Freiddie's blog

A more recent update

2009-10-10T06:44:00.000-04:00

A few days ago I decided to resume writing stuff on this site, after a few months of inactivity. The summer has been a little hectic as a result of my peculiar schedules, and the lack of interesting topics has prevented me from posting.

Now that the Fall semester is here, I have had more than enough topics to discuss, but ironically the lack of time has further prevented me from writing here. This weekend, if all goes well, I plan to write a one or two posts about some topics of interest. Stay tuned.

learning gtkmm

2009-05-28T20:20:00.002-04:00

GTK+ is a graphics user interface (GUI) toolkit for C; since I prefer to work with C++ over C, I use its related C++ binding, known as GTK-- or gtkmm. From what I have learned so far, it's actually a very elegant solution to a dilemma that I faced this week: how to build a cross-platform program with a window interface.

The keyword here is "cross-platform". MFC is not an option here, because it's targeted to Windows. In addition, my impression with MFC has been rather... disappointing. It's hard to learn and very cryptic for a new C++ programmer like myself. My past experience with frameworks like .NET has shown me far more elegant ways of graphical programming.

There are just so many ways in which GTK+ is different from MFC... other than the elegance of its structure. For example, I can make windows that are very resizable without putting a lot of effort -- because GTK+ is based on a simple "bin/container" system (where you can drop "controls" or widgets into highly flexible boxes), rather than the absolute-positioning system (specifying precise X, Y, width and height of each control) that MFC uses.

Of course, there are many other options out there besides GTK+, e.g. Qt, but right now I want to focus on one of my options (chosen rather arbitrarily) and work on it. If GTK+ satisfies my needs, then I will most likely stick with it for a while; otherwise, I can just choose another framework to work on (preferably sooner to make code modification easier).

There are so many things that intrigue me about C++ that I can't write down all at once -- it's like discovering a whole new world. I'll try and keep things updated when possible.

a shift in focus

2009-05-22T12:00:00.019-04:00

Several semesters of pure math and physics, and it's time for a (temporary) change. As I have already mentioned, my focus this summer is on C++ programming. What I probably forgot to mention is that I'm also taking some social science courses this semester, so I'll be treading on unfamiliar territory.

I don't know much about sociology, and a little about cognitive psychology. Nonetheless, those are the courses that I'll be taking the first half of summer. Without the experience, these two subjects will seem very new to me, which is a rather unusual feeling. I typically have at least a small idea of what goes on in my usual science classes, so I might not be used to this kind of feeling.

Recently, I took the first few classes of these two courses, and they went quite well so far. I find myself more interested in the psychology class than the sociology one, since the psychology class also had a lot of biology in it -- akin to the molecular & cellular biology that I just did last semester.

Interestingly, the instructors were rather young ones, which is something that I'm not typically used to (unless they are teaching assistants, but this isn't the case). The teaching methods are a little different for my psychology class, but I think I should be able to work with that. The instructor tends to use rather unusual approaches, and talks with a more "informal" tone.

So far it's only been about a week, so I can't tell how effective my instructors for the two classes are. I do hope they are helpful, considering these two classes will be harder than my average science classes.

reorientation

2009-05-15T14:35:00.000-04:00

Phew, the spring semester just ended. It was definitely more work than I had anticipated, and with my usual disorganization, my daily and routine schedule was completely destroyed.

So now that I've "sort-of" settled in my new abode, it's time to start over and reconstruct the broken schedule I had for the past few weeks: turning my biological clock back by a few hours so as to resume what a normal person should have. Because of that, I would really appreciate the summer classes starting next week, since I tend to lose track of time when I have no deadlines.

A goal that I set myself for this summer is to learn C++, for real this time. There is actually a need to do so in order to work on a certain research project, so there is no excuse this time. I had avoided it for long enough, and now it's time to embrace it. I understand that it will be much harder to learn than Python or C#, but I expect it to be a fruitful effort, considering so many programs are written in C/C++ nowadays.

One of the tough decisions is to select the programming framework. I would really want to learn one for Unix, but so far my main focus must be MFC (i.e. Windows) because that's what the current program is written in. Perhaps if I'm ambitious, I could try rewriting it for Unix, or even better, for a more generalized interface so that it works on all platforms. That would be a difficult task though. Regardless, I hope I would at least accomplish the "learn C++" part.

rapid post

2009-05-05T10:00:00.002-04:00

Since I haven't written anything for weeks, I decided to write one short post to keep it updated. I should be able to return to blogging after this finals week of exams.

That's one thing: finals this week. Secondly, and what follows, is that the spring semester is nearly over, and summer semester begin in less than two weeks. I do have classes during summer, but I think it will be much less exhausting than what I have done this semester.

There are so many things that I had wanted to do, only to be deprived of the time because of the overwhelming amount of homework (and that is precisely why I am glad my intro physics lab II is over: no more lab reports).

