; will definitely be playing as him once the Wii U version comes out (not getting the 3DS version; I'd like to spare my buttons of a painful death). I really wish the demo included Robin as a playable character, though; of the new roster, I'm looking forward to playing as him the most.
On a more academic note, this Thursday is my Ph.D. preliminary exam oral defense, so that'll be fun. I've already worked through the problems that I will be asked about, and I think I've solved all of them. Hopefully all will go well.
As you may have noticed, this summer the blogs were highly accented with my extreme absence since I took a trip to the northern UK. The reason for this absence is simple: I was studying for, and subsequently started taking, my preliminary examinations for continuation to my Ph.D. in physics. Last week for me was filled with three four-hour exams: one on Monday (Quantum Mechanics), one on Wednesday (Electromagnetism), and one on Friday (Classical, Special Relativity, and Statistical Mechanics grab bag). I am happy to say that I survived the initial onslaught of my prelims and am now in phase two: a twelve-hour take-home exam to be done over seventy-two hours (10 a.m. today to 10 a.m. Thursday). I have glanced at the problems but not worked on them yet, but I feel pretty good about the quantum section.
In other news, the new school year is set to start in a week, but I have a class starting this Thursday. That'll be quite fun. 8D
Day 5: I climbed Arthur's Seat for a second time; it was sunny, so the view was even better than on Sunday when my advisor and I climbed it together. I also got proof That I made it to the summit. 8D
Day 6: I went to Edinburgh Castle and walked around the former residence of the Scottish royal family. There were a few museums that were mainly dedicated to the history of Scottish military. I also saw the Scottish crown jewels, but was not allowed to take photos (and didn't realize I wasn't allowed until a lady yelled at me for taking out my phone).
Day 7: I journeyed to Pencaitland, which is about 12 miles outside of Edinburgh, for a tour of the Glenkinchie distillery. However, I was late for my booked tour, as the bus didn't take me the whole way to the distillery, and it was a 2 mile walk to the distillery from the bus stop. I literally was walking, in the middle of Scottish farmland, following signs that I hoped were telling me the truth and leading me in the right direction. I eventually got there, however, unharmed but late. The lady at the front desk was very accommodating, though, and fit me into the next tour. It was quite lovely, and we got to see all the steps of brewing whiskey followed by a tasting session. After tasting, I picked up a bottle for my dad and a smaller bottle for me (if they sold 50 cl bottles, they would have been the same size, but, alas, they only had them in 20 and 70 cl sizes). I tried to get on the distillery's shuttle back to Edinburgh, but unfortunately I had asked to join it after it had left; they told me not to worry, though, as there was a local barman who would come and pick me up with two other women who also took the bus and take us to his pub, which was a few seconds' walk from the bus stop. The three of us had a drink at his pub (his only request in exchange for picking us up, which was completely fair in my opinion) and we got to talking. The one lady was around my age and still in college, while the older woman was her aunt and was retired. We got to talking about math and science, since the aunt had studied nutrition science for her job and enjoyed talking about science. We also discussed beer, the tour, and previous and future travels we were planning to take. All in all, it was a lovely afternoon, and we sat together on the bus back to Edinburgh and talked some more. Once we were back in the city, we said our goodbyes and were very glad to have met each other.
Then, this morning, I boarded my flight back to the states, and now I am quite tired, as it is (as I'm typing this) around 1:30 a.m. back in Edinburgh, and my body wants to be very well asleep. I am happy to say, though, that it was a fruitful trip, both for research and fun, as now my code that I've been working on for nearly a year finally works and has reproduced the results of the paper we modeled it off of! Now, we get to push it into new parameter space to aid us in our spectroscopic analysis.
Well, that's all for now. I'm going to go eat some cookies with my friends.
- Vaguely losing consciousness on the plane ride over the Atlantic to adjust to new time zone. Would not qualify it as sleeping.
- Instead of checking into the hotel (which didn't allow checkins until 2 p.m. local time), climbing Arthur's Seat to the summit with my advisor like a boss.
