Hypothesis and Theories

Leon and Serene

2009-12-31T22:25:00.006+08:00

Serene is here to help Leon update blog coz his blog is dead.. arghhs... :X

hmm... was mapling with dear just now.. he's so pro coz his bowman and ice mage are all above 100 whereas mine's so noob, always stuck at lvl 84.. but well, grats to him for leveling to lvl 120! v(^,^)v quickly do the quest and show me ur new skill yea? :D

today is the last day of Year 2009 and its time to have resolutions for the new year!

(1) Hope Leon can get enrolled into NTU Aerospace which is his dream course as he likes planes since young...

(2) Hope I can get good results this year and hopefully hit a GPA of 3.4-3.6?

(3) The last resolution is for Leon and Me.. We've come this far since Year 2005, braving lots of obstacles...

but luckily, we're still together after all these years.. perhaps these obstacles are a test to make us closer together? whatever the reason is, i hope, we'll still remain loving all the time (even till we grow old)... i will be there for u if u ever need me.. we shall be best friends and best couple together k! :D

kk, shall end up.. cya tmrw, my dear.. Happy New Year to you in advance! Love you lotsssss! ^^

Written by: "Serene-the-Great".. muahahaa... x)

Random Randomness

2009-07-02T22:56:00.002+08:00

Project Index Season 1 Opening: Kawada Mami Psi-Missing

Code Geass Season 1 Opening: Colors-Flow

Code Geass Season 1 Ending: Ali Project-Yuukyou Seishunka

D-Gray Man: Yumi Morita Kusakari - Tsunaida te ni Kiss wo

The Tower of Druaga, Opening & Ending

Chen Jia Wei... RIP bro......

2009-05-19T22:08:00.004+08:00

Chen Jia Wei, 6th Guy from the Left with Mouth wide Open...

He was a good friend, study buddy, and occasionally a funny joker in our group. For the past 7 years that we knew him, he was always an easy going guy, never complained about anything. Many times he gave names and we disturbed each other in class, but that's what made going to school more colorful; each day isn't the same. Pleasant guy, always spinning his pen... Clumsy fella he was too, during NAPFA standing broad jump tests on one occassion he fell on his butt during the first jump, quickly he just stood up laughing. Things he didn't knew and needed help to learn, he would approach us. He was a Jovial guy; that was when we were all in Secondary School.

He retained for a year to retake O'lvls (damn, I can't imagine the papers got it wrong and stated he took N lvls TWICE wtf!!), which then he went on to Republic Polytechnic, Diploma in Business Administration. There however, we heard that people wasn't used to his character, he might have been the butt of jokes. That aside, a few months before this incident he went to church... made a couple of friends there but some on the surface accepted him, but at his back said some bad things (that unfortunately... is human nature, and I hate christians!). I do not want to jump into conclusions, but if I were him, I would really feel a kind of a social reject. However his brothers are still here, Munesh MaoQuan WeiLiang Faizal JinHui PohHeng KengHei JianPing YongJian and me, but I might have missed out on a few more, at least he could've told us about his problems? After graduation from SSS we occasionally hanged out, esp during each year's Christmas and New Year. The last conversation I had with him was on April the 2nd week about his studies and FYP, which he told me he was doing fine, and even gave me thumbs up for me getting Gold for my own FYP... he was really.... a good person, but personally I'm unhappy that he had to go this far to seal himself from us... thinking back, he hadn't told us any of his life's problems had he? It might've been a ticking timebomb ever since we knew it, but none of us realised... he was just too jovial... ...

I still couldn't come to grips at this reality, now that a certain brother and laughter is gone. Munesh and me agrees on this. Sighs.

Anyway that aside, I would really wish for him to be at peace. And may God forgive the actions done...

We will, miss him.

Achmed the Dead Terrorist

2009-05-04T22:26:00.000+08:00

ROFLLL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Consequences

2009-05-04T20:51:00.005+08:00

Well, personal information can be used against you. Be it Friendster, Facebook, Blogs and anything that reveals your personal information to the public.

Anyway the case is this, Short & Sweet: This guy was working in Sakae Sushi, Served the customer something with tonnes of Wasabi? Stomachache later I guess.

Here's the video link http://www.zshare.net/download/59120579ac2779a6/ (Which he personally took off from youtube already.)

And the forum's thread link. http://forums.hardwarezone.com.sg/showthread.php?t=2347904

So in short, don't reveal too much about yourself. :P

Anyway, time to do some reports.

Humour me...

2009-05-04T10:53:00.003+08:00

Tired, so I'll just let the pics do the talking.

Funny blog here... http://keboch.wordpress.com/2008/06/03/

Macbook Air gets Smashed!! ($2-3k?)

Schrodinger's Cat

2009-04-03T20:44:00.002+08:00

Schrödinger's cat is a thought experiment, often described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics being applied to everyday objects. The thought experiment presents a cat that might be alive or dead, depending on an earlier random event. In the course of developing this experiment, he coined the term Verschränkung (entanglement).

Schrödinger's Cat: A cat, along with a flask containing a poison, is placed in a sealed box shielded against environmentally induced quantum decoherence. If an internal Geiger Counter detects radiation then the flask is shattered, releasing the poison which kills the cat. Quantum mechanics suggests that after a while the cat is simultaneously alive and dead. Yet, when we look in the box, we see the cat either alive or dead, not a mixture of alive and dead.

Schrödinger's thought experiment was intended as a discussion of the EPR article, named after its authors: Einstein, Podolsky and Rosen in 1935. The EPR article had highlighted the strange nature of quantum superpositions. Broadly stated, a quantum superposition is the combination of all the possible states of a system (for example, the possible positions of a subatomic particle). The Copenhagen interpretation implies that the superposition undergoes collapse into a definite state only at the exact moment of quantum measurement.

Schrödinger and Einstein had exchanged letters about Einstein's EPR article, in the course of which Einstein had pointed out that the quantum superposition of an unstable keg of gunpowder will, after a while, contain both exploded and unexploded components.