As stated, I should be able to resume blogging once I sort out a more, um, "regular" schedule with more free time.

pointers

2009-04-11T20:12:00.000-04:00

Pointers are the one unique "data type" in C. Now that I'm slightly more acquainted with the language, I realized that C is all about pointers and memory management.

What makes pointers and memory management so useful is that they allow dynamic objects to exist during run-time. This dynamic behavior is absolutely essential because most of the time we don't know how much data we will get from user.

Take an input string, for example. This is trivial in higher level languages like Python, but a real difficulty in C. Normally, C has to know what length an array of characters (a so-called "string") has to be in order to input them from standard input, but if I can allocate memory dynamically, I can set this size to any size I want, and expand it if necessary.

Pointers, aside from being a useful tool for passing parameters by reference, are intimately related to memory management, because pointers is the way in which memory is addressed.

One might wonder, where are these features in other higher level languages? Most of them would be either hidden ("unrecommended") or non-existent. Why so? If pointers are that flexible, then why don't we have them in higher languages?

The hard part about pointers and memory management is that you have to know how to use them, and to use them correctly. Messing around with them lead to things like the so-called "memory leaks". I consider the name a bit misleading... It's not like memory is vanishing or anything, but rather, the program is "hogging" memory even though it no longer needs it.

That's the problem with manual memory management: it's useful, but it can be also dangerous. It's "dangerous" because it can literally cause unexpected side-effects to one's own program. It's not just a matter of "memory leaks": other and more dangerous issues include unintentionally editing the data where you shouldn't, or trying to read data from the wrong place.

Either case, if the program decides to overwrite its own data but at the wrong place, the error may go unnoticed. If it attempts to read or write to memory that doesn't belong to the program, the operating system will refuse and cause the so-called 'segfaults'.

"With power comes responsibility" describes the situation quite well here. The direct manipulation of memory allows C to perform tasks efficiently, if used well; on the other hand, if it's not used well, it can lead to all sorts of unexpected errors, which may be either obvious or, even worse, subtle.

catching up

2009-04-04T18:52:00.000-04:00

It's April, and it still felt as if I was in the middle of the semester.

As "expected", the list of things that I should/must do is growing at a much larger rate than previously, and this means free time will be a lot harder.

What I recently noticed is that whenever I'm reading or studying, I prefer to do it in a "free" mood rather than being forced upon, because I can explore things and understand things more deeply, rather than the "surface" understanding that I get from studies and revisions.

And this is why I often take longer doing math and physics homework - I need to understand it, because rushing over a problem, just like glossing over a book, is not helpful. It's a lot easier to forget if one only has a surface understanding of the subject.

But when time is scarce like during these periods, I often don't have the time to slowly work on things... and this would only affect my understanding of the material.

I don't think I can "catch up" my studying after semester, because by then I'd have little incentive to do so.

Perhaps this also explains why I don't seem to understand my modern physics class as much as my classical dynamics class. They are different in that the modern physics class is just an introductory class - things are often presented briefly, and I have to know a whole sleuth of equations that seemingly have no origin (I'm quite certain that most of the derivations would be too complicated for this level); in the classical dynamics class, there is a more in-depth perspective of things, with derivations and stuff, which makes it more interesting to understand.

My mind works on linking things together, and when new things are added, it always takes a while to chew over them. On the other hand, if it's just an improvement or generalization over something I learned previously, it's a lot easier to grasp.

And perhaps I should attend to my homework now.

the eccentric derivative

2009-03-25T23:27:00.000-04:00

When I first studied ordinary, single-variable derivatives, they were relatively simple and the rules weren't so confusing. In fact, many of them belonged to the "common sense" group. Take, for example:
dy/dx = (dy/du)(du/dx)
If you treat "d(...)" as an operator and as a single entity, and manipulate derivatives as if they are actual fractions, then the chain rule appears to be "obvious".

I can't quite say the same thing for partial derivatives, however. Some partial derivative rules are just... strange:
dy/dx = -(∂z/∂x)/(∂z/∂y), if z(x, y) = 0.
The surprising part of this equation is the negative sign. While I can derive the equation itself without issues, it appears, at least to me, quite surprising that partial derivatives don't behave the way total derivatives do. Now I realize that the distinction is indeed necessary, and this difference in behavior and rules is one reason.

Take for example:
dy/dx = 1/(dx/dy)
This is always true, but it isn't true if I replaced it with partial derivatives. Instead, the inverse becomes a "sort-of" matrix inverse, and things are more complicated. Put simply, there is a way to invert partial derivatives, but the formula is far more complicated than what is shown above for total derivatives.

There is often a common trend in math: as things become more complicated, involving "higher-order" entities, some of the simple rules that originally applied would breakdown, replaced by more general, but complicated rules. One might call this unruly, but I would consider this "elegant" for most cases. E.g. Stoke's theorem is more complicated but far more general than the single-variable fundamental theorem of calculus.

