|| Welcome to the Blog managed by the KVPY 2005 Batch || Twish asks members to comment on the blog MaKeOvEr!! || RG says: Looks like a famine situation here || Blog glows in bright shades || KVamPys tame their own minds... with new mysterious posts on TP ?! || What is TP after all ? || KVamPYs start thinking about their Summer Projects as the Entrances are about to end.. || IIT? IISc? IISER? KVamPYs wonder where to enjoy this summer.. || Obiwan and Sunita in ISSER || Arun awaiting replies to his letter. || Swetabh ( Bhakt ) and Abhilash trying for IIT Kanpur ( Along with Twish ) || What about the next year ? Apply again for KVPY ? || Bulbs light up as blog fills up with posts. || Latest News brought to u by Twish (Twishmay) and Rash (EMAIL US NEWS) || EvErY bOdY KnOwS..... KVamPYs RoCk!! ||

Monday, December 31, 2007

Period three implies CHAOS!





note on the title:this is the exact title to the 1975 paper by Yorke, an applied mathematician - who is credited with bringing back Lorenz' seminal work.Who was Lorenz?Read on!



We can relate pretty well to our intermediate school differential equations. And though they did not take as much toll as indefinite integration did - it all boiled down to some really frightening (and at times transparent) expressions that had to be moulded into a solvable form we knew of and follow the old techniques.
But we have heard of seldom-encountered-but-know-they-are-there type of UNSOLVABLE differential equations that cannot be solved. So? Some differential equations cannot be solved. We can take that in our stride right? Try this! Only some differential equations can be solved, a wider variety - infinite for all we know - are unsolvable. Its a bit like being at rest with the idea that our rational number system being infinitely dense and that makes the irrational numbers exceptions- and you get a proof out of the blue that irrational numbers are more dense on the number line, or metric space-technically speaking.
Since its inception in 1600+something , calculus has provided a novel way for studying continuous variations- infact it arose as a tool for physics (no offence to the mathematicians)- and has been the 'quantum leap' for sudy and modelling of physical systems in nature, otherwise known as PHYSICS.
An etymological observation here- quantum is a very small quantity right? so how does a 'big' leap translate to 'quantum' leap?- or is it a reference to the enormous paradigm shift the 20th century physics community had to undergo in order to accomodate the most successful theory of their time.
Returning to the main stream of thought, though the chaotic behaviour of systems (i am going to ask you to go by the 'feel' of the word here - a random unpredictable behaviour that refuses to settle down to any semblance of predictabilty) seems disorderly, it is actually deterministic-- that is you can predict, without any approximations, the outcome of some system. The science of 'Chaos'(the term was popularised by James A Yorke, an applied mathematician who is said to have rediscovered Lorenz, in his publication 'period three implies chaos') is essentially classical- there is no relativity or quantum mechanics involved here.
but people back then were being paid to find order in systems! why study disorder?

But considering its simplicity and comprehensibiliy, this science started producing papers only in the late 70s and 80s becase of the stagnantic (no such word- you DO get the sense!) set of invisible rules laid down by the scientific community-> to produce a paper that was RADICAL and DYNAMIC DEPARTURE FROM ORTHODOX was suicide! To get a grant and publish papers you had to, and still have to stay away from being too original.
You have to model physical, biological or chemical systems with the existing mathematical tools- who dares to explore systems that are random and defy modelling (read predictability). Regarding the unsolvable diferential equations we were talking of, imagine a system of two or three such equations that are coupled (meaning that in a system of x,y and z, all three can appear in any form, linear or nonlinear,in each expression.) - we are trying to gauge the amount of complexity that can be built in around these systems.these system of differential equations can, however, be approximately solved using computing algorithms. so we can get a stream of data with varying time in which given a set of initial conditions mark the starting points and the system of equations mould the path of the variables. this is all the insight we need to get into the story of Edward Lorenz





"Lorenz was born in West Hartford, Connecticut. He studied mathematics at both Dartmouth College in New Hampshire and Harvard University in Cambridge, Massachusetts. During World War II, he served as a weather forecaster for the United States Army Air Corps. After his return from the war, he decided to study meteorology. Lorenz earned two degrees in the area from the Massachusetts Institute of Technology where he later was a professor for many years."--wikipedia. for all our purposes, edward lorenz was a meteorologist. during his days as weather forecaster he built a very primitive model of the climate system of earth, with a view to predict local weather. though the work was not very successful in terms of scientific design, it became famous in his department, the system of twelve interwoven differential equations churned out a stream of data on a long roll of paper (remember that this was around 1960, give or take one year on each side).people would bet on what the weather would be that day- windy, or sunny or wet. one day, so the story dictates, he wanted to start midway instead of starting allover again - putting in the same initial conditions and wait for an hour to go back where he left- instead he looked up the data in the previous sheet and fed it to the computer.this data seems to have survived for storytellers- he put in an approximation."One day in 1961, he wanted to see a particular sequence again. To save time, he started in the middle of the sequence, instead of the beginning.He entered the number off his printout and left to let it run. When hecame back an hour later, the sequence had evolved differently. Instead of the same pattern as before, it diverged from the pattern, ending upwildly different from the original. Eventually he figured out what happened. The computer stored the numbers to six decimal places in itsmemory. To save paper, he only had it print out three decimal places. In the original sequence, the number was .506127, and he had only typedthe first three digits, .506. "- http://library.thinkquest.org/3120/old_htdocs.1/text/fraz1.txt .




Although i would like to think that there was more than one variable in the calculations. this illustration does its job pretty well though, it shows that the pattern, or sequence if you please, was very dependant on the initial conditions. For practical purposes, an experimentalist prides himself if he can determine a physical quantity to the third decimal place. Here the absence of the fourth, fifth, and sixth decimals had erased all similarities to the original sequences within three-four cycles. What lorenz aptly demonstrated after this was that long term weather prediction was impossible. To do so he stripped down his system of equations for convection to their bare essence to three eqations.afterwards it was discovered that his equations mimicked a water-wheel- "At the top, water drips steadily into containers hanging on the wheel's rim. Each container drips steadily from a small hole. If the stream of water is slow, the top containers never fill fast enough to overcome friction, but if the stream is faster, the weight starts to turn the wheel. The rotation might become continuous. Or if the stream is so fast that the heavy containers swing all the way around the bottom and up the other side, the wheel might then slow, stop, and reverse its rotation, turning first one way and then the other. " (James Gleick, Chaos - Making A New Science, pg. 29).This is a system of equations of the same family, or perhaps the same set that lorenz used, you can try plotting the behaviour of this system at home.




(i)Dx=10*(y-x)



(ii)Dy=-x*z+28*x-y



(iii)Dz=x*y-(8/3)*z



for starters, D=> d/dt(operator);x*y='x' multiplied by 'y'
Whenever physicists encounter such a system they try to think of a quantity that is conserved, or in special cases, show predictable behaviour. Think of the simple harmonic equation D**2(x)=-w*x['**'=>raised to the power; here D**2=>d/dt(d/dt)]. in "phase space"- in which all possible states of the system is representable- this translates into a circle.Please note that lorenz was not aware of this terminology because this field of mathematics came in 1971. Say for turbulent flow in a cylindrical pipe, the elements of water that collide with the cylindrical wall, act as if it is attracted by the centre of the cross section of the pipe- THAT, thus, is the attractor in this system.Note that the elements that dont collide but are bound attractively to the surrounding elements also behave as if they are attracted, albiet by some different force law than inverse square. in lorenz' system, the attractor came out in the form of a double spiral.see picture.so although the momentary behaviour of the particle was seemingly random, in the long term, it was sketched out in the form of a ever-continuing, never intersecting double-spiral.sort of gives you insight into the butterfly effect- "The flapping of a single butterfly's wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month's time, a tornado that would have devastated the Indonesian coast doesn't happen. Or maybe one that wasn't going to happen, does. (Ian Stewart, Does God Play Dice? The Mathematics of Chaos, pg. 141)"
The bottomline in this first phase of insight into chaotic systems was that certain systems behave too sensitively to their their initial conditions and that Lorenz' work established that long-term-weather forecasting was impossible. Now comes the sadder part of it, his paper was published in a Swiss Meterological Journal that lay in obscurity waiting to be rediscovered.
The next story that defined birth of this new science was the work of Robert May, an ecologist in the 1970s. When one stands in the shoes of an ecologist and tries to model the population of, say fish in a pond, one inadvertedly realizes that the simplest model would be one in which there is unlimited food and the population of one year depends linearly on that of the previous year.i.e P(n+1)=a*P(n);P(n)=>population of the nth year.Now if you start taking into account the total food being constant,and the survival for existence, you arrive at :


P(n+1)=a*P(n)*[b-P(n)]


If we want to capture the essence of the equation in , x(next)=r*x(present)*[1-x(present)]- this is the logistic difference equation that can be used to model a biological system in a closed ecological system.Believe me when i say that this is only an approximation, and is probably arrived on by hit and trial rather than some deep insight into the factors of demography. Certainly, this is an accepted recurrence relation only because it yields the results, i.e. it can mimic, within permissible errors, the population of certain ecological systems like that of fish in a pond,instead of being the the factor for the population variation. The least we can do to explore this field of the logistic equation is to study the patterns that appear for certain values of r, or the characteristics of the demographic pattern that evolves with r:(courtesy wikipedia-'logistic map'): When r is between 0 and 1, the population heads to zero, independent of the initial population.


