Sunday, February 28, 2010

The little things in life.

Today I discovered a new joy in life...typesetting mathematical equations in OpenOffice. I think it's quite strange, but writing my Partial Differential Equations paper this afternoon was an incredibly relaxing and fun experience. I'm going to see if I can find a way to attach a picture of it, because it just looks so nice -- like something you'd see in a textbook, not something created in a few hours with absolutely zero experience in typesetting prior to that (I guess that's a testament to how easy the system is to learn).
Anyway, I'm as surprised at this as most of you no doubt are, but very grateful to boot. I really needed something related to school to be fun this semester...

Just another day in Paradise.

Ahhh, another day in tropical paradise, wakened to the sweet tones of...tsunami warning alarms!?

Yes, that is part of what it means to live on a little rock in the middle of the deep blue sea. Although why they had to set them off at 6AM in the morning is beyond me...

If you haven't heard, sometime yesterday there was a magnitude 8.8 earthquake off the coast of central Chile, that spawned tsunamis heading out across the Pacific. If you look at a globe, you'll see that there is pretty much nothing between the central coast of Chile and the island of Hawai`i, which is why they began an evacuation of coastal sites everywhere on this and the other seven islands.

I was dreaming when the alarms went off, so it took me a few minutes to figure what on earth was going on. The alarms also woke up my housemate Josh, so we calmly got on the Internet and after a few minutes of relevant Google time managed to work out that we were not in imminent danger of being swept away. The ETA of the wave wasn't until after 11 AM Hawai`i time, and after consulting the Hawai`i county civil defense tsunami evacuation maps, we determined that we were outside the evacuation area. Josh has been through these a few times before, so he wasn't too worried. As of this writing, (about 2PM), the tsunami warning on the NOAA Pacific Tsunami Warning Center website has been canceled, so I'm guessing the wave wasn't too big (Josh mentioned one source said it was about 3 feet high).

So as you can see, life is never dull on an active volcano in the middle of an ocean that's surrounded by the Ring of Fire! And now I must get back to my homework...I doubt the teacher will accept "There was a tsunami!" as an excuse for turning it in late (now, if it had happened on Monday, maybe....).

Wednesday, February 24, 2010

The Sound of Music

Continuing in my vein of point-by-point laptop comparisons, today I will mention the speakers on my new computer. They are amazing. I'm not very knowledgeable about such things, but I appreciate good music, and boy, do these things deliver! I've been having great fun over the last few weeks identifying new themes and motifs that I never heard before in music that I've listened to, in some cases, hundreds of times of the last few years. I think the integrated subwoofer has something to do with it, perhaps being responsible for the vibrant bass I'm hearing (one of my best friends, who's a musician, was quite impressed by the fact that a laptop had a subwoofer, so it must be good).

Today I moved over my copy of the Messiah I got for Christmas (thanks Mom!) and was blown away by all the little details I could hear. It's incredible how much a great piece of music can be improved by having better speakers. Since I typically listen to classical music while doing homework, these speakers are wonderful. I suspect it helps me remember things better, since your brain works a lot harder when it's following the interwoven counter-melodies of a Baroque fugue and doing Complex Analysis, then when it's just doing math (at least, my brain does). And that, I believe, helps forge those all-important neural connections. By such little things, the world may be moved...

Tuesday, February 23, 2010

More busyness.

I realize I haven't written anything for a couple days, mostly due to the sheer number of homework assignments that seem to have conspired to be due around now. Right now, I have Modern Physics homework due tomorrow (thankfully completed tonight), Partial Differential Equations homework due on Friday and a 2-page writing assignment in the same class due on Monday (it's a writing intensive course). I also have an Electromagnetism test due on Friday, as well as a currently unknown(!) number of Complex Analysis problems ("at least ten") due the same day. So that is why I haven't written anything recently.

