The Obligatory New Year Post.

So today, as I type, people around the world are celebrating the start of 2012 and as usual we have Google's customary New Year doodle!

Every time some event like the New Year comes up, I start thinking. It always feels as though the year that separates two New Years, Christmases, Valentine's Days or birthdays fly by at breakneck speed.

On my seventeenth birthday I was struck by how my sixteenth birthday felt like it happened only a few months ago. I wondered why time seems to go by really fast when now and why when I think back to the time I was in Kindergarten, the one year I spent there seems like an eternity. A few days ago I came across this really interesting Youtube video which gives a possible explanation for this illusion of time speeding up. Skip to 2:13 in the video to get right to the section I'm talking about but I think it's a good idea to watch the entire video as it's really quite interesting.

I think the theory is very likely correct because I've had a similar experience. When I was in Year 9 my family moved to Malaysia. So the thirteenth year of my life was filled with new experiences. I learnt a new language, I met new people, made new friends and saw new cultures and traditions. Now when I think back to Year 9 it really does seem like the year went on for a really long time. And I do seem to have richer memories of Year 9 than of any of the following years until I started my A-Levels. At the start of the A-Levels there was again a lot of new things to get used to, like completely new teachers, new classmates and a new syllabus. So the first three or four months of my A-Level course seemed to have lasted longer that the rest of the course.

So after all those observations I have something to add to the theory. I think what makes time seem to go by really fast is a routine. If there is a routine that I strictly follow every single day over time, my actions start to become automatic. Take the example of me brushing my teeth. I've been doing it for so long that I can now get up in the morning and brush my teeth even if I am half asleep. My body has built up some sort of muscle memory that puts the body on autopilot so that I don't have to think about brushing my teeth. In fact I often brush my teeth lost in thought only returning to reality when I have to find out what classes are scheduled for the day and pack the right books. So once you fall into a routine, you know exactly how the day is going to turn out and therefore there are no surprises or novel experiences in your life.

So at the start of this New Year, I leave you with this nugget. If you want to live your life feeling that you have squeezed as much as you can out of every single second, if you want to look back on your life and say "It's been a wonderful ride.", go out and do new and exciting things, throw your daily schedule in the fire and spice things up a bit. Learn something new everyday and savour every single moment of your life.

Happy New Year People!

Let's work together to make 2012 the best year we've ever had.

The Face of Music

I'm someone who was introduced to the world of "Western" music quite late. For most of my childhood, I heard nothing but Indian music. Notice that I use the word "heard" rather than "listen" because I never really chose the music I heard. To be frank, I never felt much of an attachment to music during my childhood. I remember that I had grand total of three or four "favourites" but I never felt any connection with these songs and I liked them more for the fact that they had a catchy melody than anything else. I was never able to catch the words that were actually being sung. Looking back, I think it was because of a unique situation I was in. The school I went to had English as its medium of instruction and we were strongly advised to speak in English while on campus. So as my vocabulary and knowledge of English steadily improved as I progressed in school my mother tongue was left neglected. I always scored higher in English language tests (Relatively speaking as I never did that  spectacularly in English either.) I did feel however that English was slightly easier to learn and being a science freak, I tended to use English just as often or perhaps even more often than my mother tongue as I felt that learning scientific concepts were much easier in English and by the time I was in Year 6 or 7 my thought processes and all my mental conversations that happened in my brain were entirely in English.

When I moved to Malaysia in 2007 English became my dominant language, a change I was able to handle with relative ease because of my previous school. At this point music was something that was quite alien to my mind. My perception of what music is differed significantly from my current perception of music. Music was something that I thought to be in the same category as other occupations that entertain people in their leisure time like chess or other sports. It didn't touch me as deeply as it seemed to touch others.

As the months I started becoming interested in western classical music. Starting with a couple of sample tracks that were included in a fresh install of Windows XP, I ventured into the world of symphonies and concertos. I admit that when I first started I listened out purely for the novelty of the experience and not because the music produced in me any of the emotions that the music was supposed to convey. These subtle messages completely escaped me. Almost two years passed before I started to really feel the mood of the music.