When r is between 1 and 2, the population quickly stabilizes on the value (r-1)/r.



When r is between 2 and 3, the population again stabilizes on (r-1)/r but oscillates around the value for a while.The rate of convergence is linear, but at r=3, the rate is excruciatingly slow - less than linear even.
With r between 3 and 3+(6)**.5[~3.45], the population oscillates between two values dependant on r.



With r within 3.45 and 3.54(approx), the population oscillates between 4 values forever.





With increase of r from 3.54 onwards the the population oscillates between 8 values then 16,32,64..... and on.The period of r with the same no of oscillations decreases rapidly, with the ratio between two such intervals approaching delta=4.669.... the Feigenbaum constant- whose story we shall come in with later. Now we can throw in the term period doubling cascade- think of infinitely branching arteries.


Beyond 3.57, most values exhibit chaotic behaviour, but again some values of r are there that show non-chaotic behaviour. Like 1+(8)**.5[~3.83], these are islands of stability. In fact the bifurcation map is a fractal, if you zoom in on certain areas they seem 'similar' to the whole map again.

Perhaps we got in too deep into this mathematical system than we intended to, but this isn't even starting to get technical.Robert May thus, showed how complex and beautifully simple systems like these can be at the same time.

The third story has to be that of Yorke who with Li proved that any one-dimensional system which exhibits a regular cycle of period three will also display regular cycles of every other length as well as completely chaotic orbits in 1975.Yorke's paper was named "Period three implies Chaos"- where he coined the term for use as we know it today.
For those attracted to abstract objects/theories of beauty, Smale's work on the mathematics of chaos was the first attempt that popularised the field of chaos to physics. His work can be, at its very basic simplification, be visualised by amazingly simple means. Consider a bar, bend it into a horseshoe shape and fold the whole thing overall again. the points that were initially distinctly apart originally, come together. The action of folding, however can represented by the difference equations operating on the variables. That's pretty much all a layman, like myself, can make of Smale's work.

But there is still one matter of importance in these regions and that is an insight into the true nature of chaos as we should know it. Chaos is NOT random, as the word sems to imply. What a chaotic system IS that it is very sensitive to initial conditions. So any approximations anywhere shifts the data wide off course. So once we have the precise set of initial conditions, chaotic systems ARE deterministic.
note: i attended a lecture by prof. gadagkar of iisc bangalore, on behaviour of insects, and there he said that 'simple algorithms CAN produce complex behaviour if some feedback relation is inbuilt'-- remember smale and his shape-bending difference equations...... poetic isnt it?

Friday, November 02, 2007

IISER up next!

well well!!
post the iit exams this is going to be my first meaningful gibberish(_note that i can be quite comprehensible when i want to!).
sisters and brothers of the kvpy community! i am at iiser kolkata!
here we are taught, as we were all informed during the summer camp of last year, all the four disciplines of science... pcmb that is.
but what we are actually aiming at is fusing these lines together, and promoting the scientific community as a whole.(this was my version of the iiser brochure documents!)
now for the real picture, iiser kolkata has no hostel and campus of its own and we are the first of many future batches(technically 2nd, but egotising is an important skill these days!).
the hostel is pretty far from the institute and we reach there by bus.
the highlight though is that we have no restrictions on the noise level we make at hostels and ,this is important, no protocols for punishment.
so everything you do is a trend setter (applause!)
apart from that , all you get here is a bunch of marginally intelligent (modesty?maybe!) people packed up, and voila!!
the effects are quite satisfying!!
we have a fab physics course, lapping up the intricacies of mechanical systems in general and exploring whats been wrong with the high school matter.
the computing course(read mathematics practical) is complementing the same course- we learnt python and gnuplot and together they help us model novel mechanical systems and see how they behave-- visualization that is!
the chemistry and biology take their toll -- i am not intersted in either but still its nowhere near physics in fabricational capacity.
but our biology department is exceptional and contains both good human beings and pedagogues(they usually are.) and there is an overall interest in biology because of them.
the maths is the boring now, but i intend to take it up afterwards-- we are doing the cornerstones of calculus now.
i guess that it got a tad tooo long, but you have to give in to egoTism (egoism with a T for talk, that is) sometime!
thats it.
about other kvampyiians,
sunita panda is studying mech. in nit trichy,
abhijit awadhiya is in iiserpune or niser,
jyothi v nair (bangalore camp) is in iiser kol
......... uh thats all,
and i have material for a post or two now!

Thursday, October 25, 2007

From IIT KGP with Love ...

Hi KVamPYs,

me glad 2 be bak on the blog, and nice post somani, u just inspired the blogger in me, and here i am pushing aside all my work,..

IIT is all about the sprit, the soul of engineering and technology, a place where ppl eat, breath and drink tech... literally ...

We do all sort of things here (except study of course...;)) currently am in a the organizing of ROBOTIX 08, the biggest robotics fest in south asia ... appart from that, we have hacked into some really formidable places (well not me exactly, bt my frnds here... me nt that gud in programming - am better at embedded syetems ), making some real techie bots - like balancer bot, biped runners, stealth explores, etc, just to begin the list ...

and am working with my rock band as well "The StrinGbreaKers" ... expect our first release soon after our end sems...well no ragging here till now, but rest assured theres gonna be a lottt ...!!

And i hav turned my room into a small kind of an arthropodic santuary ... got some 500 species of insects living in harmony with humans and robots... well we r literally in the middle of a jungle .

And theres more, but i got little time ... gotta work with the god damn 8052 ...

will post more very soon, especially on my bots ...
Time signing off ..

Thursday, October 11, 2007

HIBERNATION OVER

hi guys,this is my first post
though i've regularly visited the blog i didnt get to post one so sorry about that!!!
i'm at iitkgp now in mech deptt(manfac sc branch)
sabhi hopefully peace(lingo starts here) maar rahen ho.!!!!
at kgp there is quite a bit of load but now peace prevails(midsem naam ka bhoot gaya).....
no ragging here(hoo hoo haa haa)..
regular bhaat ....
and timepass ke liye chem,electrical,maths chalta hai...

the makeover is really cool twish!!

may KVamPYians rule !!
we rock!!!!!!!!!!!!!!!!!!!!!!!!!!

Sunday, August 26, 2007

providing a platform ..................since 1988!

its like arun once said, ppl really do have qualms about posting a little post, but hop on while writing massive comments(the list included me till yesterday!).
so at your service, and start typing on about where you are now and in which stream.
we do need to update ourselves!
and i sincerely do hope that the erudite discussions continue..and so do sul and tp posts.

i have got a new topic for discussion........... although it is more sociological and psychological than scientific. survival of the fittest has been a rule for evolution all over the history of earth. but now the mammalian life forms feel a duty to protect its peers, and the peak of culmination of this feeling is the human society as we see it today.
so is the sociey neccesary and if so, why?

first comment about your present whereabouts though.

Monday, July 02, 2007

SUL (Part 1)

How many times have you encountered the language barrier? I have many times. Trying to explain the waiter in Bangalore that I want a glass of water, and he got me a glass of whiskey! This I suppose happens to all those non-polyglots. Isn’t there a way out of this? Why do we not have a universal language?

