Saturday, July 30, 2011

Favourites - The Feynman Lectures on Physics

Rereading some of my favourite sections and thought i'd share what lessons I think professor Feynman was trying to convey. Enjoy.
Each piece, or part, of the whole nature is always an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again or, more likely, to be corrected.......The test of all knowledge is experiment. Experiment is the sole judge of scientific “truth”.
~Volume I, 1-1, Introduction
A poet once said, "The whole universe is in a glass of wine." We will probably never know in what sense he meant that, for poets do not write to be understood. But it is true that if we look at a glass of wine closely enough we see the entire universe. There are the things of physics: the twisting liquid which evaporates depending on the wind and weather, the reflections in the glass, and our imagination adds the atoms. The glass is a distillation of the Earth's rocks, and in its composition we see the secrets of the universe's age, and the evolution of stars. What strange arrays of chemicals are in the wine? How did they come to be? There are the ferments, the enzymes, the substrates, and the products. There in wine is found the great generalization: all life is fermentation. Nobody can discover the chemistry of wine without discovering, as did Louis Pasteur, the cause of much disease. How vivid is the claret, pressing its existence into the consciousness that watches it! If our small minds, for some convenience, divide this glass of wine, this universe, into parts — physics, biology, geology, astronomy, psychology, and so on — remember that Nature does not know it! So let us put it all back together, not forgetting ultimately what it is for. Let it give us one more final pleasure: drink it and forget it all!
~Volume I, 3-10, The relation of Physics to other sciences
It is important to realize that in physics today, we have no knowledge what energy is. We do not have a picture that energy comes in little blobs of a definite amount.
~Volume I, 4-1
We can't define anything precisely. If we attempt to, we get into that paralysis of thought that comes to philosophers… one saying to the other: "you don't know what you are talking about!". The second one says: "what do you mean by talking? What do you mean by you? What do you mean by know?"
~Volume I, 8-2
From a long view of the history of mankind — seen from, say, ten thousand years from now, there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade.
~Volume II, 1-6 end
In fact, the science of thermodynamics began with an analysis, by the great engineer Sadi Carnot, of the problem of how to build the best and most efficient engine, and this constitutes one of the few famous cases in which engineering has contributed to fundamental physical theory. Another example that comes to mind is the more recent analysis of information theory by Claude Shannon. These two analyses, incidentally, turn out to be closely related.
~"The Laws of Thermodynamics"
If, in some cataclysm, all scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or atomic fact, or whatever you wish to call it) that all things are made of atoms — little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence you will see an enormous amount of information about the world, if just a little imagination and thinking are applied.
Poets say science takes away from the beauty of the stars — mere globs of gas atoms. Nothing is "mere". I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination — stuck on this carousel my little eye can catch one-million-year-old light. A vast pattern — of which I am a part... What is the pattern or the meaning or the why? It does not do harm to the mystery to know a little more about it. For far more marvelous is the truth than any artists of the past imagined it. Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter if he were a man, but if he is an immense spinning sphere of methane and ammonia must be silent?
~Footnote
So, ultimately, in order to understand nature it may be necessary to have a deeper understanding of mathematical relationships. But the real reason is that the subject is enjoyable, and although we humans cut nature up in different ways, and we have different courses in different departments, such compartmentalization is really artificial, and we should take our intellectual pleasures where we find them.
...the "paradox" is only a conflict between reality and your feeling of what reality "ought to be."
~Volume III, p. 18-9
...and you will find someday that, after all, it isn’t as horrible as it looks.
~Volume III, Epilogue
~"Physics is like sex. Sure, it may give some practical results, but that's not why we do it."

Saturday, May 28, 2011

Visca el Barça!


Not a treble, but an incredible season nonetheless! And what a way to end it off: A 3-1 win over Manchester United in the Champions League Final! It was a match truly fit for a UEFA finale.

Tonight, football fans from all corners of the globe faced towards Wembley, the Mecca of the beautiful game. Barcelona vs Manchester United was the dream final, however only one team’s dreams could come true. Both sides tasted domestic league success this season which would be no mean consolation prize, however, a defeat for either team would prove a bitter pill to swallow having come so close to glory. Barcelona arrived as slight favourites having endured arguably the rockier road to London. While the Catalans survived stern challenges from Arsenal and Real Madrid en route to Wembley, United made short work of Chelsea and cruised to the final having humiliated German outfit Schalke in the semis. It seemed the smart money on this fixture would remain in the wallet!