It's time like these that remind me why I love math in the first place.

tensors and transformations

2009-03-13T15:58:00.004-04:00

Transformation, in the most literal of senses, means changing the form of something... Since I dabbled in computer graphics a lot in my earlier years, I would usually think of them as graphical manipulations like resize/rotate/skew/reflect etc.

Indeed this is very related to the mathematical concept of transformations, except, one is often more interested in transforming the "canvas" rather than the "image". In more strict terms, one often transforms the coordinate system rather than the objects.

At earlier levels, I could never understand why it was even useful to perform transformations (as they were often introduced along with matrix algebra), but eventually I realized that transformations are one of the most useful tools in mathematics.

The necessity of transformations is often obscured by the ubiquity of the Cartesian coordinate system (i.e. x, y, and z). It just so happens that it isn't the only coordinate system available, nor can it describe all kinds of spaces. The Cartesian system describes Euclidean space satisfactorily (the zero-curvature kind of space that is nearly always used in "ordinary" math), but there are other kinds of spaces out there. Not to mention the fact that there are other coordinate systems that can be defined iin Euclidean spaces, like the cylindrical coordinate system or the spherical coordinate system.

In calculus, one of the most frequently used and most powerful rule is the chain rule, which I'm quite sure many have heard of:

What most people may not realize is that the chain rule is also a kind of transformation rule, i.e. it allows the transformation from one set of coordinates to another. The one-dimensional (single-variable) chain rule allows the transformation of a derivative in u-coordinates to a derivative x-coordinates.

The multidimensional "general" chain rule, shown below, does the same thing, but for higher dimensions.

It may look unwieldly, but it's really simple if you put it in summation form:

Here I just put i to represent any particular index, and used j as a running index. You might think that's the end of the story, but physicists (and some mathematicians) would do anything and everything to make their equations look neat and elegant... like dropping the summation sign altogether:

Now, I'm (partly) using tensor notation. Take note that "upper indices" are not meant to represent powers like e^x or something. Rather, they are just indices, just like the lower index in "x₁", except tensor algebra requires to have a way to distinguish between two kinds of indices, the upper or "contravariant" indices and the lower or "covariant" indices. Funny names, I'd say. Doesn't that look like our "ordinary", single-variable chain rule with a few indices attached?

Now that I've already "digressed" here... I might as well describe what a tensor is first. A tensor is a "kind of generalized quantity" that includes both vectors and matrices, and much more. Originally, I used to think of them as multidimensional "arrays" as in computer programming, but that was too simplistic. Tensors are not "just arrays of components", because they are really "geometrical" quantities that exist without a coordinate system, yet can be expressed differently in terms of numeric ("scalar") components when a coordinate system is specified. It's very much like vectors: you can express vectors (i.e. "arrows", if you like picturing them) in different coordinate systems, and doing so will give you different values for their components, but regardless of the system you use, these geometrical entities exist and don't vary with the coordinate system that you choose. And this is why tensors are useful... in fact, in tensor algebra, is all about transformations of tensors, because they obey very "straightforward" rules.

It's hard to describe what tensors really are, since I could only describe how they behave - I'd say it's an interesting property of abstract mathematics: one can talk all day about what those entities can and cannot do and what rules they follow, but one hardly bothers with what they truly are. Definitions are, after all, just a description of what they do. I can't "visualize" them so easily as vectors, which was why I had a hard time understanding it.

All these belong to some of the most elegant* branches of mathematics, which is still intimately attached to theoretical physics - and that's why I'm so interested in it. On one side, there's the beauty of tensor algebra (no kidding), especially in those unusually elegant equations I see; on the other side, there's a comforting feeling of union when I realize that much of what I learned about vector calculus (and matrices) are united into a grand set of equations in tensor algebra - just look at the chain rule, for example, or perhaps the fundamental theorem of calculus that I didn't have the space to mention. It feels like we are going onto higher and higher math, but retrospectively, we are really digging deeper and deeper into the fundamentals of mathematics.

* I would call these tensor algebra and multivariable calculus, but I'm not absolutely sure.

increasing complexity

2009-02-28T11:01:00.045-05:00

There is a trend about my math studies that goes from grade 1 to now and perhaps beyond. Other than the fact that things get more difficult over time (duh), there is a clear trend towards complexity, and by the time you reach calculus, you start to realize that there is a limit to the computational power of us humans, not to mention the fact that there are so many things that simply cannot be done in closed form.

In the most elementary of levels, you start the journey of mathematics with the "four arithmetics", i.e. addition, subtraction, multiplication, and division. Things were very simple at the time: the only thing we ever had to worry about was not dividing by zero. Everything else is straightforward. All the linear equations are solvable (with a few trivial exceptions).