The Barrier

Try running the Google search with language set to all languages. You will find at least a few thousand Japanese, Korean and Chinese sites. Well you can always run the language filter. But see the amount of information blocked by the language bottleneck. And we still don’t have a good enough translator.

Let English Be

The most obvious question you might ask is why not make English the universal language? Some might even say that English is already the universal language. But I can assure you it is not. Of course half of the world population can understand it. But what about the other half? They might as well accept English provided America conquers the world. But lets finds a more peaceful i.e. a non-American (sorry ;)) solution.

La Universale

What is then the universal language? Let me put forward some points that the ideal language should have. But before that let me tell more about types of languages. Languages are mostly three types.

1st is Symbolic language. Like English, Spanish, and all European languages. Now don’t ask me why. (Try to pronounce Rough, Cough as bough or Dough.)

2nd is Phonetic language. Like Hindi, Sanskrit, etc. and I think all other popular Indian languages. This is superior to the one above for a very simple reason that, even any odd sound can be represented in it accurately, and the words are written and pronounced in the same way.

The 3rd is a very special one and I will come back to it later.

What then is the aim of any language? Simple question isn’t it? To effectively exchange feelings, and of course information. The later is easier than the earlier. Our language or rather the scripts are utter failures in exchanging expressions and feelings and emotions. Think of online chatting. You never know the mood of the other one unless he/she uses ‘smileys’. How crude!

Well not all languages could become universal languages. The best test for a universal language is, if it can be understood and represented WITHOUT prior training in it. Impossible many will say. I say not. I will give one small example. Go to any where in the world and gesture ‘food’ (hand moving to an open mouth). Every one will understand. And such a language should be 100% efficient in expression of feelings. The lack of a script can be adjusted for the time being. So any ideas?

I have one.

You will understand the third type of language very well if you have read the book ‘Eragon’ by Christopher Paolini. It is very close to universalization of communication. What I mean is communication by images (the way Eragon and Saphira communicated). But the most important thing is that the images should not be contaminated by exposure to the outer world. Get it? Telepathy, Brainwave communication, you can call it whatever you like. That will be universal I think. A Bengali, a Marathi, a Spaniard all can of course recognize a cow when they see an image of it, unless of course it is polluted by the ever present human schemata (prejudice in a layman’s language).

The topic is open for discussion, so please join in and hope the 2nd part comes soon. And before Time signs out let me ask one thing to everyone. (Alsotry to guess what SUL is.) Remember the attempt in 1980s to contact alien life forms in outer space by sending a magnetic disk, with images and sounds of earth (and simple human words in English)? O please don’t laugh. Let me put you in their shoes; tell me what could be the best thing we can send them? See how the lack of a universal language pinches?

Saturday, June 23, 2007

Tough one

The warden of a prison meets 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another.

"In the prison is a switch room, which contains two light switches labeled 1 and 2, each of which can be in either up or the down position. I am not telling you their present positions. The switches are not connected to anything.

"After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must flip one switch when he visits the switch room, and may only flip one of the switches. Then he'll be led back to his cell.

"No one else will be allowed to alter the switches until I lead the next prisoner into the switch room. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back. I will not touch the switches, if I wanted you dead you would already be dead.

"Given enough time, everyone will eventually visit the switch room the same number of times as everyone else. At any time, anyone may declare to me, 'We have all visited the switch room.'

"If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will all die horribly. You will be carefully monitored, and any attempt to break any of these rules will result in instant death to all of you"

What is the strategy they come up with so that they can be free?

Saturday, June 16, 2007

My revenge on the previous puzzle

Acting on an anonymous phone call, the police raid a house to arrest a suspected murderer. They don't know what he looks like but they know his name is Jack and that he is inside the house. The police bust in on a carpenter, a lorry driver, a mechanic and a fireman all playing poker. Without hesitation or communication of any kind, they immediately arrest the fireman. How do they know they've got their man?

Saturday, June 09, 2007

A Simple question!

Hi....

First Of all i must say u that the question given below is not a question of IIT level....or AIEEE level....or your state Entrance exam level...or the CBSE level....or class 5 level........Itz very very easy......And i am not underestimating u guyz...but the fact is that i liked this question very much(There is some reason for that)....i'll tell u later....n remember to post the answer in the Shout Box!!!

Best of Luck ..............
IF
1 = 5
2 = 25
3 = 125
4 = 625
5 = ?


Think.......

Monday, June 04, 2007

Gujjars?

Guys, i know some of you will bash me for this...........for coming up with something so obvious on a site thats supposed to be 'kind of' intellectual. But let me assure you, i tried to pull off many times before sitting down to write it.
About ten days ago, i had never heard of the group of people called gujjars(probably, not many of you had either) and now they are all over the news channels(OK, the news people are known for highlighting the bad things more than the good ones - imagine seeing kvpy fellows on the front page of the newspaper........and now imagine seeing mr.telgi there- lets not take this further), ya....i was talking about the gujjars, or probably in a much larger sense about reservations. The basic purpose behind the agitations, the nationwide protest is not to get them reservations, but to remove them from the OBC category and put them into the ST category, sounds funny to hear that a backward class could gather so much support to burn buses and block roads.
OK, now before this turns into a news report, i'll come to the point. Just as the whole scene about reservations in iit has kind of initiated this revolt by a small section of our society(not small, if we go by the areas they are trying to destroy), there is a possibility that with the politicians looking to fan the feelings of caste division, this idea may travel places and a lot more of the local leaders may come up with similar demands. But before i sign off, i must appreciate Mr.Arjun Singh for his efforts and look - they are paying off beautifully. It seems quite obvious now, what his motives and his vision for India is like, and unless something really dramatic happens(like a young powerful PM(waise, 50 is young by IST) or something) my heart feels a little sad that things are not looking very bright for our country.

With all that useless talk having gone into your heads, I think the next time i post, it will surely be something more interesting and informative.....probably something on computer science.
Bye

Friday, June 01, 2007

KVPY Bangalore Photo!


(NOTE: Click on the pic for a normal enlarged pic.)

Ok, curse me for taking so long, but its HERE!. As you can see, our group is quite a bit larger than yours (Nyah nyah!), and a lot of these guys are seniors (BSc dudes/dudettes). Now, I shall identify some people here.
Teachers/Student Aides:
They start from the middle 2nd row:
Red shirt: Anil Sir, really really nice guy. Coordinated the whole event.
?
The one and only Dipanker Chatterjee! Also an amazing person
?
?: I believe she is in the Bio department.
?,?,?,?
Girl with a light blue shirt and jeans: A very nice, and interesting student aide. She works in the Ecology department, and I believe she's doing a lot of interesting work relating to elephant conservation. She actually does her work on field. Also, she gave an amazing presentation on circadian rhythms in bugs, and their various calls.
There were several other very nice aides, but not in the picture apparently.

Students:
Guy on right edge, with a grey and red shirt, wearing a bag: ME!!!
Guy on my left: ? but he's a senior. We had an interesting conversation on relativity and laser cooling I think, along with the guy on the top row, 2nd from left (crossed arms).
Guy on bottom row, 3rd from right, light colored clothes and bag: Chinmaya (tagged: super smart cool dude)
Guy on top row, 4th from left, with "Dhoni" hair, and NO bag: Dinesh (tagged: also awesome guy)
Guy on bottom row, from 5th from right leftwards Amol, (guy who went to IMO national camp), Sisir
Guy on bottom row, 2nd from left: Atheendra
Guy on 2nd row, 4th from left, blue shirt: Ramkumar
Guy on 2.5th row, 3rd from right (beside Ramkumar), black shirt: Venugopal
Guy on top row, middle with a Google Code Jam shirt: ? senior who went to the National camp for Indian Informatics Olympiad.


That constitutes all of my memory. As you can see, I don't know many girls there, but if you were on that pic, you are constitutionally granted to come and: a) tell me so I can put that in, b) kick me, next time we meet.

Wednesday, May 30, 2007

IIT Results

It's no secret that most of us (at least in the MPC branch) are IIT aspirants. So, how did we all do? Please post your results (and your expected marks) below.

Friday, May 25, 2007

Development

Okay, so I know most of the people visiting this blog find biology awfully boring.
Well I can't seem to complain given that I hated it too during school. Anyway lets put all that behind and try to make things interesting.

