Friday, 31 December 2010

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!

Saturday, 25 December 2010

Another Christmas Has Come and Just Gone

It's Christmas again! It's not exactly a festival I celebrate.Nowadays all festivals are characterized by holiday promotions and discounts on the price of clothes.

As do all holidays Christmas too has an interesting (By interesting I just mean that the story is not known by many people. History is never interesting (Hint: It's always boring.)) long winded and convoluted back story that describes how it evolved. It's a thrilling tale; starting with some pagan festival that was celebrated on the Winter Solstice which fell on 25 December in the Julian Calendar (We now use the Gregorian Calendar). There are interesting side-stories that describes how traditions evolved (For example the tradition of bringing home Christmas Trees was adapted from the Roman Festival of Saturnalia). But apart from this half-hearted and rather sketchy account I will not bother to recount the story in its entirety.

On a more interesting note Google apparently wanted to end the year with a huge, big bang. They have certainly outdone themselves with their latest doodle which, according to news reports took a team of five 250 hours to create. It's quite impressive and interactive. You should go check it out. It's only going up on display till 25 December. I f you miss it, don't worry you can still view it here
However, impressive as it may be,  my personal favorite is still the Scooby Doo Doodle (Or should I say Scooby Doodle!).

Here's doodle in all it's glory.


Amidst all this festive cheer there is a small part of me that is slightly alarmed. The Christmas of 2009 it seems, happened just days ago. Where did the year go? Time seems to be galloping by at breakneck speed. Yet another Christmas has inevitably come and just as inevitably, gone.

Imagine all the possibilities!

I have always felt that imagination is the most wonderful quality that a human can possess. It is our unique capacity to think of that which is not is in my opinion the single greatest driving force that has fueled human innovation and invention ever since we first started knocking stones together. 

I have always been obsessed with the concept of mental visualization, that particular skill which affords us the capacity to just close our eyes forget the world around us and delve into the depths of our mind. All children possess this capacity, but I feel that we lose this wonderful ability as we get older unless we constantly exercise it. I was not consciously aware of doing this until I was about 11 and since then I have been constantly trying to develop it further, to push the limit of my ability to visualize.

I would always look for ways to exercise my mind in this way. From trying to do geometry in my head to recalling snippets from the latest episode of Pokemon complete with sound. I had never felt I was making much progress.

It realized a few days ago however that this was a misconception on my part. I felt real excitement a few days ago when I solved a problem on 3D geometry without ever writing a single equation down. My progress had been too gradual to be noticeable. The problem was relatively simple. I was trying to find the shortest distance between two skew (i.e non-parallel, non-intersecting) lines in 3D space. I was able to derive the whole concept without any previous knowledge within about 15 minutes of intensive visualization.
I do not know if this particular approach at solving problems have any mental health benefits, but even if it doesn't I will keep at it just because it feels wonderful.

Thursday, 23 December 2010

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.



Tuesday, 21 December 2010

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.htmlI 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!


Friday, 10 December 2010

Unfashionable to be Intelligent?

A news feature about a certain Gail Trimble, a student from the Corpus Christi College really left me flabbergasted. What was the reason? Simply because she displayed her cleverness by amassing an unusually large amount of points on the BBC Quiz Program, University Challenge. Here is the news story.

For those who can't be bothered to read the story, here is the summary:
A 26 year old girl called Gail Trimble participated in the University Challenge Quiz show as part of a team of 4. She dazzled the audience with her astoundingly large bank of general knowledge and thoroughly impressed the quizmaster, Jeremy Paxman. Don't take my word for it. Watch her mindblowing performance here: 
http://www.youtube.com/watch?v=KCj4wjV-oqM

Although she received a lot of praise, within a few days unbelievebly cruel comments were being circulated about her in social networking sites and all over the internet. I quote from the article:
However, despite Miss Trimble's success, many viewers have subjected her to vicious abuse. Some experts say this behaviour exposes the sinister hostility to brainpower in our dumbed-down, celebrity-obsessed age.
While some have praised the 26-year-old as 'very sexy with a gorgeous smile', others call her 'a hateful know-it-all' and an ' annoying bitch'.
They have taken particular exception to her saying 'Oh, well done', 'Of course' and 'Quite' to her teammates.
One said she was a 'horse-toothed snob' who 'ruins University Challenge every time she is on it with her "better than thou" attitude'.
Another said Miss Trimble was 'so brain-rupturingly irritating and smug' that they hoped science would come up with 'a screen that you can reach through and punch those inside'.
'She could easily win University Challenge on her own, but I get the feeling she may well celebrate alone as well.'

