Reactive Self-Perception

I sometimes do just love these long train journeys where I get to sit 30hrs in one position and just look around and think. It just lets you introspect. It lets me analyse the world around like never before and observe the ocean humanity flow by as if I am not a part of it. Watch everything from a distance and yet not feel a part of it. Look at the world around as if I am looking from outside but with as much proximity as anybody living in it but letting a larger picture sink in unrestrained by all personal affiliations and identifications.

This state of mind lets in thoughts which I have never thought and lets me think about non-academic things at a greater depth than usual when I don't even remember the very possibility that I can have a non-academic life. Given my recent mental disposition sprouting from some recent emotional and relationship adventures (which generated the last 2 blog posts) every little human interaction was seeming like hitting back at me with greater force than ever before. But I have this ability to detach myself from such issues so that I can quickly get back to logical thinking, my natural state of mind.

And in these times reading or thinking about Economics provides something intellectually challenging to pursue while crammed in half-a-seat in an Indian train. It just looks so relevant.
Hence sharing here the thought and insights developed in those lonely hours.

Hence I started reading about this idea of "Reactive self-perception".

I was reading how some countries in the post-colonial period have failed to take full advantage of the globalization leading to the opening up of markets. It has lead to an unfair distribution of the advantages of globalization and this stems as much from the faults in the implementation of market economy in a globalized manner (like super-powers maintaining an upper-hand in terms of patent rights etc) and also because of these colonized people unable to recover in some sense from the age of empires. The countries which have been severely hit by this are the African ones and India to some extent but India has somehow escaped the terrible situation of Africa thanks to its active intellectual movement and powerful press and media which has championed the Indian identity in a very assertive way. India at least didn't see the severe internal collapse leading to civil strife and famines and blood pools which Africa has seen since the end of the colonial period. Unlike most South-Asian countries they are yet to see the fruits of democracy.
Not that south-asia has been any paragon of democracy but the implementation has definitely been much better than in Africa.

Now the interesting thing is that this has serious roots in the subject of psychology (interesting how psychology helps understand global economics!) in what is called the "reactive self-perception" .

Reactive self-perception is the state of the mind when one decides one's identity NOT as a result of an analysis of one's own self but as a response to what OTHERs think about him/her. If for centuries a set of people are ill-treated and humiliated and told that "you are all idiots" then the first generation takes it as an insult and might revolt but if the revolt is crushed then the next generations believe that their identity is of an underdog. After a century these people start seeing themselves as the "natural" underdogs and suffer from what Nobel Laureate Amartya Sen calls the "illussion of destiny". They start thinking that their natural place is at the receiving end of the world and are not supposed to be the agents of change but can only be the receivers of whatever the powerful gives them.

This reactive identity can lead to mis-utilization and under-utilization of resources and also fatalism. It can lead to a complete failure of all the goods to be achieved out of globalization. There is a market where people are ready to buy and sell but the people with the products aren't there to bargain the prices since they don't realize that they have the power to bargain! The producers coming from underprivileged backgrounds are not even psychologically prepared to challenge the buyer into giving a better price! Again even in an open market economy the advantages of fair dealings is lost because of internal psychological barriers.

I think even in day to day life and in our social life this feature shows up where lots of voices and talents are unheard and unused simply because the voice and talent belongs to someone who has been collectively ostracized by the society and hence has been implicitly led into believing that he/she is incapable or wrong!

Further this kind of Reactive Self-Perception can also become the roots of terrorism where one starts defining one's identity as a reaction to some certain set of ideas. Like even though any well-reasoned person will understand that it is hard to distinguish between what exactly is a "western idea" and what exactly is an "eastern idea" given the amount of mixed global heritage we inherit, unfortunately much of Islamic fundamentalism relies on this "reactive identity" where one starts defining as "Islamic" everything that is in contradiction to whatever is commonly called "western"! This can lead to devastating effects as the world is aware of like the recent declaration of Talibans in the SWAT valley that "democracy is un-Islamic"!

Islamic fundamentalists have unfortunately looked as "Islam" as not a philosophy stemming from certain geographic regions but as a symbol of being "anti-western"! Islam as an answer to everything that the west seems to stand for. Its roots are probably not far to seek when the west at one point did pump this Islamic identity to counter the Russian.

One day this is likely to hit-back the social memory of Africa that when the world was agog with Obama being elected in the USA, millions died in Zimbawe in famines. Its likely that the world will eventually pay for this grave error.

