Happy New Year!

It's 2011! Another year has begun.

I have a long and busy year ahead. I have both my Cambridge AS and A Level exams in front of me.

2011 has been declared the International Year of Chemistry by the United Nations. So let's celebrate the achievements of Chemistry and of Science in general this year(I've always felt that we should always celebrate Science)!

I extend my wishes to the entire world. Let us spend another year working towards a more peaceful, more harmonious, more tolerant, more rational and open minded world.

Let's work together to make 2011 the best year the World has ever had!

Once in a Red Moon

It seems that the December 21 of 2010 was quite saturated with important events. A very total and spectacular lunar eclipse took place last Tuesday. A lunar eclipse as we all know occurs when the Earth comes directly between the Sun and the Moon. The Earth casts it's shadow on the moon and the full moon disappears from the night sky for a while. Well, not quite. This is what actually happens.

As you can see the moon is never completely in the Earth's shadow. Instead at the peak of a lunar eclipse, the moon appears blood red. All of you will have seen a sunset, at least in pictures. The sun appears red because it has to pass through much more of the atmosphere that when it is directly overhead. In this case the sun's light passes through a similar amount of atmosphere before it falls on the moon. Radiation of shorter wavelengths are scattered in the atmosphere leaving wavelengths we perceive as red to go through and fall on the lunar surface. This causes the moon to glow in a most enchanting red colour. Certainly one of the more beautiful celestial events.

Winter Solstice

Today, 21 December 2010 is a day of great importance. Today is the day the Earth's axial tilt is at it's maximum of 23° 26' away from the sun. If measure the angle of elevation of the sun from the horizon at twelve noon today you will measure an angle of 69° 34'. It certainly brings back memories. If you were a reader of my blog exactly a year ago you might remember my creative technique of measuring the Earth's axial tilt. For those who weren't there, you should know that I managed to calculate the axial tilt of the Earth by measuring the angle of elevation of the sun on the day of the winter solstice. While this in itself is not very impressive, the method I used to calculate the angle of elevation of the sun is very interesting. I did not measure the angle directly. I used a more long winded but safer method of using shadows and similar triangles. If you are curious read this post: http://ashwinnarayan.blogspot.com/2009/12/tilt-of-earths-axis.html then this post http://ashwinnarayan.blogspot.com/2009/12/few-clarifications.html. I say my method was safer because looking directly at the sun is never a good idea unless you are hell bent on inflicting permanent damage on your eyes. The most impressive thing is that my measurement was very accurate. My answer was very close to the original value.

Historically, the winter solstice is a very important date. There are several festivals celebrated by almost all of the ancient cultures of the world that depend on the winter solstice. A very famous example is the Jewish festival Hanukkah. There are several magical tales and legends associated with this date. It is apparent that humans felt that solstice was a very mystic event.

Recently the date December 21 has gained quite some fame after the sudden surge in the interest the public has shown towards Nostradamus's predictions. Apparently he said that the world as we know it would end on December 21, 2012 due to the Earth, the moon, the sun and the centre of the galaxy lining up. Some people also believe that a fictional Planet Nibiru will come zooming into the solar system and knock Earth off it's orbit.

As someone strongly believes that  good science must be promoted and bad science must be debunked,  let me make an announcement. The world WILL NOT end on December 21, 2012. Period. It is a fantastic work of fiction. If you check the star charts you  will see that this alignment of the Earth, Moon, Sun and the centre of the galaxy happens EVERY YEAR. I thank my favourite astrophysicist Dr. Neil deGrasse Tyson for making me aware of this and for showing a contagious enthusiasm in science that has made the world a better place. So for those who are waiting for the end just take a step back and think for yourself. Do not be misled by pseudoscience.

On a different note today is also the birthday of my good friend Evelyn Chua. I wish you a very Happy Birthday!

A Mathematical Curiosity

I stumbled upon yet another mathematical curiosity on the web. This was something discovered by the Mathematician Hermann Minkowski. If you recall my blogpost about Space and Time you'll realize that this is the same person who reformulated Einstein's Theory of Special Relativity in 4 dimensional spacetime.

Consider the following situation:

A person wishes to travel from the first black spot at the bottom left corner of the diagram to that on the top right. He can only do it by following the grey borders. Assume that one of the square compartments have a length of one unit. If the person travels 6 units east and 6 units north he travels a total of 12 units.