- Enjoyed a Guinness. (Not Scottish, I know, but arguably fresher than those sold in the US.)
- Tossing a caber.
- Wearing a kilt.
- Playing bagpipes.
- Trying haggis. (Will probably do this at breakfast tomorrow, though.)
Last week I went home to visit my family for a couple of weeks. It's been pretty low key so far; visited some friends over the weekend, mowed the lawn (so lovely), and tried to get things a bit cleaner around the house. I also ate way too much food at various gatherings.
This weekend my dad and I pick up KK from grad school (he successfully defended his Master's!) and will enjoy two long, arduous, 10 hour-long trips. Then, I fly to Wisconsin for a conference, so that should be fun.
I also got the Back to the Future DeLorean LEGO set, and I must say it's a very nice representation. Also, Doc Brown's "Great Scott!" face is perfect.
I really want to make the purple skateboard in that set an actual hoverboard using magnets and a superconductor. One of these days...
I also went to Philly BrickFest two weekends ago, but I was only there for a couple hours since I had to leave for choir rehearsal. I did snap some pics, which will hopefully end up on my Brickshelf at some point. Maybe.
In other news, I'm still obsessed with quantum mechanics and have been playing around with various mathematical things associated with it, like deriving the ladder operators and matrix elements for the quantum harmonic oscillator, deriving formulas for coherent states, and
(This is the part where you all look at me like I'm mad, and I reply with an expression like this: 8D)
So, not too much going on with me right now, but I can't complain.
This mass is known as the inertial mass. The larger an object's inertial mass, the more it resists being accelerated by a given force. The second definition of mass also comes from Newton, but it is instead determined by his law of gravitation.
The mass here determines how much two massive objects attract one another; this is known as the gravitational mass. But here's the interesting thing about these two masses: there is no law of physics that says these masses are one and the same. Such a notion is known in physics as the equivalence principle. The weak equivalence principle was discovered by Galileo; he noticed that objects with different masses fall at the same rate. Einstein came up with the strong equivalence principle, which discusses how a uniform force and a gravitational field are indistinguishable when you look at a small enough portion of spacetime. The only reason we believe these two masses are equivalent is because experiments show that they are equal to within the precision of the instruments with which we measure them, and there are ongoing experiments trying to narrow down that precision to determine if there is any difference between the two.
What this says is that the product of the uncertainty of a measurement of a particle's position multiplied by the uncertainty of a measurement of a particle's momentum has to be greater than a constant (given by the reduced Planck constant, h over τ = 2π). This has nothing to do with the tools with which we measure particle; this is a fundamental statement about the way our universe behaves. Fortunately, this uncertainty product is very small, since ħ is around 1.05457 × 10-34 J s. The real question to ask is, "Why do particles have this uncertainty associated with them in the first place? Where does it come from?" Interestingly, it comes from wave theory.
Take the two waves above. The one on top is very localized, meaning its position is well-defined. But what is its wavelength? For photons, wavelength determines momentum, so here we see a localized wave doesn't really have a well-defined wavelength, thus an ill-defined momentum. In fact, the wavelength of this pulse is smeared over a continuous spectrum of momenta (much like how the "color" of white light is smeared over the colors of the rainbow). The second wave has a pretty well-defined wavelength, but where is it? It's not really localized, so you could say it lies smeared over a set of points, but it isn't really in one place. This is the heart of the uncertainty principle. Because waves exhibit this phenomenon – and quantum particles behave like waves – quantum particles also have an uncertainty principle associated with them.