Linking to what was being said earlier, there are reasons to believe that eventually this sense of "reactive identity" coupled with the implementation errors of globalization and open-market economy it will lead the neglected Africans into becoming a base for terrorism in the coming years. Today they are physically weak because of the famines, tomorrow they will be psychologoically suicidal and the mortal pains will become irrelevant. We are very likely to see a rise of another Osama Bin-Laden in Africa in the next half-century mimicking the Islamic terrorism that sprung from the middle east and has wrecked havoc in the last half-century.

African terrorism might be just round the corner.

And the next day after being candid.

I wake up the next day and I tell to myself

"Its all useless. Chalo forget it. Lots of work left to do"

I thank for the existence of this subject called Maths and Physics which look like infinitely deep holes to me where I have dived in and more I sink into it more seems to exist down there. And thankfully so!

Otherwise what else other than Representation Theory and Quantum Fields could help forget such things?

Another day. Newer things to learn. Newer roads to walk.

But the destinations never change just that I carve out new untrammeled paths in this wilderness.

The paradox of commerce

The other day I was eating in a shop in the Indian Navy campus and I was impressed by the shopkeeper who was selling jalebis and refused money for his jalebis since they had gone cold and were broken. Some people might say that he was not thinking economically but I think he is only being more efficient by ensuring that because of this attitude I will come back to his shop again when he would have hot jalebis which would taste better and he can then have the full right to charge me the cost.

This is probably the biggest effect years of scientific training has on you is its ability to make you capable of going through various situations in life without emotional involvement. Gives you the ability to observe subtle aspects without being touched by them. Can't say much about Physics but mathematics education definitely gives me this powerful ability.

Of course scientific training if gotten into the blood also has interesting social and personal consequences! Most innocuous of them is probably the sensation of solace and deep happiness when I can cocoon into the cubicles of the academic institutions with connectivity to the web far away from the hustle-bustle of million people outside apparently enjoying their lives. Gives me that detached perspective where I feel far away from the party outside and seem to see grander visions of universal features through the regular struggles of other people's lives.

A state of mind when you start thinking like an AI without emotional edges or ripples of human bonding or binding. A state of mind where the amorphous existence of the human race seems to crystallize into bare essentials. A state of liberation from all local identities of caste,state,religion,language,party and elevation into the state of being an observer and a thinker.

And many people see it as my fundamental inability to feel associated to anything, feel a sense of belongingness to any particular sect. And this misunderstanding leads them to think that I am an hypocrite. What they can't see is my feeling of association with the human identity. This is an identity which makes you humble at the thought that apparently we are the only one around who can think deductively. In many cases I am an unapologetic reductionist.

Its a feeling of being a global citizen minus any sense of local identification.

I don't see why people host huge parties etc on their marriages with rituals going on for days! I see the bare essential to be 2 people signing a legal paper that the Indian constitution wants them to. If the 2 people are mutually compatible then anyway they will live happily and if they are not then no amount of grandeur of parties and rituals will keep them together. If I ever ever decide to marry then she and I will one fine morning go to the marriage registration office and sign the papers. Of course we would have lived together for quite some time before doing this.

Why am I suddenly thinking of these things?

It probably stems from a sense of betrayal I felt from my visit to a restaurant in Mumbai called "Calcutta Club" which specializes in Bengal cuisines (West Bengal is a state in the eastern part of India). When in the company of people not from West Bengal I have always defended Bengal whenever people from other states start poking fun at Bengal along the same old stereotyped issues. I generally have an publicly unacknowledged advantage in such discussions since most of these stereotypical features are missing from me and many people before initial introduction thought I was from the southern states of India! But this restaurant, notwithstanding the fact that the food was good seemed to put up a weirdly hypocritical show about being a representative of Bengal in the middle of Mumbai.

This restaurant had put up posters all around of Amartya Sen, Rabindranath, Soumitro Chattopadhyay, Satyajit Ray, Mother Teresa and what not. The photographs didn't seem to have any apparent reason for being there except for the fact that all of them had something to do with Bengal. The set of photographs on the wall were completely thoughtless to say the least and seemed to be screaming out with a sense of cheap "selling" Bengal to Mumbai.

I wonder whether Nobel Laureate Amartya Sen would approve of his photograph being hung by the tables of a restaurant!

And more deplorably there were customers in the restaurant who seemed to think that this was a great thing to do since this "Brings a sense of being in Bengal" ! I was struck at the lowly levels of thinking to which people can fall to and at the gullibility of the average customer.

