Godel

Godel's theorem as it appeared in Proposition VI of his 1931 paper "On Formally Undecidable Propositions in Principia Mathematica and Related Systems I.":

To every w-consistent recursive class k of formulae there correspond recursive class-sings r, such that neither v Gen r nor Neg (v Gen r) belongs to Flg(k) (where v is the free variable of r).

which translates to

All consistent axiomatic formulations of number theory include undecidable propositions.
...
Godel showed that provability is a weaker notion than truth, no matter what axiomatic system is involved.
...

Escher

Escher takes you down Strange loop (or is he taking you up)

Two-step Strange Loop

Self-reference

Perpetual motion

Metamorphosis

More Escher pictures

Implicit in the concept of Strange loops is the concept of infinity, since what else is a loop but a way of representing an endless process in a finite way? And infinity plays a large role in many of Escher's drawings.
....
In some of his drawings, one single theme can appear on different levels of reality. For instance, one level in a drawing might clearly be recognizable as representing fantasy or imagination; another level would be recognizable as reality. These two levels might be the only explicitly portrayed levels. But the mere presence of these two levels invites the viewer to look upon himself as part of another level; the viewer cannot help but getting caught up in Escher's implied chain of levels, in which, for any one level, there is always another level aboe it of greater "reality", and likewise, there is always another level, "more imaginary" than it is.

Graduating from B.E. to B.Tech

It was August 1994. Ragging was still not banned in Andhra University. As a junior here, everyday before and after each class, whenever there was free time we were subject to bantering from our seniors. This was supposed to be an informal way of knowing your seniors :-). These seniors were from all departments of engineering and sometimes from the arts and sciences too. One thing palpable, after being subjected to this routine everyday, was I never got to know who my real seniors were, as I never encountered anyone from the EE department.

One Friday afternoon, just when I thought I could escape the prying eyes of seniors, my fast pace home was interrupted by two seniors. I knew this was going to be another of those long Friday afternoons. I gave them my SD (Self Definition/Sontha Dabba), which was a standard practice, and part of which said I joined the EE branch. From there this talk went into unchartered territory as they started asking me about Thevenin's theorem, Norton's theorem. This was very unlike the ragging I had encountered earlier where you are at times subjugated to phyiscal and mental humiliation. But this was turning out to be not one of those. This was one of the most interesting talk I had with anyone on the campus and probably in retrospect I could say that this was the start of a four year long endearing memories.

That talk in short says all about the EE department and its students. This department had earned a reputation of being rigid, stern and highly disciplined. This department had in its faculty, members like Prof. Ratnam, Prof. Govind Rao, Prof. Sitaramam, Prof. Ramamurthy and Dr. Bapi Raju to name a few. You could easily see the demarcation as to how the classes and labs were conducted and how the students of these department were. It says a lot about the institution that these people built. It rose above mediocrity (that is not to take away anything from the other departments), often times challenging the entire university apparatus. It takes a lot of courage to rise above the average and then make everyone else believe the same. It takes a lot of character to set higher standards and then follow them under all adversity. I am sure these Professors had endured a lot of flak while building the institution, at times from their peers and others from their very own students (and they still do). What I saw, during my four years there, must have been the result of years of unperturbed dedication.

Today, when I look back, I realize how fortunate I am, to have done my undergrad from that department. I feel very proud to say that I did my undergrad from the EE department of AU. It is no mere coincidence that this department within a span of two years had produced the GATE topper twice (one of whom is a very dear friend of mine) and one GATE second ranker (one of the two who ragged me and was probing my understanding about Thevenin's theorem). This is, again, not to take away anything from those rankers. They thoroughly and richly deserved it. It couldn't have happened to any more brilliant people, but I am sure they too would acknowledge the sleight of that wonderful faculty.

Alas, those achievements turned out to be just like an earthern lamp which when lit gives light all around, but then it also exudes its full brilliance right before it starts to wane down. On my last visit there, I could see first hand how the department had slipped down. We met some of the older faculty members who have since moved to private colleges. It was a sorry plight to see the once revered department being run by people who interpreted their seniors way of running it all wrong. While the Professors before them believed in always setting the bar high up, with emphasis always on attaining higher learning (transient state to steady state by Prof Govind Rao), exploring beyond the realm of text books (any of Prof Ratnam's lectures). They sometimes seemed a bit stretched, especially, when you saw themselves in the context of students from other departments. We had been asked to leave 7 lab's at a stretch when we couldn't answer a seemingly innocous question What is voltage rise ? , or were made to look like idiot savant's for not knowing the meaning of moron :-). I am sure much of this was intended to get us out of our shells and to disband any preconceived notions we might have had about how our next 4 years would be like. Unfortunately, the part which caught on with the junior professors, readers and lecturers was the nagging part. They just thought that they could have their way and keep us under leash by always keeping us on our toes. This was a classic case of Lost in Transition. One group of people were looking to liberate us and the other trying to restrain us.

Today, AU is being considered for conversion from a University to an IIT, a rare honor for any Indian university. How I wish, the UGC could have woken up atleast 5-8 years earlier, that is when they would have seen this department (I cannot speak for the university) in its full splendor. Even today, if I still haven't forgotten some of the lectures, terms, and the process which I had learnt there, it is because of the quality of teaching. I am not sure how different IIT's mode of teaching is, but I am sure they too would have admired the EE department of AU and would not have found it wanting in any respect.

How happy they will be in seeing the institute graduate from a BE to BTech. It would have been a fitting ode to the distinguished faculty to have seen their hardwork, dedication, vision pay off this way. But then they didn't work for this honor right, because no work can be as resplendent as this when driven by the fruit. The fruit should always be the by product of karma, not the guiding light.