But as I learned more and more advanced stuff in math, I soon realized that everything becomes a lot more complicated. For example, quadratic equations are not always solvable in terms of real numbers. The only way to properly solve them is to invoke a new dimension of imaginary numbers, which complicate things a lot. A well-known property of complex numbers is that complex exponentials are often multivalued (such as "i" to the power of "i").

Nonetheless, numeric algebra is not as difficult as what I was to learn next. Calculus. It is one of the most powerful tools in math, yet it is also so complicated. Differentiation: straightforward to do, but for any expression that is more than a handful, it will certain produce a rather overwhelmingly long and often ugly expression. But the real trouble here is integration: not everything can be integrated to produce a closed-form expression. There are lot's of integrable functions, but we just don't have the symbols to describe them.

As if that wasn't enough, then came differential equations. It was pretty much like entering a thick quagmire. There are very very few differential equations that can be solved in closed-form; nearly everything else must be done in numerical solutions, and numerical solutions aren't always correct. This is in direct contrast to numeric equations, which do often have closed-form solutions and are often easy to find (this is typically true of low-order polynomial equations). Indeed, numeric equations often have a very simple set of rules that allow me to solve them, while differential equations often require the use of ad hoc 'tricks' or certain very limited methods (that only work in specific scenarios, such as separating the variables).

This is where I am now: slowly treading through the differential equations. Most of the time, the actual problem sets given are not too difficult to solve, since they were designed that way. But what about in real life? Most real phenomena are not that easy to solve.

Looking far ahead, I believe that I'll be studying other more exotic things like linear algebra and differential geometry, since they'll be absolutely essential for the physics that I intend to learn. They are very daunting, and they still appear to be so. Hopefully, by then I would be prepared to learn them.

And the conclusion? Nature is very complicated, but I must admit that this is exactly what makes it so interesting to study. If it weren't so complicated, it would be just "simple harmonic motion" everywhere, which - frankly - isn't all that fun.

gnuplot plumbing

2009-02-12T18:44:00.036-05:00

For over 2 weeks, I've been trying to figure out what's wrong with gnuplot...

Firstly, some background for my readers: gnuplot is an open-source program that plots stuff: graphs, data, curves, surfaces etc. Not only does it have a GUI that allows users to plot stuff, it allows programmers to send commands directly into the program through a mechanism called piping. For those who has some skill in *nix shells, you probably know a little about it, since it can achieved by the "|" (pipe) operator.

Recently, I have been working on a few Python scripts that analyze some experiment data. Once the analysis was done, it should display a graph of the data, using gnuplot. To communicate to gnuplot, I used the program "pgnuplot", which is a pipeline interface for gnuplot (and is bundled with gnuplot). However, no matter what I tried, the code always fails with a strange error:

[IOError 22: Invalid Argument]

I thought I was doing something wrong, and tried different methods several times. Later, I discovered (through Command Prompt) that the command:

echo plot x | pgnuplot

for some reason fails if the working directory is not the directory of pgnuplot, but works fine if I am in the right directory. I later tried changing the working directory in Python, but that didn't work either.

I nearly gave up on this idea, but I soon found something else strange. I used a snippet of code that searches the PATH environment variable of the OS, so that it can retrieve the absolute path of the pgnuplot executable. And guess what I saw? It was pointing to something entirely unexpected: a different file that is also named "pgnuplot". So that's what it has been doing!

All this time, my Python program was referring to the wrong pgnuplot executable, so all I needed to do was to use the correct absolute path, and - voilà - it worked like a charm. No more funny-looking error messages when I try to pipe to pgnuplot.

That sure made my day.

notational inconsistencies

2009-01-30T17:53:00.055-05:00

As a physics student, I find it really annoying when people use so many different (and sometimes unfamiliar) mathematical notations for the same thing. Worse still, there are times when notations clash, causing ambiguity.

Let's take a simple example:

f(x)

Even if I don't say anything about it, people will often agree that it is a function "f of x".

But what about this?

t(1)

Now here's an ambiguity (even if you don't realize it immediately): is that supposed to be "t times 1" (a product of t and 1) or "t of 1" (a function t evaluated at 1)?

Chances are that people don't encounter this very often, since it is often explained whether t is a function or not. However, in physics it is common to mix functions and numbers, because equations work for both.

There are other less noticeable issues as well. Consider the following:

x²

Most people will say this is "x squared", but if you've done any tensor algebra, you'll know that it can also mean "the value of vector x at index 2"

That's the problem: upper indices use the same notation as for powers, which can be ambiguous sometimes. Although powers don't usually occur with tensors, it is still important to keep the notation consistent and unambiguous.

So far I haven't thought of a reasonable solution for this superscript problem, but I have been thinking about the function/bracket issue mentioned earlier.

