Saturday, February 24, 2007

On thinking - Part I

The text that follows is probably not really coherent. One reason for this might be due to the very topic chosen and the other reason being yours truly writing on the same. I really like what Neils Bohr has to say on this: 'Never express yourself more clearly than you can think'. Having said that, I want to be able to put my thoughts some place easily accessible so that I can work on them later on. Views, critiques and comments are welcome.

-------------------------------------------------------------------------


The focus of this blog is on: How much of what we call thinking is a mere rearrangement of prejudices and how much is sheer logic. And by the way, what is thinking?

The word think, I think, is taken for granted, so much so that when we say, "I don't think that's a good idea", for instance, we are merely communicating the prejudice we already have about that idea (for example: drunken driving is not a good idea..there is no thinking here) unless ofcourse, we pause for a while..really think and give that reply. You could also pause to recall what your prejudice is, but that would not qualify as thinking or would it?

Look at the number of definitions given by the dictionary for the word think.

One of the definitions given is: to have a conscious mind, to some extent of reasoning, remembering experiences, making rational decisions, etc.

Some key words in these definitions are: conscious mind, rational analysis and recall.

These words are by themselves a bit ambiguous. For example what do I mean by conscious mind? Atleast, when I am awake, I am aware of a mind that does my thinking. Now, I can go one step further and say, who is that 'I' in "I am aware of a mind that does my thinking"? Is that I different from the mind. As in if you say I am aware of my mind, you are larger than the mind right, only then can you look at it as a whole. Now, a great many people are skeptical of the 'I' analysis, they have labelled it philosophy and rightly so.

But I can't proceed even a nano meter further, if I am not clear about what 'conscious mind' means. At this point, we give up and make an abstraction of the term 'conscious thinking' and leave it at that. This gives me an idea that thinking is fundamentally related to what assumptions we make on the meaning of words so as to understand the world. This may seem obvious, since the world we see is mostly described through words and if we are not clear on the meaning of these words, but anyway make descriptions, our model is fundamentally flawed. And the assumptions we make on the meaning of words gives us a coloured, prejudiced view of the world unless the prejudices are proved to be indeed true. And these assumptions are also the building blocks for another word: perspective
Since, thinking seems to change or refine the assumptions we make about the meaning of words, thinking therefore has to do with broadening of our perspective or the model used to view the world.
Contd...

Tuesday, February 20, 2007

A taste of phd life

Firstly, phd life is a way of life. Period. Phd life is a little..nay, a lot different from a masters' grad life (Mgl). In Mgl, you have a vague idea of what research is and most of your time is occupied in course work, in Phd grad life(Pgl) courses are a secondary thing but as far as research is concerned, you have no idea of what your research topic is for quite some time. Add to that, the uncertainity of area of reasearch and you have got yourself a non-starter. Add to that social and psychological dynamics and it is truly an experience, a humbling and at times close to melancholically numbing. But the good thing is, you get used to statements such as "I have given up in life" or "Life is a mess..but that's cool" or "This week was peaceful..I didn't get any work done but my advisor didn't say anything either".
Actually grad students, zombies and hippies fall in the same category. Most of the time, there is no sense of 'time' and life keeps going on despite the fact you have lost touch with reality. There ofcourse will be occassional bursts of activity and things would seem great until complacency and procrastination sets in and then you are back to auto-pilot.. Wake up -> Surf the net -> Eat -> Surf -> Go out -> Surf -> "Think about doing research" -> sleep -> Eat, etc.
Ok, this text seem depressing enough to me, I will get back to doing something productive.

Finite simple group of order two

Its pretty obvious that these words have something to do with Maths (or Math, depending on the English you prefer). I have no idea what these terms mean. Finite - ok, simple - I know the meaning, group - hmm, order - huh.. Anyway, its interesting that such a uber geeky expression "Finite simple group of order two" has been creatively composed into a song(and sung well too), that even if you don't come from a Maths background, you can very well appreciate the same. When you watch this song, you will know the different meanings of 'One to one'' and expressions such as 'I am getting "tensor" everyday' and "When we first met, we were connected(graphs)" to name a few. How about, "And by corollary, this shows you and I to be, purely inseparable...QED". Watch the video if you dig more of these 'math nothings'(I switched english) here.