However, before wrapping up tonight, I'd like to mention the results of a test I ran to compare the processor speed of my old and new computer. I found a rather large and detailed scene I'd made in Blender, a 3-D modeling program, and rendered it on both computers. The results? Old computer: ~2:05. New computer: 0:09.75, or a whopping 12.82 times faster. It's interesting that both processors are rated at the same speed, 1.6GHz, the main difference is that my new computer has 4 cores running at that speed compared to one in my old (there are a few other small differences as well). Now, the speed increase is probably not due entirely to the processor, since this computer also has 16 times more RAM and a 1GB video card (my old computer doesn't even have a discrete video card), but the processor is certainly a large part of it. So next time you're considering a new computer, take it from me: quad-core is the way to go. Dual-core, at least.


(I hope to eventually expand this into a sort of series of reviews doing point-by-point comparisons of my new and old computers in various categories. We'll see how far I get.)

Friday, February 19, 2010

It's a Wonderful Life

Today I learned that what I want to do with my life is arguably the most difficult subject ever undertaken by humans.

Joy.

My calculus professor, Dr. Ivanova, whom my cosmology professor Dr. Heacox pointed out as the most promising source of knowledge on the math I need, informed me that theoretical cosmology uses math so difficult even pure mathematicians avoid it.

Wonderful.

The reason for this disclosure is because today I decided that a directed studies program would likely be the only way for me to start learning the tensors that are so important in theoretical cosmology. I talked with Dr. Heacox first, who after pointing me towards Dr. Ivanova and offering to set me up with some books, remarked "It's a beautiful subject, but it hurts your head" (and he's been working with tensors in cosmology for over 40 years). Dr. Ivanova had more to say, because she's one of the few math faculty on campus who knows anything about differential geometry, the extremely high-level and abstract field of math in which tensors (and more exotic stuff) reside. Part of her remarks, along with much helpful overview information, were the aforementioned "Cosmology uses such heavy math, even pure, theoretical mathematicians avoid it", and that cosmology is so difficult, very, very few people have ever really understood it.

I have always had an idea that what I wanted to do was complicated, but never before truly realized the extant of what I had planned. It's like discovering that wanting to put up a shed in your back yard requires you to learn how to survey land, study atomic bonding theory, and be able to calculate strains in materials (which, incidentally, requires tensors for fullest treatment).

But she also said that anything less would be a waste of my mind, which I'm going to take as a compliment. It will be an interesting life, if nothing else...

Wednesday, February 17, 2010

General Busyness

Well, the post I wanted to write yesterday never happened, due to running out of time and having to work on homework. This post will be short for the same reason. I got my paper and USB cord for my printer today, so I was able to set it up and get it running. I haven't had much reason to use it yet, but it seems to be working just fine.

My trip to the Vis on Saturday went fine, although there weren't many people from the UAC there. Which was not a problem, because the local amateur astronomy club was there with several extra telescopes set up. Which was good, because I could not believe how many people there were up there! We probably had crowds getting up into the 70's or 80's for quite a while, and though it got quiet later on, it never completely slowed down (usually, we might have 20-40 people on any given night at our busiest).

One of the guys who works at the Vis commented as we were setting things up at the beginning of the evening on the clouds rolling down the mountain like water, and how he would like to make a time lapse movie of it some time. Well, I had my camera on hand, and as soon as everything was set up, I set it up on the balcony and proceeded to take a hundred shots over about five minutes, which I plan to put together into a really cool movie showing the clouds flowing down the slopes of Mauna Kea when I have time. It's an amazing thing to watch, and easily visible to the naked eye if you look for more than a few seconds. It happens fairly often at the beginning of the evening, when the cooling air causes the moisture to condense and move down the mountain. I'll have to see about linking to the video of it when I have time...

Sunday, February 14, 2010

fried eggs + electric stove = bad

Today's post will be a little collection of various random things I've had in my head over the last week but didn't have time to set down due to getting my new computer. Which, by the way, I still plan to write a comprehensive review on either Sunday or Monday. But today is just a quick post, so I can get to all the homework I have.

Sunday was a pretty momentous day for me. As I mentioned last week, I took the drive test up at the Vis and am now a certified driver for MKSS (Mauna Kea Support Services). Sunday was the first time since then that I went up. Strangely, that day, the other certified driver who was scheduled to go couldn't make it, so I was the only person who showed up. To be sure, I had been hoping to drive on Sunday, but not by myself! It was with no small trepidation that I started up the assigned minivan and headed off. But despite my worry, and the fact that Saddle road is a genuinely dangerous road if you're not careful, I made it safely. I guess I'm REALLY a certified driver now.