To further illustrate the putative incompleteness of quantum mechanics, Schrödinger applied quantum mechanics to a living entity that may or may not be conscious. In Schrödinger’s original thought experiment he describes how one could, in principle, transform a superposition inside an atom to a large-scale superposition of a live and dead cat by coupling cat and atom with the help of a ‘‘diabolical mechanism.’’ He proposed a scenario with a cat in a sealed box, where the cat's life or death was dependent on the state of a subatomic particle. According to Schrödinger, the Copenhagen interpretation implies that the cat remains both alive and dead until the box is opened.

The thought experiment

Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; quite the reverse: the thought experiment serves to illustrate the bizarreness of quantum mechanics and the mathematics necessary to describe quantum states. Intended as a critique of just the Copenhagen interpretation—the prevailing orthodoxy in 1935—the Schrödinger cat thought experiment remains a topical touchstone for all interpretations of quantum mechanics; how each interpretation deals with Schrödinger's cat is often used as a way of illustrating and comparing each interpretation's particular features, strengths and weaknesses.

Schrödinger wrote:

"One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks."

The above text is a translation of two paragraphs from a much larger original article, which appeared in the German magazine Naturwissenschaften ("Natural Sciences") in 1935.

Schrödinger's famous thought experiment poses the question: when does a quantum system stop existing as a mixture of states and become one or the other? (More technically, when does the actual quantum state stop being a linear combination of states, each of which resembles different classical states, and instead begins to have a unique classical description?) If the cat survives, it remembers only being alive. But explanations of the EPR experiments that are consistent with standard microscopic quantum mechanics require that macroscopic objects, such as cats and notebooks, do not always have unique classical descriptions. The purpose of the thought experiment is to illustrate this apparent paradox: our intuition says that no observer can be in a mixture of states, yet the cat, it seems from the thought experiment, can be such a mixture. Is the cat required to be an observer, or does its existence in a single well-defined classical state require another external observer? Each alternative seemed absurd to Albert Einstein, who was impressed by the ability of the thought experiment to highlight these issues; in a letter to Schrödinger dated 1950 he wrote:

"You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality—if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established. Their interpretation is, however, refuted most elegantly by your system of radioactive atom + amplifier + charge of gun powder + cat in a box, in which the psi-function of the system contains both the cat alive and blown to bits. Nobody really doubts that the presence or absence of the cat is something independent of the act of observation."

Note that no charge of gunpowder is mentioned in Schrödinger's set-up, which uses a Geiger counter as an amplifier and hydrocyanic poison instead of gunpowder; the gunpowder had been mentioned in Einstein's original suggestion to Schrödinger 15 years before, and apparently Einstein had carried it forward to the present discussion.

In the Copenhagen interpretation of quantum mechanics, a system stops being a superposition of states and becomes either one or the other when an observation takes place. This experiment makes apparent the fact that the nature of measurement, or observation, is not well defined in this interpretation. Some interpret the experiment to mean that while the box is closed, the system simultaneously exists in a superposition of the states "decayed nucleus/dead cat" and "undecayed nucleus/living cat", and that only when the box is opened and an observation performed does the wave function collapse into one of the two states. More intuitively, some feel that the "observation" is taken when a particle from the nucleus hits the detector. This line of thinking can be developed into Objective collapse theories. In contrast, the many worlds approach denies that collapse ever occurs.

Steven Weinberg said:

"All this familiar story is true, but it leaves out an irony. Bohr's version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wavefunction (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?

Considerable progress has been made in recent years toward the resolution of the problem, which I cannot go into here. It is enough to say that neither Bohr nor Einstein had focused on the real problem with quantum mechanics. The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wavefunction, the Schrödinger equation, to observers and their apparatus."

Everett's many-worlds interpretation & consistent histories

In 1972 Hugh Everett formulated the many-worlds interpretation of quantum mechanics, which does not single out observation as a special process. In the many-worlds interpretation, both alive and dead states of the cat persist, but are decoherent from each other. In other words, when the box is opened, that part of the universe containing the observer and cat is split into two separate universes, one containing an observer looking at a box with a dead cat, one containing an observer looking at a box with a live cat.

Since the dead and alive states are decoherent, there is no effective communication or interaction between them. When an observer opens the box, they become entangled with the cat, so observer-states corresponding to the cat being alive and dead are formed, and each can have no interaction with the other. The same mechanism of quantum decoherence is also important for the interpretation in terms of Consistent Histories. Only the "dead cat" or "alive cat" can be a part of a consistent history in this interpretation.

Roger Penrose criticizes this:

"I wish to make it clear that, as it stands this is far from a resolution of the cat paradox. For there is nothing in the formalism of quantum mechanics that demands that a state of consciousness cannot involve the simultaneous perception of a live and a dead cat".

although the mainstream view (without necessarily endorsing many-worlds) is that decoherence is the mechanism that forbids such simultaneous perception.

A variant of the Schrödinger's Cat experiment known as the quantum suicide machine has been proposed by cosmologist Max Tegmark. It examines the Schrödinger's Cat experiment from the point of view of the cat, and argues that this may be able to distinguish between the Copenhagen interpretation and many worlds.

The Ensemble Interpretation states that superpositions are nothing but subensembles of a larger statistical ensemble. That being the case, the state vector would not apply to individual cat experiments, but only to the statistics of many similarly prepared cat experiments. Proponents of this interpretation state that this makes the Schrödinger's cat paradox a trivial non issue.

This interpretation serves to discard the idea that a single physical system in quantum mechanics has a mathematical description which corresponds to it in any way. The problem should be renamed Schrödinger's cats.

Objective collapse theories

According to objective collapse theories, superpositions are destroyed spontaneously (irrespective of external observation) when some objective physical threshold (of time, mass, temperature, irreversibility etc) is reached. Thus, the cat would be expected to have settled into a definite state long before the box is opened. This could loosely be phrased as "the cat observes itself", or "the environment observes the cat".