One thing I had noticed was that parentheses, square brackets, and also curly braces are often used to denote the order of operation. However, I think it's redundant and unnecessary to use all three different kinds of brackets just to do the same thing. It's a "waste", I would call it. Perhaps we could use square brackets for functions instead of the usual parentheses? It is compatible with the typical use of brackets (since functions are sometimes indicated with square brackets, though not as often). So I could say "f(x)" to mean the product of f and x (of course it would be rare to write it like this; it's better to say "f x") while "f[x]" to mean the function f acting on x. I wouldn't call this convention-breaking (since it's fairly compatible with the original notation of functions), but it certainly would be unusual.

There are other cases of ambiguities in math & science. For example, consider "e". "e" is the natural base, but it's also the symbol for the elementary charge, so how do I differentiate them? (Again, it's unlikely that an equation would use these 2 at the same time, but it's still possible.) My subtle solution is to use italics for elementary charge ("e") and upright for the natural base ("e"). It's a very minute difference, but I prefer it this way to avoid confusion.

Similarly, I would use the upright form of "π" to represent the circular constant, and italics for anything else (unfortunately, sometimes it is very difficult to distinguish between upright and italic Greek letters in some fonts). The reason why "π" and "e" get an upright font is because they are very special mathematical constants.

Besides constants, I also prefer to use the upright "d" for derivatives to avoid confusion with variables or functions that are named "d". There are quite a few textbooks that actually use this convention.

I really wish there was a specific "committee" of some kind that regulates mathematical syntax and conventions (sort of like the IUPAC for chemistry, or SI for scientific units).

filler post

2009-01-25T23:02:00.000-05:00

The past week has been a series of awful time management, which is why I can't scoop myself an hour to work on my blogs. Nonetheless, I'll try to summarize the whole week with a short 15 min post.

The classes began on Jan 12, as I may have mentioned earlier. This 17-credit semester consists of 7 courses, of which 3 are physics (including a lab), and the remaining 4 being chemistry, biology, math, and computing.

The great things are: I get to learn cool new physics, math, and a new programming language (i.e. C). The annoying things are: lot's of written homework. I can't stress that enough: written homework. I don't like written homework; I prefer to type things out neatly rather than hand-in a page containing 20% cancellations and pencil-carbon smudges.

Besides the 2 physics and math classes that require written homework, there's a "lightweight" single credit computing class that I stumbled by chance: an opportunity to learn some C, and perhaps gains some real programming skills. I mean this is the first time I get to do anything in C; normally I'd be in a persistent fear of C (or C++, both are pretty scary and nasty) because I'm clueless as to how I can do anything useful in those languages. How do I write a file? How do I draw a line? How the heck to I even construct a window? (I must have been too dependent on GUI-based programming like MS Visual Studio.)

Those are questions that can be hopefully answered, or at least I would know how to answer them. I really need to get into a mood of programming... it's been months since I'd wet my hands with some real programming.

Okay, that's my filler post. I really hope I can do some better time management next week, considering the "dormant" physics lab will begin classes on Tuesday, which implies lab reports and more lab reports.

twin para-dogs

2009-01-14T18:42:00.001-05:00

I can't help notice the fact that "paradox" sounds surprisingly similar to "para-dogs". Funny, I could've made a pun out of it, but I'll save the embarrassment.

Back to topic: Spring semester just started on Monday, so my regular routines come back into play, which means I feel a lot more organized now. However, this means there's plenty of homework and assignments to keep track of (and not forget).

The first thing that frustrates me in a semester is the textbooks. Buying textbooks is a pain because they always cost a lot more than you'd typically pay for an average book. This time, there is the additional problem of a book (Calculus III, Marsden & Weinstein) that isn't available in bookstores, so I had to order them.

Besides all the book chaos, my physics classes quietly began on Monday. Today, I suddenly got a big surprise: I'm already starting to learn special relativity in my modern-physics class, yet I never thought about it in this light. (And hence the title of this post: the twin paradox concerning special relativity.)

Unlike the one for last semester, the calculus class for this semester requires us to hand-in our assignments weekly, which means no slacking-off for me. In addition, there are also written assignments required for my classical-dynamics class. On top of that (and all the other electronic homework on LON-CAPA and OWL), I have a physics lab, so I'll have lab reports to work on (again).

Still, I hope to have a great Spring semester.

start of another year

2009-01-03T15:34:00.001-05:00

Oh it's a new year. Didn't felt like much though; the extra leap second gained felt like nothing.

The new year of 2009 has already begun, which means I'm not too far from Spring semester (a week away!). Thinking back, I could've been a bit more productive during this break.

I wonder if I'll ever grasp C++ (I got a bit of my programming spirit back recently). I wonder how the next semester will go. I wonder how the International Year of Astronomy would be. Lot's of anticipation, and lot's of doubts.

Nonetheless, I wish everyone happy new year (despite being 3 days late).