Now Twish had some really interesting posts which definitely might have made all of you think about the brain in terms of circuits, processing, perception and a whole lot of other things. However before I put up a post about the workings of the brain, I have to first get everyone to know how the brain or for that matter any organ develops. (wait, it doesn't start getting boring here, I am gonna talk about circuits in a totally different way).

So lets start with two cells i.e the resultant of the fusion of the sperm and the ovum. So what happens next. How is it determined which cells become what in the course of division of these two cells to form the millions of cells that is us? How is it that the neurons are formed only in the brain and the spinal cord and other regions? What makes the heart not be in the place of the kidneys and the blood cells to be as they are? (No, this is something that isn't easily ascribed to the creations of a higher power namely God)

So what happens is a completely different branch of biology that is called Developmental Biology.
I can't promise you that I shall give you the answers to what makes the heart cells to not become neurons and vice versa but what I can say is that probably some of you might see the analogy between genetics and circuits.

So now lets get to the start of development. You have 2 cells and they divide something like 9 times over. Till this point none of the cells are in anyway different from one another (or atleast no one has been able to prove that they are). So these cells are called embryonic stem cells (ESC). Now once this stage has been reached what happens is that the embryo starts getting polarised, by polarised I mean to say that now you have distinct regions within the embryo which you can differentiate. Hence we now have an anterior (mouth) end and a posterior (anus) end. Similarly we have left and right sides and up and down distinctions.

But in turn how do two cells differ simply becuase of positions. This is due to a clever trick brought about by diffusion of protein products that have been passed on with the ovum(the sperm is a poor guy who contributes only DNA and no proteins).

So how do these circuits work?
Due to the proteins passed into the embryo by the ovum, these protein create a gradient by simple diffusion and the varying levels of these proteins at different areas "switch on" or "switch off" certain specific genes and these genes form certain other proteins and so on and so forth. Now the products of these genes are important for the activity of other genes and so forth. Thus what you have is a series of AND/IF/OR gates which function together in a highly complexical manner leading to different cells showing different reactions to the same stimulus.

Thus in most simple words, this is the basis of differentiation of cells to form neurons and muscle cells and liver cells.



I think this much is enough at one go, shall write more once I feel it has been adequately understood.

Sunday, May 20, 2007

polarized light------- part 1

read between the lines:- "this guy is so lazy that he posts on what he has been doing for his summer project."


the first part calls for a recapitulation of sorts----I've been reading a really lovely book on optics by hecht---i don't know who he is guys......but i am a fan!


so , we can start with the polarization states of light---
(i) natural / randomly polarized light(never unpolarized,no!)
(ii) plane polarized light (P - state)
(iii) circularly polarized light----divided further into right handed(clockwise)--R-state
left handed (anti-clockwise)--L-state
(iv)elliptically polarised light --can be right/left handed or horizontal/vertically polarized-depends which way it has a larger amplitude.


essentially every state can be generalised into the elliptical light category-- i mean plane polarised and circularly polarised light are but special cases of the elliptical category.

the mathematical treatment too is very general - assuming the polarized (or randomly so) radiation to consist of the orthogonal components -- horizontally and vertically polarized light respectively.

assumption: propagation of the ray is along z axis.

in the x-y plane, A(x)= acos(wt - kx)
A(y)= bcoswt(wt - kx+ 0) "sorry 0 for theta



adding up amplitudes , A(tot)= acos (wt - kx) + b cos(wt - kx + 0)
= a' cos(wt - kx + 0') where a'= ........ you know the drill


now,
apparently this represents the general elliptic equation, you know where the pricipal axes dont constitute the major and minor axes.
(my knowledge of gemetry and maths is seriously limited)

so when the phase difference in the orthogonal polarized states of light(0)is zero-
we get plane polarization
when 0= 45*(degrees) ,and the two impinging amplitudes are different the elliptic phase takes over,
while for 0=45* and equal amplitudes, circular polarization takes up.

i dont why i explained all this, but this is only the beginning............ most of you should know this but i started dutifully.

in the next part i will take in something that we dont know till now and expand on it.
this article actually deals wth mathematical methods of denoing polarized light.
but what makes it interesting is that we can treat polarization optics entirely through matrix algebra. i mean denote the incident light with a matrix, multiply it with a square matrix that is specific to the optical element to which the incident ray is subjected, and you obtain the emerging ray.
the simplicity of the whole process drew me in, and i perfomed my project on the same thing.

Saturday, May 19, 2007

Turing And his Great Machine!

This is a big comment on the prev. topic (TP II). Its just soo long, and more than less disconnected that I thought I'd post it out here.

Twish: I'm basing this on memory, so I may have a few gfacts sketchy, but what Turing proved was that there were functions/programs (algorithms) that could not be solved. Wait, thats what you said. Ok, let me go into a little histoire here:

Alan Turing made a theory for what is called the Turing Machine. The Turing machine can perform certain actions, and helped solidify what an algorithm is. It is a function that the Turing machine can perform. Now I don't know how he proved it, but Church and Turing made the Church-Turing Thesis for the Universal Turing Machine. Catch this very carefully: A UTM, can perform ANY action any machine can perform, albeit not very well. Theoretically, given the time, power, and memory, a UTM can perform any task a machine can perform, i.e. every single algorithm.
In exact words:
"Every 'function which would naturally be regarded as computable' can be computed by a Turing machine."

However, he also found the Halting Problem. An algorithm that could never be decided whether it halts or not. Remember that this machine can process any algorithm a machine can process... but it can't determine the halt-ability of this algorithm (note that it can still run the algorithm.) That means that the UTM, and any other turing machine (algorithm) can not find whether this halting problem will halt or not.

Once again, I'm sure to have confuzzled you all. So what do I mean by halting. Suppose you have a problem: find an odd number ending in 3. It halts very quickly (every number ending in 3 is odd). Suppose I were to switcheroo this question. Find an even number that ends in 3. It would never halt. Determining if a problem can halt or not is the object of the Halting Problem, but unlike us, it can't see the very obivious fact that an even number can't end in 3. More about this later. Bascially the program will have to continue trying for every single even number to see if one of them ends in 3.

WARNING: This is going to be *very* confusing. I've lost my sanity thrice while reading this (twice before, once right now). First some teaching of this kind of axioamatic functions. Axiomatic functions happen to be strings. That's what axiomatic systems are all about, strings. Now, a function operates on well... another string. So remember, everything is a string. Note, this may seem confusing, but I'd like to point out to say Twish or Rash, who program a lot, in OOP, functions are objects too!. If you've ever done ASM, you'll know that the functions that are called are binary too! There is not biggie here.

Lets have a possible (?) program called (Captial names are programs) Halt (str, in). This takes an axiom function string (str) and an input (in), and returns true if prg halts for input in, and false other wise. Now, this is precisely what Hilbert-garu wanted, but alas, he's going to be disappointed.

Now, lets create another function called Disappoint (t), and put in its argument (input) some string 't'. Now this Disappoint's function is evaluate Halt (t,t) (this is where Cantor's diagonal argument comes in actually), and to loop forever if the Halt returns TRUE, and stop if it returns FALSE. We can just represent it at Disappoint (t). Nothing very out of the ordinary really. These are all functions within the great UTM's scope. Now for the final blow, suppose we take the very input (t) to be nothing but the program string for Disappoint? This is again something to do with the quirk of self-action. Dissapoint is applying the program string upon itself! Now...

* Lets say that Disappoint(t) stops. That means that Halt(t,t) must have returned false! But that must mean that the program "t" didn't halt! But the prg "t" is nothing but Disappoint(t)! So, if Disappoint(t) stops, it must mean that Disappoint(t) did not stop!!! *zing* You have just gone insane ;)
* Now, suppose Disappoint goes on forever. That could only imply that Halt returned true, or it hasn't finished yet. If Halt stopped, then well that means that "t", i.e. Disappoint (t) stopped, but then again it hasn't!.

Now of course you will say, what if Halt(t,t) itself does not halt EVER, but then isn't a suitable function. That is to say, Halt(t,t) is a function that is supposed to find whether a given function halts or not. Now if it never halts itself, it can not tell you if the given program (t) halts. So it is insufficient to determine if a program halts or not.

The objective of the Halting Problem is to prove that there can not be a particular algorithm/program that can find out if *any* program will halt or not.