If the person travels along the blue line he again travels 12 units. The figure below is a bit stretched. But with a little bit of imagination you can see that the distance travelled by the person remains 12 units even if the height of on step is reduced so much that it looks like a sawtooth. You can take my word for it but feel free to draw it out and confirm this.

Now Minkowski asked a very interesting question. What if the height of each stair became closer and closer to zero? The path taken by the person become closer and closer to the straight green line. So even when the height of the stair is only 10^-8 units the distance of the path is 12 units. Now's the time a keen mathematician's spider sense starts tingling. What is the length of the green line? According to the Pythagoras theorem it is (6^2 + 6^2)^0.5 = (72)^0.5 which is the same as 6(2)^0.5. But according to the reasoning we just followed it's 12!! So what happened to all that extra length that disappeared when we used the Pythagorean Theorem?

I'll try to give a solution in the next blogpost.

  

Kingdom Hearts Birth by Sleep

First of all, let me tell you: I'm not a big fan of video games, especially those excessively popularized and advertised games like Warcraft, Halo or Devil May Cry. I used to play a lot of video games, but those were in the same league as Pokemon Emerald, Fire Red, Leaf Green and such. In fact I prefer such peaceful games to those involving violence and carnage.

There is however one game which deserves special mention. There is one game which should belong to my detested list but somehow managed to capture my attention. I am referring to Kingdom Hearts Birth by Sleep. I can only conclude that the generous dose of Disney characters (For I just love Disney Films) attracted my attention enough for me to give the game a try.

So there it is. The one and only action role playing game that captured my attention: 

Of Space And Time

It is with great pleasure that I announce the most recent expansion of my knowledge database.

I have gained a  preliminary understanding of the mathematical framewrk of Albert Einstein's Theory of Special Relativity. More specifically, I have understood, at least in part, the Minkowski Spacetime Reformulation of Relativity which treats time as a fourth dimension. I now understand the derivation of the time dilation equation.

  

Before this sudden revelation, I could only stand far back, like a spectator and wonder at the quirky implications of the theory. But now I can get up close and appreciate the true beauty of the theory which lies in its use of non-Euclidean geometry 

It's interesting to note that Albert Einstein did not construct the theory this way. He started with the assumption that the speed of light was the universal speed limit. However in Minkowski's Reformulation, this does not need to be assumed. The fact that assuming four dimensions solve many of the problems that Special Relativity faced suddenly makes the 11-dimensional universe suggested by the M-Theory more plausible and believable. An understanding of Higher dimensional Geometry is just within my grasp. 

Why Don't We Run Out of Music?

I have been thinking about this for a long time. It's quite a conundrum.

Every time I hear a really catchy, melodious tune, I think "How come no one discovered that before?"
There are only a finite number of musical notes, and humans have been composing music for centuries. How come we don't deplete that bag of permutations that contain of catchy tunes?

And if by any chance we haven't used up all the possible combinations of musical notes, I ask the question: "Will we ever run out of new music?"

And God said...

and all was light!*

*For the sake of clarity the equations above are the four of the most famous and important equations in all of Physics. They describe how the electric and magnetic fields relate to their sources,charge density and current density. As we all know, light is made up of oscillating electric and magnetic fields and these equations dictate how these fields work. So they did shed light on the world both literally and metaphorically. Get it?

IGCSE Results are out

The IGCSE provsional results are out and I finally have some time to blog about it. Before I reveal what I got I will remind everyone which subjects I took. I was examined in nine subjects. They are: Physics, Chemistry, Biology, Mathematics, Additional Mathematics, ICT(Information and Communication Technology), Economics, First Language English and Foreign Language Malay (Core Syllabus).
And here are my results:
Physics                         - A*
Chemistry                     - A*
Biology                         - A*
Mathematics                 - A*
Additional Mathematics - A*
ICT                               - A*
Economics                     - A*
First Language English    - A*
Foreign Language Malay - C

I am not in the least disappointed with the C I got for Malay. I took the core Syllabus for Malay. If you take the core syllabus for any subject the maximum grade you can get is a C. So I got the maximum possible grade for all my subjects.

John Conway's "Game of Life"

Recently I became very interested in cellular automaton. Have you, the reader ever come across John Conway's "Game of Life"?

It is a very simple game. The game is played on a two dimensional grid. Each cell in the grid can have two states: alive or dead. Every cell has eight neighbouring cells and the states of these cells affect the state of the central cell. Each step the fate of a cell is determined by the following rules.