Objective collapse theories require a modification of standard quantum mechanics, to allow superpositions to be destroyed by the process of time-evolution.

In theory, since each state is determined by the one previous to it, and that from its previous state, ad infinitum, pre-determination for every state would have been achieved instantaneously from the initial "threshold" of the Big Bang.[citation needed] Thus the state of the dead or alive cat is not determined by the observer; it has already been pre-determined from the initial moments of the universe and the ensuing states that have successively led up to the state referenced in this thought experiment.

The experiment is a purely theoretical one, and the machine proposed is not known to have been constructed. Analogous effects, however, have some practical use in quantum computing and quantum cryptography. It is possible to send light that is in a superposition of states down a fiber optic cable. Placing a wiretap in the middle of the cable which intercepts and retransmits the transmission will collapse the wavefunction (in the Copenhagen interpretation, "perform an observation") and cause the light to fall into one state or another. By performing statistical tests on the light received at the other end of the cable, one can tell whether it remains in the superposition of states or has already been observed and retransmitted. In principle, this allows the development of communication systems that cannot be tapped without the tap being noticed at the other end. This experiment can be argued to illustrate that "observation" in the Copenhagen interpretation has nothing to do with consciousness (unless some version of Panpsychism is true), in that a perfectly unconscious wiretap will cause the statistics at the end of the wire to be different. Such a test would only work if the collapse occurs after (as opposed to before) observation, otherwise it would appear collapsed whether it had been wiretapped or not.

Although discussion of this thought experiment talks about two possible states (cat alive and cat dead), in reality there would be a huge number of possible states, since the temperature and degree and state of decomposition of the cat would depend on exactly when and how, as well as if, the mechanism was triggered, as well as the state of the cat prior to death.

In another extension prominent physicists have gone so far as to suggest that astronomers observing dark matter in the universe during 1998 may have "reduced its life expectancy" through a pseudo-Schrödinger's cat scenario, although this is a controversial viewpoint.[9][10]

Another variant on the experiment is Wigner's friend, in which there are two external observers, the first who opens and inspects the box and who then communicates their observations to a second observer. The issue here is, does the wave function collapse when the first observer opens the box, or only when the second observer is informed of the first observer's observations? Another extension is a scenario where the inside of the box is videotaped, and played to an audience at a later time, or played back to the cat while in the box. If dead there would be no observer to cause detanglement, if alive detanglement would occur.

Superstrings

2009-04-03T20:24:00.003+08:00

Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings. It is considered one of the most promising candidate theories of quantum gravity. Superstring theory is a shorthand for supersymmetric string theory because unlike bosonic string theory, it is the version of string theory that incorporates fermions and supersymmetry.

The deepest problem in theoretical physics is harmonizing the theory of general relativity, which describes gravitation and applies to large-scale structures (stars, galaxies, super clusters), with quantum mechanics, which describes the other three fundamental forces acting on the atomic scale.

The development of a quantum field theory of a force invariably results in infinite (and therefore useless) probabilities. Physicists have developed mathematical techniques (renormalization) to eliminate these infinities which work for three of the four fundamental forces – electromagnetic, strong nuclear and weak nuclear forces - but not for gravity. The development of a quantum theory of gravity must therefore come about by different means than those used for the other forces.

The basic idea is that the fundamental constituents of reality are strings of the Planck length (about 10−33 cm) which vibrate at resonant frequencies. Every string in theory has a unique resonance, or harmonic. Different harmonics determine different fundamental forces. The tension in a string is on the order of the Planck force (1044 newtons). The graviton (the proposed messenger particle of the gravitational force), for example, is predicted by the theory to be a string with wave amplitude zero. Another key insight provided by the theory is that no measurable differences can be detected between strings that wrap around dimensions smaller than themselves and those that move along larger dimensions (i.e., effects in a dimension of size R equal those whose size is 1/R). Singularities are avoided because the observed consequences of "Big Crunches" never reach zero size. In fact, should the universe begin a "big crunch" sort of process, string theory dictates that the universe could never be smaller than the size of a string, at which point it would actually begin expanding.

Our physical space is observed to have only three large dimensions and—taken together with time as the fourth dimension—a physical theory must take this into account. However, nothing prevents a theory from including more than 4 dimensions, per se. In the case of string theory, consistency requires spacetime to have 10, 11 or 26 dimensions. The conflict between observation and theory is resolved by making the unobserved dimensions compactified.

Our minds have difficulty visualizing higher dimensions because we can only move in three spatial dimensions. One way of dealing with this limitation is not to try to visualize higher dimensions at all, but just to think of them as extra numbers in the equations that describe the way the world works. This opens the question of whether these 'extra numbers' can be investigated directly in any experiment (which must show different results in 1, 2, or 2+1 dimensions to a human scientist). This, in turn, raises the question of whether models that rely on such abstract modelling (and potentially impossibly huge experimental apparatus) can be considered scientific. Six-dimensional Calabi-Yau shapes can account for the additional dimensions required by superstring theory. The theory states that every point in space (or whatever we had previously considered a point) is in fact a very small manifold where each extra dimension has a size on the order of the Planck length.

Superstring theory is not the first theory to propose extra spatial dimensions; the Kaluza-Klein theory had done so previously. Modern string theory relies on the mathematics of folds, knots, and topology, which were largely developed after Kaluza and Klein, and has made physical theories relying on extra dimensions much more credible.

The five consistent superstring theories are:

The type I string has one supersymmetry in the ten-dimensional sense (16 supercharges). This theory is special in the sense that it is based on unoriented open and closed strings, while the rest are based on oriented closed strings.

The type II string theories have two supersymmetries in the ten-dimensional sense (32 supercharges). There are actually two kinds of type II strings called type IIA and type IIB. They differ mainly in the fact that the IIA theory is non-chiral (parity conserving) while the IIB theory is chiral (parity violating).