That's the proof. Now that you've lost your marbles, I'd like to profess that the first time around, I didn't get it, but this time I did! Yay! (Well to my defense, the first time around was with a much denser material, with a bunch of axiom maths in it too). So what have we learnt? Hilbert was twarted just like Russell. Just for interest, Russell spent a good 10-15 years I think, to come up with a system that he said was complete. Poor guy was gunned down by Godel. OUCH!

Well, what does this have to do with our lively discussion? To start with, our mind, can break through this barrier. How, I don't know, but it can. We can understand that there is no such thing as an even number ending with 3. BUT, that very same mind can also say that there no consecutive primes after 2. The very same system can do both. There is a slightly larger proof of this argument (Turings), that proves the same result for any (finite ?) set of methods (i.e. if you argue with me that we have two specialised methods for both the above problems). But, we are able to transcend that rule. Again, how, I have no idea, but that is the greatness of our mind. There are bits and pieces dealing with rebuttals that I've left out, but I think that this post is long enough as it is!

Friday, May 18, 2007

TP Part II : Insight


I was more than pleased to see so many comments. It was a greatdiscussion. So why delay for Part II ? Of course the observations and "comments" affect the system ( A sleek example of Uncertainity Principle like effect is real life ) so now the posts I had thought of are no longer going to be the same. I was supposed to write about all this an year ago, but got lazy. To me, this is DAMN interesting ! I hope you all too would realize the importance, consequences, and implications of the ideas that follow.

Temporal Programming
Hats off to Time and all of you for mentioning this. For this ceratainly is a great field of current research. A hot field indeed where people fix neuro-networks with electric chips and try to control them and stuff. The aim of course is to combine electrical and biological systems to create "cybernetic organic matter"... sounds Terminator-ish ehh ? lol

However TP is NOT equal to Temporal Programming. If I were to mention it, it might sound 'dubious' and trivial/unimportant/crazy. But I'd insist, that if not of all the importance, it sure is what I began with. So more about TP on Part III. Till then I would like to have a time travel session ( yoh Time get the machine ready man ... ) back to history (a subject I hate from the core of my heart ) ...

Many of you ( Im sure Arun would ) would already know about many of these facts. However, please bear patience, for the others would be fascinated indeed. Countdown Time...
10
9
8
7
6
5
4
3
2
1
0
-1
...
(oops forget it)

Old Hilbert had Problems
In the early 1900s ( not early... infact the very year 1900 ) the great mathematician Hilbert listed out a few "good" "classical" problems in mathematics. Many of these have been solved now. What he emphasised further, was a need to organize mathematical reasoning. He said that a formal axiomatic system should be both `consistent' (free of contradictions) and `complete' (it represents all the truth). Further argued that a mathematical problem should be "decidable" in the sense that there exists an exact procedure or set of instructions (however complex) to decide whether a proposition is TRUE or NOT... an algoritm !

Around the same time, people were talking about unification of physics. This, in a sense, was a unification or generalization of Mathematics. But it's been tested ... that nature seldom appreciates such acts of (folly???). The 2 problems can be listed...

  • a complete system of axioms
  • an algorithm ( procedure ) to deduce a give proposition as TRUE or FALSE
But things have never been simple...

Everything is Relative
While other mathematicians were working, trying to formulate a standard set of axioms, the genius of Kurt Godel prooved (Boolean Algebra) that there can never exist a complete logical system, all by itself. For the daredevils and brave-hearts the two theorems of "incompleteness" can be found below :

Wikipedia - Incompleteness theorems

The exact proof ( With Godel's history and stuff )


PARENTAL ADVISORY is Required... click at your own risk ! (I'd advise not unless you have chewing gum for a brain cuz thats what is going to happen lol)


How to do it ?
People yet searched for Hilbert's second quest... the algorithm. But a wise guy called Turing was wise enough to show that this too was impossible. Now I am not explainging how because I take the liberty to post about it as a follow up, for its a favourite topic of mine and deserves special credit.

Implications
Hilbert's dream was shattered. My history is not good enough to tell you, whether he lived to see that day, but I guess not. The two quests were PROOVEN to be impossible. There could not be a self-consistant set of axioms. Hence mathematics must rely on (some) assumptions. Also, there was no set of algorithms. So there was no way to predict if a proposition was TRUE or NOT ... infact... you could proove it TRUE, but never FALSE. Its like Physics. U have a theorem. U keep experimenting. But cant proove it. Same applies to maths for some of these classical ones. An infamous example is Fermat's Third Theorem, which reamained unprooved for decades, and was finally prooven in the 1980s. Who who' s ? Maybe it could have been wrong. The point is, is it true that ALL THINGS TRUE CAN BE PROOVEN ?

Back to the Brain
Now most of you must be thinking " This crackspot ... last I knew he was talking of the brain and something wierd called TP ... and now he switches to abstract mathematics ... "
I empathieze with you (my brain does). But explaining all of the above was important. The implications are not small.

AI
This aint another TP... but Artificial Intelligence yeaah... So now Im talking about a field, which promised to change the world in the 1950s but over these many years, has been an utter failiure. When people expected to see walking talking humanoid robots, all they get is stupid toy dogs that act like pets. The technology has failed to deliver. Now Ill dismantle and disect certain subtle points of the subject.

Humanoid or not ?
An aim... one of them... has been to make machines "think". There are two basic problems. One - we hardly know what is "thinking". Two- The approach. By the approach, Ill bring out a certain result that recently, wierd looking robots have outperformed human-like (humanoid) ones for various tasks. They are as effecient, if not more, while imitations of humans have been unsuccessful. The point is, we are trying to COPY nature.
Switch to an analogy. Aeroplanes. ( Im sure TIME wouldn't agree but I still believe that conventional aerofoil based planes are better than ornithopters ). Initiall people fixed wings and tried to fly resulting into calaities. Most the designs they thought of comprised of moving wings. However imitations of nature failed. The flying planes we have today are based on different design principles.
So why IMITATE human thought at all ?
I mean... machines, lots of them, can do better than human at lots of things. Like... playing scrabble, chess, even football ... and I am not talking about humanoid ones ! So why make a humanoid thing at all ? I guess this has more to do with the curiosity and understanding ourselevs than imitating a birds flight. Ohkay now Im diverting from the topic ... ( but wats the topic ? )


My Doggie is Conscious
Forgive that subheader. I am getting wierder with each passing hour. Though my point is, can machines be conscious ? Back to the game eh ? Well to understand this, we must look into our own machines... our brain... Now how exactly our brain works is not known. Perhaps we can say (or we do) that it follows algorithms. Like a computer program or a computer. So a machine can follow algorithms too. Whats the big deal ? The deal is... that we have prooven... that there is no perfect algorithm. Infact for the set of all algorithms, there is another which is unbounded, or not an algorithm at all ! ( Turing did all this )
How exactly it says what it does would be clear only when we study Turing's method(s). But the result is... maybe our brain does not follow an algorithm !
Hah ! I can hear God laughing. "Do what you can *.......* you cant copy your own mind"
Now our kind of machines follow algorithms. What can be done if a thinking machine does not follow an algorithm ? Nothing. Hopeless. Maybe somewhat like, popping of the wave function! (Arun's comment - deserves a post on its own).

Wrapping Up
I mentioned ( or you did... ) yoga and hypnotism. I was to write about them, related to my own escapades(TP). However, my brain tells me its tired. So Ill let those two hang up.

Till then something to think about.

(1)
Is it the mind which carries out experiments or the world which provides inuput ? If its the mind... what about my mind and your mind ? Are u a figment of my imagination ? ( Ive tried conveying this message to ppl. The replies were not very positive so Ill not try it again hehehe )

(2)
This publish button I see below is ORANGE. This Save Now button I see is BLUE. Ohkay. I can differentiate between frequencies. But then... do you see ORANGE too ? Yes you would say you do. But do you see the SAME orange as I do ! ... I guess there is are no means to answer this, that I can think of. MAybe you see my RED as your YELLOW and my BLUE as your RED. Maybe its not of much importance... but will the beauty of the RAINBOW be the same for both of us ? If not... this could be a reason why things like art,beauty are subjective ... that is ... "lie in the EYES of the beholder".

(3)
I believe that the EARTH is conscious. Only it doesn't bark.