Speaking of which, tonight is the second Saturday of the month, which means that the University Astrophysics Club of which I am vice president gets to bring as many people up as they want to help out at the Vis, so I'll be heading up there tonight. From what I've heard, a goodly number of the certified drivers won't be able to make it, so I'll probably get to drive up again. It's nice to be driving again, although a little weird given that I've been walking most of the time for the last 6 or 7 months.

Anyway, I need to finish this and get on to other things today.  I have...let's see...three homework assignments and a take-home exam to work on, which makes me very happy it's a three day weekend this week!

A hui hou!

Friday, February 12, 2010

Yes, I'm still around.

Sorry for the long delay everyone, I'm still alive and well. There are two reasons for it: one, I still have a fair amount of homework to keep up on, and two, my new computer came Monday! So I've been busy getting it all set up and poking around to see what it's like (I'm writing this post on it, in fact).

This is just a quick update, as I plan to do a detailed review later (perhaps over the weekend), but I will just say that I am really pleased with my new computer. Windows 7 is proving to be a stable and useful operating system, and the sheer computing power of this thing blows my mind. I can't wait to start transferring files from my old computer over (another weekend job) and comparing the time it takes for certain CPU-intensive tasks to complete.
Anyway, I need to run, so stay tuned for some more posting over the weekend! 

Sunday, February 7, 2010

Every Cloud has a Silver Lining.