I am sure many customers in that restaurant would happily walk out of the resturant full of photographs of Rabindranath and Satyajit Ray and drink like a hog in some nearby bar and return home drunk in a totterring state. Wonder if that also makes them feel like a Bengali!

While I was wondering about these things people around were busy wondering what a long time it has been since they ate proper Bengali food and debating over apparently irrelevant questions like whether item X should be had before Y or vice-versa. I have eaten a hell lot of different kinds of foods in my life and I have learnt to appreciate culinary skills of the human population without a sense of attachment to any particular type. Again a scope for the cynics to attack me.



This situation reminded me of a dialogue by Amitabh Bachchan in the movie "Cheeni Kum" where he as the chef of an Indian restaurant in London proclaims that

"We are not like other cheat "Indian" restaurants in London which put up posters of elephants and tigers and sell anything in the name of Indian food to ignorant english people"

Unlike Tabu in that movie, I was in the company of people who were highly appreciative of "bengal" atmosphere of the restaurant and hence because of social restrains had to control my bursting rage at the misuse of these great people and walk out of the restaurant immediately.

No wonder I run into so many social conflicts since when other people around were appreciating the food, I was feeling a sense of betrayal. I couldn't get my mind off the fact that this restaurant was downright immoral by misusing the names of these people.

I wonder when or if ever India is going to come out of such cheap business models which try to sell by rousing cheap local sentiments. Why go and blame the politicians for making hollow speeches if we keep patronizing such restaurants which adopt such hypocritical business models?

Of course this attitude of trying to "sell" doesn't restrict itself only to restaurants but also penetrate deep into the society and disastrously reflects in the way Indian education is compromised. I am scared of the day when corporate sector shall start determinig syllabuses in colleges so that they can "produce" efficient workers.

I am already seeing such trends in the Physics education scenario.

Growing up is learning the art of silence -Part 1

3 years ago when I was studying about the Dirac Equation, a few months later a question came to my mind as to how would one go about writing a representation of the Clifford algebra for arbitrary dimensions. I somehow felt very uncomfortable with the idea that Dirac was picking up the 4-dimensional representation and it was sort of a magic that it was giving me the spin 1/2. {Today I hopefully understand more about what is going on here given the studies on spin and representation theory that I have done over these years.}

But then at that time I was a kid compared to my present self. I went to my classmate Swarnabho and asked him to explain this to me since I knew at that time we was studying Representation Theory. What I got from him was a load of sarcasm and lecture regarding why I was dabbling in such "hi-fi" stuff when I didn't know basic group theory etc etc etc. But neither for once did he even give me a reference which I could look up. I felt damn irritated. (This was neither the first nor the last time I got some non-sense reply from him. I definitely respect him for his huge knowledge of mathematics but I am sorry to say that I never got any help from him whenever I asked him. I this respect I got tremendous help from Vipul who is definitely one of the finest brains in among science students that I have ever met. )

What this interaction with Swarnabho resulted in was me running down to the computer room in CMI and write a blog about this "characteristic attitude" of mathematicians. This blog of mine irked a lot of people around and rightly so.

I clearly remember the email reply I got for the blog from Nivedita. She lashed out at me. Again rightly so.

Recently when I met Nivedita a few weeks ago I was wondering at the back of my mind whether she was still talking to the author of that blog or to me. I am optimistic.

Surely I did a stupid thing then by writing that blog.
May be that action of mine was more stupid than Swarnabho's enlightening sarcasm.

People live and learn. I am optimistic that I do that too.
At least I am sure I won't write such a stupid thing today! Today such an experience would probably result in a blog post or probably silence.
{I have just gotten used to so many weird experiences about human relationships!}

Deep down I know I am a completely different man today than the guy who wrote that blog then. But then again as Vipul said to me once

"Even if you change overnight, some people will never change how they perceive you"

:D

Its actually so very difficult in life to communicate what one really wants to say and its so easier to send out a wrong image. At one level I believe its just not worth one's time and energy to ensure that everyperson interpretes things correctly. Its probably again that silence can come to the rescue and let one focus energies on ensuring that a select group of people see the right things.

Silence gives birth to selectivity.


This is probably the essence of growing up. Somewhat CMI life forced me to mature faster as a person than what might have naturally happened. Probably it was the intellectually charged atmosphere of CMI in those days and the completely hay-wire courses where in-class comprehensibility was low and various social factors which forced me to grow faster. Today when I look at people from colleges in various other parts of India I feel this one thing significantly as to what a massive impact the challenging environment of excellence in CMI in those days could have on a receptive mind! It sent my scientific maturity of thinking way ahead. {Though I must say that the terrible Physics curriculum of CMI didn't teach me much when compared to the Physics courses of IITK} I absorbed more essential things like global maturity of thinking from the environment than I did from the classes.