She is qite well educated. 
Miss Trimble achieved 11 GCSEs - including 10 A*s and one A at the fee-paying Lady Eleanor Holles school in Hampton, South-West London.(HA HA HA Kian Seng!!!)
She then took four grade As in Latin, Greek, English literature and maths at A level, followed by a first in Latin at Corpus Christi in 2004. She is now studying for a doctorate in Latin literature.


I bet I got you interested. I encourage you to read the article.

There are two things that this response shows about the world in general.


Firstly, the obvious discrimination against women. It seems that society still struggles with the concept of intelligent women. In fact the Youtube video I linked above discusses the issue. I completely agree that as a species that has reached such a level of technological development we should be moving towards a society where everybody has equal opportunities. We're in the 21st Century for God's Sake!! Gender discrimination is for the Dark Ages.

Secondly, the "uncool" nature of intelligence. In many places intelligence is being viewed with distaste. In fact there is an increasing amount of brilliant children being forced to "slow down" and disguise their intelligence for the sake of avoiding ridicule and teasing from peers. I can connect with this because I experienced this kind of ridicule when I moved to my new school in Year 9. To put it in the words of my self proclaimed "cool" classmates, Trying hard in school makes you "gay". Books are also "gay".Getting good grades makes you a nerd. Trying new things and cultures makes you a freak. New well-founded ideas are "radical" and "un-cool".

 Why are we moving towards a society where we celebrate intellectual mediocrity? Why is it wrong for a woman to be intelligent? Why is it unfashionable to be intelligent? 

Thursday, 9 December 2010

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.

  

Tuesday, 7 December 2010

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: 



Wednesday, 1 December 2010

A Very Ubiquitous Emoticon

In this post I shall talk about a very ubiquitous emoticon. It is an emoticon that is casually added to the end of sentences to announce amusement. Sometimes it appears to stand alone powerful enough to play the role of a reply to a question. I am of course talking about the famous "XD"

The Urban dictionary gives the following definitions.
XD :
 
 
1. A phrase which genrally expresses the randomness, hilarity, embarrasment, etc. Often used in chatrooms of various kinds.

PERSON 1: Two hamburgers walked into a bar and the barman said, 'Sorry, we don't serve food.'
PERSON 2: XD

A: We squashed oranges in the canteen at lunch.
B: XD

2.An text-smilie with a usage somewhere between 'lol' and ':D'. Visually similar to the clenched eyes of South Park characters.
"Hey, wanna cyber???"

"XD"

3. A symbol with X being the eyes and D being the mouth, to make a seeming of the person having squinched eyes and a mouth wide open laughing. This is usually used to replace rofl, as the X for eyes indicates that they are laughing so hard they may have fallen off their chair. Usually used in mmorpgs and chat lines.

Example 1:
Person 1: Hah i hacked some n00b's account then went and spammed lots of people and got it reported!!1!

Person 2: Omg XD haha he must be so pissed!
And finally, the most hilarious definition of all:
1. An internet expression that will hopefully replace LOL as the laughing symbol.


2. An internet expression that gets annoying if overused.
1. (the right way to use it)
Person 1: *tells a dumb joke*
Person 2: You try so hard that's it's funny. XD

2. (the wrong way to use it)
Person 1: I walked my dog ealier.
Person 2: XD
Person 1: Then I fed the cat
Person 2: XD
Person 1: AHH I'M TALKING TO AN AUTO-RESPONDING XD MACHINE!
Person 2: XD
Person 1: Die.
Person 2: XD
A very fitting definition I think. XD!

Tuesday, 30 November 2010

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. 

Sunday, 3 October 2010

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?"

Tuesday, 28 September 2010

A Poem I wrote in 2008

Below is a poem I wrote in 2008. I had just turned fourteen; hence the rather childish structure. But I found it an interesting insight into a very important stage of my life.

Somehow the title of the poem reminds me of the saying "Empty vessels make the most noise."


The Empty Vessel

Behold the empty vessel in the Atlantic,
Sailing Westwards,
To find the Land of the Spices,
Which was in the East.