The years after I moved were those of great changes for me in many areas of my life. I started taking a genuine interest in mathematics, learnt to think critically and creatively, and most importantly I learnt to think for myself. I learnt scepticism, about the fallacies of the mind, about how information should always be judged upon evidence and not the authority of the source of the information. I also became more open minded to change. I went from being moderately reluctant to change and new ideas to being fiercely supportive of new ideas. I came to realize than change was quite literally the vehicle of progress and the necessity of abandoning old ways of doing things in favour of newer, more efficient ways of doing things.

It was this change that spurred me to try contemporary western music. When I think back to those moments of discovery I loose any of the regrets I have about not discovering this genre earlier. For most people these moments are part of their early childhood when the brain is less analytical in my opinion less capable of appreciating the complexities of perception. Because I was venturing into this new genre of music at this (relatively) late age every time I listened to something new, every time I stumbled upon a gem, a new melody I was able to "observe" what goes on in my mind with the excitement of a scientist who has stumbled upon something new and revolutionary. Now when I listen to music "properly" I sit down on my bed in the dark after everyone's asleep, put on my headphones, turn the volume up to a comfortable level. I then close my eyes and concentrate on the sounds. I try to mentally decompose the music into the separate instruments and the voice. It's like trying to pick out a conversation from a buzz of noise in a huge room full of people. I then notice how each separate sound fits together with the rest how they combine to give a resultant sound which is sometimes completely unexpected. It's like mixing together ingredients with different tastes when cooking to give a new, unexpected taste. The ingredients are the notes from the different instruments and voices used. The net result is the final dish that you eat. Cooking with sound...

I noticed that rarely I stumble upon music that is so good that I take to it the very first time I  hear it. For most songs however the moment of "liking" is less well defined. It's lot like my experience with meeting people. The first time I wander into a group of strangers for example when I move to a new school everybody looks similar and my mind is a confusing mass of faces. But as I get to know the people in the crowd better their faces or at least my perception of their faces change. They get friendlier, less intimidating and more distinct. They start to stand out from the crowd. And if you have a huge mass of faces with a couple of my friends in it familiar faces are easily distinguishable from the "noise". Its the same with most of the music I listen to. When I first hear a track it's a bit intimidating. It's new and I don't know how to think about it yet. Eventually it grows on me and when I hear it again, my brain hails it like an old friend.

James Randi Does His Stuff

I am often surprised at how even highly educated  people can sometimes be fooled by slightly unusual things. In my opinion it's nothing but intellectual laziness. If intellectually lazy people see something that's not in the textbooks they immediately jump to the conclusion that something mystic is going on rather that trying to find out what might have happened.

This is a video I found on Youtube about a "mysterious" reaction which apparently has no explanation. As a person who has learnt quite a bit of Chemistry I tried to figure out what could possibly have happened. My explanation may be slightly off or even completely wrong but I have to start somewhere.

Here's what I think happened. If you look at the video you'll see that a few drops of liquid is added to the distilled water before the blue universal indicator is added. Since the Indicator is blue in alkali that "something" was probably an alkali. I remember that pH indicators are frequently weak acids or weak bases and that only a few drops of alkali was added at to the beaker at the start of the experiment so the concentration of alkali must be very very low.

The universal indicator solution is made up of a mixture of several pH indicators, some of them weak acids. From my experience in doing titrations with I've seen that near the endpoint if you keep swirling the flask the solution turns clear (using phenolphthalein as an example) but the titration is not quite done yet because once the swirling is stopped the solution turns a very very  slight pink. You then have to add one more drop to complete the titration. I reason that the agitation may may be affecting the reaction to a certain extent (I still haven't figured out how but I will soon.). I think this is a similar situation. 

One of the acidic indicators in the Universal Indicator mixture reacts with the miniscule amount of base and neutralizes it. After neutralization, the remaining mixture of indicators take on a yellow colour either because the new ions formed are yellow or because the remaining portion of the Universal Indicator has a yellow colour. The colour will probably return to blue if the stirring is stopped.

I hate to burst the bubble of that aspiring magician (He did look awfully pleased with himself) but sometimes the truth is more important.