What CMI atmosphere did to me in the first year was to kill all possible narrowness that might have existed in my mind and open up my thinking to make it receptive to radically new ideas which students from other colleges would not be able to appreciate readily. It was becoming natural for me to see by the middle of my second year of BSc. as to why one needs the idea of "parallel transport" on curved spaces to make sense of Newton's laws.

The most essential ingredient of this growing up process is the art of silence.
The most important tool that one develops as one grows is the power of silence.

The importance of the moments when you look inwards and think harder through everything and get clarified about precisely what all things you understand and what all you don't. Its a process which leads good results whether the question is scientific or not.

Its about learning when to be silent. Its probably a big thing that I learnt while at CMI that no conflict is ever resolved by speaking or talking or discussing. Its best resolved by thinking silently and then coherently putting down in words and sharing the writing with relevant people.

The identification of the "relevant" is also a part of the growing up process. That as you grow up you learn to pick out from the surroundings who are the relevant people i.e who are the people who serious enough about the issue that they would like to understand the reason and the resolution of conflict. When I was kid in the first year I was full of optimism about this that everybody is interested in questions and issues I am interested in.

Its a useless waste of energy to try to make lots of people see a subtle point about which you are excited about and hence efforts should be concentrated on the relevant people and not communicated via public mails.

Long long ago in the past I used to have the optimism that I can make many people see why I think something is worth thinking about. That something was at times why spin of a particle should be defined by irreducible representations of SU(2) instead of any other "physical" idea or why smoking/drinking alcohol should be banned inside institute premises.

Silence is the route to resolve the relevant set.

In very simple cases like that of curved space-time I realized as I grew up that not many are interested and in more complicated cases like whether there should be reservations in colleges, even lesser people are interested!

Its a hard fact that the process of growing up teaches you is to recognize that 99.99% of the people around are not interested in things that you might be seriously interested in. And it would be massive foolishness expect any larger fraction of people to be interested! More important the matter is on a larger scale lesser will the people interested in it. But this scenario should not be a deterrent to you pursuing the cause if you are yourself convinced that the cause is important.

This is also again one of the realizations that arise out of silence. The determination to pursue what you think is important regardless of what other people have to say about it. Silence is a tool that helps to not get lost in the crowd.

Silence is a way to take firm decisions.

When I was a "kid" in BSc. if I thought that the teacher in the class was saying nothing sensible the I used to directly say that in the class and object. And hence got into serious trouble. Today I know that this simply doesn't help since me pointing out the trouble doesn't suddenly raise the intelligence or the knowledge level of the teacher (unless of course the teacher is exceptional who appreciates subtle points like say Prof.Amol Dighe in TIFR) and almost always most of the class doesn't see the subtle point. Its a useless waste of energy again.

Today I choose the silent way out of such situations. I simply bunk the class at times or I might send my feedback about the stupid class when I am officially asked for it.

Again silence becomes an artistic tool to fight life.

But then one should be beware of the pit-falls of silence:

1. On should not resort to silence as a mode of communication! Like if I my girlfriend (lets assume one exists and is unique for this discussion!) resorts to silence when relationship is in trouble then the situation only becomes grim. Silence might become the route of further confusion by becoming a gap in the communication. In such situations each side must probably think in silence and write out everything coherently and communicate in writing rather than start shouting at each other.

Thinking and writing frees the mind. (why I blog!) Its an art as to how to use silence.

2. One should not become suddenly silent without trying to sort the trouble! Its as bad a solution as just passing by like a stranger whenever this person with whom you are in trouble with is passing by. Its best to first to be silent and think about everything through and then try to talk with the person and get things sorted and if then things don't work then assume complete silence but by giving a notice to him or her like

"After thinking a lot, I think you are hopeless and brainless and useless talking to. Hence I am becoming silent. Do you have any further clarifications to give before I shut off? "

I have been at both ends of this problem! I would have greatly appreciated if the people who at times assumed silence with me to have given me a notice like the above becoming so! :P

Silence is an important art that one has to acquire while growing up but not at the cost of losing frank honesty.
But then honesty is a very big thing that only nanoscopic number of people can appreciate and hence again through silence one has to resolve this "relevant" set with whom one can be honest without wasting energies.