Today I bought a printer, USB cable to connect it, and 500 sheets of paper for $0.97, plus shipping and tax.
If you're wondering how that came about, it's a bit of a story...
As some of you may know, I have wanted to get a new computer for some time now. My current laptop is rather slow, has little RAM, has already gone through two batteries, and has no dedicated graphics card, which makes it a poor fit for what I like to do: multi-tasking and multimedia. In its defense, I will say that it is a very stable machine, and despite running slow still runs quite well, although battery-less it is basically a glorified desktop, and one that runs slower than all but the cheapest of those.
But! the point is that, when mom and dad surprised me at Christmas by paying for my current semester here at Hilo (thanks guys!), I decided I would put some of the money I had intended to use to pay for tuition towards a new computer. And that's where this tale really begins.
 Hoping that if I acted quickly I could have my new computer before I left California, I started looking at computers Christmas day. I set myself a $1,000 spending limit, and began to see what I could find. To be honest, I didn't do much research. In fact, since my current computer is a Dell, and our family computer is another Dell, and they had both always run well, I went straight to Dell's site and began looking around. After some looking and comparing, I finally settled on a 17-inch with specs that I could live with. I wasn't perfectly happy with it, but I'm 1) a perfectionist and 2) a bit greedy; what I really wanted was the most powerful computer out there, one that could handle pretty much any situation that had even the slightest chance of coming up. Instead, I settled for a good mix of specs that was just over a thousand dollars, and ordered it.
As I said, my original plan was for it to arrive before I flew back to Hawai`i on the 8th. The estimated shipping date was the 5th, but I was hoping it might ship early, and I had gotten free 3-5 day shipping. To be short, it didn't come. I had known all along that this might happen, so, while disappointed, I wasn't too surprised (I figured maybe they were busy with all the holiday sales).
So, I flew back to Hawai`i, very happy to return to the land of warmth and sun from frigid Northern California (I think I can hear those of you in Nebraska and Washington laughing).
Time passed, until maybe  a week later -- I remember it was close to the middle of the month -- I got a somewhat strange e-mail from Dell saying that my order had been delayed. Not just delayed a few days, but delayed till the end of the month! No explanation given, and a notice that they would have to cancel it if they didn't hear from me in 24 hours. For some reason, I didn't feel right about it, and called mom to ask her what she thought. She agreed that it seemed weird, so I made the decision to let the order lapse and take another look around (I figured I could always re-order it if I didn't find anything better, and it would probably take the same amount of time either way). So, I went back to looking.
Now, you may be surprised to find out that while I know a lot about what makes a good laptop, I had never paid much attention to brands, which is why I had gone with Dell initially: much simpler than actually looking around and comparing from other manufacturers. However, I'd gotten a recommendation from a friend while in California about HP, so I toddled over to their site and started looking around, and what I found completely blew me away. While looking through their laptops, I came across a 17-inch model called the dv7t Quad Edition, boasting an i7 Quad Core processor. Now, if you haven't kept up with the latest in Central Processing Unit designs over the last few years, the i7 is currently about the 4th most powerful the most powerful chip available in the general laptop (or even desktop) market right now. About maybe ten years ago, someone in some CPU design department somewhere had the brilliant idea of making a chip that would be able to do two things at once, instead of merely focusing on making a chip that could do things ever faster. Well, that idea turned out to be golden, and now a fairly large proportion of computers run on dual-core processors (I think 'Dual Core' is actually a registered trademark of Intel, whose dual-core Pentium chips command a very large market share).  Anyway, dual-core chips were a wonderful step forward, because it's extremely difficult to double the computing speed of a single-core chip, whereas simply adding a second core and making the two play nicely together gets you the same effect. It just took someone to take that important first conceptual step. I'm sure almost as soon as it was seen that it could be done, people were already wondering how high they could go, and just a few years ago now, they introduced the quad-core line of chips. That's right, these chips have four, count 'em, four separate computing cores in each chip. Each core, individually, doesn't even have to be all that fast. The things are still incredibly powerful and fast, and, according to reports, nearly impossible to bog down no matter how many programs you have running.
Now, after that long digression, I should say that I have wanted a computer with one of these pretty much since I first knew they existed.  However, computers with them have always been priced above what I was willing to pay for them. Until...I came across this particular model which had an instant rebate of $200 on it. Which put it under a thousand dollars. Now, I am not a very impulsive buyer, I tend to dither a lot when spending large amounts of money (for me, that's more than about $25). I also like reading reviews about things I buy before buying them, so I started looking for some. And lo and behold, what should I find, but a coupon code for that particular model that was an additional $350 off. And not just any configuration, but one that actually increased the system specs way beyond what I had resigned myself to. To put it bluntly, this was truly a heaven-sent deal. I ended up getting a system costing $1,528.99 for a mere $978.99, plus a measly $40 in taxes. The final tally was
  • Processor: i7- 720QM Processor (1.6GHz, 6MB L2 Cache, 1333MHz FSB) w/Turbo Boost up to 2.8 GHz (That's a really good processor. I mean really good...)
  • Memory: 8GB RAM. (this...made my jaw drop. My current system has 1/16 of this [half a GB]. This is currently the maximum amount of RAM that can be stuffed into a computer. And RAM is, after your processor, the most important factor in how fast your computer runs. More RAM = faster computer.)
  • Graphics card: 1GB Nvidia GeForce GT 230M (this is a whoppingly big graphics card. My current laptop doesn't even have a separate one, so there's really no comparison. This card in your computer is responsible for all the graphics you see, so a better card means you can do more fancy stuff with graphics. And I love doing things with graphics...)
  • Hard Drive: FREE Upgrade to 320GB 7200RPM SATA Hard Drive with HP ProtectSmart Hard Drive Protection  (I really didn't care too much about the size of the drive, because I don't regularly save full-length movies on my computer and I'm not a professional photographer, but hey...can't beat free. My current drive is 60 GB, for comparison, and I still haven't filled it up after 2 & 1/2 years, so this one should last me for a long, long time.)
  • Display: 17.3" diagonal HD+ High-Definition HP LED BrightView Widescreen Display (1600 x 900) (I currently have a 15-inch display, so this will be even bigger. Perfect for graphics work.)
 The rest of the specs will probably not be of much interest to you (for that matter, these may not be of much interest to you), so I will leave off raving about it now. Suffice it to say, this is a computer beyond my wildest dreams of what I hoped to be able to afford at this time in my life, and all I can say is soli Deo gloria.

But I realized I still have not explained the printer...
 