Ill quit writing before you book me for the asylum. lol.

Ill be Bak

~ Twist ~




Monday, May 14, 2007

T.P. - Part I


If you toss a coin seven times to get seven heads, you know there is something wrong with the coin.
Introduction
This topic is going to be weird so please be prepared for it. It is a controversial topic. I've been thinking about it since long. It has literally "consumed" whatever little mind I had! I won't jump straight to the point and start with some background information.

Slaves or Masters
I had once written a long post about consciousness and its existence etc. This is closely related to that, yet very different. Consciousness, I guess we are all aware of. But my question this time is, other than taking lots of critical(maybe) decisions, what is the role of this 'consciousness' ?
Okay. You want to walk from point A to point B. So your conscious brain gives orders to your brain to walk/run etc to point B. And then you walk/run watever to point B. Apparently simple. But it certainly not so. Walking itself is a very complex thing, when you wonder about the nerve impulses involved, which muscle to relax, when to relax, when to contract, coordination, balance, destination, etc. But, the catch is, when we walk, are we aware of all these things happening ? No. All we say is WALK and a certain program gets executed in the BRAIN which makes us walk, by following various very very complex procedures.

The Brain and Us
From the last example, we could see that we(consciousness) have an important role in giving orders, but no role at all in following complex instruction sets. That is done inside our brain. Think of all the other tasks that we do and the skills we posess. How effectively, the brain is able to bring about these complex changes, and we are unaware.


Practice makes it Perfect
Back to the same example. How did this 'walking' program get executed? A possible mechanism can be this, that all these "programs" are stored in memory and recalled when we need them. To store them in memory, such automated programs, we practice a task. For example, any sport. When we play football, as a beginner, we try and get better. We try to dribble the ball, keep it in control, and try to aim it where we want. Then we practice. Resultantly, these skills come naturally to us. The next time we play the game, we dont have to think about doing all these things. It almost becomes a "HABIT". We take it for granted. This is an example of how our brain learns. We decide on something. Practice it. And a PROGRAM for the same is created in memory which gets exectuted when we need it.

Power of the brain
We hear it everyday that the human brain can be very very powerful. It is true indeed, if we notice the above examples. Well, maybe some of the processes are carried out by or in coordination with other organs as well, yet the capabilities of learning and then reproducing the learnt skill so effectively is impressive indeed.

The Question
I end this post, keeping it short and not touching my origional subject at all. Though the question I look forward to ask is, now that Ive given an example of how the brain learns these skills :

Can we TEACH our brain, a skill, which is seemingly impossible, yet possible in theory ?

I guess I framed a weird question.
Let me just ask,

CAN WE TEACH THE BRAIN ANYTHING WE WANT, if it is possible theoretically ?

I would also like to see if one one you could guess what the heading of this post stands for. HINTS: The Sub-headings.


See you soon with TP - Part II

~ Twish ~


Thursday, April 26, 2007

isi lurking + an unrelated problem

here is a sum that held me in due to oversight on my part.it has got only one twist- thats all!
here goes-


imagine a rubber string, fixed at one end, is streched linearly in a horizontal plane so that the free end always has a velocity 'v0'.if an insect at the free end starts moving towards the fixed end with velocity v1 , at T=0, and initial length of string is L, find the time at which the insect reaches the fixed end.
my question is that wat shud b the min value for v1/v0.

sorry for for the accccute wording though- cudnt help it.

u know i already feel like reading for college- i feel exhausted with this standard syllabus already.
if u ppl hav applied for isi-bstat admission,discuss in this thread.

Monday, April 23, 2007

Flap Flap ... Times Back



So, ppl ... wonder where i had vanished all this time, been on some very distant time travel into the depths of future. Nah. busy with IITJEE. well tats gone so now i can do some thing closer to my heart. This is what i have been working on.

ORNITHOPTERS

Seems a very far fetched name. But wat lies within is even more weird. Ornithopter as d name suggests is 'flight like birds'. flapping wings. no propellers. The key difference between an ornithopter and an airplane is that the driving airfoils move up and down instead of rotating. For both the airplane and the ornithopter, most of the lift results from forward motion through the air. In the ornithopter, lift is produced by the flapping wings, often in conjunction with some additional fixed wings. Birds likewise use their body and tail as a fixed lifting surface.

Why Ornithopter ?
My sudden intrest in ornithopters can be attributed to the recent air mishaps- crashes. i was very upset. the current air plane designs are over a century old. fixed wings. high forward thrust, some thing new is required. Ornithopters are better in following ways:
  1. Very high maneuverability
  2. low noise
  3. high lift
  4. good fuel efficiency
Ornithopter isnt a new concept. the first ornithopter was built in early 1900s !! manned flights on ornithopters hav also been achieved. but considerable work needs to be done before u and i can ride one.
Now wat am i working on? am on a fold wing type model which will have a very strong downstroke, enabling it to 'climb'. i will write the details one i have made a successful model. But there is one problem. This isnt a basic science topic and hence i cant take it up in KVPY program. :(

Well then, i think 3d matrices will be good enough for the summer project ...
waiting for ur responses (and refueling my time machine)
TiMe

Thursday, April 19, 2007

PANIC!!! New Blog Look

First of all, I'd like to apologize my absolute disregard for all the hard work Rash and Twish did for the site. I thought I could play around with the site so that the comments page would be a bit wider (since we tend to have long comments), and just change the look a bit.
As a result I made a huge huge mistake of not saving a template backup. I thought that there would be a rollback option at the stage, but it seems that there wasn't. Again, I'm so so sorry that I screwed up all your hard work, and I'm desperately hoping that you have a few back up. If not, tell me what all you had, and I'll put in the work to make sure that its back.

I hope you like the new look. I feel its a bit brighter, and easier to navigate. If you've any objects, comment about it.

Wednesday, April 18, 2007

The KVPY Summer Programme: Discussion

As I laid out in the 'above' thread, this is the discussion thread. Please abuse...

The KVPY Summer Programme

All of us have been caught up in the exam, and I think its time for us to get back to the task at hand, the KVPY Summer Programme. I'm sure that each of us has some ideas if what to do in their bulbs, but really a lot of us haven't the least idea on how to do that. Then again, it could just be me, but I'd like to see you come out and prove me wrong, and then help me out.

So this is how it works, this first post is for each of us to list out what we plan to do, and possibly where we plan to do. You can be as descriptive as you like, and you can write a cute love story between you and quantum physics if you like. But, you get only one post, and you can edit it however much you like. (Copy the entire text and delete your old post if necessary). I want it like this so that we can keep it clean. Do post what you've done, plan to do, etc.

Now, there will be a second post following this one, where we shall discuss as freely as we'd like one what was written in the first post, as well as talking about penguins.

I hope you all pitch in and we're able to create enough volume to help each other out.

Tuesday, April 10, 2007

THE KVPY SCHOLARS

[Click on the Photo to Enlarge]

As far as i remember the people in the photo are:
Bottom Line (L-R): Rasagy "RaSh/Gr81", Debasish, Priyanka, Abhinav Uppal, Mr. S Mallick (our cordinator of the camp), Another Coordinator, Debanjan "ObiWanKenoby", BhagyaShree, Sunita, Prateeti, Somani (Standing behind).
2nd Line: Sandeepan Parekh "Spidy" (2nd from Left) & Saurya Prakash "Time" (Blue Shirt, behind Debanjan)
3rd Line:Swetabh "Bhakt" (Behind Twish), Twishmay "Twish/Twister" (Red & White) ..... Lagnajeet (Yellow), Manish (Blue), Pravar D Mahajan, Ankit "Pandey" (Black).
Last line: Abhishek Bhatnagar (Red Shirt), Ankit sagwal (Orange Shirt), Tanmay and Ashish.

PS: Isnt that Arpit on extreme Top Right?

Any one else whom u can identify, plz comment....

(Updated last on 17/4/7 by Gr81)

MY PASSION

This post is not about metaphysics as many of the posts on this page are.. It is something u must be knowing...