Lyrics to the song(borrowed from here):

The path of love is never smooth
But mine's continuous for you
You're the upper bound in the chains of my heart
You're my Axiom of Choice, you know it's true

But lately our relation's not so well-defined
And I just can't function without you
I'll prove my proposition and I'm sure you'll find
We're a finite simple group of order two

I'm losing my identity
I'm getting tensor every day
And without loss of generality
I will assume that you feel the same way

Since every time I see you, you just quotient out
The faithful image that I map into
But when we're one-to-one you'll see what I'm about
'Cause we're a finite simple group of order two

Our equivalence was stable,
A principal love bundle sitting deep inside
But then you drove a wedge between our two-forms
Now everything is so complexified

When we first met, we simply connected
My heart was open but too dense
Our system was already directed
To have a finite limit, in some sense

I'm living in the kernel of a rank-one map
From my domain, its image looks so blue,
'Cause all I see are zeroes, it's a cruel trap
But we're a finite simple group of order two

I'm not the smoothest operator in my class,
But we're a mirror pair, me and you,
So let's apply forgetful functors to the past
And be a finite simple group, a finite simple group,
Let's be a finite simple group of order two
(Oughter: "Why not three?")

I've proved my proposition now, as you can see,
So let's both be associative and free
And by corollary, this shows you and I to be
Purely inseparable. Q. E. D.


Thursday, February 15, 2007

Where am I headed?

This post might seem suspiciously similar to a blog with a similar title I posted a while back: Where do you go?. Well it is similar in the concerns expressed, but the context(expect a lot of word and meaning dance on this word) is different.


The following text is structured into 4 sections. Each section is independent of the other and can be read as such with minor interlinkages. Section II is essential to this post and is relevant to my current state of things, the rest of the sections are add-ons and sometimes plain fluff. But, you might find sections III(connecting three seemingly different fields) and IV(inter-linkages and abstraction) more interesting than the other sections if you dig technical stuff.

Section 1
Section 2
Section 3
Section 4


I. Introduction
 Jump to II 


Where am I headed? I find myself asking this question often, so much so that I have a notion of being "lost in life", and it comes up as a status message on google talk inadvertently while I keep reverting back to 'available' and my friends seem amused. Not sure the previous sentence made sense, but yeah, the sentence is open to interpretation: The meaning you look for, you shall find. Anyway, where am I headed? Right now, nowhere in particular, I mean I need to get back home and catch some sleep, but that can wait.
But seriously, where am I headed? Well again, nowhere in particular. I mean I have just started out on a Phd, where do you think graduate students are headed? I mean for another 4-7 years, depending on my procrastinating abilities, I shall waddle around looking at the ducks at the Drumheller fountain in the campus, as I pass by them to my lab and back everyday. So yes, there is research and temporary coursework to fit in the details of these 4-7 years, but the big question is where's the big picture?


II. Levels and states

Go back to I
Jump to III
Or IV

There are three broad levels and many states that can describe 'where I am headed'.

The broad levels are basically all plausible possibilities that I can see myself getting into, say 5-6 years down the line. The states are essentially what happens within the context of these levels, it can describe what I think of where I am headed at any given point. The levels and the corresponding states are described as follows:

Level 1) Get into the industry after my phd, earn dollars or rupees and life goes on.

State
: This is a fuzzy thing right now, I am not particular about earning big money and hence my aspirations in this field are negligible as of now.


Level 2)
Continue research after a Phd, which can happen in a few ways: Faculty at a university, Research scientist at an organization or industry.
I am describing a few possible states at this level:

State a)
Big picture clear, but the details are fuzzy: Here I refer to the 'area of research' as the big picture. This state is more or less a temporary problem and is usually considered normal. Can be worked out. I mean you will have glitches in your research and you may be less motivated at times than others, but you are sure which area you want to work on right.

State b)
Deatils are on, but the big picture is fuzzy (similar to 'lost in life' I mentioned earlier):
Now, this means that you are doing research and course work, things that grad students do, but you are not sure if you want to stay in the area of reasearch you are currently on. Now, this by no means is a temporary problem, indeed to determine if this is a problem at all requires time and thinking. It's like when you say, 'give it time, things will sort out for themselves'. Only that, we are talking 4-7 years in a given area and once you are decided on an area its hard to shift to areas that are a little unrelated.

Hence area of research needs to be more or less the same, with minor variations over time.
My state right now is that my big picture is a little fuzzy in that I am undecided on the level of theoretical or mathematical rigor I would like in my research. I am also undecided on whether to decide anything about this undecisiveness. To understand the previous statements in detail, visit section III.


Level 3) ??. The ?? or question marks are fuzzy areas: Things that I am 'open' to, things I am not clear about, dreams, etc. For instance, I am 'open' to the idea of being an entrepreuner, but I recognize fully well that I lack the skill sets especially on the financial and managerial aspects required for a successful start-up.

