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.

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…

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.

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

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.

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.

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.

My SPOJ account