Published at June 30, 2007
in Science.
While recently dining in rays cast by a certain solar entity shining through our bay window, I noticed that when my shadow and that of the table were about to combine, they sort of bubbled out to meet each other. I took pictures of the effect, and GIMPed them into the following concise example of this phenomenon (yes, this is a picture of shadows on a rug, please excuse the fuzz).
As shown in the image, when one shadow moves closer to the other, they tend to expand slightly to meet each other. So, being the person that I am, I decided to think of a viable reason why.
What I came up with is this. As you can kind of see, the shadows have a slight gradient of blurring around their edges, caused by the light source not being pinpoint (being spread out over a distance, say the surface of the sun). As the shadows move closer to each other, these fuzzy edges combine to form a shade more easily visible, making it appear that the shadows are bubbling out. Sounds good?
But why does the shadow on the left appear to bubble out more than the one on the right? My explanation of this is more of a hypothesis than anything, but I think that the curvature of the shadow has a great effect on this. On the right, the shadow is flat, while it is curved on the left. This may cause the condensed blur to appear as more of a part of the curved shadow than the flat one. I will need to experiment a little bit more to verify this however.
So, a week into summer, the kid is already looking into obscure mathematical functions with absolutely no apparent use, just for the heck of it? Yes, granted, there are better things I should be doing (like getting better at ping-pong). But how can I resist exploring new math stuff when I run across it?
The story goes like this. I was reading xkcd web comics (I consider these to be the best humor on the web), and I happened upon a reference to A(g64, g64) (an incredibly huge number, as you will know once you understand all concepts involved). Of course, I had to Wikipedia the Ackermann function, a recursive function that grows exponentially (in figurative terms, not mathematical) as its two variables increase. You can check out its definition here. Then, of course, I decided to write some code to calculate Ackermann numbers, so I did, using Python. It is as follows:
Well, yes, that is just an image of my code, strictly because it looks cooler with the syntax highlighting. And no, I didn’t just copy this from Wikipedia, I came up with it myself. Now, as soon as I figure out what to use Ackermann numbers for, I am ready to do something that will certainly prove to be interesting and educational…any ideas?
Published at June 26, 2007
in Math.
I was recently toying with my graphing calculator (yes, I toy with mathematical tools), and I found anther item to add to my list of things that are weird/cool about the Euler number. By the way, if you don’t know calculus, you might as well disregard this post, as the key weirdness involved is one that contains integral calculus.
Anyway, I was calculating random definite integrals of the function ex, and I noticed that
I says to my self, I says, this is very strange! But then I realized that it is just an excellent demonstration of the first part of the fundamental theorem at work. By said theorem, the above integral is equal to the antiderivative of ex evaluated at 1 minus the antiderivative of ex evaluated at 0. Yielding e-1. Cool, eh?
Published at June 25, 2007
in Linux.
Some may remember my post earlier reporting my none too successful bid at video editing using a Linux OS. Other, more perceptive readers may even recall my immense dissatisfaction with the availability (or lack thereof) of good tools for this endeavor. Well, I would like to revise my review of Kdenlive from a disapproving one to a satisfied one.
I was in one of my lazy lets - see - what - I - can - do - with - this - while - I - procrastinate - from - doing - whatever - else - I - am - supposed - to - be - doing moods recently, and I pulled up my old rival, the aforementioned video editing software, Kdenlive. I had previously suffered difficulties with it, in the form of its many crashes whenever I attempted to execute various routine editing tasks. Well, in my experimenting of late, these have been entirely unapparent. Maybe I downloaded the next version without noticing, or maybe I just was being an utter dunce last time I was trying to use it, but I had no problem saving and opening files as I did before, and using a handy tool in one of the menus, I was able to easily make clips of images, what I had most difficulty doing before.
I am thus stripped of that which made me ever regret touching Linux with video editing intentions, and am left with the ambition to promote its ability therein. Using Kdenlive, I was able to successfully create a video masterpiece, documenting a giraffe I befriended at a local zoo (just for fun, you can check it out here). Well it is really no masterpiece, but it was fairly easy to create, and demonstrates several of the things I will want to be able to do in future video editing. So that’s that.
Published at June 19, 2007
in Life.
As summer is quickly approaching (three days!!!) I feel the need to announce another one of my summer projects, namely learning the language Esperanto to a point at which I can speak it moderately well. With any other language, it would not be feasible to to imagine learning it very much at all in a single three month period, though Esperanto is different. Being a man made language, it has no irregularities, and is intelligently designed to be easy to learn with a background in other romantic languages (I have the epitome of this, having taken Latin at school the two previous years). Esperanto is a language without nationality, being spoken by a handful of people of almost every nationality you can imagine. I think it is pretty cool, to have an international language which I can expect some people from any number of other countries to understand. So why haven’t you heard of it before? I guess it just hasn’t caught on yet. It only has been around for roughly 100 years. Hopefully it will soon come into use as a common international language.
A friend of mine and I are learning it from lernu.net; if you are interested I suggest you check it out.
I have recently stumbled upon a new, unheard of, and perhaps exotic programming language: Processing. It appears to be very similar to Java, though with a more graphically oriented bent. Actually, it may just be Java, only with slightly altered language features (though not vocabulary and grammar). It appears that, once the user has written the code, the Processing IDE converts it to Java code and compiles it to an executable-wrapped JAR file. Very interesting idea, and cross platform too!
I have yet to experiment with it much, as my current programming time is delegated to reading the book Beginning Python, for the purpose of (as you may have guessed) learning Python. Maybe this summer, which is rapidly approaching, I will have time to play with Processing, and perhaps even create some cool graphical web tool, which seems to be the specialty of the language.
Once I have taken the time to check it out in greater depth, I may post a review of sorts here; until then, check out the site (linked above), which is quite informative.
While recently showering, I was deeply involved in a great pastime of mine, namely thinking. I also realized I was engaged in something else: strange vocalization bearing a striking resemblance to song. So, combining these two activities, I began thinking about the activity of singing in the shower, examining the cliche. This post is the result of that thought.
Why, of all places, is a shower sung in by people who sing nowhere else (such as myself)? Well, after much consideration, I have locked upon three factors that I think may provide the reasoning behind this strange behavior. Here goes:
- In the shower, the noise of the great volume of water running all over the place gives the (mistaken) impression that others cannot hear the singer’s voice. This leads those who desire to croon without being examined by the ears of another to believe they are doing so.
- The humidity of the air during a shower could perhaps serve to grease the pipes, if you will, moistening ones trachea and making it easier to emit noise. This makes even the most squeaky shoe of a singer able to vocalize like a great opera star.
- Any noise sounds awesome with the reverberation added by most bathrooms. The lack of a great amount of stuff in a bathroom allows the sound to bounce around more before being muted.
The combination of these three factors can (and in many cases do) lead to what I have termed “showersong”: shower-bound vocal emissions. Next step: construct a waterproof recording studio in a shower! Imagine what magical compositions the popular singers of today must weave while showering…