The heterotic string theories are based on a peculiar hybrid of a type I superstring and a bosonic string. There are two kinds of heterotic strings differing in their ten-dimensional gauge groups: the heterotic E8×E8 string and the heterotic SO(32) string. (The name heterotic SO(32) is slightly inaccurate since among the SO(32) Lie groups, string theory singles out a quotient Spin(32)/Z2 that is not equivalent to SO(32).)

Chiral gauge theories can be inconsistent due to anomalies. This happens when certain one-loop Feynman diagrams cause a quantum mechanical breakdown of the gauge symmetry. The anomalies were canceled out via the Green-Schwarz mechanism.

Please note that the number of superstring theories given above is only a high-level classification; the actual number of mathematically distinct theories which are compatible with observation and would therefore have to be examined to find the one that correctly describes nature is currently believed to be at least 10500 (a one with five hundred zeroes). This has given rise to the concern that supersting theories, despite the alluring simplicity of their basic principles, are, in fact, not simple at all, and according to the principle of Occam's razor perhaps alternative physical theories going beyond the Standard Model should be explored. This is aggrevated by the fact that it is exceedingly hard to make predicitions from any supersting theory which can be falsified by experiment, and in fact no current superstring theory makes any falsifiable prediction.

General relativity typically deals with situations involving large mass objects in fairly large regions of spacetime whereas quantum mechanics is generally reserved for scenarios at the atomic scale (small spacetime regions). The two are very rarely used together, and the most common case in which they are combined is in the study of black holes. Having "peak density", or the maximum amount of matter possible in a space, and very small area, the two must be used in synchrony in order to predict conditions in such places; yet, when used together, the equations fall apart, spitting out impossible answers, such as imaginary distances and less than one dimension.

The major problem with their congruence is that, at sub-Planck (an extremely small unit of length) lengths, general relativity predicts a smooth, flowing surface, while quantum mechanics predicts a random, warped surface, neither of which are anywhere near compatible. Superstring theory resolves this issue, replacing the classical idea of point particles with loops. These loops have an average diameter of the Planck length, with extremely small variances, which completely ignores the quantum mechanical predictions of sub-Planck length dimensional warping, there being no matter that is of sub-Planck length.

Kaluza-Klein Theory Overview

2009-03-31T23:14:00.002+08:00

Another great theory... if only my maths didnt sucked...

In physics, Kaluza–Klein theory (or KK theory, for short) is a model that seeks to unify the two fundamental forces of gravitation and electromagnetism. The theory was first published in 1921 and was proposed by the mathematician Theodor Kaluza who extended general relativity to a five-dimensional spacetime. The resulting equations can be separated out into further sets of equations, one of which is equivalent to Einstein field equations, another set equivalent to Maxwell's equations for the electromagnetic field and the final part an extra scalar field now termed the "radion".

A splitting of five-dimensional spacetime into the Einstein equations and Maxwell equations in four dimensions was first discovered by Gunnar Nordström in 1914, in the context of his theory of gravity, but subsequently forgotten. In 1926, Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of very small radius, so that a particle moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension. This extra dimension is a compact set, and the phenomenon of having a space-time with compact dimensions is referred to as compactification.

In modern geometry, the extra fifth dimension can be understood to be the circle group U(1), as electromagnetism can essentially be formulated as a gauge theory on a fiber bundle, the circle bundle, with gauge group U(1). Once this geometrical interpretation is understood, it is relatively straightforward to replace U(1) by a general Lie group. Such generalizations are often called Yang–Mills theories. If a distinction is drawn, then it is that Yang–Mills theories occur on a flat space-time, whereas Kaluza–Klein treats the more general case of curved spacetime. The base space of Kaluza–Klein theory need not be four-dimensional space-time; it can be any (pseudo-)Riemannian manifold, or even a supersymmetric manifold or orbifold or even a noncommutative space.

As an approach to the unification of the forces, it is straightforward to apply the Kaluza-Klein theory in an attempt to unify gravity with the strong and electroweak forces by using the symmetry group of the Standard Model, SU(3) × SU(2) × U(1). However, an attempt to convert this interesting geometrical construction into a bona-fide model of reality founders on a number of issues, including the fact that the fermions must be introduced in an artificial way (in nonsupersymmetric models). Nonetheless, KK remains an important touchstone in theoretical physics and is often embedded in more sophisticated theories. It is studied in its own right as an object of geometric interest in K-theory.

Even in the absence of a completely satisfying theoretical physics framework, the idea of exploring extra, compactified, dimensions is of considerable interest in the experimental physics and astrophysics communities. A variety of predictions, with real experimental consequences, can be made (in the case of large extra dimensions/warped models). For example, on the simplest of principles, one might expect to have standing waves in the extra compactified dimension(s). If an extra dimension is of radius R, the energy of such a standing wave would be E = nhc / R with n an integer, h being Planck's constant and c the speed of light. This set of possible energy values is often called the Kaluza–Klein tower.

Examples of experimental pursuits include work by the CDF collaboration, which has re-analyzed particle collider data for the signature of effects associated with large extra dimensions/warped models.

Brandenberger and Vafa have speculated that in the early universe, cosmic inflation causes three of the space dimensions to expand to cosmological size while the remaining dimensions of space remained microscopic.

The space is compactified over the compact set

C

and after Kaluza-Klein decomposition, we have an effective field theory over M.

The fifth dimension is a compact space, and is called the compact dimension. The phenomenon of having a higher-dimensional manifold where some of the dimensions are compact is referred to as compactification. Compactification does not produce group actions on chiral fermions except in very specific cases: the dimension of the total space must be 2 mod 8 and the G-index of the Dirac operator of the compact space must be nonzero [1].

The above development generalizes in a more-or-less straightforward fashion to general principal G-bundles for some arbitrary Lie group G taking the place of U(1). In such a case, the theory is often referred to as a Yang-Mills theory, and is sometimes taken to be synonymous. If the underlying manifold is supersymmetric, the resulting theory is a supersymmetric Yang–Mills theory.