In a second post I shall dwell on the more complicated issues about silence like should you be silent when you see a crime being committed? Does growing up mean remaining silent to crime just because survival instincts and matured judgement tell you that speaking-up might mean danger to you? Is maturity of judgement only about diplomacy and hence compromise with honesty?

About doing science and research

When mortally pressed for time one compromises with quoting other people than taking time out to coherently report one's own mind. And hence here I plan to put up links to a some exciting writings about doing science and research about which I could myself go on for pages albeit it comes from only 4 years of experience.

{I shall be biased towards Maths, Physics and Theoretical Computer Science since these are the 3 fields with which I have some acquaintance. Its been a long time I have been committed to Physics and flirting with the other two. Again among the other 2, I have been courting Maths for the longest time and have only been looking at from far away at TCS. Eventually I don't plan to meet the day when I shall need to choose! :P}

Hence the job is best left in the hands of the giants like Dyson, Hamming and Atiyah etc:

1. "Advice to Young Mathematicians" by Atiyah

2. "Heretical thoughts about science and society" by Dyson

3. "Birds and Frogs" by Dyson

4. "You and Your Research" by Richard Hamming

5. "Kill the messenger" by Sunil Mukhi


And yes before I sign off I will tell you to watch the movie "October Sky". It really captures the idea of doing research .

The passionate insanity of doing science and research and that addictive feeling of being involved with an idea forgetting everything else.

Curiosities in Computer Science. Can one go beyond finite and discrete data ?

My knowledge of Computer Science is near 0.
My knowledge of Mathematics is epsilon.
Officially I am supposed to know some finite amount of Physics.


My only slight non-trivial brush with CS was with the exciting course that I took with Prof.Madhavan Mukund at my Alma-mater Chennai Mathematical Institute (CMI). Prof.Madhavan Mukund is definitely one of the best 5 professors I have ever seen in IEMS (Rourkela), St.Xavier's Collegiate School (Kolkata), CMI, IMSc, TIFR and SINP. (4 institutes of India where I have spent non-trivial amounts of time).

{Of course St.Xaviers is a special case in this list from where I can hardly recall a single good science teacher. I definitely got some great English and Hindi teachers. And IEMS (Ispat English Medium School), Rourkela is the school in Orissa in which I studied till class 6. I was in Rourkela for 11 years. IEMS had an intensive mathematics and science environment and that instilled in me a love for these subjects right since my childhood. That school has produced many awesome students and its a pity that today that school is crumbling because of government's apathy towards it and lack of funding. I would urge people to collect together to do something for that school which has given Indian some of the finest students in science in the 1990s and the late 80's.}

Prof. Madhavan's course was awesome to say the least. (those unforgettable days when I used to stay awake for days at a stretch trying to do his innovative assignments...I could atleast get a working code ready for all of the questions, though almost always my algorithm was nowhere close to the slick solutions of some of my awesome batchmates like Hrushikesh, Arnold or Preyas.} For me whose only exposure to programming in school was ISC exam level programming with C++, this was an introduction to the completely new world of CS. I always wished that I could take up more courses in TCS but given my professional commitment to Physics I never could get the time to study TCS more seriously, but I keep hoping that someday I shall study more of it. At least I hope to understand someday Automata and Complexity Theory. Little that I see of it from talking to my various friends who work in these fields, I feel they are exciting things to know.

I later sat through another course of Prof.Madhavan Mukund..just listened to the lectures. But anyway thanks to his lectures in the 2 courses, it sparked in me an interest for CS. It drilled in me a basic fact that CS is NOT programming as is commonly and erroneously conceived.

Anyway here I want to talk of some naive thoughts about mine about CS. These are mostly some questions about CS which I have been curious to understand and know but never got the time to do serious reading about them. I am sure most of what I will be talking here will be naive to professional CS people but then I have been filled with childish curiosity to know about a million things since I was a kid. I have no fears to ask questions no matter how naive they are.

I would be glad if some CS or Maths person reading this blog decided to explain these things to me. I have been thinking of these questions for quite some-time but as usual given my primary commitment to Physics I have never been able to do serious reading along these lines and hence have made no substantial progress. All I have is some questions to ask. Let me at least ask them publicly!

So let me begin.