Barcelona were rocked by the eleventh hour absence of Carles Puyol and Javier Mascherano was offered the opportunity to attempt to shore up the massive gap left by their talismanic captain. In the opening minutes Manchester were clearly on top as Barcelona failed to find their rhythm. Chicharito found himself through on goal twice in the opening ten minutes, however he was unable to beat the offside trap. The Catalans seemed vulnerable at the back, and numerous mix ups and route one efforts from the Mancs meant Valdes had to be at his most alert to rush off his line on a few occasions to keep his side in the game.

Messi was played through by Iniesta on 22 minutes, however, an epic tackle by Vidic denied the Balon d’or winner and as Rooney broke through on the counter, Mascherano snuffed out the counter attack. At this stage of the game Barcelona really settled into their rhythm and dominated possession. They knocked repeatedly on the Manchester door with good chances falling to Pedro and Villa but Ferguson’s troops continued to ride their luck. It was only a matter of time until the Blaugrana broke the deadlock, and Pedro was on hand to latch onto a Xavi through ball to send Van Der Sar the wrong way to rattle the net and take the lead. Their celebrations were short lived however as Rooney picked up an Abidal throw in to play a delightful one two with Carrick and then Giggs before powering a right footed shot beyond Valdes to tie the game. At the half time break Sir Alex was the more content of the two managers as Barça seemed incapable of capitalising on their numerous chances.

Barcelona resumed the second half in total control and Alves and Carrick were both awarded yellows for rash challenges. Messi proved yet again to have an ace up his sleeve and produced a trademark moment of magic on the hour mark by rifling a left footed thunderbolt from the edge of the area after some good work from Busquets in the box to win the ball back from the United defence to take the lead again. At 2-1 Barcelona were not content to sit on their lead and Villa was at hand ten minutes later to make it three with the most sublime of curling chips from the edge of the area to put the ball and the cup just beyond the reach of the helpless Van der Sar. Guardiola, sensing a two goal cushion, gave Puyol and Afellay a run out in the dying minutes, as the Catalans made United look like a pedestrian pub–side rather than Champions League title contenders.

It ended at 3-1, securing a second Champions League and a tenth title for Guardiola in a three year period. A buoyant Eric Abidal was offered the captain’s armband and given the chance to lift club football’s most coveted prize in a fairytale ending to a season that will live in his and many other football ball fans’ memory for decades to come.

Monday, April 18, 2011

Tempus Fugit

Wow, it's already been a year since I created this blog. A lot has changed since then - I'm almost done high school and starting university next year (post to come). Surprisingly, I've only managed to write 40 posts during this time, a record I don't think i'll be able to break considering i'll be even more busy next year. I'll still try my best to keep posting stuff frequently though.

Happy April 18th!

Tuesday, April 5, 2011

Treble Season for Barca?


Seems very likely now, doesn't it? The recent 8 point lead on rivals Real Madrid in La Liga has catapulted Barcelona to possibly win the league this season, with only 8 games to go. Told you Mourinho couldn't change anything!

Today, Real Madrid played Tottenham in the first leg of the Champions League quarter finals with a 4-0 win that gives them the edge for the second leg match next week. Surprisingly, Inter Milan lost a devastating 5-2 to Schalke 04, something I would have never predicted. Inter Milan has been doing very poorly lately and even lost to Serie A rivals AC Milan 3-0 last week. It would take a lot for Inter to still make it to the semi finals of the Champions League, in spite of winning it last year.

Tomorrow, Barcelona plays Shakhtar Donetsk, one match i'm looking forward to simply because it's going to be a thrashing defeat on Shakhtar's end. I'm certain Barcelona will make it to the finals of the Champions League this year. It is very likely that they will win the finals with the unprecedented amount of success they're having so far, breaking numerous long standing records along the way. And no, I don't believe in "jinxing" something. Only time will tell ...

All I have to say regarding the Spanish Cup finals in a few days amongst Barcelona & Real Madrid is that Barcelona never fails to step up to the plate, and delivers when it needs to most. I still remember the last El Clasico in which Barca won 5-0, it was a thing of beauty.

I'm anticipating that this is going to be another Treble Season for the red and blue like the one back in 08-09. Recent statistics show that of the 30 La Liga games the Blaugranas have played so far, they have won 26, tied 3, and have lost only 1 match against Hercules back in September, having scored 82 goals with Messi leading the top scorer of La Liga coupled alongside Ronaldo, each with 27 goals. They have an unbelievable record of going 28 games unbeaten this season, and it would be a shame for Barca not to win a Treble.