Refuting Intelligent Design: The Game of Life and Irreducible Complexity

A long time ago I wrote a blogpost about John Conway's Game of life, which used simple set of rules to make dots on a page evolve. This zero player "game" is an excellent example of how complex systems can evolve from simplicity. All we have is a grid in which each cell has two possible states dead (shaded) or alive (empty) and four simple rules:

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

 If the system is then left to evolve on it's own given certain initial conditions highly complex patterns emerge that seem almost unthinkable with such simple rules. Here's an example.

This pattern was created by humans who worked out the initial conditions using computers. But think about what would happen if you took a huge grid containing millions of squares and kept populating them randomly while allowing the system to evolve for millions of years. Although the probability of such complex patterns forming on their own is pretty low, because of the huge timescales involved, complex patterns will inevitably develop. In fact I wouldn't be surprised if some apparently lifelike systems which replicate themselves evolved. Now if someone who had absolutely no idea of the starting conditions observed this complex system and tried to work backwards he would find find himself with an outrageously complex problem. Although this person may be able to work out how the little structures in the system function and replicate he would have little or no idea about how the system came about. 

Now think about the world as it was nearly 4.5 billion years ago when our planet was in its infancy. We had a big primordial "soup" of chemicals as the "initial conditions". The laws of physics and chemistry were the rules which our "system" which is the Earth and the primordial soup of chemicals followed. Considering the fact that the laws of physics are considerably more complex than the set of four rules for John Conway's Game of Life and that atoms and molecules have a substantially larger set of possible states that alive or dead is it not conceivable that after a about a billion years--the estimated time it took for the first life forms to appear-- by some lucky coincidence very simple prokaryotic life forms had developed?

Irreducible complexity is a concept that is very commonly used by Intelligent design proponents and creationists to justify the existence of an Intelligent Designer. They claim that in it's current state, life is too complex to have evolved by chance. This is another example of the inability of our brains to intuitively grasp extremely small probabilities. "Common sense" is often misleading when we look into the world of the very small. I think the Game of life provides an excellent example of how seemingly irreducibly complex systems can arise from some initial conditions and a set of rules. We may not have the computing power to reverse engineer evolution at present but I think the day will come soon enough.

The illusion of irreducible complexity in a bacterial flagellum. The complexity of the flagellum was shown to be reducible by  Zvonimir Dogic.

Large Numbers and Premonitory Dreams

Ever heard of the saying "If at once you don't succeed, then try, try, try again."? Have you ever thought of approaching the problem mathematically? The idea just popped into my head today during math class. So now I shall play the role of a theoretical Mythbuster and explore the validity of age old adages using a a purely theoretical approach.

First let's simplify the problem. Let us assume that the probability of you failing horribly at something (and succeeding at it) remains constant and does not depend on whether or not you failed horribly in your previous attempt. We need to find the minimum number of repetitions of a particular task you need to carry out before the probability of success is 99%.

Mathematically this is a trivial problem which can be solved using a binomial distribution. If $X$ is the Random Variable that represents the number of successes, then $X\sim B(n,p)$ where $n$ is the number of repetitions and p is the probability of success. Let us assume for the purposes of this discussion that you are such an incredible moron at doing this task that your probability of success is only on in hundred or 0.01. We want to find n when the probability of succeeding at least once is 99%. So doing the math,

$X \sim B(n,0.01); P(X\geq 1) = 1-P(X=0) >0.99$

$1-(0.99)^{n}>0.99$

$n>\frac{\log 0.01}{\log 0.99}\Longrightarrow n>458.2$

Repeating the task over 458 times ought to do the trick! So this old proverb does have a mathematical basis!

Premonitory Dreams

So what does all this have to do with Premonitory dreams? As it turns out a similar concept can explain in a very simple and elegant manner why people have premonitory dreams.

There are thousands of reports every year of people dreaming about the death of a friend or close relative days before it happens. The superstitious always think of this as "evidence" for the existence of the supernatural. But despite the fact that science cannot explain individual premonitory dreams, a very simple explanation exists if you consider the population as a whole. Read this extract from an article by Michael Shermer.