Strange Loops

Strange loops occurs whenever, by moving (up/down), through the levels of some hierarchial system, we unexpectedly find ourselves right back where we started. Sometimes I use the term Tangled Hierarchy to describe a system in which a Strange Loop occurs.

Hofstadter is talking about one of the types of recursion here. Recursion, that eternal principle which is the core of all programming. I don't think its pure coincidence that it rears its head at all times at the most unknown places.

It, being a common tenet for all programming, is because recursion is present all around us. Its the basis for mathematics, sciences and life as a whole.


I, for one, believe that the universe is a manifestation of a small pattern repeated over and over again by using recursion principle. (More on this later ...)

Whenever we encounter recursion, we always look for a terminating condition to break out of the loop:

while(true)
{

TryAgain();

if(M)
{

break;

}

}

In the above psuedo-code we break out of recursion when M is achieved. This can be achieved while we go through this another loop TryAgain which at some point will break you free of the loop.

But as we will see later on there is more than one way to break out of the loop even without achieving M here ...

The strange loop which Hofstadter is talking about is when you are in a circular loop. People familiar with a circular linked list can easily identify with it. Its a hierarchy with a parent node showing way to a child node. But somewhere along, while traversing the hierarchy, the child node loops back to one of its parent nodes and we end up in a tangled hierarchy.

GEB

I recently finished my reading of GEB and based on one of my close friends idea I would like to present my thoughts as I read through each of the chapters.

For the unintended and for someone looking for a reason to read this book, let me try to paraphrase what this book is about. Before I do that, a statutory warning: Numerous people before me have tried and failed and I know I myself might become one of them, but nevertheless let me give it a go.

First and foremost let me try to define the target audience: This book has an unprecedented fan following on the net throughout the world, so that would mean a huge chunk of the cyberworld population. The kind of people who will find it instantly likeable is someone who likes programming, mathematics, philosophy and above all someone who is looking to find meanings in forms.

Now what this book is about: This book takes you through an unforgettable intellectual journey, something which will stay with you for a long time to come. For me this book is all about discerning patterns where Hofstadter tackles Math, Arts, Music, DNA, Turing and Zen among other things and reunites them all under a common thread.

In case you have started wondering how in the world can these discordant things be connected at all, I highly recommend you to take this journey where Hofstadter with a prelude of dialogues follows it up with profound images of self reference and the likes which is bound to keep you hooked.

Play by their rules and you will survive

Do I have to subscribe to one of the ism-s to survive? Why this fixation within society and with men that he has the best method of solving problems and his ideology should be ceded to by one and all. And see the paradox, he wants other men, the same creation to pledge support to him and to do what -- to prove that he is right. When was this social milieu created? But on the other hand, I do feel that this is the thread which is keeping the social order in place, else there would be anarchy if true freedom prevails. The beast that man is, the needs to be baited always, and enough to keep the savage inside him crushed. We have been seeing and will see more in future the rise of this barbarian under different hoods, he will rise and rise until freedom is achieved. If you ask freedom from what - freedom of expression, freedom from oppression, freedom of thought. This freedom is gonna bring a few things, but will peace be one among them. I doubt it. Then will it be worth it. Yeah, maybe.



What has Capitalism achieved us? What has Communism achieved us and for that matter what has most of these ism-s achieved us. More delusions. The only thing they have accomplished is push us into more chaos. No, don't get me wrong, I am in no way intending that this is bad. I think what it has achieved is just ephemeral. But then these are just smaller parts of the bigger revolution which seems to be happening as we speak.

What is a living being?

Who or what is a living being? Let me try to see if I understand it right ...

We don't call a thing as living being if that thing can just breathe. Also its not an object which can move. Then what constitutes a living being? Is it just its ability to reproduce? If I do see some nodding heads then I would like to dwelve a little deep as to what we mean by "reproduce".

So reproduce is producing oneself again, or basically copying one over. So works well for the modern definition of living beings where we have covered all taxonomic groups. Fair enough. But with our understanding of Genes and how we replicate ourselves, lets see how or why we need to make some changes.

Gene theory tells us that there is a certain DNA structure which is copied over after some permuations and combinations between the two sexes (atleast in most cases). Now we know this gene is a molecular structure which given the right conditions and a set of definite time is able to decode and arrange a given set of molecules in a certain way and hence successfully replicate itself up. So a couple of things which I think needs emphasis -
1) right conditions without which the culmination and hence the replication might never happen
2) definite time which varies based on the complexity and a lot of unknown factors (lets say its the time of implemeting an algorithm)

Well there is our reproduction flowchart. Apply it and wow, you can copy yourself up. But wait a minute, isn't that how NaCl, O₂, H₂O, CO₂ and everything around us (and actually the so called US) have been formed. There are not 100% NaCl molecules around us, neither are there 100% O₂ molecules and why is that. Its the same magic principle, the reproduction flowchart. Continued later ....

What today constitutes our antipathy to "man" ?

What today constitutes our antipathy to "man" ? - for we suffer from man, beyond doubt-- Nietzsche

So what am I waiting for ? Where do I think this next revolution will come from. Am I not becoming one among them ...... This really sucks, this whole drama enacted so perfectly and here I am playing away my part. Why is that I no longer feel the urge to come out of it. Why has my spirit been handed a premature death.

No but there is hope too, I know the next big change is around the corner, it has already started exuding, yes I know it wont be long. This is more of an idiopathy. Yes, the maligned tumor which has been growing is now too big to be controlled.FREE US, GET THE SELFLESS SPIRIT OUT, yes, LET IT FLOURISH SINCE THATS THE WAY IT WAS SUPPOSED TO BE.