Vamanos Blaugranas!

Wednesday, March 16, 2011

Happy Half-Tau Day!

Yea, I know i'm late, but that's not the point of this post. Also, seeing as how many of my fellow bloggers are posting about this, I thought I should too.

After reading some articles online, i'm more inclined to the fact that half-tau day is more correct (logically) than pi day. However, since we humans have been using pi for so long (circa 2000 BC), maybe it's more of a tradition and we should just go with the flow. If you've read one of my previous posts, you'll notice that i'm not very fond of pi and it has annoyed me for a very long time now. This video explains exactly what I mean:

Monday, March 7, 2011

Tuesday, March 1, 2011

Arsenal .. lucky

While preparations for the second leg match between FC Barcelona and Arsenal on March 8th are underway I would like to discuss my thoughts on the previous match they had and why Arsenal didn't deserve to win.

First off, I have nothing against Arsenal, in fact they are my favourite team in the Premier League, and that pure class 83rd min strike from Arshavin was a thing of beauty. Even though Barca was in a state of severe fatigue since it was during February, and some major players were missing from that match, that's still no excuse given the results. But, based on the given statistics it seemed more of a miracle that Arsenal actually pulled through with the win. Furthermore, Messi's headed goal wasn't offside and the fact that Arshavin intentionally got a hand ball near the end just adds up to the mere chances Arsenal had in order to win. To me it just seemed impossible for Barca to lose after the amount of success they were having this season.

One thing I am certain of however is that when Arsenal arrives in Camp Nou in 7 days, it will result in an entirely different outcome as the energy and sheer madness that Barca fans bring with them will ultimately end with the demise of the Emirates.

Circles?

As I was doing some last minute practice problems before tomorrows CCC I thought of a possible mathematical paradox involving a simple geometric problem with circles. The problem itself is not the interesting part but the thought is:

As everyone knows, a circle is defined as the locus of all points equidistant from a center. Furthermore, a circle has both a diameter(d) and a circumference (c), and the relationship between the two is: c=\pi\cdot{d}.\,\!

However, one must realize that pi is an irrational number (some of you might know where i'm going with this), which means we can never say with absolute certainty what the value is. Therefore, even if we know the diameter with absolute certainty, we can never know the circumference, and if we know the circumference with absolute certainty, then the diameter is in doubt. Therefore, we can say that one can never know both the diameter and circumference of a circle. Since a circle has to have both a definable diameter and circumference. We run into a mathematical paradox.

Then I began to think, "Ok, so what does this mean? What's the resolution to this paradox" and soon enough I compiled a list of possible outcomes:
1) There are no such things as circles or any other geometric figure that's dependent on pi.
2) String Theory is to blame as higher dimensions account for the uncertainty in circle geometry (ie. 2D Euclidean Geometry is a simplification even in the flattest worlds).
3) Pi is not a constant but somehow we say it is. Kind of like a mathematical illusion.
4) Pi is in fact a rational number.
5) Because Chuck Norris said so ..

Another thing to consider after this realization: Is circle uncertainty the mechanism behind Heisenberg Indeterminacy? If so, how does it effect observation?

... Worth a thought? At least this distracted me for a while so that I don't fall asleep before the competition.

Wednesday, December 1, 2010

El Clásico!

What a match - One that will go down in history between bitter rivals FC Barcelona and Real Madrid. Barcelona's brilliant performance on Monday was absolutely mesmerizing, to the point that I literally had my jaw dropped by the 90th+ minute. Vamanos Blaugranas! 5-0 in favour of Barca.

Not only is the result so astonishing, but the fact that Real Madrid's perfect winning streak during la liga was finally broken, and Barcelona took over the leader-board as headed by Barca's great coach, Pep Guardiola. In my opinion, Guardiola has done so much in his young career, he has the potential to be the greatest coach Barca has ever had. Much better than Real Madrid's Jose Mourinho.

However, as always, there was some great controversy to be handled during the match in Camp Nou. First of all, when Cristiano Ronaldo (aka; the greatest poser to have ever lived, over hyped, and one who has no respect for the beautiful game) had the audacity to push Pep Guradiola, in order to get the ball for a throw in. Second of all, when Sergio Ramos deliberately tackled Lionel Messi, and later on continued to shove fellow national team mate captain Carles Puyol in the face to finally get a red card. (Not to mention he got a red card from his previous match along with Xabi Alonso). All I can say is that Real Madrid played a very dirty game, while Barcelona's performance was simply breathtaking (Over 600 passes made!).