We can employ a similar back-of-the-envelope calculation to explain death premonition dreams. The average person has about five dreams a night, or 1,825 dreams a year. If we remember only a tenth of our dreams, then we recall 182.5 dreams a year. There are 300 million Americans, who thus produce 54.7 billion remembered dreams a year. Sociologists tell us that each of us knows about 150 people fairly well, thus producing a social-network grid of 45 billion personal relationship connections. With an annual death rate of 2.4 million Americans, it is inevitable that some of those 54.7 billion remembered dreams will be about some of these 2.4 million deaths among the 300 million Americans and their 45 billion relationship connections. In fact, it would be a miracle if some death premonition dreams did not happen to come true! -  Michael Shermer,September 3, 2008. Why Our Brains Do Not Intuitively Grasp Probabilities. Scientific American, Retrieved from http://www.scientificamerican.com/article.cfm?id=why-our-brains-do-not-intuitively-grasp-probabilities 

As we can see from this article, our brain is not very good at intuitively grasping probabilities, especially when the numbers involved are disproportionately small. This results in the intolerably widespread delusion that premonitory dreams are a result of supernatural influences. It doesn't help that most people are prone to what is called a confirmation bias. When people believe in something they tend to look for events or pieces of evidence that confirm their belief and tend to "filter out" anything and everything that contradicts their beliefs. All those who claim to be psychics take advantage of this cognitive bias. Take tarot card readers as an example. People always remember the time the street psychic predicted their promotion of pay raise but always forget the times they failed to predict anything substantial. In fact if you measured the success rate of psychic predictions you'd probably find that they are not much better than what you would expect from someone who was guessing intelligently. So in the future if you meet somebody who claims that premonitory dreams are proof of the supernatural you can gleefully prove them wrong!

How to (Legally) Jump a Red Light.

So I went on an extended hiatus from blogging for a while because I was very busy by my AS-Level examinations. Now with only one exam on physics (MCQ) left I shall temporarily re-enter the blogosphere.

With physics buzzing about in my mind I thought I'd do something about physics. So today I am going to tell you how to jump a red traffic light and get away with it (even if you're caught) using the indomitable power of physics.

Imagine yourself in this situation. You're speeding down a long deserted highway, it's an emergency and you're confronted with one of those annoying red lights. You need to get home as quickly as possible but those sneaky cameras are always on the watch for people who want to bend the rules a bit. What do you do?

Use the Doppler Effect.

I wonder how many will get this reference?

Many people are familiar with the Doppler Effect that's observed with sound. They may be able to recall that the sound of a train which is speeding towards them is at a higher pitch that the sound of the same train when it has passed you and is moving away from you. In simple terms this is because the sound waves in front of the train get squeezed together and has a shorter wavelength and consequently a higher frequency that the waves in front which are stretched out.

The amazing thing is that this Doppler Effect will work with light too because light essentially consists of electric and magnetic fields oscillating at right angles to each other. The colour of the light depends on it's frequency and wavelength. In light it is called the Relativistic Doppler Effect because the effect was first brought to light by Albert Einstein.

So to jump the red light, all we have to do travel fast enough for the red traffic light to be blushifted to a green colour. 

So we apply the equation for the Doppler shift of light. $\frac{\lambda_s}{\lambda_0} = \sqrt{\frac{c-\nu_s}{c+\nu_s}}$.

$\lambda_s$ is the wavelength at the source, which is equal to 650 nm (Typical for red light).

$\lambda_0$ is the wavelength observed, which is equal to 520 nm (Typical for green light).

$c$ is the speed of light which is 299792458 m/s .

$\nu_s$ is the speed of the source away from the observer which is what we need to find. 

If the calculation is carried out you will find that the required speed is about $6.6 \times 10^7 m/s$ or about 237 600 000 km/hr.

And there you have it! Travel at 237 600 000 km/h and you can legally jump the red light because at that speed the red light is no longer red. It is green.