• Any live cell with fewer than two live neighbours dies, as if caused by under-population.
• Any live cell with more than three live neighbours dies, as if by overcrowding.
• Any live cell with two or three live neighbours lives on to the next generation.
• Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction

To better visualize this situation look at the following pictures. The "game" is played on a grid that looks like the one below. At the beginning of the game the player chooses which cells to populate. this is called the initial state of the grid. At each step (sometimes referred to as a generation) the cells surrounding these populated cells and the cells themselves are changed according to the rules given above.

The above rules may appear to be strikingly simple. But the beauty of this game lies in the fact that extremely complicated patterns can be created using these simple rules. I'll start simple. Say you populate three horizontal rows and then allow the game to start. Here is the result.

If we start out with a shape that is a bit more complex.

These are however unimpressive when compared to the highly complex patterns that have been discovered. For example:

The game of life is not just a game. The complexity produced by these simple rules are a prime example of how complicated structures can evolve from simple physical systems. In particular the arguments put forward by creationists and supporters of intelligent design can be refuted. Since the human body contains billions of atoms it is possible for this group of atoms to develop complex behaviour such as locomotion, and thought and an intelligence.

The patterns that I have shown in this post are the simplest of all discovered. High power computers have been used to generate highly complex structures that exhibit extremely complex behaviour.

A Thought Experiment

I have been pondering over this thought experiment for a few weeks.
Here is the experiment:

Imagine a perfectly spherical ball and imagine that the inside of the ball was a mirror. Imagine that you are standing inside this mirror ball with a portable light source such as a flashlight or a fluorescent light bulb (I'm trying to be green here!). You turn on the light source to illuminate the inside of the sphere. What would you see?

This thought experiment seems to have a deceptively simple solution as mirrors are something we are very familiar with. I started off with thinking about what would happen if we were in a cube in which the inner walls were were mirrors. Mirrors placed parallel to each other produce an infinite number of images. So I would see infinite copies of myself each successively smaller. But what of the lighting conditions? At first I thought that the room would be very bright. But after a bit of thought I realized that my surroundings would seem very dark indeed. I realized that I would be very brightly illuminated but the parallel universes on the other side of the mirror would be very dark except for my reflection.

Now how do I complete the analogy and carry the argument on to a perfectly spherical mirror? It is very difficult to develop an intuition for curved mirrors. In this case my best guess is that I would see infinite reflections of myself but the reflections would be distorted.

Now what if I turn off the light? This part of the solution is fun to figure out and alltogether less mysterious. The light that is inside the mirror would keep bouncing around until all the radiation is absorbed by my skin and clothes. So when I turn off the light I guess I would still see myself but as the radiation is absorbed I would slowly get dimmer and dimmer until all the radiation is absorbed.

But what if I just keep the light shining? In a ruby laser light bounces back and forth between two mirrors until it gets so intense that it escapes from one of the mirrors which is only partially silvered. So I think that would mean that if I kept the light shining I would slowly get brighter and brighter until the intensity of the radiation is so high that I will have to close my eyes to protect them from permanent damage.

All this is assuming that the mirrors are perfectly reflective. In reality no mirror is perfectly reflective and always absorbs some of the radiation.

Now this situation is very hypothetical and my reasoning may not be correct. So this post is open for comment and discussion. I would like to hear the opinions of others and have a discussion in the comments page. Maybe that will clear up some of the grey areas.

The Solar Eclipse

 

Yesterday, January 15, 2010 was the day of an extremely rare celestial event: A solar eclipse. Yesterday's solar eclipse was special because it is one of the longest ever recorded last for around 11 minutes. It was also an annular solar eclipse, meaning that the sun would not be completely covered during the peak of the eclipse. A ring of light would have been visible. 

Where I am staying the solar eclipse was only partial, with less that 40 % of the sun being blocked but I still managed to observe it happen. I projected an image of the sun on a white paper using a a pair of binoculars and watched as the moon slowly covered the sun and then moved away. Even though the eclipse was only partial it was still an amazing experience. It was the first time I had ever observed a solar eclipse. I even took a few photographs of the eclipse. I will try to upload them soon.

“The monotony of a quiet life stimulates the creative mind.”

—Albert Einstein --- From Civilization and Science, October 3, 1933. Quoted in The Times (London), October 4, 1933.