.. Yes, this is biased. So what?

Here are some of the highlights of the game (I recommend for any avid fan to watch the entire match):



Barça, Barça, Barça !

Saturday, October 30, 2010

Life as I know it

In honor of my grandfather, whom I've learnt everything from.
“There are only two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle.” – Albert Einstein
“The best years of your life are the ones in which you decide your problems are your own. You do not blame them on your mother, the ecology, or the president. You realize that you control your own destiny.” – Albert Ellis
“The trouble with not having a goal is that you can spend your life running up and down the field and never score.” – Bill Copeland
“If what you’re doing is not your passion, you have nothing to lose.”
“The person who says something is impossible should not interrupt the person who is doing it.”
“It is never too late to be what you might have been.” – George Eliot
“All our dreams can come true – if we have the courage to pursue them.” – Walt Disney
“What the mind can conceive, it can achieve.” – Napoleon Hill
“It is not because things are difficult that we do not dare; it is because we do not dare that things are difficult.” – Seneca
“Great minds discuss ideas. Average minds discuss events. Small minds discuss people.” - Eleanor Roosevelt
“If opportunity doesn’t knock, build a door.” - Milton Berle
“The sky has never been the limit. We are our own limits. It’s then about breaking our personal limits and outgrowing ourselves to live our best lives.”
“Don’t say you don’t have enough time. You have exactly the same number of hours per day that were given to Helen Keller, Pasteur, Michaelangelo, Mother Teresea, Leonardo da Vinci, Thomas Jefferson, and Albert Einstein.” – Life’s Little Instruction Book, compiled by H. Jackson Brown, Jr.
“First they ignore you. Then they laugh at you. Then they fight you. Then you win.” – Mahatma Gandhi
“When you can’t change the direction of the wind — adjust your sails.” ~ H. Jackson Brown
“Everything you want should be yours: the type of work you want; the relationships you need; the social, mental, and aesthetic stimulation that will make you happy and fulfilled; the money you require for the lifestyle that is appropriate to you; and any requirement that you may (or may not) have for achievement or service to others. If you don’t aim for it all, you’ll never get it all. To aim for it requires that you know what you want” ~ Richard Koch
“Confidence comes not from always being right but not fearing to be wrong”
“Your time is limited, don’t waste it living someone else’s life. Don’t be trapped by dogma, which is living the result of other people’s thinking. Don’t let the noise of other’s opinion drowned your own inner voice. And most important, have the courage to follow your heart and intuition, they somehow already know what you truly want to become. Everything else is secondary.” – Steve Jobs

Monday, September 6, 2010

Hawking on God again - "The Grand Design"

I woke up this morning to the news that, according to Stephen Hawking, God did not create the Universe but it was instead an “inevitable consequence of the Law of Physics”. By sheer coincidence this daft pronouncement has come out at the same time as the publication of Professor Hawking’s new book, an extract of which appears in todays Times.

Before I express my viewpoints, I'd like to establish that I do not believe in God, and yes, that means i'm an atheist. Therefore, my remarks might seem biased, but that's what keeps the debate on religion vs science going. I'm sure I will have several more posts on this topic in the future.

Stephen Hawking is undoubtedly a very brilliant theoretical physicist, though I wouldn't rank him in my top 20 all time physicists. However, something I’ve noticed about theoretical physicists over the years is that if you get them talking on subjects outside physics they are generally likely to say things just as daft as some drunk bloke down the pub. I’m afraid this is a case in point. And it's quite saddening to think that numerous fans follow every one of his remarks - no matter how religulous they may be.

God and physics are in my view pretty much orthogonal. To put it another way, if I were religious, there’s nothing in theoretical physics that would change make me want to change my mind. However, I’ll leave it to those many physicists who are learned in matters of theology to take up the (metaphorical) cudgels with Professor Hawking.

Though I haven't read the book yet, i'm sure it will be the usual nonsense some people put just to get media attention for a while to fund their studies. No offense to Professor Hawking, whom I respect very much.

Wednesday, September 1, 2010

Everything is Emergent ... Really?

It’s funny how when one thing is going good, it’s going great. And no one portrays that better than Erik Verlinde, who has made a claim that the reason why physicists do not understand the fundamentals of gravity is due to the fact that gravity is an emergent phenomenon, or an “entropic force”. As usual, the media gets all hyped, and so his claim ends up in the New York Times.

