i screwed up again!

Argh something's wrong with this brain of mine...it works so slow, i couldn't complete the physics paper quickly enough...left all those "state definitions" and other open-ended word answer questions blank...then didn't have time to go back and fill them up...argh!

just wonder why i'm so stupid...why am i so slooow? [insert stuff in last post here]

i hate myself...and to seek temporary relief of my pain, i'm reading "mathematics for physicists" and trying to bluff myself by making me think i'm smart enough to understand that...yeah and perhaps 100 yrs later when i finally get it, i'd also realise my brain's too sloooow.

oh well its gonna be over...just as how Pu Yi's father said to his young crying son at his coronation, in the twilight of the Qing Dynasty. Perhaps next March i'll learn that i'm finished too...what an awful thought i cannot resist.

what can i possibly do? sigh. i hope i don't sink into depression again...i've only a month before NS catches up on me, and i'll need to find some confidence in me. So much to do to save oneself, so little time to do it. And i'm so sloooow.

math, physics and curry...drugs to cause hallucinations of achievement and high mental capability, even in the absence of. There is no cure to a painful inferiority complex in which that awful reality is projected into the inner space of my heart.

There's only math, physics, curry. Indulge in psychological analgesic.

and so it goes..

my boring life...yeah i don't know how others lead theirs, but i fear my life must seem terribly boring to many other pple...yeah i know its the exams, and exams make life dull sometimes, but oh well who cares what other pple think right? More important to have some self confidence that'll go a long way. What matters is i find what i do challenging and interesting!

spent lotsa time last night and today adding a few features to this blog, most visible being the floating links bar to the left. Well been looking at many other blogs, so interesting-looking, but mine's still a default template, though subject to some tweaking to accomodate that javascript...boy that was tough trying to make the menu float! and the mending procedures following that too!! also, i can add post notes like these * ! Yay! it works! Hopefully this comes in useful for technical articles in future!

Note:

(hide)

Testing 1,2,3.

Note:

(hide)

Peek-a-boo!!

Talking about looking at other blogs, hehe reveals my "voyeuristic tendencies". Yeah its interesting looking at what other people are posting. Like girls talking abt their boyfriends and such...haha! oops! But i'm also glad i came across some other blogs such as iraquna.blogspot.com at last i've seen the famous blog written by an iraqi as seen on the papers! I've got lots to discover in the blogger's world! *wink*

And now, for some more "random ramblings on physics for possible future use":

What sort of geometry could we be talking abt with space?
Does only "space" need to have a topology?
How abt energy too? Cycles...yin/yang...symmetry in topology, how abt topology of physical laws? Topology of a topology? Russian dolls with symmetry, i.e. the "largest" doll fits into the "smallest" one?
Laws and laws which govern laws...sets of laws applying to only particular universes...compare with eignfunctions of the schroedinger equation, and Hawking's wavefunction of the universe
Constants? Physical constants? Hmm...
why does quantum mechanics have the Planck's constant?

Some commonly made assumptions:
energy is conserved
there is a fundamental particle
existence of the Planck energy/distance/whatever else
why does the "single unified force" at higher energies have to split into 4 forces at our energy? Only 4 forces?

so much for wild questioning...perhaps they may be useful years later haha! well, if not for physics, at least to entertain the masses abt my stupidity??!

yep tt's all.

the self-contradicting loser that's me

Dammit!!! ARGH! Shit today i just found out i'm gonna lose another 6 marks! DAMMIT!!!
And they just gotta be on electronics!! It sux big time when you make mistakes on stuff that's so close to your heart...really feeling very bad...i'm so inclined to being pessimistic abt my A levels, and i wonder if i might lget B for physics instead! F*** i just cant express the anguish i feel in words. I really can't care less abt my studies and grades, but this is the A LEVELS! If i screw it up, i won't get a scholarship, i'll lose a 6-year employment opportunity that's part of the bond of the scholarship, i'll not qualify for a good university, and if i'm stuck in a local university with a stressful education and "overly pragmatic students", what's the purpose of living??? I've had enough of studying in this place! My school life has never been really happy, only the stress i've got just because i've always wanted to pursue my passions and interests. Great, so now i've lost the gamble, screwed up two years of JC life, and am paying the price for my A levels...and the doom is unfolding before my eyes!!! SHIT!(*$&%*#&$#@

sigh.