Also, I thought I could post some funny links:

Have a grand new year!

existence

2008-12-27T12:10:00.005-05:00

Recently I have been ponder about the meaning of "existence". No, I am not asking what the purpose of life is (which I consider a meaningless question). Rather, I am try to accurately define the meaning of saying "X exists."

When a person says "the table exists," I can understand this as an attribute of this table. The attribute "existence" in this case is true. However, I don't think this is reasonable: such an abstract attribute of an item (at least this is one way I understand "existence") also seems to be meaningless to me.

I think the real meaning of "existence" should be defined as subset operator. In other words, X exists if and only if X is a subset of the universe at a particular time. Existence is always a time-dependent boolean quantity. If anything is not part of the universe, then it is by definition non-existent.

Now if I press the question further: "how do I define the universe?" I can reuse the definition of physicality (previous post). Physical things are part of the universe. Physical things, because they interact with other physical things, are typically testable, though it may not be practical to test.

Still, I'm not exactly sure if this analysis is correct, but this is how far I have managed to achieve.

stardust

2008-12-19T18:59:00.000-05:00

There's a lot of ways to be amazed; here's one: everything that humans have ever touched is stardust.

Sometimes, it's still amazing whenever I think about it. Of course, astronomers are probably well aware of that, but recently I still got a minor amazement when I realized this to its full extent.

There are those times when I still wonder how the illusion of consciousness has been achieved, but I have never been able to get far. Nature is strange like that (or as someone else puts it, "preposterous").

There are still times when I lie in the bed awake thinking about this, but I don't know if it is even a valid question to ask.

winter break begins

2008-12-11T23:41:00.003-05:00

It's winter here; it's been winter since September. However, beginning on Saturday, the official MSU winter break begins.

Last week and this week 'til Friday, I completed all my finals for my classes, which means all my classes are already completed by now. This gives me a lot of extra time than usual, since my typical day in this semester has mostly been about lab reports (you probably noticed that in my Tweets).

I do sincerely hope that I can do some more "work" (as in things I wanted to do during the semester but never got to them) during the break, and not just goof things up and waste my time reading too many feeds or something.

Anyway, that's all the stuff I have to "report". Have a good Winter Solstice.

faster than wind

2008-12-01T17:26:00.011-05:00

Update: It looks like Mark has changed his mind. So it seems, that faster-than-wind travel is indeed possible. I'm awaiting Mark's detailed analysis of the problem.

On Word Munger, I saw this really tough physics problem (below is my rephrasing):

Is it possible for a machine to harvest energy from only wind, yet capable of travelling faster than wind, yet in the same direction as the wind?

So far I haven't figure out if it's possible. Over at Word Munger, there is an argument going on between Dave and Mark, and I haven't been able to tell who is right yet.

Under "normal" conditions, a cart with a sail can't move faster than the wind speed; Dave argues that with the correct setup, it is possible to move faster than wind.

The counterintuitive part is that if the cart moves faster than the wind, the relative velocity of the wind becomes negative, resulting in a drag instead of a push. Yet somehow Dave is able to mitigate this by allowing the wheels to thrust the cart with a propeller. I'm not sure if the latter part is possible, since it feels like a "pull oneself out of a swamp with one's own hair" kind of problem. How can a wheel thrust itself? This is one thing I don't understand.

I wanted to come up with a mathematical model/equation that describes the cart's motion (in a simple way), but so far I haven't been able to do so because I don't know how propulsion thrust depends on rotational speed, nor do I know how wind thrust depends on relative wind speed. I might make some linear assumptions, but those are only assumptions.

If anyone has any idea about this, let me know.

17th birthday

2008-11-24T22:51:00.001-05:00

Today's my 17^th birthday. It happens to be on the same day as a chemistry exam. Ah well.

The post isn't about how I am celebrating it; rather, it's just another digression on things I'm interested in.

* * *

Firstly, I would like to reiterate that an examination should be a way of testing if the students understand and can apply the subject. It is not meant to be a device to trick students into all sorts of pitfalls. This is what gives exams a bad name: why should exams be a place where you force people to get it wrong?

The most devious tricks I can recall right now are:

Deliberately putting an answer for a person who forgot to convert units.
Use ambiguous words/ask ambiguous questions.
Make statements that have exceptions (no matter how minor) to them.

The one I want to highlight is the second one: use of ambiguous words. When a person says something, the meaning must be absolutely clear for someone who is acquainted with the subject. If I say, "what is the f of a camera?" I am causing a confusion for the student. The student can wonder if I am referring to the "focal length" or the "f-number", which are quite different. In multiple-choice questions, ambiguity is especially harmful, because one mistake and you get no credit at all for the question. Specifically, I am insinuating that the poor usage of the phrase "valence shell electron pair" makes it ambiguous as to whether double-bonds count as one so-called "pair" or two pairs. That is why I did not like the first question of the chemistry exam.