We know that given a linear map between 2 finite dimensional vector spaces one can represent it by a matrix by a choice of basis in the two spaces. A lot of interesting things begin to happen if the linear transformation is an automorphism and then I have interesting structures to play with like the eigenvalue, eigenvector, trace and determinant etc. Now we know that even if the matrix representation is dependent on the basis one can write the characteristic polynomial of this linear transformation and then the coefficients of this are basis invariants. The coefficient of the highest and the first power are most familiar to us by names of "determinants" and the "trace". And the determinant of of a matrix written without the signum function in its defintion is the well-known "Pfaffian". {There are some very exotic definitions of Pfaffnians through graph theory and through differential geometry but I shall avoid all that stuff here}( I shall avoid getting into the complication of differentiating between the minimal polynomial and the characteristic polynomial and whether the field is algebraically closed or not and what its characteristic is. I shall brazenly sweep these subtleties under the carpet so that I can get my essential questions across to the reader. Reader is requested to assume the best case scenario whenever required :P )

{Most common difficulties will arise when the algebraic dimension and the geometric dimension of an eigen value doesn't match but then if one restricts oneself to algebraically closed fields like the complex plane this problem is gone. So kindly do it if you run into problems :D }

Q1. We needed a choice of basis to define these n-basis-invariants (let the vector space be of dimension "n"). Can we define these basis invariants without a choice of basis?

Q2. So isn't it possible to the give a linear transformation as an "input" to a computer program by giving it these n invariants along with their multiplicities? Can't everything that can be known or said about the linear transformation become deducible to the computer as soon at it knows these n-invariants?

I can see this much that one can solve the characteristic polynomial to uniquely determine the linear transformation (upto permutation of the basis) if there are no degeneracies in the eigen-value.

Q3. The most naive way to specify an automorphism of a finite dimensional vector space to a computer would be to give it a matrix representation of it. But can't there be situations when it is advantageous to the computer to get the linear transformation as a set of its invariants ? {it saves memory for one thing..in the first way it has to store n^2 data and in the next it has to store n data}

On the same strain if I have a finite group then everything about the group is known if I know its group multiplication table.

Q4. Hence isn't it possible to give a finite group as an input to the computer by specifying its multiplication table?

Q5. We know that in some cases the group is generated by a generator set using some relations. In those cases can't memory be saved by giving the computer an group not as a multiplication table but instead as a generating set and the relations?

Q6. Isn't it possible to input to the computer in this way a free abelian group on a set? Or to get very fanciful, is it possible to make the computer understand the "free abelian group" on a set as a solution to an universal mapping problem?

Q7. Conversely given a table which "looks like" a group multiplication table isn't it possible to write a program to take this as an input and test whether this represents a group? This definitely can be checked in a finite number of steps but I suppose one should be able to come up with a slick algorithm which does this checking in less than that.

Q8. If the above can be done then isn't it possible for the computer to check whether two finite groups are isomorphic given their multiplication table? This again seems to be a finite process but can someone give a slick way to do that?

Obviously the non-trivial question is when the cardinality of the 2 groups are equal. Since we know that there can be non-isomorphic groups of the same cardinality.


Q9. Thanks to Lagrange's theorem we know the possible values of the cardinality of the subgroups of a finite group. Hence given the multiplication table we know the subsets of it that we need to search to detect subgroups of a group. Given any subset of the matrix checking whether it forms a subgroup isn't very difficult.

Hence can't one write a computer program which will take the group multiplication table as an input and then generate all possible subgroups of it?

In the all the above cases the saving grace is that there is a sense of finiteness about the data being taken by the computer whether in form of a vector space dimension or cardinality of a group. But this is where I want to let my fantasy take a bit of flight.

Can't we get computers to get to operate with things which are not finite and discrete?

Apparently Topological Spaces seem to be such a non-finite and non-discrete data unless the underlying set is a finite set.

So we can think of the following possibilities:

Q10. If the underlying set is finite then it should be possible to give as input to the computer the set and the open sets and then ask it to find out, say, whether this Topology is Hausdorff. This seems possible since it is more or less a search algorithm.

Q12. Even if the underlying set is not finite, but say the Topological Space is second countable and further the basis is finite. Then can't this be given to the computer as input?

Q13. Similarly other immediate notions of "finiteness" in topology that might be a good area to try computability would be:
a. If every point has a countable basis of neighbourhoods.
b. If the space is compact.
c. If the space is paracompact.

Q14. Further if the space is not only compact but also can be embedded in some euclidean space and can be gotten as the 0-set of some equation. Then too probably one can try a method of doing topology on it with a program


Q15. We see that the essential trouble with programming topologies is that we don't know of any way to make the computer understand logic which involve ideas like:

a. "For any 2 points..."
b. "Given any point one can find...."
c. "Given a curve.."
d. "Given an open set containing.."