Now, if there is one model in physics that I am truly not very fond of, it would be the Standard Model. However, Verlinde has took his claim one step further with the help of Peter Freund, to claim that the Standard Model is also an emergent phenomenon. In fact, Freund has a new paper out on the arXiv entitled “Emergent Gauge Fields” with the following abstract:
Erik Verlinde’s proposal of the emergence of the gravitational force as an entropic force is extended to abelian and non-abelian gauge fields and to matter fields. This suggests a picture with no fundamental forces or forms of matter whatsoever.
And the appreciation:
I wish to thank Erik Verlinde for very helpful correspondence from which it is clear that he independently has also arrived at the conclusion that not only gravity, but all gauge fields should be emergent.
Geoffrey Chew's failed "bootstrap program" of the sixties - much the same reminiscing theoretical idea:
It is as if assuming certain forces and forms of matter to be fundamental is tantamount (in the sense of an effective theory) to assuming that there are no fundamental forces or forms of matter whatsoever, and everything is emergent. This latter picture in which nothing is fundamental is reminiscent of Chew’s bootstrap approach, the original breeding ground of string theory. Could it be that after all its mathematically and physically exquisite developments, string theory has returned to its birthplace?
It is still puzzling to me as to why this is a good thing. During David Gross' (a former student of Chew's) Nobel prize lecture, he explains:
I can remember the precise moment at which I was disillusioned with the bootstrap program. This was at the 1966 Rochester meeting, held at Berkeley. Francis Low, in the session following his talk, remarked that the bootstrap was less of a theory than a tautology…

Wednesday, August 11, 2010

God's Number is 20

As many of my friends know, I am a competitive speedcuber (one can search up my WCA profile).

I love solving puzzles, and more importantly, I love the mathematics behind it. For some time now in the cubing world there has been some progress made into solving an algorithm which produces a solution having the least possible number of moves, the idea being that an omniscient being would know an optimal step from any given configuration. This is known as God's algorithm. The number of moves this algorithm would take in the worst case is called God's Number.

Recently
Morley Davidson, John Dethridge (also a TopCoder), Herbert Kociemba, and Tomas Rokicki proved that God's Number for the standard 3x3x3 Rubik's Cube is exactly 20.

Why is this a great leap forward for cubers? Simply put, imagine constructing an algorithm to optimally
solve all 43,252,003,274,489,856,000 positions of the cube. Easy, no? It took 3 decades to get to this stage ..

Here's the
article for further reading.

Monday, August 9, 2010

P != NP ?

Stumbled upon this interesting article today on the famous P versus NP problem. Thought I should share it with my fellow CS enthusiasts.

For more, please visit here.

(Aug. 9) -- News that Hewlett-Packard employee Vinay Deolalikar may have solved one of computer science's most confounding mathematical problems -- known as P = NP or P versus NP -- is buzzing around the smart side of the Internet. The problem was formulated by Stephen Cook and Leonid Levin in 1971, according to the Clay Mathematics Institute, which has been offering a $1 million prize for its solution. Now, mathematicians are in the process of scrutinizing Deolalikar's proof, released on Friday, which says that P is not in fact equal to NP.

P versus NP
Roughly, the mathematical problem asks if "questions exist whose answer can be quickly checked, but which require an impossibly long time to solve by any direct procedure," according to the Clay Mathematics Institute. In other words, are there really problems whose solutions can be easily verified but not easily solved?

To illustrate the type of problem that could occur if this were true, Clay imagines a college housing scenario wherein 400 students have applied for rooms at a college that can only accommodate 100 of them. A selection of 100 students must be paired together in rooms, but the dean of students has a list of pairings of certain students who cannot room together. The total possible number of pairings is ridiculously large -- more than the total number of atoms in the universe -- but the solutions, i.e. the list of pairings finally provided to the dean, is easy to check for errors: If one of the dean's prohibited pairs is on the list, that's an error.

If P = NP, then problems that appear hard to solve (as the one above) actually have very easy solutions. Deolalikar says he has proven that P does not equal NP -- as many mathematicians have believed -- meaning problems do exist that are easier to solve than to verify.

P
In the equation P = NP, P stands for "polynomial time" and refers to a set of problems whose solutions are easy to find.

NP
NP, meanwhile, stands for "non-deterministic polynomial time" and refers to a set of problems whose solutions are hard to find, but easy to verify.