When I ordered the computer in mid-January, the estimated shipping date was February 1st. Since I was getting my dream computer, I didn't really care how long I had to wait for it (the fact that it was custom-configured is probably why it was so long). Well, along comes the 1st, and what should I get but an e-mail from HP saying that my order had been delayed. But what a difference! Instead of two weeks delay, it was only until the 4th; and to top it off, they sent along a $50 gift certificate for their online store, which I thought was awfully nice, considering they didn't have to send anything. So that is the origin of the $0.57 printer, $0.29 USB cable, and $0.11 ream of paper. The printer originally cost $29.99, the cord an additional $14.99, and the paper $5.99, which came out to a mere $0.97 above the certificate. The entire rest of the charge was the shipping and $0.26 tax, so the whole thing cost me $6.48. And now I have my own printer, and don't need to rely on printing things at the library anymore like I have (or, I will when it comes in about a week).

Oh, you're wondering about my computer? It shipped on the 4th as predicted, and is currently in Anchorage, Alaska, on it's way here. If everything goes smoothly, I should have it by Wednesday, so perhaps the next update will be written on my spiffy new system. So stay tuned! And remember to watch out for those silver linings!

A hui hou! 

Thursday, February 4, 2010

In which earth-shaking things are revealed.

Yesterday...

How to begin? "Yesterday I learned a new mathematical operation"? "Yesterday I was taught something that rocked my knowledge of vector calculus to its core"? Or maybe "Yesterday I learned of mathematical quarks".

I'm sorry, it's a bit hard for me to explain, but yesterday I did have a very profound revelation in math as it relates to the commutativity of the dot product when one of the "vectors" is the del operator.

Oh dear, this is just getting worse, isn't it? Let me start by explaining that we have homework due in Electromagnetism. Most of the problems were fairly straightforward, if a little long and time-consuming. But there were two product identities that simply rebuffed all efforts to prove. This was the more downright bewildering because usually such proofs are very simple: just write out every single term explicitly, and cancel until you're left with zero on both sides of the equals sign. But these two repeatedly withstood every attempt, by me and several other people as well. My only thought was that I must be doing something wrong, but what? As far as I could tell, all the terms were correct, but in each proof I'd end up with 20 or more terms that wouldn't cancel.

But yesterday...

I and a classmate were working on the homework, and having finished the rest of the problems, were getting increasingly frustrated with our lack of progress, or indeed the lack of any conceivable way to make progress. I should mention that we were working in the main hallway in Wentworth Hall, the main Astronomy/Physics/Chemistry building on campus. We were venting our frustration by reviewing everything we knew about vectors and their operations from the beginning, our conversation going something like

"But that's a vector!"
"Right!"
"And if you dot a vector and the del operator, you get..."
"A scalar!"
"Right!"
"And if you multiply a vector by a scalar, you get-"
"-a vector." 

At which point Dr. Heacox, one of our professors from a different class happened to walk by and overhear us. With the desperation of two drowning sailors, we turned to him and poured out our troubles, about how the identities wouldn't work, and we must be doing something wrong, but what was it, and did he have any idea what was the problem was? To his everlasting credit, he stopped and came over to look, and in about 30 seconds had identified the problem: dotting the del operator with a vector is not commutative.

That's a rather complex statement, so I will explain. To be commutative in math means that you can do things in any order and it won't affect the results. For instance, addition is commutative: \(2+3=3+2\). So is multiplication: \(5*7=7*5\). But subtraction and division are not. \(3-4\ne 4-3\), and \(8/2\ne2/8\). Knowing whether an operation is commutative or not is very important.

You can think of vectors as essentially numbers with direction.  For instance, velocity is a vector. You can say things like "50 mph to the east", or "2 feet per minute straight up". Speed, in contrast, is a scalar, a number with no direction. Saying "50 mph" gives me no information about what direction this speed is directed towards. Many of the numbers we deal with in everyday life are scalars (like temperature, price, and speed). Others are vectors, like forces and accelerations (I almost said weight was a scalar, until I remembered that it does have a direction: towards the center of the Earth).