State: This is ofcourse a wild dream, but I am just open to it as of now. Entrepreuners are the order of the day and are needed big time back in India, is one idea I believe in. We have a lot(or many??) of IT startups but how many technological start-ups? What are the core needs that India might face in the next 10 years? Well these are really broad questions and may have little to do with one being an entrepreuner per se, but one needs to be aware of the state of things before plunging into it and I am sure I would be more aware of these details as I proceed down the time line. But its nevertheless fuzzy right now.

III. Brief diversion into intepretation of optimization in Math, Industrial Engineering and Transportation:

Go back to II or I or Jump ahead to IV


This diversion is essential to understanding the context behind my dilemma and can be read independent of the rest of the post.
Consider the three broad areas of transportation engineering, industrial engineering and Maths. At first these may seem unrelated areas, but a closer look can bring out possible connections.
Transportation engineering has to deal with operation and management of transportation systems. (I am more into the operations part of it, though management and operations are inter-related for example in decision support systems). Transportation systems could be systems involving rail transit, bus transit, air, shipping, etc. Transportation, again is a very broad area, atleast to transportation engineers(you see how narrowed down research can get) and the area I want to work on is optimization applications in transportation. Now here, what we have is a methodology (optimization) being applied to a field (transportation). For instance, I can have a problem where I want to optimize the operation of a transit system i.e optimize the routes and schedule of the transit to minimize costs, waiting time, etc.
Now, industrial engineering is again a pretty broad field with connections to mechanical engineering in inventory control, etc, and operations research. Operations research is the science of optimization: how to twiddle or tweak the parameters of a system so that the system performs better. It basically is a methodological field with applications in many fields including manufacturing, electrical systems , transportation, chemical engineering, basically any problem that entails "better performance".
So you have the nail(optimization) and the head(transportation in my case), you can't really separate them out, but you can state the degree to which you would like to use each of them or look at each of them - basically your focus.

Now, we are already heady with all the nails and heads and the hammering, along comes math to make it even more bumpy. Math is again a very broad field with topics ranging from abstract algebra, number theory, optimization, calculus, harmonic series, etc.
Did you just notice that optimization came in the list. So how is "mathematical optimization" different from what industrial engineers call "operations research".
Again its the area of focus: Mathematicians tend to be more rigorous, they are more into the mathematical "exactness" of the subject. There is a structure, there are axioms, theorems and proofs. You can't just state something loosely about optimization methods without inviting criticism from Math professors (and this has been my personal experience). Everything needs to be laid down in white and black.
Everything's got to have a proof. That's the bottom line.

So we have just seen three broad areas of research and as you proceed from Math (optimization) to Industrial engineering (operations research and its application) to Transportation Engineering (Pure application), things get pretty watered down in terms of 'preciseness' and the 'theoretical rigour', but they also get pretty exciting, since the real world is by no means laid out in black and white and unpredictability arouses excitement. By the way, there is a whole area of research on unpredictability: Stochastic processes. Reasearch in transportation is sometimes very data oriented(e.g. Intelligent transportation systems) and hence a whole lot of time is spent interpreting data sometimes in an unstructured manner and this is where I am currently facing a problem. This is where I am 'lost', I want to decide very soon, the 'degree of theoretical rigor' I want in my research and this could mean shifting directions, shifting research and getting more of the 'nail' than the 'head'. Getting more of the nail, could either mean bringing in more theoretical rigor into research(can get very boring at times) and possibly shifting into researching better optimization algorithms and techniques or could mean taking the middle path also known as operations-transportation or OR-Transpo and actively update myself on current state of the practice in optimization, all the while keeping tabs on potential applications in transportation(congestion in container ports, public transit, intermodal transportation, etc).

So what am I doing about me being lost? Well, I am alert, I am keeping options open and let's see how things go.

So to describe my state in level 2, I have brought in my understanding(or lack thereof) of optimization in math, industrial engineering and transportation - Interesting.



IV. Related and unrelated final comments

Go back to I or II or III
Post-script and Gripe:
This whole division of areas of research into engineering, science, philosophy(yes even that), humanities, arts (making a good power-point presentation is an art, as many would agree) at a very broad level don't make sense, since new science, new engineering are merging rapidly with other fields. Quantum physics necessiates the need for an observer, it brings in subjectivity and consequently philosophical paradigms. Many inter-disciplinarly fields of quantum-bio-computing, mathematical finance, and possibly Philosophy of science(really?) call for inter-disciplinary collaborations and we are now seeing a shift from traditional divisions of knowledge into such and such areas to this, that and them areas put together. I see this in some universities: Department of electircal engineering and computer science or department of civil engineering and engineering mechanics, etc.