However, this is arguably not the most bizarre thing about the uncertainty principle. There is another facet of the uncertainty principle that says that the shorter the lifetime of a particle (how long the particle exists before it decays), the less you can know about its energy. Since mass and energy are equivalent via Einstein's E = mc2, this means that particles that "live" for very short times don't have a well-defined mass. It also means that, if you pulse a laser over a short enough time, the light that comes out will not have a well-defined energy, which means that it will have a spread of colors (our eyes can't see this spread, of course, but it means a big deal when you want to use very precise wavelengths of light in your experiment and short pulses at the same time). In my lab, we use this so-called "energy-time" uncertainty to determine whether certain configurations of the hydrogen molecule, H2, are long-lived or short lived; the longer-lived states have thinner spectral lines, and the short-lived states have wider spectral lines.
So while we can't simultaneously measure the position and momentum of a particle to arbitrary certainty, we can definitely still use it to glean information about the world of the very, very small.
The triangular numbers are the numbers of objects one can use to form an equilateral triangle.
Anyone up for billiards? Or bowling? (Image: Wikimedia Commons)
Pretty straightforward, right? To get the number, we just add up the total number of things, which is equal to adding up the number of objects in each row. For a triangle with n rows, this is equivalent to
This means that the triangular numbers are just sums from 1 to some number n. This gives us a good definition, but is rather impractical for a quick calculation. How do we get a nice, shorthand formula? Well, let's first add sequential triangular numbers together. If we add the first two triangular numbers together, we get 1 + 3 = 4. The next two triangular numbers are 3 + 6 = 9. The next pair is 6 + 10 = 16. Do you see the pattern? These sums are all square numbers. We can see this visually using our triangles of objects.
(Image: Wikimedia Commons)
You can do this for any two sequential triangular numbers. This gives us the formula
We also know that two sequential triangular numbers differ by a new row, or n. Using this information, we get that
Now we finally have an equation to quickly calculate any triangular number. The far right of the final line is known as a binomial coefficient, read "n plus one choose two." It is defined as the number of ways to pick two objects out of a group of n + 1 objects.
For example, what is the 100th triangular number? Well, we just plug in n = 100.
T100 = (100)(101)/2 = 10100/2 = 5050
We just summed up all the numbers from 1 to 100 without breaking a sweat. You may be thinking, "Well, that's cool and all, but are there any applications of this?" Well, yes, there are. The triangular numbers give us a way of figuring out how many elements are in each row of the periodic table. Each row is determined by what is called the principal quantum number, which is called n. This number can be any integer from 1 to infinity. The energy corresponding to n has n angular momentum values which the electron can possess, and each of these angular momentum quanta have 2n - 1 orbitals for an electron to inhabit, and two electrons can inhabit a given orbital. Summing up all the places an electron can be in for a given n involves summing up all these possible orbitals, which takes on the form of a triangular number.
The end result of this calculation is that there are n2 orbitals for a given n, and two electrons can occupy each orbital; this leads to each row of the periodic table having 2⌈(n+1)/2⌉2elements in the nth row, where ⌈x⌉ is the ceiling function. They also crop up in quantum mechanics again in the quantization of angular momentum for a spherically symmetric potential (a potential that is determined only by the distance between two objects). The total angular momentum for such a particle is given by
What I find fascinating is that this connection is almost never mentioned in physics courses on quantum mechanics, and I find that kind of sad. The mathematical significance of the triangular numbers in quantum mechanics is, at the very least, cute, and I wish it would just be mentioned in passing for those of us who enjoy these little hidden mathematical gems.
There are more cool properties of triangular numbers, which I encourage you to read about, and other so-called "figurate numbers," like hexagonal numbers, tetrahedral numbers, pyramidal numbers, and so on, which have really cool properties as well.
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Real Name: Forever Shrouded in Mystery
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Hieroglyphs And The Like
Gravity Falls is an awesome showThe Duchess Approves - Oct 03 2014 07:33 PM
My latest video gaming conquestsAkano Toa of Electricity - Oct 03 2014 04:26 PM
My latest video gaming conquestsVoltex Oblige - Sep 16 2014 08:50 AM
My latest video gaming conquestsLyichir - Sep 16 2014 07:30 AM
My latest video gaming conquestsThe Duchess Approves - Sep 16 2014 03:26 AM