Algorithm
A set of instructions used to solve a problem. We use them without thinking about it in everyday life, such as when trying to figure out why a lamp doesn't turn on.

N
The number of elements involved in an algorithm. The time it takes to execute many common algorithms is proportional to N or N raised to a power. For example, to determine why a lamp is not working, we might consider three elements:
1. The lamp is not plugged in.
2. The light bulb is burnt out.
3. The lamp is broken.
With only three elements to consider, our algorithm will not take very long to complete. But, if we are trying to determine why our computer won't turn on, we are presented with more elements to consider: Is it plugged in? Is it frozen? Does it need to be rebooted? Does the operating software need to be re-installed? Is it broken? And so on.

Polynomial time
Refers to a "fast" or "efficient" amount of time needed to execute an algorithm, as in N or N raised to a power. Problems classified by "P" in P = NP are those whose solutions can be solved in polynomial time. Problems classified by "NP" can be verified in polynomial time but require exponential time (in other words, far, far more time) to solve.

NP-Complete
The set of NP problems (the majority of NP problems, in fact) that could be solved by adapting a single, easy solution, if an easy solution were possible.

Read more about P = NP on
MIT's website.
pnp12pt

Friday, July 30, 2010

Inception

... It's weird how I can tell if a movie is good just by looking at the trailer.

Inception was absolutely brilliant. Watched it the first day it was released, along with Despicable me and The Sorcerer's Apprentice. Reviews on those movies perhaps at a later time, or not at all.

From the director of the The Dark Knight, Nolan has crafted a movie that's truly beyond genius, and layered both narratively and thematically. Believe me, you have never seen anything like Inception, though many say it is similar to Matrix, it is not. You'll want to see it again and again.

"You’re waiting for a train; a train that will take you far away. You know where you hope this train will take you, but you can’t be sure. But it doesn’t matter – because we’ll be together."

DiCaprio was in my opinion the perfect lead for this movie, as he captured the role flawlessly. “If you’re going to perform inception, you need imagination.” Inception requires so much exposition that a lesser director would have forced theaters to distribute pamphlets to audience members in order to explain the complicated world he’s developed. No wonder it took him over a decade to write the script. Even I can't explain the plot in depth, as the movie required total concentration on what is happening (perhaps I shouldn't have gone out for snacks during the movie). Why is it so difficult to explain the plot in depth? First, I don’t want to spoil you. Secondly, the film layers dreams on top of dreams to the point where a unique keepsake called a “totem” is required in order to inform a character as to whether or not he or she is still dreaming. Then you have people in particular roles like “The Architect”, “The Forger”, and “The Chemist” in order to pull off the job. Furthermore, dreams have rules: dying in a dream forces the dreamer to wake up, delving too deeply into a mind can cause an eternal slumber called “Limbo”, using memories to construct dreams is dangerous because it can blur the line between dreams and reality. In addition, intruding in the dreams of another will cause the dreamer’s “projections” (human representations created by the dreamer) to attack the intruders like white blood cells going after an infection. And these explanations only represent a fraction of the terminology, rules, exceptions, or details that are necessary for creating the world of Inception. With set pieces so intricate, so jaw-dropping, and so breathtaking, you’ll already be swept up in the whirlwind.

There’s a lot to take in, but the imaginative and thoughtful delivery of exposition keeps the viewer riveted despite the amount of information required in order to understand the premise, setting, and plot. It’s not a confusing movie if you provide it with your full attention.

“Dreams feel real while we’re in them. It’s only when we wake up that we realize something was actually strange.”

I'm more active in my dreams than in real life. It's a wonderful place to be. The idea here is - what if you can control your dreams? Other people's dreams? A concept so powerful, it'll be a shame if it doesn't get an Oscar.

Rating: 9/10




As a physics student, I am astonished by the set of laws inception breaks, but remains logical at the same time. I'm going to research more on the physics behind dreams. Should be an interesting topic.

Saturday, July 17, 2010

World Cup 2010

IN PAUL WE TRUST

Well, it's over - Spain deserved it.
South Africa was a great host, but it was a horrid world cup. Which proves my point why nothing compares to Champions League glory.
Let's just hope Brazil 2014 will do futbol justice.

Saturday, July 10, 2010

SPOJ - JEDNAKOST

Getting back to more programming after an inspirational summer camping trip. Saw one of my friends attempting this problem, thought I should give it a shot.

Recently solved problem #3752 - JEDNAKOS.

