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.

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.

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.

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!

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 ~

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 ~