If i screw up my results, i've gotta get to plan B...which goes something like, "hey i've got this really sucky result slip here, but at least i'm smart enough to do ___________, so can you give me that chance to study at your place?? Pleeeeaaaasssszzzeeee?"

Maybe i shouldn't try too hard...maybe i wasnt made for this...i'm not supposed to do electronics or physics, cos i've got a mathematically impaired brain..yeah and i'm easily confused, have a very volatile memory, and i forget what i say 2 sentences earlier, i'm VERY careless, very stupid, lousy grades...yeah plus i'm always overly ambitious and overestimating my abilities perhaps...i mean, how can someone like me so wishfully hope to do electronics and physics, when my math SUX? how can i get anything right when i'm so CARELESS? How can i understand all that difficult stuff when i can even get my schwork in order???!!!

So does that mean i stop doing what i like doing best? does that mean i'm really too stupid? Perhaps i am...yeah i've not seen any proof of any intelligence in me...yeah so what if i can take 6 years to slowly learn QM bit by bit? If this was schwork, i bet everyone would master in it like a few yrs! That i do sth other pple dont does not show if i am capable of anything more than trying to bluff myself into thinking i've got some brains...i've really lost my self-confidence...after 6years of trying new stuff, doing things differently, have i gotten anywhere? Slaved so hard in the last two years, only to have the UAV project fail...man i've never succeeded even once! I don't even trust myself!

The truth is, i don't have any talent or particular skill...neither have i proven myself in what i've tried to do. and so now i'm wallowing in self-pity.

I hate it when pple say i'm good in physics and all that. The fact is, i'm not! I didn't study, and i got a D for my prelims. and pple still say i'm good in physics!!! Don't they understand that its making me really upset? So what if i can talk abt QM and think i know what little i know abt QM? It doesnt even matter a shit when i panic and screw up my papers or not even handle a simple mechanics question properly! All i am, is someone who's interested in physics, but really is an asshole who can't do physics properly and yet has the audacity to think he can point out inconsistencies and imcompleteness in the A level physics he's studying, or fret abt any incompleteness...yeah the truth is, its a way to hide the fact that i'm too stupid to understand physics!!! ARGH!

okay, i've scolded myself enough now. covered all the pts i've wanted to cover. now i've gotta get over my depression.

not had this feeling for a long time...

had two physics papers today! argh very scared of careless mistakes, and i know i've got some mistakes already, be they careless or due to my lousy brain...must not think about it anymore!

anyway, been really slack today...i've not done any studying the whole day...except studying string theory...haha that sounds so lame! i've only seen it for a few days, and reading some layman accounts of it...very absorbed by Michio Kaku's book, Hyperspace...yeah when i first saw that bk in the sch library, and i saw the words "10th dimension" i thought...oh no not another more-than-4 dimension popular lame and over hyped what-the-hell-is-that?! thing. I must be excused for this! after all, i'm rather tired of seeing pple so interested in relativity and einstein-is-great and sprouting abt 10, 20 or N-dimension universe parallel universe when they take up such magazines as Discover and Scientific American. Hell i had no idea what these things were! I've been rather bewildered why everyone likes to talk abt relativity! Not that i think many pple know what they're talking abt...I've totally ignored (almost completely) relativity and focused on understanding Quantum Mechanics instead. But QM books are often placed alongside things with names such as "supersymmetry", "superstrings"...and a few days ago i guess i decided i must not be left out...