Chaos Theory Overview

2009-03-31T23:01:00.003+08:00

Beginning of the insensible.

In mathematics, chaos theory describes the behavior of certain dynamical systems – that is, systems whose states evolve with time – that may exhibit dynamics that are highly sensitive to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, which manifests itself as an exponential growth of perturbations in the initial conditions, the behavior of chaotic systems appears to be random. This happens even though these systems are deterministic, meaning that their future dynamics are fully defined by their initial conditions, with no random elements involved. This behavior is known as deterministic chaos, or simply chaos.

Chaotic behavior is also observed in natural systems, such as the weather. This may be explained by a chaos-theoretical analysis of a mathematical model of such a system, embodying the laws of physics that are relevant for the natural system.

Chaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices. Observations of chaotic behavior in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and molecular vibrations. Everyday examples of chaotic systems include weather and climate. There is some controversy over the existence of chaotic dynamics in plate tectonics and in economics.

Systems that exhibit mathematical chaos are deterministic and thus orderly in some sense; this technical use of the word chaos is at odds with common parlance, which suggests complete disorder. A related field of physics called quantum chaos theory studies systems that follow the laws of quantum mechanics. Recently, another field, called relativistic chaos, has emerged to describe systems that follow the laws of general relativity (Einstein's Theory of General Relativity)

If.

2009-03-23T13:44:00.003+08:00

Everyone's living in this peaceful world. So much so that they've been so accustomed to it. To them, there're just... living in this world. Getting into small fights over ego. Putting self first. What is friendship? It's just so easily broken. When cracks appear, people will just give up. That's the resolve this generation has. That's the spirit, that's their commitment... their "I will not stay till the end" rule. No honor, no self-sacrifice...

It might have been better if the world is embrioled in anarchy. Gangsterism and no-rules era would suffice. These people will then know the hardships. Maybe we're here in Singapore, a tiny island that is so 'secure' that everyone's life is not threathened. In other words, pampered. They don't know how important the people around them are... to them, friends are just people walking by the street... it's just to know once, and walk away... brothers-in-arms? Extremely rare.

Or maybe I'm just too outdated. Maybe there isn't such things like them anymore. These beliefs I hold, I will protect. Even when people around me break their oaths... that is my resolve. These answers will just be known in death... as at moment of death, decisions from your life's experiences can be made.

But I really wonder... why my resolve for the past months dropped... maybe personally, I've became more lazy and harbour selfish thoughts. It's really human to do so though... but at least I've found out now. I've to work rebuilding my resolve now... I won't give up easily... thanks Faisal, for letting me know that I'm actually acting like that.

Now just a little more dose of discipline...

no comment

2009-03-23T13:35:00.002+08:00

As usual, just some plans. Not what I'm deeply thinking...

Planning to sell my computer and downgrade... it was really impulse buying the last time, purchasing stuffs that are nice looking and high-spec-ed, stuffs which I don't need. Impulse buying... signs. Also am underutilising them, didn't use the computer much the past weeks. If it's NS, worst. And I have a retarded 5.1 soundcard... selling it too...

Tuesday RMA harddrives.

Wednesday Gym.

Hopefully I am able to find a job within this week. Need to burn my time and thoughts away... kept spacing out.

recap...

2009-03-22T22:09:00.003+08:00

I've not touched on why I've even decided to create and maintain a blog till now... Well... it occurred to me once when I started this blog, I will have to state the exact purpose of this blog so any statements here will not deviate from the blog's purpose... but somehow I just forgot about this along the way. Well. Expected.

So the purpose..? Basically to pass some time, speak out my mind and comment on stuff's that's either at times trivial or annoying. This blog has never touched on my personal emotions ever before, and I really do hope it will stay this way. Better to keep everything myself, and letting only the people I know about the stuff's that I'm going through and thinking, instead of letting everyone to see. Maybe I have enemies, I am not sure. Because even if I have, I would tend to just totally ignore them... and so if they're reading this blog, tough luck... they won't know anything more about me. Except maybe the things they want to think that I am, such that they will feel happy. Let them be for all I care... So it's just only thing's that are of non-importance to my life will be mentioned here.

Maybe I'm too conservative. I don't know... Is it that I don't want too many people to know me? I didn't like being in any limelight in the first place. So maybe naturally, I'd just keep things to myself most of the time. I restrict the information I send. For example, I didn't even display my Birth Date here. If anyone's noticed. An email if it is weak, can easily be hacked using your own birth date. Even USA Texas governor Sarah Palin's official email got hacked into. That explain loads, that's why information is very limited here.

Anyway OT, just yesterday, I've involved myself into an extremely complicated issue. I have no choice but to do so... after 2 weeks of 'escaping' requests from the people I know to speak the truth out. Ok, will stop here... it's really an annoying matter, freaking long story. It started off when someone just pissed another, and their egoes made them quarrel like faggots in forums. I definitely wanted to stay out of it, but I am totally forced to interfere in it. If you wanna know, it's all here...

http://forums.sigmagamehosting.com/index.php/topic,447.0.html

http://forums.sigmagamehosting.com/index.php/topic,448.msg1352.html#msg1352

Even when I don't mention things here, it's not like it's not on my mind... Some matters that remains private, will stay.

"Assuming is the one worst mistake that can ever be made."

72nd CIBTC J'07

My life's always in a mess. Maybe... no one can help me except myself... my mom's words. I will make things right... trust me...

the tooth fairy

2009-03-19T19:11:00.002+08:00

HEHEHEHEHEH... my sister had her tooth extracted today! Root length: 1 inch long? Am now making fun of her... wahahaha... reduce stress too. Maybe. (She just asked me to shut up while I'm typing this, angrily waving her extracted tooth in front of my monitor and bobbing my head up and down in protest...) Hoped the dentist didnt had a hard time extracting that tooth (Heave-Ho!).