It is not clear how a program can be made to understand ideas of "any" when the number of possibilities is uncountably infinite.

I would be delighted if some computer programmer or mathematician reading this blog can think about these questions and try to come up with ways of bypassing these limitations.

Q16. Can one do some kind of lattice approximation to topological space.
Like try to convert topological properties into lattice calculation?

I know it is a very fanciful thinking. But still can you do it?

Q17. On a probably simpler note I think it would be great if people can collaborate to create a database for Homotopy, Homology and Cohomology groups of known spaces and write programs which can take input like "X union Y" ("X x Y" would be trivial ) and compute these groups for these spaces by searching the database for the groups for spaces X and Y.

The issue of computability has always seemed an interesting question to me. Those questions which can be "programmed" always seem to belong to a different kind of understanding than those which can't be programmed.

Like one can write a program which will take a matrix as an input and will decide whether the corresponding linear transformation is invertible and can also decide if not then how large is the null-space.

Q18. But it doesn't seem to be possible to write a program which will take a function as an input and will decide whether it is continuous or differentiable at a point. It isn't clear how to program the idea of "taking the limits".
And as far as my intuition goes I don't think a lattice idea will ever work here since things can go wrong on a measure 0 space which a lattice can never get to.

One can also try making this following idea computable:

Q19. Given a Lie Group find its Lie Algebra.
Even mathematically it is a hard question unless quite a lot is known about the group in terms of its topology or it being understood as a zero-set of some polynomial ring.

Or a more difficult and basic question would be to understand how to give a Lie Group as an "input" to the computer?
The issue here becomes circular since in most cases a natural way to give this data to the computer at least for finite dimensional Lie Groups would be to input a chosen basis in the Lie Algebra as matrices! And that means to solve what I wanted to solve I need to know the solution!

Obviously I am thinking very naively and I would urge CS people to give some serious thought about this question.

And making the above question programmable shall be of great utility to Physics.

Q20. I would encourage computer scientists to look into these questions about general manifolds as well where there is a hint of finiteness to help compute things about apparently continuous and infinite data:

1. Triangulable manifolds (all differential manifolds are triangulable)
2. More hopes lie with manifolds which are homotopic to some polytope.


This was a brief glimpse into my world of scientific imagination about which very few people know.

I hope this glimpse would motivate some Computer Science or Maths person to think along these lines.




PS: I would recommend people to read: http://pauli.uni-muenster.de/~munsteg/arnold.html

PS: If any of you readers have any ideas about how to go about these questions then kindly put the idea in the comment. Let there be an online discussion of the ideas. If something non-trivial can be developed through these blogs!

Some thoughts about elections.

{ This has also been put up at this blog. }


Recently got my legs pulled and jibed at by a senior of mine, Vipul (from my alma-mater CMI and currently at UChicago doing a PhD in Mathematics,) about the stagnant situation of this blog and whether democracy can really be reformed by people who blog about it only once in 2 months.

{ Actually one can look at in this way: I have not been able to put up updates on this blog since I was too busy with my Physics whose professional requirements have been mounting off-late. Hence I was spending more time with Physics. Now is this a bad logic that I have actually been contributing more to the nation by trying to do my Physics well rather than blogging here? }

Anyway thanks to Vipul's comments and pokes, it accelerated the process of me finally writing down some things which I have been thinking of recently. The election round the corner seems to provocate enough number of dinner and coffee table discussions to keep one's mind thinking and hence thought of sharing some of the thoughts which I discussed during these discussions.


1. One thing has always worried me as to whether election makes any sense in a country where most voters are illiterate and are probably have little or no information about the political scenario and the plans of the parties and the larger questions that the country needs to face. Can't really blame the people because if one has to struggle day in and day out to make one's both ends meet one simply can't afford to keep track of the larger questions! The larger issues are simply a luxury when you are not assured of your next meal.

In this situation what is the difference between large number of uneducated/mis/non informed or non-thinking voters voting and voting by a random number generator?

It seems to me that a random number generator will be better since it will be unbiased and might help a better party win in comparison to a corrupt politician being able to "buy" these non-thinking voters by dubious means.

Here one also sees why issues like "caste" and "religion" and "telengana" issue based voting makes such an impact in India. When the population is so huge with no net coherence of thought then if some local issue can cause a local correlation it has large contribution to the net scenario since the rest of the system is anyway randomized! Thats what politicians use, cause local polarization (especially with a non-thinking mass) based in local issues hoping that there is no large scale coherence.