So now i feel that same way as i felt 5, 6 yrs ago when i first read popular accounts abt QM...it feels intriguing, interesting, beautiful! and keeps me stuck to the book...i'm sure its a good beginning. perhaps a few yrs down the road i can start understanding more math and reading more abt the theory, which is rather new and everything's like all over the place, unlike QM where i can look at a couple of basic postulates that give me a good summary of the basic principle... dammit, i severely lack the math man! Even for QM, i'm still taking a long time to take in the stuff, reread and reread again...but i think its very very beautiful when all the things start to fall in place, no matter how slowly it happens/is happening, and when the things you read in popular accounts are starting to REALLY show up as MATH!

Anyway, i'm gonna start recording in this blog, some questions and identifying assumptions and all that...i've learnt that assumptions are very crucial things...gotta hunt down the elusive assumptions we constantly subconsciously make, to break new ground...so here goes:

what's with dimensions? What are dimensions?
Is there something more general than dimensions?

can there be more than one set of dimensions? (ie. instead of 1st,2nd...etc dimensions, could we have like the 1,5 dimension?)

Non integer numbers for dimensions? e.g. 1.5th dimension?

do the extra 6 dimensions as claimed by string theory have to be too small to see? could they also be too BIG to see? Does the difficulty or even impossibility to perceive them necessarily be due to relative sizes of dimensions?

Often a distinction has been made between the dimension of time, as a temporal dimension, as compared to that of the spatial dimensions, as in x,y,z,whatever-follows...is this distinction necessary? could time be another spatial dimension, which due to our nature, we experience it the way we do?

I like the way Hinton (as described by Kaku) talks abt the perception of a higher dimension object from a lower dimension object's perspective...

math paper

phew today's math paper2 wasn't so bad...managed to do the stuff, with not so many careless mistakes...at least i hope! then there's this notorious question 27...haha hope i did it right, but oh well...its over...yes A level Math is over!!!

although math'll probably still be with me for a long time, cos its a necessary evil for physics and electronics. if only one day, i'd discover a hidden talent in maths! that'll sure help me...but i see no sign of mathematical intuition inside me though...argh talent...i guess excessive self doubt forces any talent into hiding! but its gonna take a while b4 i regain that elusive self-confidence...its not easy after all, to recover from 2 yrs of trauma and stress and depression and loss of mental ability and then the post-traumatic stress...argh and the bipolar maniac depression syndrom...goodness it gets worse the more i say it!!

i've got abt 6 days of exam left. I've not covered my Bio option topic adequately, which is so crucial bcos i've screwed up the main paper BIG TIME. But i'll do one topic at a time, per day...
then there's physics! i'm gonna finish covering it, but i wont know if i can do well until i get some practice, and the problem is getting it done fast! That'll be the priority tmr.

Started reading up on string theory yesterday...hmm after a really long time, i'm back how i first started: reading layman nonmathematical accounts of string theory. Last time it was quantum theory...but even now i'm thinking of going back and reading a couple more accounts of quantum theory, just for fun...as for the math, well i'm hoping to get past the expansion postulate and stuff...and then perhaps start learning more math so i can really understand and do the stuff...there's so much to learn, its gonna be fun!

[INCOMPLETE ]Thermodynamics Stupidisation - Thermodynamic Processes

Okay now i'm done with characterising the ideal gas.

oops...forgot abt PV = nRT
Ideal gas equation is a relation between the macro parameters of a gas. The relation was deduced by experiment, thanks to Charles, Boyle, Guy-Lussac...who else? hmm anyway, in the previous post i've shown the equation relating the pressure to macro level parameters...which essentially is the speed of the gas particles! Equating the macro and micro equations, we have the following:
1/2Nm = 3/2NkT

Rearranging for T, we also see that temperature is due to the speed of the gas particles.