Well, also went to Faisal's house today. Gosh... his computer temps hit easily a ONE-OH-OH DEGREES CELSIUS. 100!!! Scary lar... that's bloody hot. Reccomended him to add fans into his chassis as his computer didnt have any exhaust fan at all (All the heat is trapped in the casing).

Oh, and it just dawned to me that maybe the thermal paste on his heatsinks went EOL (End of Life). Maybe that explains the high temperatures too.

Tomorrow exam. Just enjoy another day first... (How many days am I going to enjoy -.-)

wtf titles again!

2009-03-18T11:31:00.005+08:00

Finally... graduated. That's all I need to know. And filled with mixed feelings though. Don't know how to express them, but anyway that's all that is needed to know to proceed on.

Graduate and choices to choose that decides the next path in life. Reminds me, the many choices made in life determines you, the way you live, react, and all sorts of things. The choices... yea...

20 years passed in a blink of an eye, when work starts, it'll be even faster. That sums up for the morning. Ja.

So tomorrow...

2009-03-17T23:48:00.003+08:00

It's something that comes too fast.

3 weeks of break, or so it seemed. Tomorrow will be a day that decides how many paths will be available.

Well, that is, in a sense. There're other, broader, and extreme solutions to consider... but it'll not be in the equations for now.

Somewhat, I just feel the variables are more than the constants and that, Shrodinger's Cat... just makes things really unpredictable.

To sum it up, it's a Two or Three.

yawns. titles again...

2009-03-16T21:43:00.002+08:00

My OS's getting freaking unstable... from Blue Screen of Death to debug LED number 75. Most probably going to RMA my system disc and reformat again for the third time in 3 weeks. Annoyance.

Worked at the IT fair. Mediocre, nothing much there. Well everything seems this way now. Weird, looking forward to NS. In a sense it wouldn't beat boredom right now here. I cant forget. Has everything been done's useless? The truth is being hidden or faked?

Forget it. Just find another job. Not a scam job hopefully.

titles..? nah can't think of one.

2009-03-11T19:44:00.006+08:00

Nothing much to add, quitted my job in less than a day. Scam job zzz... anyway, I still have a temp-job to fall back on. IT Fair Exhibitor, again that is... so don't expect me to blog again anytime soon for the next 4-5 days...

Anyways, here's some pic's for you to enjoy... my completed mini project. Took 6 days to complete and done nicely.

My previous ASUS EAH4870 1GB Card. Loved the Heatsink design.

Powdercoating! Some secluded place in Defu Lane.

Results of Powdercoat: Brand New!

Hardware Testing (Temperature, Voltage and Stability)

Fixing the 'organs' into the 'body'.

Say NO to Seagate, Big Welcome to Western Digital! Extremely Stable HDDs.

Dang! Something's wrong again.

Assembling... 1 Full Day 'cause of cable management.

Second Trial Run.

Everything's fine! Custom Acrylic Window made.

Mounted the final BLUE CCFL at the top.

Final Product: Blue Themed

Shot taken with CCFL UV lights off.

LED Blue dazzle.

The Asus EAH4870X2 2GB card. Monstrously heavy and a power watt hogger.

Here's another musical piece played on Piano... wah!

Post?

2009-03-08T22:51:00.001+08:00

Exam results' be out on the 18'th March.

Happened to chance upon this while searching for Opening Songs (OP). This's from the OP of Bokurano, doesn't seem interesting to watch but the OP's nice. Not the scenematics, the song being played in piano... though I don't understand what the song's about the symphony's nice. Classic ftw!

The second one's from Ga Rei's OP.

Bokurano OP Full

Ga Rei: Zero OP

Closure of a Chapter opens yet Another

2009-03-06T20:01:00.002+08:00

Back to blogging after a long break.

Seems weird, but recently I've stopped looking forward to holidays. There's alot of uncertainty, closure of a chapter opens yet another. The other chapter is one that should be walked alone? I think so. Life's decisions are decided by oneself, and it should be respected by others. No one can influence you. I will not elaborate but these has been in my thoughts since the past week.

Anyway just completed my own personal mini-project, which is refurbishing my computer hardware..? Will post some pictures soon. Reformatting the third time in five days, I hope the software limitations of the Microsoft Vista 32 bit will be remedied by 64bit Operating System.

I guess my circadian rhythm's messed up. Still feeling tired after 1 week of rest, late sleeps and waking up that is. Currently looking for jobs, ain't really used to having so much free time. It gets really bored after awhile doing nothing. Gaming just pauses life's problems... that's what I realised long ago. Am really disappointed that instead of discouraging, I'm being encouraged to continue... but well, am looking for a job already so no point in worrying!

I've lagged too far behind now. It should be time to saddle up and make a go. It must be. Thanks for the encouragement today brothers. :)

Happy Lunar New Year! And it's the F-22s, too!

2009-01-26T11:56:00.002+08:00

Today I'll let the pictures speak for itself. :)

A sense of Calm before the Storm: Chinese New Year!

2009-01-25T13:51:00.002+08:00

It's Chinese New Year's eve today. Not in a celebratory mood though, it's 3 more weeks to exams. Which means in 2 weeks I'll have to be proficient in all modules to score the As... hmm. Not quite there yet but should be able to hit expectations.

Schedules planned and drawn up, it seems that I'll be hardly left with any spare time the coming weeks. Weekends will be the very little personal time left to recuperate and relax. Anyway, I can't be bothered with people who are so selfish such that they don't consider my plans and keep pressing their schedule onto mine. Hell, it's like wtf. It's my future that's at stake here, not your's. If you don't respect my decision, leave... since you ain't bothered about my future, why should I in any way care for yours?

That's what I see as a trend in alot of youth these days: "Convenience Friendships": making friends just to have times of fun together, breaking that bond once the differences starts to appear. Heh, that's pretty fragile isn't it? In depth, one can see the level of commitment and character on a personal scale...