* * *

Recently, I have been working on computer simulations of differential equations, but I haven't been too successful so far. I managed to successfully simulate the differential equation of a rigid pendulum of any angle using numerical approximations. However, when I attempted to simulate 2D wave equations, things not only got messy (numerically approximating a Laplacian is difficult), but the waveform became "polarized" (the wave crests and troughs gets sharper and sharper) as time goes on, implying that my simulation was rather unstable. I was also a bit ambitious and wanted to simulate the 2D Poisson's equation for gravity or electromagnetism, but became confused about how the equation works. It sounded like I have to find the "inverse" of the Laplacian on the density function, but I have no idea how that could be done, or if it's even possible. I did all the simulations with Python and pygame.

* * *

Enough about simulations. I'm back in my "story mode" again: on my daily walks I tend to fantasize about all sorts of crazy tales of characters - it really reminds me of how I used to play with "anthropomorphic items" (at least I felt they were; imagine a talking hair-clip... weird) and give each of them a character to role-play. It's sorta like a role-playing game, but where I'm the director and I just tell them to make a movie. Nowadays, since I don't have them accessible, nor do I have the time to play with "dolls", I began a new way of expressing creativity: telling stories within my mind. It's a way of passing time, because walking 30+mins a day gets routine over time.

* * *

Now Thanksgiving is pretty close, I might as well spend some extra time revising for finals and complete some incomplete tasks on my task list. Anyway, Happy Thanksgiving!

science/humanities

2008-11-18T22:19:00.001-05:00

In grades 1 to 6: every subject was relatively easy. I would - honestly - say that my science classes were a bit hard for me. As I progressed further up, I found science getting easier and easier.

In grades 1 to 6: the hardest subject of all was language (any kind of language). Writing essays was by no means fun - it was a chore.

In grades 7 and up: I realized that subjects in humanities are "intrinsically" harder for me. I knew that humanities were harder than sciences, but I didn't know whether I liked science. I just loved math for the sake of it.

In grade 8: I broke up with history and art. I took geography (though quite a lot of it was human geography) in preference to... what was it called again? "Development studies"? What's that? I never did development studies, nor did it sound remotely interesting. I also avoided business studies and accounting, which are - frankly - boring. Science is way cooler, at least in my opinion. I also picked computer studies over art because I have a greater interest in computers than in drawing.

In grade 11 to 12: I began to realize that biology and chemistry are by far not as intriguing as physics and math. Therefore, physics and math became my favorite subjects. I also thought pure math was - um - too pure and bland, so maybe some applied math might be better. That's not to say I don't like pure math at all: to some extent, I still like abstract math, but I get bored easily by the plethora of theorems and proofs.

Well, that's about my summary of my contact with various subjects - I was a bit sketchy with the list. Okay, as a not-so-related finale to this post: here's what I've been thinking about humanities recently:

Simple question: why are humanity* subjects so lacking in pictures? What, can a person just truly understand a topic without even a single picture? (My philosophy textbooks contain no pictures - just text.) I personally have to visualize things, make up pictures in my head, just for the sake of understanding what these words truly mean. Why don't they just insert a few pictorial representation of things in the books? (My physics textbook has a lot of nice illustrations, even for abstract things like magnetic fields.) It would make the topics a whole lot easier to swallow, at least in my opinions. (Perhaps this is why reading books with pure text is difficult/boring for me.)

So are humanities are just as abstract as the sciences?

* Well, this may not be true for all humanities subjects, but it certainly is true for some of them. In addition, some might argue that the dichotomy between science and humanities is incorrect, but this is a personal distinction that I make myself.

unphysicality

2008-11-16T22:41:00.005-05:00

This is a strictly philosophical post on physical and non-physical objects.

I call a thing is physical if it can affect (or had affected) another object that is physical, or vice versa.

If I define the Earth as physical, then it naturally follows that humans are physical, because humans can affect the Earth. Similarly, the Sun is also physical because it can also affect the Earth, etc. Therefore, defining any part of the universe as physical automatically implies that everything in the universe is physical.

By convention, the everything in the universe is physical.

A thing is non-physical if it is not physical.

Question: do non-physical objects exist?

The problem with this question is how I should define existence. If I define existence in the narrow sense that "A thing exists if and only if it is a subset of the universe", then it naturally follows that non-physical things do not exist.

If I define existenece in the obscure sense that "A thing exists if it is a subset of some entity greater than the universe" (whatever that entity is), then the question can be answered with a bit of logic.

Suppose a non-physical thing A exists. Since A by definition can never, had never affected, nor can be affected by, nor had been affected by a physical object, the thing A is irrelevant with any physical objects, i.e. us. Therefore, the existence of non-physical objects is of no interest to us, nor can we ever find out their existence. So the answer is: we can never know whether non-physical objects exist, and their existence is entirely irrelevant to us.