If you want to solve the problem yourself - stop reading now.

Solution - Recursion + Memoization

Easy problem really

1) Treat numbers starting with zero as special cases.

2) Let minplus[sum][pos] be an array that is the minimum number of pluses required to obtain the value 'sum' using the postfix starting at 'pos', then it's just simple recursion.

3) To avoid initialization, the array stores the number of pluses plus one.

Thursday, July 1, 2010

On the G20 protests

Quick post on something that should be expressed by a Torontonian.

For all these years that I have lived in Toronto, I have never been more disappointed in our people than I am now. I applaud the police for using force with tear gas and rubber bullets against those who have caused tax payers millions of dollars in damages.

It's quite a disgrace to think vandals such as the Black Bloc
would deface such a city for no particular reason at all.

Freedom of speech is something that should be treasured in this nation, peaceful protesters however got little media coverage while numerous news casts broadcasted the events surrounding these vandalisms, and therefore did not get their message's across the nation on issues that actually mattered.

People can be very stupid.

~Happy Canada Day

... Sigh

Wednesday, June 23, 2010

Great People In History II - Leonardo Da Vinci

Leonardo Da Vinci, the great Italian renaissance man who changed our views of both art and science in such a way that modern civilizations still adore and admire his work. His accomplishments are unprecedented, a worldly known brilliant polymath whose unquenchable curiosity was equaled only by his powers of invention. There is no doubt that he is perhaps the greatest person in history, the only man to have attempted to know everything there is to know. His influences encompassed the world of arts, science & technology, and even invented new mechanisms that have revolutionized mankind. Astonishing feats of engineering were established 500 years ago, perhaps surpassing that of our modern era. He is a portrait of a genius of extraordinary diversity.

Leonardo was and is best known as an artist, the creator of such masterpieces as the Mona Lisa and The Last Supper, the most well known paintings of all time. His astonishing works of beauty still captivate and inspire people worldwide. His paintings became famous, and only rivaled by Michelangelo’s creation of Adam. When drawing his masterpiece, the Mona Lisa, his dedication and perseverance in achieving perfection caused him 10 years of his life, only to have painted the lips. In 1466, at the age of fourteen, Leonardo was apprenticed to the artist Andrea di Cione, known as Verrocchio. Other famous painters apprenticed there include Domenico Ghirlandaio, Perugino, Botticelli, and Lorenzo di Credi. Leonardo’s earliest known dated work while there is a drawing in pen and ink of the Arno Valley, drawn on August 5th, 1473. He was commissioned to paint the Virgin of the Rocks for the confraternity of the Immaculate Conception, and The Last Supper for the Monastery of Santa Maria delle Grazie. In January 1478, he received his first independent commission, to paint an altarpiece for the Chapel of St Bernard in the Palazzo Vecchio and The adoration of the Magi in March 1481 for the monks of San Donato a Scopeto. On Octover 18, 1503, he spent two years designing and painting a great mural of the Battle of Anghiari, with Michelangelo designing its companion piece, the Battle of Cascina. In both theory and practice, Leonardo’s artistic influence in the 16th and 17th century Europe, notably France, Spain, Flanders, and Germany was immense, as to have dedicated numerous museums and organizations in his honour. To this day only 15 of his paintings have survived, which have inspired and captivated millions world-wide.

Leonardo’s scientific contributions are brilliant and revolutionary for his time. His new views of the universe and nature are very accurate according to modern science, which is without a doubt a staggering feat for a man who had little to go by. His vision of the world is essentially logic rather than mystery. His personal notebook, which was discovered all over Europe in pieces, reveals correct interpretations of the human anatomy, explanations of physical concepts such as inertia, and sketches for various engineering marvels, such as conceptualizations of a helicopter, a tank, concentrated solar power, a calculator, the double hull and outlined a rudimentary theory of plate tectonics. Additionally, there are compositions for paintings, studies of details and drapery, studies of faces and emotions, of animals, babies, dissections, plant studies, rock formation, and even whirl pools. As a child, Leonardo received informal education in Latin, geometry and mathematics but did not show any particular signs of aptitude. Leonardo’s approach to science was an observational one: he tried to understand a phenomenon by describing and depicting it in utmost detail, and did not emphasize experiments or theoretical explanation. In the 1490’s, while studying mathematics under Luca Pacioli, he prepared a series of drawings of regular solids in skeletal form to be engraved as plates for Pacioli’s book De Divina Proportione, published in 1509. A recent and exhaustive analysis of Leonardo as a scientist by Frtjof Capra argues that Leonardo was a fundamentally different kind of scientist from Galileo, Newton, and other scientists who followed him, whom were more of specialized rather than diverse.