Anyway, the real stuff's in today's post's is something I would like to take in. As a hobby maybe, and expensive it is.

Desktop Rig-Modding.

Bought a little Fluroscent tubings, and I'm gonna purchase some LED lightings and UV reactive equipment. However, I will mod them after my exams! Sadly I will have to daydream about them till the day comes... Here are some nice examples of Rig-Modding.

That's all. And Faisal's pesting me to take a bathe now. -.- Signing out.

Hibernating... Again.

2009-01-14T15:00:00.003+08:00

Past week has been real... ... couldn't find the real words for it. Project's prototyping and finishing phases are FINALLY over after like 8 months. Right now's one final week of compiling reports, before we have Project V.I.V.A. taking place one week ahead of official schedule (to give ourselves mroe time to study for the exams). Out of a few hundred projects in SPinnovex and others that weren't selected for the exhibit, Skybox's got us a Gold, and I think that's a feat. Our rival team also obtained a gold. Our supervisor's gonna be damn happy, the cause for jubilation? 10% of the golds this year went to his projects. haha... Skybox and Shawk. Well, I don't know what does FYP stands for, not anymore. Anyway, hey my project's featured officially in SP webby. Though it's really, lame music in the background. Spoils the mood lol.

http://www.sp.edu.sg/SPweb/appmanager/home/default?_nfpb=true&_pageLabel=SP_FS_Courses_MME_FT_AE

Still, there're like tonnes of work awaiting. Notes that had been stacked and work being delayed due to rushing of exhibits and projects, and also some really time wasting events that had occured recently.

Will not be updating this blog until my final exams are over. It's time to start purely stressing to study and stop relaxing. With some luck I might be able to hit 3.1GPA...

Preparation for Exhibition

2009-01-06T20:10:00.006+08:00

This's more or less the exhibition area that my project will be displayed in for the next four days.

Behind the Skybox is the Shawk, that particular UAV was initially OUR PLAN!!! Stolen by them after we ditched it. :( But cheers to them though. They have more manpower (5), our group only have 4.

Here's the original video taken by Jin Hao. ^^

Enjoy, signing out!

?

2009-01-05T20:02:00.007+08:00

A great start into the new year. Nothing much can be said, it just seems bleak. And more bleak. And more and more bleak. Whatever.

Just completed the flyers today. Here it is! Can I say it's 95% my work? ><

Helped Mr Agility Skill (NEW ACRONYM!) & Technique with his proposals last night @ Indian Court. lol both of us kept confusing ourselves with HDB (Housing Development Board) and HPB (Health Promotion Board). Kinda funny actually.

Spent $80 just on clothes for upcoming exhibition... I feel its just a freaking waste of money. Spent another $380 today 'cause of some matters. Freak man... I'm outta cash. Zzz damn stressed.

Almost got into a car accident today. Or got into? Me right arm hit the car while I was chasing a Bus, afraid to be late for a test. Fortunately for me and the driver (a woman), I just hit against her sideview mirror. And that was a hit and run. Not the car which sped away, but me. Mind's still thinking about the fear of being late, so ignored the pain and continued chasing after the bus after waving to the driver apologetically. -.-

Anyway for the record, things just suck right now. Gotta think about it and really start to take some pre-emptive action instead of wellowing in self-pity. NO, I will not be those who indulge in self-pity. That really goes without saying.

But still, its a start to the new year. Cheers, everyone. This song's for you.

Wind Of Change - Scorpions

Steve is DEAD!

2008-12-26T18:59:00.005+08:00

Chanced upon this while researching on Thrust Reversers for different variants of the Boeing 737. A little distraction lol. Just notice how clean the MRO area is. Cleaner than my room I'd bet!

Hope this doesn't happen to anyone in real life. In actual work, the engine would be detached from the pylons anyway. =) *Ouch!* Watch @ 1min 20 secs... Steve nooo Steve!!

Also this particular video, shows the damage done to an Airbus 320 during a crosswind landing in Germany. Almost resulted in an accident.

Ok, back to work. ><

X'mas!

2008-12-25T21:32:00.003+08:00

Found a video, the manner in which the song's sung funny. LOL.

Also the completed product for the FYP.

The sunset @ East Coast Park on the 21st of December 2008. =)

That's all, back to work. Signing out

(Noob) Overclocking!

2008-12-24T12:08:00.006+08:00

Just bought some new PC parts 2 weeks ago. Bought a budget Intel Quad Processor and overclocked it! :D Overclocking gets you extra speed, and also saves you some money. These are the components I bought

Components:
--------------------
Central Proccessing Unit: Intel Core 2 Quad Q6600 Kentsfield; G0 Stepping, Factory Clock @ 2.4GHz
Mainboard: DFI LP Dark p45-T2RS Plus (Crossfire)
Memory: 2x2GB Team Xtreem Dark PC2-6400; DDR2-800Mhz @ CL4 (4-4-4-12)
Graphics Processing Unit: Powercolor 4870 PCS+ GDDR5-512MB
Power Supply Unit: Aerocool Modular Power @ 750 Watts
CPU Cooler: ASUS Silent Knight II
Harddisk: Western Digital Caviar Black (32MB Cache, 640GB)
--------------------

Cost:
--------------------
$1,331
--------------------

I bought the GPU second hand, so saved around $100. But since I sold my previous card, MSI-9600GT GDDR3-512MB OC at a loss of $97, there is relatively no savings. :) Especially when I sold my old Pentium 4 PC (Bought for $2,000) at only $135?? Sianz.

Overclocked stats

A 2.4GHz processor costs $29x+ these days. However a 2.83GHz chip costs an astronomical $520? It's like robbing your bank.

