Probably Approximately Correct

Here’s one I’m pretty sure every IIIT student has had to endure at some point. It goes like this:

Non-IIIT person: Hey, do you know how to deal with (random computer problem)?
IIIT student: Uh, no…sorry.
Non-IIIT person: What? You go to IIIT, don’t you? And you can’t fix a COMPUTER?!?

The way I fix a computer is I buy a new one. The perception that all CS students can deal with anything related to a computer is based on ignorance and stereotypes. True, a lot of people at IIIT work a lot in computer science, and a lot of work is done with computers, but just because everyone eats food doesn’t mean they all know how to cook.

And another one:

Non-IIIT person: Do you know what the answer to (random question) is?
IIIT student: Uh, no…sorry.
Non-IIIT Person: Ha, IIIT Boy here doesn’t even know how to solve it!

Ok, Tardtastic. Just because I did well enough in high school to get into IIIT and somehow managed my multiple choice options to get into IIIT; it does NOT mean I can solve every single problem ever conceived. I can barely even solve the problems in my own field of study. If I knew so much, do you think I’d be talking to you? No, I’d be thuggin’ into the likes of Newton, Guass, Hawking.

I think people from schools like IIIT/IIT are automatically put at a disadvantage due to this amazing ability that everyone thinks they have. If people have few expectations of you, it’s easy to surprise and impress them. But if expectations are always high, disappointment is a single mistake away. It’s gotten to the point where I’m reluctant to tell people I go to IIIT/IIT because I’m afraid of what they’ll automatically assume.

On the social front, though, the IIIT reputation can work to our advantage. If you have the ability to converse with other humans and have a good time with minimal awkwardness, people will often say, “You don’t seem like you go to IIIT!” Their expectations were so low that just being able to act somewhat normally impressed them.

[Esc] :wq

The set theory taught to us in the secondary school levels has a big trouble — It cannot be called a theory in the first place. For it suffers a contradiction, viz.,

Let us call a set “abnormal” if it is a member of itself, and “normal” otherwise. For example, take the set of all squares. That set is not itself a square, and therefore is not a member of the set of all squares. So it is “normal”. On the other hand, if we take the complementary set that contains all non-squares, that set is itself not a square and so should be one of its own members. It is “abnormal”.

Now we consider the set of all normal sets – let us give it a name: R. If R were abnormal, that is, if R were a member of itself, then since R only contains normal sets, R must be normal, which is contradictory to our original hypothesis: R is abnormal. So, R cannot be abnormal, which means R is normal. Further, since every normal set is a member of R, R itself must be a member of R, making R abnormal. Paradoxically, we are led to the contradiction that R is both normal and abnormal.

This paradox is, often, referred to as Russell’s Paradox. Fortunately, consistent set theories exist — One of them is Zermelo–Fraenkel set theory.

Coming back to the informal set theories taught to us — these are attributed to the legendary Georg Cantor. Besides set theory, he gave us the wonderful notion of countable sets, uncountable sets and infinities. In a revolutionary result, he claims the following–

Not all infinities are of the same size! He, also, claims - Give me an infinity and I shall construct an infinity bigger than yours!

Informally, he claims In particular, the power set of a countably infinite set is uncountably infinite.

There are few more interesting things that come out of Cantor’s Results –

• The ratio number of problems that can be solved on a computer to those that cannot be solved is exactly equal to the ratio of number of Natural Numbers to Real Numbers.
• He, also, goes on to prove that set of real numbers is the smallest infinity that one can find.
• The number of Real numbers between 0 and 1 is exactly equal to the total number of Real numbers!

No, No. I am not referring to the English(Indian) Premiere League or Serie A. Those are the ones I am least concerned about these days. The past week or so has been very hectic for me. Hmm…..Hmm….. So, after an indecision/dilemma for about an year or so - its finally decided and fixed.

I will be graduating this convocation with a B.Tech (Hons) and a Masters by Research in Computer Sciences. The last week was spent in writing and compiling the first draft of this thing.

The title of the work will be “Agreement can be Easier than Point-to-Point Communication”. Informally, it is about the following — Given a network of computers, it may be possible that the computers will not be able to reliably communicate/route messages to each other but they can agree on something. Per se, agree on whether a database operation has aborted or been committed. In this work, we characterize the networks over which agreement is possible but Point-to-Point Communication is not (that is, we give the give the connectivity requirements of the network and the ratio of faults to non-faulty computers).

The result sounds both baffling and fishy at the first look as we generally expect any sort of agreement/consensus measures to have reliable communication as a prerequisite or may be even a sub-routine call in the process of reaching a consensus. Our results, however, prove otherwise - Consensus/agreement protocols seem to be more fundamental to network/distributed computing than Point-to-Point Communication!

I am nearly done with my burden and hence, hope to get back to blogging on things I left behind. A couple of drafts have been lying on the hard disk for sometime now :-)

[Esc]:wq

 In 1942, the logician Kurt  Gödel and Albert Einstein became close friends; they walked to and from their offices every day, exchanging ideas about science, philosophy, politics and the lost world of German science in which both had grown up. By 1949,  Gödel had produced a remarkable proof - “ In any universe described by the Theory of Relativity, time cannot exist.“ 

   Einestein endorsed this result reluctantly, but he could find no way to refute it, and in the half -century since then, neither has anyone else.  Among all the contributions of  Gödel - this one is certainly the Queen and most of the times goes unnoticed.