So, the implications of a gas consisting of particles moving at a certain average speed, is that, it has a certain temperature, and exerts a certain pressure, and occupies a certain volume...nice cause and effect!...

wait! i think we gotta interpret this volume-pressure thing really carefully...its quite lame talking about a gas occupying a certain fixed volume, if its not bounded by a container...after all, the gas is gonna dissipate if there was no container to hold it! How then can we talk abt volume and pressure? I think we should amend the statement above to this instead:

Given a gas consisting of particles with a total amt of internal energy U (solely kinetic energy, cos its an ideal gas we're talking abt), there is a relation between the volume in which the gas is being enclosed inside (by means of a container), the pressure it exerts, and its temperature. This relation is, well,
PV = nRT

rearranging, gives T = PV/nR
shit...how can increasing V increase temperature? NO WAY! NOt unless i give the gas energy!!
damn...so how to interpret PV = nRT? argh!!!

okay lets look at other cases (variable that's not discussed assumed to be kept constant):
P = nRT/V - increase temperature, increase pressure...well that works fine. but inc. temp must be due to some energy input right?
increase volume, decreases pressure...that's true...
V = nRT/P - increase temp, increases volume...

BUt increase volume doesn't increase temperature! unless there's energy input! argh whatever this is all getting very confusing...i suppose this is where thermodynamic processes come in...

okay...i think i get it...PV=nRT still remains true...if i could just increase volume while keeping pressure constant, temperature has to increase! Just think abt the microscopic level of things...if the gas needs to exert the same pressure, ie. the same force on the walls, the particles have gotta move faster to keep up the same rate of collision with the walls!

hence PV = nRT is an empirically proven relation between the variables of a gas. And it is logically consistent! How certain things can happen, such as increasing the volume while maintaining the pressure constant, and hence increasing the temperature, is not the business of the ideal gas equation. It just tells us that if we want to do this, the consequence has gotta be temp. increase. The rest of thermodynamics tells us how we can accomplish this.

In fact, this is in essence, the First Law of Thermodynamics! So, we want to increase volume, at constant pressure...that's called an isobaric process. For this to happen, the particles must move faster. That means more kinetic energy, hence this means the internal energy of the gas must increase! By the conservation of energy, this energy must be supplied from some source outside of the system. This implies that all our heat energy goes to increasing temperature...but we must be careful! But we first note that the first law of thermodynamics is an expression of the conservation of energy in a close system involving a gas.

We could supply heat energy so that both temperature and volume increase at constant pressure. Now that's isobaric. So what happens is that some heat energy is used by the gas to do work in expanding...the rest goes to increasing the KE of gas particles, and hence its temperature.

Another possible way is to first increase the volume, perhaps by pulling out the plunger of a syringe, and then then heating it to cause an increase in temperature. That would be TWO processes. Increasing the volume would do negative work on the gas...i.e. the gas loses internal energy. Then heating it at constant temperature would give

Thermodynamics Stupidisation - Ideal Gases

i hate this topic...yucks. its so heaty...when i think i know it, i don't...
lets see if i can put the big chunks in order...we have ideal gases, macro and micro behaviour...then we've got the actual thermodynamics that deals with gases (ideal and non-ideal) and their processes...then we have "thermal properties of materials", which really is a pretentious cover for "heat capacity, latent heat and their measurement"...hmm i think i can get started now:

Ideal Gases
Gases are one of three commonly observed states of matter (you don't see Bose-Einstein Condensates everyday do you?) i suppose its hard to define a gas, i guess (pun!! not intended...) i could say that if the particles which constitute some "thing" aren't clumped together, then its a gas i suppose.

So lots of things could be gases, if we could give them the energy to become a gas...and the particles could be complex molecules, ions...so to start out simple, and then by extrapolation deepen our understanding of gases, we start with the notion of the "idea gas"...

So here goes...An Ideal Gas is:
1. composed to infinitesimal point particles, which actually have mass! i.e. point masses
2. NO forces of attraction between gas particles, or between gas particles and any container which holds the gas. In fact, ZERO potential energy exists in the whole system.
3. the gas particles obey Newton's laws! (argh i hate Newton's laws!)

in addition, we also assume that the gas particles undergo perfectly elastic collisions with the container walls, of zero duration, and that the container is totally rigid and of infinite mass (otherwise we won't get a change-in-direction-with-no-change-in-speed particle-wall collision condition)

So, gas particles like to move around. And when they hit the walls of a container, they exert forces on those walls. This would be the pressure of the gas. So how do we figure out the pressure exerted on a container by N gas particles?