Anyway, I managed to hit 3.5GHz on this processor, but it is unstable due to mounting of CPU cooler. Tuned it to 3.1GHz and its working fine, dramatically faster. Gotta thank Dave tonnes for helping me to stablise my temperatures! Previously hit the 100 Degrees Celsius threshould (Will destroy CPU at this temperature) Mainly temperature control is done by control of voltages through many components, so I'll be looking forward to learn that when I have the time. Anyway, back to compiling my report and projects + revision for the upcoming exam.

Currently @ 3.003GPA. Already chances for scoring As for 2 modules out of 7 are gone. Guess I'm headed to a 2.9 GPA? Sian-ed. This semester looks bleak. So they said: "Core A modules are always tougher than Core B"

X'mas Mood

2008-12-24T11:41:00.004+08:00

Nothing much to add on about.

Really lost the mood to study, with all the frequenting for FYP. Complete it till looks nice, at the expense of studies, social life, commitments and health. Seriously the group leader thinks everyone is able to follow his commitment. And there he is wrong, thus he failed to lead. I've settled my stance, from now on I'll stop supporting whatever his statements are. Everytime I point out that I think thing can be done faster in a sense, he'll go and reply: the others say liao. Of course who doesn't, even when my other teamates are already like "heck it" attitude. Can't he see that they're tired of doing FYP on a daily basis? Things are right in front of him; he's just either plain blind or doesn't care really. I've given up arguing on how things should be done long ago. Playing along, that's the only thing that will make the FYP ends the "fastest" way he likes. Democracy style of his? It's veiled. I don't find him as such a motivating leader, though he tries to 'lead ' by 'example', communication wise, really turns people off. Sometimes in communicating with him, you'd find he's just plain re***d. Anyway forget about it. It's ended (with 1 week of break wasted away).

Up next:
FYP Report (Tonight)
Airframe Systems Test (28/12/2008)
CMPB Medical Checkup? (29/12/2008)
Product Design Selections Sketches x2 (30/12/2008)
Statistics PBL (02/01/2009)

That's all I know. I'm still guessing whether I missed any assignments. Jeez...

Off Tracks

2008-12-01T23:59:00.004+08:00

Nothing much really. Sat-Sun, was working for Kaira Technologies selling their Logitech stuffs. Kinda regretted getting a 4870 card; could've gotten a GTX 260 Core 216, which is better in performance with regards to the latter. It could have been a blessing in disguise however, I kinda saved a hundred bucks.

Recently, there was another Terror attack (again) by some retarded fanatics. Killed many innocent civilians. Jihad? Go to H**L. These guys aren't even muslims. The muslims I know respect their faith. Not bending the words of their faiths to their Ideology. Browse the death lists and you find many innocents, really. I wouldn't be surprised if there would be a movement against these retards as well. Would be nice to see an organisation like the IRA against the Fanatical Bast**rds. I'm just so against these mindless killings just to make a point. Such weaklings resorting to violence, really. Fortunately the mogues at Mumbai rejected the bodies of the 9 fanatics. Reason being their actions are un-Islamic. These people have no sense of honor, I believe they only have revenge on their minds instead, as their actions have shown. Islam is a victim of Terrorism... may its many true believers rid it of fanatism one day. One of the many innocents that lost their lives: Ms Lo Hwei Yen. This paragraph is dedicated to you and the many Innocents whose lives were lost on that fateful day. Rest in Peace.

Anyway the start of the week went horrible. I will not mention the name, but my class tutor pointed out about the implications of posting our project video online (Which I was even much more surprised, since when did our FYP recieved publicity?) So stunned I was, to the point of not rebutting his points. Well anyways I found out later that the link was actually forwarded to the ENTIRE SP MM STAFF. WTFZOMFG. I've however got the points to rebutt his now. Though I think the video seriously requires some editing; the music theme and overall is nice. Kudos to Alex! Here's the link.

2 ICAs today, Debate on the Topic of: Outsourcing of Aircraft Maintenance (Opposing) and Statistics. Well, for the debate seems very much a draw. Both teams had each other at their throats. Anyway, Good Luck for all of us! The class tutor will fail the "losing team". I really don't like that, even if let's say we really win, it's not really fair when the opposing team did their research well. We're D.A.R.E., for god's sake. Not some ragtag you know what. Partly that's the reason that really de-motivates us to do a research-cum-report proper. Plus the pessimistic streak of his. Very de-motivating, since Day One. Speechless. Maybe he should go for some Teaching Lessons. Get a 1st Class Honours Degree before coming to teach us and talk big about stuffs. DARE, DASE, and alot of course classes I heard, found him _____. <-- Fill in the Blank.

Statistics test? Well. Question A1- Not sure of Answer. A2-A4 same as A1. Questions B1-B4 - Just do blindly. GLHF (Good Luck Have Fun).

Also, time to go for some photoshop lessons. I badly need it. Anyone able to coach me? :D

Back... For A While

2008-11-26T21:25:00.006+08:00

Ok... Just finished a little editing of the template. Seems better and much simpler than the previous blog template.

Studying for the upcoming Quality Engineering and Management, Statistics, Aerospace Materials and Human Factors tests.

Did so many drawings this week; I guess I've become the average artist already. Dang, I'm 1 week behind time I suppose.

Kept turning down many meetings (some last minutes, some arranged the week before)... kinda sucks but couldn't help it. I got a couple of test details and dates wrong (AGAIN), so here comes a re-overhaul of the schedule. Maybe if the schedule I'd set left a little free time (for others and myself), I supposed certain things can be re-arranged. But that's not the case. Too late anyways. Sorry guys! :(

Many events happened last week, well, most of them are great. Or rather all? Will blog them when I have the time. Well below's something what you can say has gone really well. Other matters are private! Don't bother asking a million times. ^^

Working at the Expo for spare cash, in hindsight really ain't worth it. $240+ and skipping school and time that can be dedicated to studies? Bad bad bad. ARGH how could I have missed the details!!

Well anyways, time to start work. Time to control the extent of damage.

And oh. Just realised that the font is small. As in tiny. Minuscule? If you can't see it. =P