By now, the more intellectually keen reader might have spotted a huge gaping hole hole in this grand plan. A big question will be burning in their minds. The will say, if we are travelling at 237 600 000 km/h are we not breaking the speed limit? However, as it turns out my plan is unbelievably foolproof. At 237 600 000 km/h, you're travelling so fast that any speed trap foolish enough challenge you (which by the way utilizes the Doppler Effect to measure the speed of your car) will find that by the time, it's microprocessors are done calculating your speed and ready to snap a photograph of your numberplate, you'll be miles away. Even if there existed a microprocessor that could calculate fast enough, you'd just be an unrecognizable speed blur on the photograph. 

Well now, we have a another problem don't we? Have you seen it yet? You might be thinking, that if the cameras are too slow to photograph you when you travel that fast, why did I go to all that trouble to calculate the blueshift of light? Why didn't I just tell you at the very beginning, without going through all this rigmarole, that all you needed to do was zoom by at 237 600 000 km/h?

I just felt that getting around the problem using Relativistic Doppler Shift Equations were a more elegant way of bending the rules than just "speeding". That's all.

[EDIT: I watched an episode of the famous Mythbusters in which they showed that all you need to do to beat the speed camera is a car that travels at over 300 miles per hour which translates to about 483 km/hr. So that's the minimum speed you need.]

Warning

Disclaimer: The author is not responsible for any unpleasant effects the enthusiastic experimenter may suffer from as a result of carrying out this experiment. Any damages suffered by the experimenter such as those due to relativistic time dilation, time paradoxes, getting lost int time, changing the course of human history etc. are the sole responsibility of the experimenter

LaTeX Testing

I've started using $\LaTeX$ for so that I may embed mathematical equations in my blog without resorting to uploading images each time I want an equation up here. This is just a test to see if everything is working properly.

[Note: Those viewing the mobile version of this website will just see lines of meaningless code unless of course you are adept at coding in $\LaTeX.$]

$R_{{\mu}{\nu}} - \frac{1}{2} g_{{\mu}{\nu}} R + g_{{\mu}{\nu}} \Lambda = \frac{8{\pi}G }{c^{4}} T_{{\mu}{\nu}}$

$G_{\mu\nu} = R_{\mu\nu} - \frac{1}{2} Rg_{\mu\nu}$

$e^{ix} = \cos x + i \sin x$

$G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}$

$\sum_{n=1}^{N-1} 3^{-n}cos(2n\theta)= \frac{9-3^{-N+2}cos(2N\theta)- 3cos(2\theta)+3^{-N+1}cos[2(N-1)\theta]}{10-6cos(2\theta)}$

$\sum_1^\infty \frac{1}{n^2}=\frac{\pi^2}{6}$

$t=\frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}}$

$F_e = \frac{1}{4\pi \epsilon_0} \frac{Q_1 Q_2}{r^2}$

And for
$CH_3COOH_{(aq)} + CH_3CH_2OH_{(aq)} \longrightarrow {CH_3COOCH_2CH_3}_{(aq)} + H_2O_{(l)}$
$K_c = \frac{[CH_3COOCH_2CH_3][H_2O]}{[CH_3COOH][CH_3CH_2OH]}$

A Chess match with my father.

Had quite a long and drawn out chess match with my father. We were quite evenly matched. I was almost going to beat him, but I made a slip up at move 47 (can you find it?) and in the end he beat me.

Play online chess

An Interesting Observation

 

Crazy..... 

An Unexpected Finish

A very unexpected finish to a chess game. I was really tired and playing a bit blindly, not thinking much more than a move ahead. I made a move only expecting to fork the opponent's king and rook but as it transpired that move checkmated my opponent. I checkmated my opponent without realizing it! Imagine that.

This was blitz chess, played in under 2 minutes with 12 extra seconds awarded to the player after each move. I'm playing as white of course.

As this is the first time I am embedding a chess game in my blog I will give some directions. Look underneath the chessboard. Click on the button with ">" in it to see the game move by move. You can also click on one of the moves in the list on the side to jump directly to that move.

Play online chess

PS: I'm not sure why the scroll bar of the move list suddenly decided it was more comfortable -> lying between my blogposts like some freakish cyber bridge. No amount of fiddling with the code could correct that issue...

Breaking Free

Most of what I put down in this blog is influenced by what happens to me in my life.