[oh well too lazy to type the derivation...i suppose i remember it..hehe]

Some problems with the theory
I think there're some problems...maybe the problem is really me, but i say that there's some incompleteness in the theory that was printed in our notes. i'll list them here:

1. It was said that the particles are in constant, random motion. However, the derivation given does not seem to be consistent with this claim. Instead, we have taken one particle, assumed it to be moving from one wall to the opposite wall, and back, and forth...and assumed that (probably by thinking this implied random motion...i beg to differ) 1/3 of the particles will oscillate between one of 3 pairs of opposite walls.
the point is that random motion really implies that the particles could travel in oblique angles such that they strike the wall at oblique angles. In such a case, the time taken to travel between consecutive walls would differ...

2. Look at the equation: P = 1/3(rho)(mean sq. speed) [darn i can't insert Greek!]
again, i say that this was based on the assumption that 1/3 of all the particles are oscillating between one of 3 pairs of opposite walls. But doesn't this only happen when all 1/3 of the particles are striking the wall simultaneously? If that does not happen, the pressure would be lower than calculated right? Well we could say that since everything happens so quickly, it would seem as if all 1/3 strike at any one time. BUT the problem with this is that, there are so many possibilities of combinations of particles striking the wall, that having all 1/3 striking simultaneously is a highly improbable event? Well, suppose we forget abt the 1st point i made above, so that the particles' motion is truly random. even so, even though we can claim that statistically, all walls get hit by the same no. of particles at almost any instant, we can't expect all the particles to be hitting the walls at the same time...i.e. there's gotta be some particles which don't touch the wall at some instant, and i've pointed out that the probability should be quite high shouldn't it? So the pressure should really be lower than what
P = 1/3(rho)(mean sq. speed) gives us...right?

stupidisation of mechanics

This studying for the A levels is getting on my nerves...i'm sick both physically and mentally and the stuff refuses to get in my head...and i've not done any practice on my papers yet! damn i don't want to end up not finishing all my papers on time anymore...2 days left man...shit

anyway, i suppose typing out the stuff as if i'm compiling notes may help me make sense of all that physics i've gotta cram...juz wonder if i can get everything done in time...i've already done some for some mechanics, but that was incomplete, and did not include a couple more examples i would like to...maybe i should address them here...then i gotta move on to thermodynamics, electricity and electromagnetism and modern physics...i love modern physics...newton's stuff stinks! i don't see how commonsensical classical physics is...i reckon that pple say its common sense because there's too many assumptions people UNKNOWINGLY make when they solve mechanics problems! I sought to address some of these deadly assumptions by digging out the axioms of classical mechanics (without bothering with the presence of electromagnetismor anything else). Then i used them to give a thorough (okay i still think its rather incomplete but adequate enough for now...hey at least i know its incomplete! not everyone who makes assumptions is aware of that!! tt pisses me off!) axiomatic treatment of some simple mechanics problems...so far everything works fine...but some problems are still pissing me off...dun wanna talk abt them now, but when i get some reasonable answers i'll add them here. I've sent this as yet incomplete treatise of classical physics to my class's mailing list...i wonder if anybody's gonna read it...or maybe they'll just heed my warning that i could confuse them, and delete it. Cos its "out of syllabus" ARGH! i hate that phrase! New to blogging...perhaps it'll take some time b4 i figure out how to put that file up here...copy and paste!??! thats 2000++ words for you man! nvm i'll get down to it...for now i gotta get down to the rest of the areas i've not touched...dis gonna be a looong night man...

urgh this is my first blog i'm so pissed and stressed i need a land of nonsense where i can type everything i'm thinking and dump all that bullshit into this pit called "nonsenseland".