Post-Post script: Why does optimization fascinate me. We all seek perfection in life, in work, in relationships, etc. However optimization is not just about perfection, which could also mean being effective. We are looking for efficiency in this effectiveness, the thought that there is one possible way or a set of possible ways in which a system can perform at its optimum is something fascinating. But then a question arises on the context of this optimization. What scale are you looking at? How big is your system, etc. You can be efficient in a given system but can cause unfavourable ramifications in a system nearby or a related system. So you see, subjectivity comes into optimization too. But operations researchers are very clever, for that matter engineers too, they restrict themselves to the 'scope' of the problem. This restricting to the scope is something environmentalists don't appreciate apparently(in a related context). But all is not lost, this 'scope' is broadening, as we see the effects of our technology on the environment and we are in a general sense, becoming more aware of the need to broaden this scope - this inter-disciplinary thing is one way in which that can happen.

Post-post-post-script: This post purely describes or questions where I am headed in terms of a career in life. Other possible connotations are out of scope of this blog and are left to the reader's imagination.

Update: Things seem to have come to a head. I am on the verge of entering a new realm in research, a few more days and I might know or may be not

Saturday, February 3, 2007

The thought - creation paradigm

The basic premise of this paradigm is that, creation is but a product of thoughts and nothing else. An immediate consequence of this paradigm is a change in perspective: "Weird things are happening in my life" would be interpreted as " I have been involved in the creation of the weird things I am experiencing right now". So, if what you think is what you create, that is to say, what manifests in your reality as life, shouldn't you be thinking thoughts that you desire in life.
For example, if I want to be able to work in a focussed manner in the near future, I sometimes just "think" about working in such a manner for quite sometime or atleast I keep that thought at the back of my mind among the many other thoughts that keep visiting my mind. And soon, the desire to work in a focussed manner as I intended in the first place, becomes strong enough to propel me to work in such a manner. This actually reminds me of a phrase I have heard before: "The power of intention".

The connection between what some might say are 'mere thoughts' and physical reality known as 'life' is not immediately clear. I came across this paradigm in a book and I have tested it out, now and then, in my experience and found it to be true.
There are two things you can do with this paradigm:
1) You can verify the truth in this paradigm by looking for experiences in your life that fit this model.
2) You can use this paradigm, provided you are sufficiently convinced about the veracity in the workings of the paradigm (for you can't trick your mind about that), to proactively create your experiences.
[By tricking your mind, I mean: You can't just say, "Ok I need to get this work done. Let me just think about it for an hour and see if that happens." Your mind would just laugh at you and say ofcourse that can't happen. Its not just thinking that's going on here, its more of a focus of thought into doing the right thing for the right result. The emphasis here is on focus of thought converting into action; you can't escape action.]

An example for the first case that comes to my mind is when you have been thinking about contacting a friend, just to see how things are going on with him/her. I mean you have been thinking about it, but then due to your current circumstances of being busy or out of town, you are not able to contact him/her. It might so happen that your friend might have left you a message on orkut or might have sent you an email. Well, that might just be a coincidence you say. I don't disagree but then it does fit into this paradigm.

The second case is something which might come as a pleasant shock to many people and might also alter their experience in life from then on. But then, to manifest a thought into physical reality is not an easy exercise. It is more a kind of an exercise in thought control. Some might also call it prayer, for prayer is essentially a single thought or maybe a group of related thoughts that are repeatedly called upon in the mind. And by our thought-creation paradigm, this repeated focus on the thought should result in its manifestation in physical reality. So, this paradigm might be a possible explanation for why prayers might work.
Also, the intensity with which a thought is thought matters a lot. The intensity of the thought might also determine when this thought would manifest in physical reality.

A natural question that arises right now is what if I were to be thinking a set of thoughts, repeatedly, that are totally unconnected or might actually be in contradiction to each other. For example, I might be thinking repeatedly of the following thoughts: Working on my upcoming deadline, playing soccer in the evening, visit friends and maybe some other thoughts. The result of this thought process might be a myriad of experiences: a bit of everything, one might say.

Ask some people, "how's life" and they might say, "A lot's going on in my life. It's really going out of hand". I say, they have been thinking a lot on a lot of things. Ask someone else the same question and you might get a reply: "Right now, I am just doing such and such a thing. It's tough but I need to get this done". This might mean they have been doing some focussed thinking on doing a particular thing and that's manifesting itself in their current reality. Anyway, this is all I have to say about the thought-creation paradigm and this is something I need to think on a bit more to gain deeper understanding on its workings. But I bet a reader who has come thus far might also want to think on this paradigm(I infact implore the reader to do so) since if it really were to work, it might have astonishing implications for the reader.