This actually shows why "blogs" are potentially powerful. They can become centers to cause these correlations among a certain section of the population and that can become non-trivial.


2. The point about becoming an effective voter is whether as a voter I am a "thinker" who takes a well-thought decision or a "believer" who goes by the hype and votes for the party which best hypnotizes me into believing in them.

As Vipul put it in a catchy question to me

"Do you think you are believer or you believe that you are a thinker?"


Let us first realize that the essential reflection of whether one is a thinker or a believer is in the way the person makes "choices". Its the process of decision making that amounts to making a choice is what differentiates between "thinkers" and the rest. It can start from simple things like working on a maths question where at every step one needs to think to decide the optimal next step and also in bigger questions like choosing one's life-partner.











Let me try to list out here as to what all a person needs to be a "thinker" apart from the basic minimum intelligence which unfortunately a person cannot change :

1. Freedom of choice.

Unless one has choices there is no use of the ability to think. If one gets excessively constrained that one's choices then there is nothing that the person can do even if he/she can think. Now choices can get constrained by internal as well as external reasons. Internal as in, I fail to see the choices that exist or may be for external reasons where some external force closes choices for me. like as a dalit landless farmer facing the guns of the rich upper-caste landlords, my choices in life are too constrained.

A large section of the Indian electorate is deprived of this fundamental thing as in freedom to choice.

And pretty paradoxically this section of the people who are artificially deprived of choices are the one's for whom a good government might make the biggest difference. Rich businessmen and people in research are probably more immune to political perturbations.

2. Relevant and correct information.

This is the next step. I have enough intelligence to think and say I have choices but still I need some substance to start thinking on. An Economics Nobel Laureate simply can't think about a question in Quantum Theory unless she/he knows enough Physics. <>

Thats the basic kind of problem a large section of the Indian electorate faces. Many simply can't afford to get time to get themselves informed about the parties and the larger issues since they have their first priority to arrange for food! Who cares about what happens to the nation when I am hungry and have no food to eat? And another considerable section of the population simply doesn't care to find out though they have lots of resources since either they are too busy with their profession or busy hanging out at the malls. Somehow given the kinds of lives we live cocooned inside research institutes worrying day and night about courses, assignments, exams and science, politics and larger questions of India seems pretty distant.







Given that large sections of the population don't cast a well-thought vote..I don't know what sense democracy makes in a country like this.




Now there are 3 sides to see in this:

1. If everybody is busy with his/her life striving for professional excellence isn't that by economic ideas an optimal state for the country? How does it then matter whether each person is thinking about the future of governance and larger national questions since anyway every person is trying for professional excellence?

May be the above idea can be put in analogy with the idea of economics that "we get our bread because the baker wants to make profit". The idea is that such a set of people is creating "positive externalities" for each other and the system is thus progressive and then why would anyone need a government? Somehow isn't it possible for such a system of "self-optimizing systems" to show some kind of spontaneous large scale collaboration like what in statistical physics is called "self-organized criticality"?

The associated idea is that a single man's vote is irrelevant to the election since one vote cannot make difference to the future and the energy and time needed to spend to inform oneself and vote knowledgeably is huge. And at the end of all this research the party for whom this party voted might not win. Hence the "net payoff" in this process tends to 0 and hence this makes no economic sense for a person to drop commitment to one's profession and educate oneself about the larger national issues.

So why should anyone vote?

2. When every person is trying to achieve personal professional excellence then everyone is tending to get into a tunnel vision where one is slowly missing the larger picture and anyway people are only going to create positive externalities only locally and not cause large scale collaborations to happen.

This is where the government chips in with an external view of the larger picture to cause macroscopic reallocation of resources to optimize its utilization by the entire population as opposed to the only local optimization that you and I can cause.

Hence one needs a good government.

3. Education and ability to think brings in with it a sense of individualism and independence of thought. How likely is it that a set of such people will show cohesion and coherent thinking? Why hasn't it happened that all the good students across the various world class institutes in India like CMI, ISI, IIT, TIFR get together to form a party which will surely have an average IQ and education billion times any other existing party?



The question is where does the market equilibrate between these 3 competing factors? Can a government have this global ability to cause large scale optimization by macroscopic rearrangement of resources? Can a government be expected to have enough insight and information to cause this?

If the answers to the above question is "no" and if anyway most voters are "non-thinkers" (and hence 1 thinker's vote counts for nought) and even economically it makes no sense to try to be a "thinker" w.r.t voting, why should I vote or worry about casting a good vote instead of doing Physics and Maths properly?