Life is what you want it to be. I figured that out a long time ago. Those who celebrate mediocrity and yearn for normality unwittingly make their lives mundane and commonplace. Those who want to have an exciting life, those who want it filled with surprises, those who want it filled with excitement will make it so if they are willing pursue it.

Over the years I have some to realize that yearning for excitement is something that is deeply ingrained into my character. After falling head over heels in love with mathematics, I began to realize that I was positively feeding off the intense feelings of excitement that follows a moment of discovery. I began to realize that even the most mundane everyday objects come alive once you start using mathematics. There are many who feel that science is boring, methodical, and mechanical. But these are people who have not experienced science fully. Those who think of science as a rigid framework of arcane rules could not be more wrong. Science is methodical and logical but that does not make it boring in any way. Those who are bored are those who are unaware of the delightful surprises, of the unexpected twists and turns and of the outrageously unbelievable conclusions that logic can lead us to. Science and mathematics is a dynamic, ever changing entity; it's almost a living thing. Those beautiful things in nature and those commonplace things that we take for granted have their beauty multiplied a hundredfold when you look at them through the eyes of a scientist.

I could keep at this forever, but I believe I have said enough to get my message across. For me science and mathematics gives me all the excitement I need.

With my interest in math came the downfall of my gullibility. I had entered a wonderful new world. A world where logic, evidence and healthy skepticism reign supreme. I learnt about why people are so gullible, why people believe in supernatural phenomena. I became aware of the cognitive biases that lie at the heart of supernatural phenomena. Slowly, like someone being lifted out of the depths of mental depression I came into the light. I entered a world where things were clearer. The world was no longer a dark and mysterious place to me. Instead it was a testament to the elegance and successfulness of science in explaining the world around us.

I came to realize why the world was progressing so slowly. In my opinion there is no greater hindrance to the advancement of human civilization than tradition, dogma and authority. By authority, I do not mean the laws that are in place for the peaceful functioning of a nation. I am referring to belief in authority; when authority is given precedence over evidence. Authority is a social evil when people believe things based on the authority of the source of information rather than evidence.

The world is an ever changing place. The only way humanity can make the next giant leap is by changing. If the cavemen had refused to give up their stone tools and use iron and bronze because the usage of stones was their 'tradition' would the world be where it is today? Scientific progress was held back for decades when the dogmatic refused to accept the heliocentric theory of the solar system. There is clear evidence that change is the vehicle for human progress. Progress occurs when change is embraced with open arms.. If the people of the world so adamantly cling to the past like leeches on human skin how can progress take place? When times change, so must we. A lot of the traditions that people follow are obsolete remnants of a past civilization that existed hundreds of years ago. Why do people think that all the concepts of life that were cherished so many generations ago are still appropriate for today's age?

Of course, I do not deny that there are many old concepts that are still applicable. There are and these concepts should continue to flourish.

But when concepts that are clearly relics of a bygone era stand in the way of progress, I am offended. Such dogmatic practices are like a ten ton anchor chained to the limbs of a drowning man. They anchor humanity to an unchanging level of progress. They create an Iron Curtain which humanity has to struggle through.

But the future is bright. Humanity is breaking free of the debilitating chains of dogma, slowly but surely. The Iron Curtain is thinner than ever before and is on its way to disappearing completely.

But occasionally when I see how much science is progressing with its newfound freedom, I feel cheated. I feel cheated when I realize how much more science could have progressed if these chains had disappeared earlier, if the Iron Curtain had been drawn open to remove the necessity of struggling through it.

If we had broken free.

A Very Knotty Incident

The past few days have been needlessly tiring. The 'orientation' activities that are supposed to familiarize the new students with the other two batches includes a long list of pointless activities such as lengthy, time consuming introductions, sports and the like. It was all utterly boring. Until today.

We played a game called the "Human Knot" where we are supposed to break up into relatively large groups of 5-6 people and link our hands together in a knot. A moderator will then judge the complexity of the knot by trying to untie it.