Every one of you must be having a weakness for something. Someone 's crazy bout programing in computers. some one likes bikes..etc..
Similarly my passion is "Airplanes".
Airplanes have always fascinated me from the beginning. When i was small i told dad to take me to the Bhubaneswar airport in the weekends to see the airplanes landing n take off.
FLYING.. Is what people "do" now a days. It has become a part of their lives. It's no more a luxury to fly as it was to hold a cell phone in the early nineties.
Over a century ago , when two ambitious cycle mechanics "The Wright Brothers" first shared the idea of flying with their friends .. they just laughed away at it. This made them more determined and they worked hard and succeeded in making a FLYING MACHINE " THE WRIGHT FLIER" from the scrap they had in their shop.It was a single engine aircraft which could fly at a height of a few meters . Though their first flight at Kitty Hawk on 17th December, 1903 lasted for seconds.. but it was enough to start a new era for the mankind. Within years the aeroplanes were used almost everywhere.. for transport, for rescue, for met studies..and for WARS.
WRIGHT BROTHERS
Coming to the actual point , today there are aeroplanes which are run by super computers. Super sonic airplanes have become a thing of past. You might be knowing of CONCORD which reached 1.9 Mach during trans-Atlantic flights in the late eighties. (Though it is phased out from active service now). Today there are fighter planes which carry laser guided fire 'n' forget missiles. Moreover there are aircrafts like the B-2 spirit bombers which can take off from the USA , bomb the "Tora-Bora" hills in Afghanistan and return home on the same day without the need for refuelling even once and without giving a single blip in the enemy's RADAR!! Planes have also reached Hypersonic speeds( greater than 5 mach) in some test flights. Within 100 years man could increase his speed from a mere 60 km/hr( on a horse) to 5 machs !!ALso there are fighter aircrafts like the F-22 raptor which have "Thrust Vectoring Technology" which moves the exhaust nozzle in the required direction for better acceleration and maneuvering. Now-a-days Airplanes completely made up of Carbon Fibre have been built. ( ex. LCA (Tejas) of India has almost 90-95% carbon fibre which makes it the lightest multi role combat aircraft in the world.)








LCA




F-22 RAPTOR


You also might have heard of Unmanned Aerial Vehicles(UAV). The "Predator" ( an UAV of US) was extensively used during the IRAQ n Afghanistan wars. These aircrafts are controlled by pilots sitting comfortably in their home land and these intelligent airplanes just come n bomb n go.. The enemy never knows where did the bomb come from? No radar signatures, no noise, no infrared radiations.. India too boasts of having a powerful fleet of UAVs ( The "Lakshya") . The " Lakshya" was first test flown in Chandipur(The Interim Test Range) in my home state(Orissa).
Here i would like to ask a question : Is there the need of Pilots in today's airplanes? Can we leave these intelligent flying machines alone in the battle field? Can we rely on these brainy planes to carry hundreds of passengers safely across the pacific? Can these planes take split second decisions in combat zone and rescue operations??
Here the discussion is directed towards : Artificial Intelligence ~ Human Brain
Here's the OPEN question ..
CAN ARTIFICIAL INTELLIGENCE EVER REPLACE HUMAN in some vital JOBS like flying aeroplanes and surgery?(to name a few). OR SHOULD THEY BE RESTRICTED TO MUNDANE JOBS IN THE OFFICE and leave the humans to take up these "more important" jobs??

What I Was Trying To Say

Okay this is just a small post...

When I mentioned a Universe with multiple epicenters, you apparently took it in a way I did not mean. When I say "epicenter", I am NOT referring to "the point from which everything is moving away"; rather, I am talking about the "point where the event first took place".

In other words, I was talking about the mouth/neck of the balloon, not its "center" per se.

Contrary to what you might imagine, the idea of multiple co-existing universes does not contradict the "everything is moving away from each other" stuff. Think of a balloon with its mouth towards the north. Now think of another balloon within this one with the mouth towards the east. We can have many such balloons, but the condition is that each one must expand at a faster rate than the one within it.

If you will give it a thought, this does mean that each and every object (an object is like a point on any of the balloon's surfaces) moves away from every other.

Monday, April 09, 2007

Easy IITJEE paper

Lovely!!!!You come after 3+2+3 hours of hard work

9-12 :- almost a shaky start, and some nervousness arising due to the need of getting the essence of the past two years (actually more) into one crucial day and to do all this in a place you have never been to , before.
12-2 :- might seem the easiest part of the day but is actually the toughest. Getting some food into your stomach and expecting to digest it without any oxygen supply coz the brain has taken it all, is as likely as ending up with JEE rank 1. And then the pressure of not looking into the first paper (you wouldn't like to have a depressed mind, or even an over-confident one - entering the second test)
2-5 :- Get back to work.And it doesn't really matter if the afternoon is hot and the electricity supply is, well ...... typically Indian. The exam is the most important thing during the three hours and a slight dip in concentration may spell disaster.

Ok, after having excerted yourself for the eight hours , you hear people saying it was an easy paper, and... and even though you know those speakers might actually never make it, you are literally forced to believe that you missed out.

Were the eight hours 'easy'? Definitely not. The questions might have been easier but the paper, it was by no means easy. Anyways, it doesn't really matter if the questions are easy or difficult , its going to be the same set of people (with minor changes) who actually make it.

IITJEE is never difficult. Its not the high level of knowledge, or the complicated theorems, its just plain application of what you know, how well you know it, and ofcourse how well you use it. The questions were tricky, no doubt. There were ocassions when the questions trapped me, and literally induced mistakes. Deadly 'match the following'. All in all an excellent question paper, trademark IITJEE.

I hope you'll leave comments, and also an estimate of your scores (the solutions are available at www.fiitjee.com - i know most of you already know it) . Any guesses for what the top score is going to be???

Thursday, March 29, 2007

The Periodic Cycle of Construction - Destruction

There are certain phenomena about which there is no doubt as to their existence, yet they are hardly understood by man. This is summarized in the epic struggle of chemists to place elements in a periodic table, with properties being governed by relative location. The fact I wish to emphasize is, there was knowledge that there is a pattern to the properties of elements, but this pattern was not understood.

Similarly, the magnetic north and south poles of the Earth are reversed periodically, while the exact reason remains unknown. Speculation and theories are rife, but the questions of why and how remain largely unanswered. (By the way, if this reversal had included a period of complete absence of the field, there would be no atmosphere on Earth)

Moving on, we come to the Universe. As I have just mentioned elsewhere, there is no tangible concept of the "birth" of the universe itself, but because the universe's boundaries are being defined by the points where the farthest celestial objects exist, the big bang is taken as the origin.

The big bang was something which propelled matter outwards from a concentration which may be taken as a point.

This might even be periodical. Like the ice ages, perhaps the big bang has a reverse phenomena which occurs after a period of time, to be again followed by the bang itself.

What could possibly reverse the big bang? Something like an object achieving the speed of light. Infinite mass would have an omnipresent gravitational pull, with an infinite force that would immediately begin pulling every object composed of matter towards itself. This, or something like it, may cause the "death" of the universe, just as the big bang caused the "birth".

And the bottom line is, there is nothing we could do to prevent it.

Monday, February 26, 2007

The Boards....

Just a short post wishing you all...

BEST OF LUCK FOR THE BOARDS!!

If you ever come online between the boards period, do comment with your experiences (Not just about the paper, even about the center/ invigilator/ people around)

Lets see how the boards went throughout the country!!

;)

Thursday, February 15, 2007

A post in a hurry...

Well I apologize for not posting this yesterday!


And yes this is not about the Valentine Day... :p


Its wishing:
Lagnajeet Das a (Belated) Happy Birthday!!

Seems like the blog is becoming a Birthday Wishing Blog :p
So mayb everyone should leave their birthdays in the comments... :D

I wont be coming online often, so ALL THE BEST FOR THE BOARDS!!
:D

Friday, February 09, 2007

HaPpY BiRtHdAy TwIsHmAy!


Well sorry got a bit late...
Its already Evening... :p

Today is a very important day for all the members of this blog (I know there are very few who take out time to read this... still!)

Because today's the Birthday of the FOUNDER of the blog:
Mr. TWISHMAY SHANKAR! (aka Twish aka Twisted!)

HaPpY BiRtHdAy!!

Monday, January 22, 2007

Intro

Thats me, Dhrubajyoti Samanta a.k.a. DJ. Sorry for this late intro. Just couldn,t think of anything to write. I had joined the summer camp at Calcutta with all the others. I had also played football with others. So long for now. Waiting for your comments.