Anyway, the point of this is that the dot product (one of the two ways to multiply vectors) is commutative: \(A\cdot B=B\cdot A\). However, it is not commutative when one of the two "vectors" is the del operator. I put vectors is quotes, because the del operator is just that: an operator, not a vector (some operators you may be more familiar with are \(+, -, \times,\) and /  or \(\div\)). You are allowed to treat it like a vector for purposes of notational simplification, and so I (naively) assumed that it did indeed behave like a vector at all times. But what I learned, and what really rocked me to my core, is that \(\nabla\cdot A\) does not equal \(A\cdot\nabla\) (the del operator is the upside-down equilateral triangle. The actual symbol is called a “nabla”.). The quantity \(\nabla\cdot A\) is a very common mathematical and physical quantity, called the divergence of A, since it measures how much A is spreading out or contracting in. But \(A\cdot\nabla\) is another beast entirely. In fact, it is without physical meaning until multiplied by another vector. That's why I whimsically began this long rant by saying I had discovered a mathematical quark.

Quarks, in the Standard Model of physics (the most successful theory of matter that we have to date), are what make up certain sub-atomic particles like protons and neutrons. Both protons and neutrons are made up of three quarks, and when one of those quarks changes its type (from being, say, a 'down' quark to an 'up' quark) you can have a neutron change into a proton, or vice versa (extremely rare).

The catch is, quarks have never been observed by themselves in any experiment, so the best we can say, since they seem to fit all the data, is that quarks can never exist freely in nature. Much like the little mathematical beastie \(A\cdot\nabla\) which has no meaning until multiplied by a vector.

"Why is this such a big deal?" , you may well ask. I think the answer, for me, is a combination of the fact that I had never heard of this before -- had seen nary a mention of it in all the math classes I've taken so far. I had no inkling of its existence, yet there it was just waiting to be the solution to my problem. Also, the fact that I was rather...worked up when I learned it. I'd already spent over 4 hours over several days trying to get the one identity to work, and it was driving me crazy when all of a sudden...the answer just fell into my lap, as it were.

After dispensing this astonishing piece of knowledge, Dr. Heacox amiably bid us good day and went off to wherever he was going, while my classmate and I sat and tried to decide whether to laugh long and loud at our stupidity or go over and kick a wall, repeatedly. Unable to make up our minds, we settled for finishing the homework, which went over completely without incident after that (although it still took us an additional 2 hours).

So, that was that. Not especially life-changing to most of you I'm sure, but it was a very moving experience for me, as you can see by the length of this post. You can now go about your life with some interesting information about vectors (perhaps tomorrow I'll tell you more about the other way to multiply vectors, the cross product), while I ... will be taking Dr. Heacox cookies tomorrow.

Tuesday, February 2, 2010

Fine food.

Just a quick entry today to say that I may not post for a couple days due to large amounts of homework. I do have one or two things of note, however:

Yesterday I went up Mauna Kea for stargazing, where Nathan taught me about how to do scientific data reduction. Reduction, in imaging terms, means taking an image and squeezing as much useful information as you possibly can out of it. There are various procedures for doing this, but I'll postpone a description till I have more time.

Also, I took the drive test, so I am now a registered driver! Able to drive the official MKSS (Mauna Kea Support Systems) vehicles if I need to. Since I've never changed a tire before, that was part of the test, so I learned how to do it. Pretty interesting. If it wasn't dark or cold or rainy, and I didn't have to be somewhere urgently, I could see it being kind of fun.

Other random news: I went to the local Safeway today, for my weekly grocery shopping. On a whim I decided take a picture of everything I bought today. Digression: riding my housemate Jonathan's moped in traffic on a 3-lane highway got a little too much for my nerves, so last week I started walking to the grocery store. It's about a mile, the same distance as it is to school, and I simply carried my groceries home on foot. Since I was carrying around 20 pounds of food in each hand, this had the interesting effect of making me mostly unable to lift my arms for the rest of the day (as a result of the strain of having to continuously hold all the bags away from my legs for 25 minutes while I walked. Try it sometime). This time, I came prepared and brought my backpack along due to a brilliant suggestion from a friend (something I probably would not have thought of for quite some time on my own), so I managed to carry at least as much weight if not more home with no ill effects. Anyway, this is what $80.44 can get you in Hawai`i. I'll let you draw your own conclusions on my healthy eating habits, or lack of them.


(I should point out that the contact solution was $20 by itself, but removing that would give you a pretty good idea of what I spend per grocery trip. Yes, food is expensive here)