The empty vessel carried by the waves,
Going West instead of East,
To find the land in the East,
The Land of Spices.

"Land ahead!" they shout,
"I see the Land of Spices,
The land of riches where,
There are temples paved with gold."

"Weigh the anchor!!"they shout,
and weigh the anchor they did,
And on their little boats they all went ashore,
Ashore in the land of the West.

The land of the west where,
They found all but spices and riches,
The land of the West where,
They found nothing but tepees.

Oh Christopher! Oh Christopher!
Oh great Christopher Columbus!
Tell me why you went West,
Looking for the East.

Thursday, 23 September 2010

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?

Thursday, 9 September 2010

Why I am Incompatible with Violent Movies

No occasion is more unique and singular than discovering something about yourself that was previously unknown.

I have never been a fan of violent movies but I was always under the impression that I could watch one if I wanted. I have now discovered that this impression was nothing more than a delusion. I usually read some novel when I have my dinner. But a few nights ago I was unable to find anything good. I decided to watch television with the rest of my family for a while. They were watching a Tamil movie and I reveal for those who are unfamiliar that violence constitutes a substantial percentage of every Tamil movie's storyline. At the time the movie was going through a particularly violent phase. As I watched my heart rate started to go up. Within a minute my cardiac tissue was practically flinging itself violently at the inner side of my unfortunate thoracic cavity. With my heart rate rose a compulsion to avert my eyes. I was quite literally struggling with myself. It was as though a separate mind was in my brain trying to turn my head in the other direction. Eventually my compulsion won.

I was quite mystified. Why would a movie which is quite obviously a unrealistic portrayal of imaginary events provoke a reaction of such inflated magnitude? I decided to confirm that the reaction was indeed part of me and not due to the conditions of that evening alone. Perhaps, I reasoned, it was an occasion on which I was unusually susceptible to stimulus. For a cause to be assigned to an event I have to remove all the variables from the experiment to ensure that the cause which I wish to investigate is the only thing affecting the experiment. So, on a day on which I was sure I was completely clear minded I grabbed my opportunity during lunch when the final section of the movie "The Incredible Hulk" was showing. First I established my resting heart rate which turned out to be 62 beats per minute. I started watching this rather unsettling scuffle between two giant green monsters (That was perhaps the understatement of the year.). I got the same reaction. My heart rate actually went up to 130 beats per minute!!

I remember I wasn't always like this. There was a time when I was younger perhaps at the age of ten or eleven when I used to watch violent movies without flinching. That was before I fell in love with mathematics (when I was thirteen). Now at 16 years and 6 moths I think the years I spent looking at harmless equations (Some people call equations vicious! Imagine that!) has mellowed me. Perhaps that is the reason that over the years, I have developed a curious affinity for Walt Disney films or films very like it. I watch movies like "Bolt", "The Wild", "The Chronicles of Narnia", "The Incredibles", "Johnny English", "Mr. Bean" and "The Sorcerer's Apprentice". And, on giving the matter some thought I realized that I was really glad of this development. I may be called a weakling by some but I am extremely proud of the fact that I find violence even in imaginary situations quite repulsive and revolting. I feel happy when I realize that I have become a better person, a more complete person. I feel a sense of satisfaction when I know that I will always be an advocate for peace.

One thing's for sure. I'll never watch violent movies again.

Friday, 3 September 2010

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.

Sunday, 29 August 2010

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.

Sunday, 15 August 2010

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.

Friday, 13 August 2010

Two Mathematical Jokes

An infinite number of mathematicians walk into a bar. The first goes up to the bartender and says, "I'll have a pint of lager, please." Each next one says, "and I'll have half of what he's having." The bartender says, "You're all idiots," and pulls two pints.


Person 1: What's the integral of 1/cabin?
Person 2: A log cabin.
Person 1: No, a houseboat – you forgot to add the c!

Hilarious.

Note to laymen: You need to be quite familiar with advanced math to understand these jokes. So do not panic if you find yourself scratching your head over this one.

Saturday, 31 July 2010

An 'i' for an 'i' !!!

I'm learning about complex and imaginary numbers right now. Now, the previous sentence probably throws my less mathematically inclined readers into a state of utter confusion. I'm afraid it just can't be helped because this little mathematical curiosity is so interesting that I find myself unable to delay the moment of revelation even to give a short overview about what complex and imaginary numbers are. If you are very keen on understanding this post I suggest you brush up by clicking here and here.