      In case, you are intersted to know more about this particular result of Gödel – refer “The Forgotten Legacy of  Gödel and Einstein” by Palle Yourgrau.

 ——-

        For those readers, who are unaware of  Gödel’s contributions to Computer Sciences and Mathematics; I compose this brief overview about Gödel’s result from Aaronsons’ lectures.

There’s an amazing result called Gödel’s Completeness Theorem, which says that these rules are all you ever need. In other words: if, starting from some set of axioms, you can’t derive a contradiction using these rules, then the axioms must have a model (i.e., they must be consistent). Conversely, if the axioms are inconsistent, then the inconsistency can be proven using these rules alone.

I am a student from Xth year of B Tech, I intend to do a summer project/honors/BTP/Dual Degree at center Y. How do I chose my stream? Where should I go? How should I succeed? As T says

Just do a simple experiment- whatever task faculty member gives, complete it ASAP and go back with next set of questions to be tackled or to seek new things to be done, do this regularly, you will find faculty member showing lot more interest in your work, and you get better guidance.

I think any student who has followed this recipe is bound to succeed or at least have an idea of where he is heading. I also think this recipe is perfect for any student — including dual degrees and enough to ensure your degree on time. Rather, I stand as a testimony to the success of this scheme/experiment. All I can tell is it worked for me - why not give it a try? I can even proudly go ahead and state that this is the recipe for achieve anything - right from to job offers at your Google, Amazons to PhD/MS admits at a good place. I go ahead and ask “four questions” which might strike  anyone of us.

Question 1: How do I choose a center?

Answer: IIIT gives you reasonable depth over the first four semesters - so you would have had an idea by now. In case, you neither have a choice nor unable to decide for some reason -   few faculty members (Prof. Kamal, Prof. Srinathan, Prof. Bipin, Prof. Navjyoti, Prof. Madhav Krishna) are open to this idea of CYOP - create your own project. These faculty also work in multi-disciplinary areas. You should meet  them and discuss your interests and aims/ambitions. In case, you are totally confused, I can suggest one solution from my experiences - keep speaking to as many faculty as possible and things will get a lot better. Try to spend some non-trivial amount of time on any book -I bet you will fall in love! In case, you still have a problem as T says - “Prof Kamal is the best person to talk to.” In any case, keep interacting with a lot of people. You keeping quiet and never opening your heart/interests to any responsible person (includes peers, seniors who can advice you or any faculty member) can be the biggest damage you can ever do to yourself. The onus is upon you to act.

Question 2: Do I need to seriously consider the statistics (like placements, MS/PhD admits etc) before I choose a center?

Answer: NO. There have been students from every center in IIIT who have excelled on all fronts. So, I believe any one else can do it as well. For instance, there are students from (any) center you consider who have done well in getting an admit in MS/PhD/MBA programmes at good places around the world; same is the case with placements. So, it is up to you to choose a center of your choice. For me, statistics are the least important things here.

I can go ahead and give names of those people, but I felt again that taking their names is not the requirement. The requirement is for you to realize - “Nothing is impossible from IIIT”. You have not lost anything yet. IIIT is an excellent place and has set it up nicely for you. The game is for you to lose.

Question 3: Which faculty member to choose?

Answer: Well, to find this out -  The best people to meet and inquire about are the students of the faculty member you are targetting. Just hang out with for a while you will get a feel and may be bug your (prospective) peers with the general trivia you are interested in.But, again your choice of peer should be good or you should take inputs from a good number of people; you cannot approach an outlier (a sample that is an exception) and decide on his inputs. So, you have to be careful. However, I think most of us choose a faculty mentor based on our own experiences with him - like the courses we have done under him etc.

Question 4: What should I do when - the faculty member is not giving me a time slot to meet or  I am not able to find the faculty member in his room?

Answer: From a personal perspective - let me tell you a story –

Yaso happens to be fond of catching scorpions and crabs. On a particular day - I find him standing on the bank of a river and trying to catch a scorpion in the river. Each time he catches tries to catch it, he gets a sting and lets it off. I watch him and after I was tried of seeing him do this atleast 50-60 times, I rush to him and ask - Yaso, don’t you understand the inherent nature of the scorpion - it gives you a sting whenever you catch it. You should be mad in doing this again and again. Surely, there is something wrong with you. To which Yaso says, “Dear Prasant:  Such a small creature is so stubborn that it is not abandoning  its natural instincts, Why should I?”

You should be like Yaso who was willing to take a sting but never swayed from his natural instincts. The natural instincts of a student is to seek - seek knowledge and should be ready to take in a sting or two on the way.

This story was an eye opener to me just for a simple reason - It is your future/progress is at stake. So, is it not your responsibility to catch hold of your advisor? Of course - the faculty also must play his part. But, certainly the onus is on the student to catch hold of his advisor and seek from him. In short, a student should be a seeker. You should chase your faculty - you may ask me why should I, he has given me a project; is it not his responsibility to call me, tell me what should I read and how should I make a decision. All I can say is one thing - Your faculty member cannot more interested than what interests you show in your problem nor can he spend more time than you in the problem. In short, he cannot be more interested to meet you than what interest you are showing in meeting him. So,  understand that it is your interests in the problem and the urge to meet him that decide the fate of your project. 

All I can say is - “Nothing is impossible from IIIT”. You have not lost anything yet. IIIT is an excellent, exceptional place and has set it up nicely for you. The game is for you to lose!