Friday, January 19, 2007

CALL FOR HELP

Arun , or ne1 else, plz get me a DATASHEET for the Transistors TL - 188
and TL - 187 ... EMERGENCY !

Sorry for posting this but I really need this ASAP !

TWISH

( Soon get bak with a REAL Post )

Friday, January 12, 2007

HaPpY BiRtHdAy Mr. TiMe!!

Happy Birthday Saurya (Time) Mishra!!

Hope you enjoy Your Day!

Time flies doesn't it?? Better come up with time travel soon....


H*A*P*P*Y* .* .*.* .* .* .* .*.* .* B*I*R*H*D*A*Y
*.* .* .* .* .* .() ().() () () () () .* .* .*.* .*
.* .* .* .*.* .* || || || || || || || .* .* .*.* .*
.* .* .* .* . *@@@@@@@@@@ .* .* .*.* .*
.* .* .* .* .*@/////////////////////////@ .* .* .*.* .*
.* .* .* . *@@@@@@@@@@@@@@@@ .* .* .*.*
.* .* .* .* @//////////////////////////@ .* .* .*.*
.* .* .* @@@@@@@@@@@@@@@@@ .* .* .*
.* .* .* @///////////////////////////@ .* .* .*
.* .* .* @@@@@@@@@@@@@@@@@ .* .* .*
.* .* .*.* .* .* .* .*.* .* .* .* .*.* .* .* .* .*.* .* .* .*

Keep Posting!!
:D

Monday, January 08, 2007

Basics of Electronics: Transistor Time!

Woo! Transistors! Drool, drool. Ok, my childish reactions apart, transistors are the backbone of electronics as we know it. They represent a control structure, where you can control one part of the circuit with another (as a master-slave relationship). As an overview, a transistor has 3 terminals (I'm talking about BiJunction Transistors' (BJT) here), which are called the Emitter, Base, and Collector (EBC). By changing the potential difference between the Base and Emitter, the current between the Emitter and Collector can be varied. I'm going to use acronyms for EBC's from now on, because I'm lazy.

Generic NPN transistor diagram below:

Ok, we'll discuss the NPN (negative-positive-negative) transistor right now. The PNP transistor is nearly the same, except the polarities are reversed. So the NPN transistor consists of three regions, a N junction (see previous article for junctions), a P junction and a N junction. They are the Collector, Base and Emitter respectively. If you want to, you can look at the transistor as two diodes, with the P junction fused. You can take two PN diodes and try to make a transistor out of it, but it'd be really crappy, because the P junction must be very very thin for reasons we shall soon see.

Let's connect up our transistor to a battery, and try and understand how it works:

Firstly, note that the C is connected in reverse bias (i.e. the positive end is connected to it), with respect to the EC connection. The BE is in forward bias though. Remember the depletion zone (from the previous article) right? Well, its here too. By varying the potential difference between the BE, we are able to change the 'thickness' of the depletion layer. That allows more current to flow. Initially, the layer is pretty thick, and electrons can't flow from the E to the C, so there is no current in the EC circuit. Now, as we increase the potential between BE, the layer thins down. So now electrons are allowed to flow into the B region.

Remember that the EC in reverse bias? That means that the C can't give electrons because of the gap, but it does mean that it is very very eager to take electrons. Thus, it sucks up the electrons that enter the B region. The B region must be very thin so that the electrons are not absorbed by the B or taken away from the circuit.

There you have it folks, by varying the BE potential, you vary the depletion layer. This allows a current into the B region, which is taken up again by the C region (so the Collector collects the current). Through a model, the relation between the V(BE) and I(EC) is Ice is proportional to exp(Vbe) (exp is e power). There are other components called FET (field emmission transistors), which vary as Ice proportional to Vbe^2.

In the next article, we'll discuss Op-amps, Comparators and Logic Gates

(Did I catch yous in time for the PBs?)

Sunday, January 07, 2007

Basics of Electronics: Diodes


Well, this is going to be a lengthy specialized article. I don't know how many of you have worked with circuits (as in solder circuits), but I atleast can vouch for myself, and Twish. I'll just explain what goes on behind the diode, the transistor, and the op-amp. We've already covered the others, i.e., resistors, capacitors and inductors in our syllabus (technically, diodes are in my syllabus too, but we've not covered them). I'll then go on to explain a very very simple IC, the 555 timer. I'm not sure at this point whether do post them as parts or as a whole. But I resolved to finish the entire article today, so at least I can post the bits and pieces over a few days.

Diode:

First, lets look at the generic diagram of a simple P-N junction diode:

The 'P' junction is a semiconductor (generally silicon) doped with a trivalent element, like boron, so that it becomes an electron-deficient species. They have electron acceptors, or 'holes'. As always, the guys behind this liked to complicate their lives and ours, so by convention, we talk of the 'holes' moving, rather than electrons. The trivalent dopant atom (Boron), cannot properly bond with the neighboring Si atoms; one of the four bonds lacks an electron, which it readily will accept from any source it can lay its hands on.

The 'N' junction is a semiconductor doped with a pentavalent element, like Arsenic, so that it has an extra electron (as compared to the usual four). They give out electrons. The As atom has an electron, after using four of its electrons to bond with its neighbors. The bond energy of this electron is pretty weak, and the electron can easily be cajoled into leaving.

Let's move on to the function of this simple device. As soon as you join these two 'junctions', the electrons from the N junction immediately 'neutralize' the holes of the P junction. This creates a void space in the middle in which there are no charge carriers. Note that a conductor conducts only due to carriers, and hence the absence of them makes the void space an insulator (a very thin one though). This region is called a depletion zone.

Now, as with all insulators, and all materials in fact, if you force it enough, you can get electrons to flow. When the holes and electrons have met, they leave behind a positive dopant ion, and a negative dopant ion. Yup, you know where I'm going with this, a field is established in the reverse direction. So, if you establish a sufficient potential difference between the two ends, the electrons have enough energy to make it through this gap, and current can be established. In general, I've seen most references say that the gap closes, but I feel that is simply a convention established, to easily explain the phenomenon.

A good question to ask at this point is after the electrons jump the gap, shouldn't they fall into the holes again? In fact, they do, and that is why there is some potential drop across diodes. A key difference between semiconductors and conductors is the number of electrons/holes it has is finite. That means that you can fill them all, and go on with life. That is why the graph of the I-V of a diode isn't just a right angled line.

There are two ways a diode can be connected, forward bias and reverse bias.

Forward Bias: In this setup, the positive (or higher potential end) is connected to the P junction, and the negative (or lower potential end) is connected to the N junction. This will establish from P -> N. That means the electrons are pushed from N -> P, which is a good end. The N junction has excess of electrons anyway, and the depletion layer potential is in the P -> N direction. So the external field overrides the internal field, and the electrons merrily cross the depletion layer. Once the potential of the depletion layer is reached, the current jumps up to its normal value, from a meager trickle earlier.

Reverse Bias: If you were to flip the connections, and connect the P junction to the negative terminal, and vice versa, then you would create a field in the direction of the internal field, increasing the gap. You would get no current in this manner. However, if you increase the potential enough, the material of the diode breaks down, and suddenly allows a lot of current to flow. This is called avalanche breakdown.

Now you know how a diode works. I know most of you already know this stuff, but I had to clear the way for the other topics.

Coming Soon: Transistors...

Friday, January 05, 2007

Biology & Astronomy - Questions, not Answers

Alright. Two things being tossed off my mind here.

1) Why February?

So when the calender was first made (gregorian), the months were given days according to the motion of the moon. Also, it was noted that a year is about 365.25 days, so a leap year was added every four years to negligate the approximation of 365.

However, it was noted that the days in one month had to be truncated to fit in 365. And then they truncated them from Feb. And now we can't rely on the day of the month to find the location of the moon.

But why were these days removed only from Feb? Why weren't the number of days in every month made equal?

2) Negative Half-Life?

Although a half life is negative, as in it is for decomposition, is there anything opposite to the phenomenon of exponential decomposition?

Take the example of Cancer cells. They divide, then the two cells again divide etc. The rate of reproduction increases over time. My question is, is there an accurate exponential formula for this? There really should be, according to physics, but there may be factors which inhibit the reproduction of a particular daughter cell of a cancereous parent...

3) Time travel

You will just have to wait for the release of my book.