During his lifetime, Leonardo was highly valued as an engineer & a gifted inventor. He created mechanisms never thought of that had influenced people of average status to soldiers in the military. One of his famous inventions, still in use today, is an everyday tool – the scissor. He greatly advanced the state of knowledge in the fields of anatomy, civil engineering, optics, and hydrodynamics. After knowing Ludovico il Moro, Duke of Milan, he went on to produce many different projects for him, including the preparation of floats and pageants for special occasions, designs for a dome for Milan Cathedral, and a model for a huge equestrian monument. When Ludovico was overthrown, Leonardo fled Milan for Venice, where he was employed as a military architect and engineer, devising methods to defend the city from naval attack. He devised a system of moveable barricades to protect the city from attack. While in that position, Leonardo went on to create several maps, which were extremely rare at the time and it would have seemed like a new concept, even though only a few handful of people had seen and known how to use a map. When he returned to the Vatican in Rome, he made a mechanical lion which could walk forward, then open its chest to reveal a cluster of lilies, and also designed wings and shoes for walking on water. Da Vinci also invented musical instruments, such as a keyboard instrument with strings, which made sound via a wheel, horsehair strap, and a bow – a lot like a modern violin. His list of inventions rivals that of Thomas Edison, and continued to do so when building hydraulic pumps, reversible crank mechanisms, finned mortal shells, and even the steam cannon. Big leaps in thought were established during this ‘Da Vinci’ era.

Born in Vinci, Florence on April 15 1452, Leonardo di ser Piero Da Vinci, a man born with remarkable talents that some say transcends from God, displayed infinite grace in everything he did and cultivated his genius so brilliantly that all problems he studied were solved with ease. As Giorgio Vasari once stated, “all his actions seem inspired and indeed everything he does clearly comes from God rather than from human skill.” As a painter, sculptor, architect, musician, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist, and writer, his works and accomplishments speak for themselves, and through extensive research there is no doubt that he is perhaps the greatest man to have ever lived that has influenced people of such broad perspectives. His death on May 2nd, 1519 only marked the beginning of a new era that has forever changed mankind. In 2003, American author Dan Brown based a fiction novel entitled “The Da Vinci Code”, that sold 80 million copies as of 2009, and went on to be produced into a blockbuster movie.


World Cup Predictions

School is over and summer has begun - life is good.

Note: This post is mainly to organize my predictions for the World Cup.

Top 16

Group A
Uruguay & Mexico (Already confirmed - very disappointing for France)

Group B
Argentina & South Korea (Pretty obvious)

Group C
USA & England (Hopefully)

Group D
Germany & Ghana (Ghana is one African nation with a good chance of advancing)

Group E
Netherlands & Japan (Netherlands has a good shot to take it all)

Group F
Italy & Paraguay (I'm not very fond of Italy)

Group G
Brazil & Portugal (Tough group and a sad loss for Ivory Coast)

Group H
Spain & Chile (Poor performance from Spain thus far)

Therefore, the top 16 teams are:
  1. Argentina
  2. Brazil
  3. Chile
  4. England
  5. Germany
  6. Ghana
  7. Italy
  8. Japan
  9. Mexico
  10. Netherlands
  11. Paraguay
  12. Portugal
  13. South Korea
  14. Spain
  15. Uruguay
  16. USA
Quarter Finalists
  • Argentina (Eliminating Mexico)
  • Brazil
  • England (Capella will ruin England)
  • Germany
  • Japan
  • South Korea (Eliminating Uruguay)
  • Spain
  • Netherlands
Semi Finalists
  • Argentina
  • Brazil
  • Germany
  • Spain
Finalists
  • Argenina
  • Brazil
2010 World Cup Winner: Argentina, even though Maradona has no idea what he is doing.

You might have noticed I changed my finalists from Argentina & Spain to Argentina & Brazil. Simply put, after Spain's poor performance in several matches, I don't have much hope for them advancing through to finals, though they do have the potential. Brazil, however, has stepped up to the plate and has delivered quite a show for each match. I could be dead wrong, but for now lets enjoy the beautiful game.

Overall, this world cup hasn't been good, and i'm quite sad for the African nations.
Rating: 6.5/10

Let's just hope this isn't another World Cup like that of the 1990's in Italy.