As is usual when I start learning about a topic I started to fiddle around with the concept. A little bit of manipulation here and there goes a long way.  Very soon I stumbled across a mystery which I managed to explain to myself. We all know that
i 2 = −1
i^{4n} = 1\,
i^{4n+1} = i\,
i^{4n+2} = -1\,
and 
i^{4n+3} = -i.\,


So I took this simple problem: i^5 and decided that it could be represented as (i^4)^(5/4). Since i^4 = 1 the expression can be simplified to 1^(5/4). 1^(5/4) = 1.


I was mystified. I could use this technique to prove that any power of i is equal to one. Had I discovered some disrepancy, some fallacy in mathematics? Not likely, I thought. So I set out to analyse my results. 


I wish to prove that i^(5) is i and not 1.


Very soon I found the error in my calculations. I was just beginning to understand how quirky imaginary numbers can be. My mistake lay in assuming that 1^(5/4) = 1. After some thinking, I figured out that it was not. Here's what I did. I reasoned that 


1^(5/4) = (1^5)^(1/4)
           = (1^(1/2))^(1/2)                      Now since 1^(1/2) = +1 or -1
           = 1^(1/2) or -1^(1/2)
           = -1 or 1 or i or -i


So in the end I concluded that by breaking up the exponent of 5 to 4 and 5/4 I was actually introducing 3 new solutions into the problem. It is similar to a situation in which you have a linear equation and by squaring the equation you introduce new spurious solutions which were never part of the original problem. Since (i^4)^(5/4) is not equal to i^5, i^5 remains equal to i and only i. Q.E.D


Interesting isn't it?

Tuesday, 13 July 2010

Weapons of Math Instruction

I found this online. It's Hilarious!


A public school teacher was arrested today at JFK INTL Airport as he attempted to board a flight while in possession of a ruler, a protractor, a set square, a slide rule and a calculator.
At a morning press conference, Attorney General Alberto Gonzales said he believes the man is a member of the notorious Al-gebra movement. He did not identify the man, who has been charged by the FBI with carrying weapons of math instruction.
“Al-gebra is a problem for us,” Gonzales said. “They desire solutions by means and extremes, and sometimes go off on tangents in a search of absolute value. They use secret code names like ‘x’ and ‘y’ and refer to themselves as unknowns’, but we have determined they belong to a common denominator of the axis of medieval with coordinates in every country. As the Greek philanderer Isosceles used to say, ‘There are 3 sides to every triangle’.”
When asked to comment on the arrest, President Bush said, “If God had wanted us to have better weapons of math instruction, He would have given us more fingers and toes.” White House aides told reporters they could not recall a more intelligent or profound statement by the president.

Sunday, 9 May 2010

Monday, 5 April 2010

Mr Raj! Your Streamyx Monkey Administration is spreading!


























This is the screen that welcomes me when I click on the link to any youtube video.

A team of highly trained monkeys? YouTue administrators(Google) must be playing a prank. Either that or Mr Raj's Monkey Administration is taking over the world!

Saturday, 27 March 2010

May the Force be with You

"Master" Looi Kian Seng, if you are indeed going to New Zealand for your further studies, be cautious you must be. For once you stray down the Dark Path there is no return. May the Force be with You!

Friday, 26 March 2010

More Proof That The World Is Full of the Mentally Retarded - The Jedi Census Phenomenon


Quote from Wikipedia:
The Jedi census phenomenon is a grassroots movement that was created in 2001 for citizens of a number of English-speaking countries to record their religion as "Jedi" or "Jedi Knight" (after the quasi-religious order of Force-attuned knights in the fictional Star Wars universe) on the national census.
 I think that we can safely say that the world astoundingly crazy. 

Sunday, 14 March 2010

Vivaldi's Birthday

The great Violinist Antonio Vivaldi's birthday was on March fourth. If you have listened to the background music  on my blog, you may know that it is by him. It is a piece called "Spring" from his famous "Four Seasons".

Today is the birthday of another respected and famous violinist who was also Nobel Laureate.
 None other than Albert Einstein! In addition to being one the famous Physicist, he was also a violinist.

Albert Einstein is in my opinion and in those of many others the greatest Physicist who ever lived apart from Sir James Isaac Newton.

Saturday, 16 January 2010

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.



Saturday, 2 January 2010

“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.