Alright, that's my short anecdotal philosophy post. I'm not sure if my logic/definitions are valid, but that's my conclusion so far.

interferometric weekend

2008-11-15T14:35:00.004-05:00

On SciLearn, I wrote a post on wave interference. Go check it out.

On Thursday and Friday, I've been trying to line up a He-Ne laser so that I get an interference pattern (using the Michelson interferometer). Apparently, it was easy to say on paper, but hard to do in practice. In addition, I had to make sure the lenses were placed in the correct positions, so they don't focus or diverge the laser, but keep them parallel (I doubt I managed to do that).

I also wanted the laser to strike the mirrors at their centers and pass through all the irises without being truncated anywhere, but that's an ideal situation I doubt I can achieve. The mirrors were aligned for other experiments as well, so I was not to adjust them in any way, making things hard for me, I guess.

In the end, I did get some sort of interference pattern, but they were straight, vertical stripes/fringes- definitely not what I had intended. I also got some fuzzy circley rings, but they didn't look quite like what I had in mind. By the end of the day, I dismantled the setup and, hopefully, next week or the week after, I can redo it and obtain something better (and more expected). I felt the beam splitter must have been doing double reflections, which might explain where all the vertical stripes came from.

Once the interferometer is set up, I'll have to find a way to count those fringes (electronically, of course). The next part also sounds difficult: where am I going to find a fringe counter?

And this is why it's hard to be an experimentalist: I'd rather be a theorist.

Folding proteins

2008-11-10T17:27:00.001-05:00

I have to say, this really caught my attention: http://fold.it

It's called Foldit, a neat little program/game that allows you to fold proteins for fun, while at the same time contributing to science. It's also no trivial task, since not only do you need to know some basics of protein structure (i.e. intermolecular forces such as hydrogen bonds and dispersion forces etc.), you have to be creative and have a knack for 3D shapes. (You'll have to register an account to play it, but it's free and only requires you to pick a nickname, a password, and an email.)

Basically, the interface is really simple that it shouldn't take a long time to get used to, and it's not all the overwhelming either. Just follow your way through the tutorial, learn some basic terminology and you are ready to go and do real challenges, and don't forget - it's a game that helps biologists study proteins!

mnemonics don't work

2008-11-08T12:11:00.004-05:00

In science classes, instructors and textbooks often introduce mnemonics as an aid for recalling. However, what I have noticed is that most of the time, mnemonics don't work. Recalling a piece of information entirely unrelated to science is often difficult, and relating that to the actual subject is equally hard.

Some mnemonics are relatively easy, and these are usually abbreviations. These mnemonics have the advantage that you only need to recall a smaller piece of information in order to retrieve a larger one. The main problem with these is that they are ambiguous. "ROYGBIV", a mnemonic for the colors of the rainbow, could represent many things, although the limitation to color words would reduce this ambiguity. "ELI/ICE" is a mnemonic to recall that "inductor (L) voltage (E) is followed by current (I); capacitor (C) current (I) is followed by voltage (E)". The ambiguity here is that I could also say: "inductor (L) voltage (E) follows (I); capacitor (C) current (I) follows voltage (E)", which is entirely the opposite of what it is meant to mean.

Other mnemonics are not so easy, at least for me. For example, there's the sentence (for resistor color codes): "Better be right or your great big venture goes west" (Wikipedia). These mnemonics require one remember quite a lot of information, so they aren't so easy to remember, unless one happens to remember sentences better than color codes. A more appropriate approach to remember this would be to recall: "black, brown, {colors of the rainbow except indigo}, gray, white", which is much more systematic and is actually related to colors (and you just need to know 4 colors in order + colors of the rainbow except indigo, which makes sense since indigo is hard to distinguish from blue sometimes).

The best way to remember scientific knowledge, in my opinion, is to:

Use mnemonics in limited situations. One can still use mnemonics to remember things initially, but as one becomes more and more familiar, the use of mnemonics should be replaced by direct recalling of the information. For example, it might be OK to learn "SOHCAHTOA" (mnemonic for "sin/cos/tan") in high school, but I don't expect people to still use that when they are in college. In addition, remembering too many mnemonics will cause a lot of confusion, so don't overuse it.
Deriving from earlier knowledge. Unless the derivation is very messy or takes a huge amount of time, one can learn the process of derivation and derive formulas and equations from either first principles or known equations. Of course, one should be able to recall these eventually as one becomes familiar with them, and then derivation would no longer be necessary.
Image memory. If you have a really good memory at remembering images, then this is an advantage if you use it properly. Sometimes, the diagram in textbooks can help remember information. Even better, practical demonstrations in class are the best way to remember things if you watch them carefully and recall them as "mental videos".
Understanding the subject. The best method is to simple understand what you are talking about. Unless it's something that is meaningless (e.g. resistor color codes) or purely conventional (e.g. the direction of the cross product), it's usually best to remember things by understanding things.