As a person who has fallen in love with mathematics I am always reading up on new and sometimes old interesting happenings in the world of numbers. Having been at it for nearly four years I know many unexpected and unlikely places where mathematics can be applied. As soon as the rules of the knot game were declared I noticed a striking resemblance between the game and a branch of mathematics known as the knot theory. In the game as a knot is being untied, we are not allowed to unlink hands but a range of possible moves are allowed. They include the following.

As it turns out these are the exact same moves that are allowed on mathematical knots. In fact they are called Reidmeister moves.

 So having learnt bit about the knot theory I decided to apply it. Most of the knots we have ever tied with our hands are mathematically not very interesting because they become straight lines with two free ends after going through a finite number of Reidemeister moves. Mathematical knots are much more interesting. They have no free ends and are physically un-unravellable. Bearing this in mind I set out create one of the simplest mathematical knots, a trefoil knot which cannot be untied by any amount of Reidemeister moves. But alas! I made a wrong turn and without realizing it had made two unknots. All was not lost however.

When the others tied to unravel our knot, they got the surprise of their lives! After several twists, turns and stepping over crossed arms, those watching us went silent as our knot split into two clean separate circles. That was something that did not happen often! So in the end the slip up served its purpose.

The above anecdote proves that the applications of the wonderful subject called mathematics can be found the most unexpected of situations. It just keeps popping up everywhere doesn't it?

School Starts Again

School has reopened and the usual truckload of work joyfully  resumes it's consistent daily drive into my 'to do' list. Consequently, quality sleep continues to elude me.

With the exams looming ominously like a charged thundercloud, it's time to begin a hectic revision. Four months seems to undergo some quirky relativistic length contraction but time dilation, which is supposed to slow down time, seems to be acting in reverse. I might not get an opportunity to update my blog as often as I have been for the past month.

The new batch of A-Level students have arrived and we are now undertaking the infinitely boring task of 'orientation'. I fail to understand how some people are able to enjoy meeting new people so much. Personally, I find that it takes a Herculean effort to keep track of the names of so many people. After a day of pointless introductions I find myself mentally exhausted. It is for this reason perhaps, that I don't remember having made more that 10 friends in my entire life. (I think ten is a gross overstatement but I think it's a safe estimate and a nice round number.) Relativity comes into effect here too I suppose. Once you realize how deep and meaningful the questions posed by Science are, once the wonder and mystery of the Universe ensnares the senses and captures your imagination, you start to realize how meaningless it is to worry about something as mundane as what shirt you're going to wear tomorrow. The problem is that people are too engrossed in the synthetic world we have created around us which sweeps us away with an avalanche of simplistic pleasures such as shopping, films, promotions and the like. So engrossed that they almost never get the time to ponder on the deep mysteries of the universe.

They are those to whom the emotion of experiencing the mysterious is a stranger. The do not pause to wonder or stand rapt in awe. Their eyes are truly closed.

What a Way to Start the New Year!

In many places around the world New Year was not as happy as people would have liked.

From what I heard on CNN and BBC, there has been an explosion outside a church in Egypt, killing about five people. A bomb exploded in a public area in Nigeria, with an estimated but disputed death toll of 30.

To cap it all, huge flood has put quite a damper on New Year celebrations in Queensland, Australia.

Due to the idiosyncrasies of the International Date Line, calendars North America is still read 31 December 2010. The whole world is watching and waiting for the New Year Ball Drop in Times Square New York, one of the most famous New Year's Eve celebrations in the World.

I will now take a moment to highlight my favourite Scientific Discovery of 2010. Put your hands together for the amazing, the versatile, the exotic Graphene!

 

With it's exotic and wonderful electrical and physical properties, graphene has won the hearts of thousands of physicists and physics lovers around the world. It is arguably one of the most important scientific breakthroughs since the invention of the integrated circuit. It is therefore not surprising that the Nobel Prize in Physics for 2010 went to Andre Geim and Konstantin Novoselov for the discovery of wonder material. Scientists around the globe are still discovering new and wonderful properties of graphene. It could be this two dimensional sheet of material that fuels the next wave of technological development. Hats off to graphene!

On a completely different note, the morning news revealed that the social networking site called Facebook has overtaken Google as the most visited website in the US. What an alarming trend! Why are people so obsessed with this thing? What is so great about this website?