Becoming a successful researcher

The following articles address the following questions:

1) What does it mean to do good research?
2) What are the important factors in doing good research?
3) How does one successfully and confidently do a Phd?
4) How important is it to have a good and compatible advisor?

Article1
Article2
Article3
Article4


Other articles on becoming a successful researcher (including problems faced by junior faculty)here.

What makes a phd life tick?

This is something that I have been thinking about for quite sometime. Phd life is life lived in 4-5 years. Its been just 1 year so for me in my program and I have had numerous ups and downs. What I have understood is that to come out successfully out of the Phd program there are a few things in non-academic life that need to be taken care off.
Phd life = Academic life (research + a few courses) + Social life (friends) + Some other passion (books/physical activity/music/...). These three components need to be well-balanced for a Phd life to tick. Lets look at these components in detail:
i) If you lose interest in your area of research, its very difficult to continue through a Phd. You may lose interest because you might have had a different concept about what a Phd might be before you began the program. You may lose interest because its a relative thing... you are more interested in working in some other area. You might lose interest because you are tired of the rigors of a Phd program.
ii) You got to have a few close friends you can count on when you need them. It has been my experience that I am immersed in research for one or two weeks, and when I come out of the research world, I am craving for social interaction.
iii) Many times doing research could be frustrating , so you would be looking for some change in your life. This is where an already existing habit or hobby such as book reading or physical activity such as running might prove very useful.

Balance is the key word. All the three components need to be balanced for a smooth ride through the Phd life. Imbalance could lead to minor frustrations or even major episodes (depression, etc).

Motivation

What motivates one to do research. Researchers don't usually see their research or work as 'work'.
I had rather call my research as creative work, since that is actually what I am doing. The motivation in doing research, in being able to stay in the lab throughout the day even during weekends is basically the idea that what you are doing is fun. If something is fun, wouldn't you want to do it all the time.
But even during work, there are periods when you are slumpy and not getting much work done and other periods when you are really really productive. Now, what is the reason for this?
People may call this the 'cycle'. But looked into a little more deeply, it may become clear that productivity is either motivated by deadlines, either set by your advisor or yourself or because you have suddenly entered an interesting phase of research.
Interest in the research area in general is a must, but that alone may not be sufficient, since there is a tendency to get lazy. What's needed is a vision, a vision that is both short-term and long-term. A vision of how you think your research should be unfolding as the time progresses. This vision is essentially a way to set deadlines for yourself, but a vision is something more than that. A vision is a dream that gets lived as time passes by. A vision when 'well-visualised' can be really motivating, since your vision shows you doing great things in the future and you can't wait to get started towards that path. Living a vision or a dream is the best thing that can happen. That's why visions are so powerful and form the basis for a long-term motivation in research.

Playing on reality

What is reality? Is it something that is perceived to be real or is it something that is real no matter what?
The question being asked here is whether reality is a function of perception and perspective or is it something that is real whether you look at it or not.
Quantum reality is a reality based on perception, based on an observer and the observed. In quantum reality the observer effects the observed and vice versa. Quantum reality has been found to hold good in the microscopic world, the matter within an atom for example but it has not yet been verified to hold good in the macroscopic world we see and experience.
The reality of the macro-scopic world that we see is based in duality. Duality is the nature of our perceived reality.
There is another reality that can potentially exist. It's called the ultimate reality and ultimate reality is a singularity. The moment just before the big bang would be an example of a singularity.
So when do these realities, namely the quantum reality, the duality based reality and the singularity manifest in our perception and why are we even bothered about these realities? Why is the nature of our world based in duality and what does it mean to experience singularity. To answer these questions, duality must be properly understood.

What is duality? Duality usually refers to pairs of opposites that coexist in a single reality. The good and the bad, the tall and the short, the sweet and the sour, peace and war all exist in the world we see. Why is duality necessary in our world and why can't the world be more singular? That is to say why can't life be always sweet, free of tensions, free of anger and resentment, free of rejection, etc. Well let's say life was more singular in nature. Let's say life was one happy and smooth journey from birth to death. No ups and downs, no crisis, no pressing problems, etc. That is to say life was one happy period. How would you experience your happiness 10 years down the line? It would become mundane.
Someone asks you, how are you? You would say, "Ah.. the same old. I am happy...and it sucks". That is to say, to enjoy happiness, you must first know what it means to be sad and depressed. Only then will the joy of happiness be fully felt and experienced.

We all like dramas don't we. The good and bad, the happiness and sorrow all in one big drama.
Life and dramas have many things in common including their basis in duality. Life has also been described by many as a magnificent and never-ending drama. Only that, you are a part of that drama along with your co-actors that include your family, friends and others you interact with during your life.
So that sort of gives a hypothesis on the need for duality in our present reality. Now moving on to ultimate reality. What is it and what does it look like?

What makes a good phd student?

Indeed what does? Know more here .

Frustration

I know what to do. How to do it is not a problem, atleast not a big problem. But am I doing it? That is the whole problem. The coming two months are really crucial to my career and am I doing anything about it. Its all well to say that things are really fuzzy, its all well to blame others, blame the situation, etc. But the least productive thing that can be done is to be productive in work. Amidst all the chaos, if I can bring about some consistent and concerted work, that should see me through this mess, through any mess actually. Because that's the only way out.
Focus on the essential things and leave the details to work it out by themselves, or work on it once the essentials are out of the way. This is to be done because a man's perspective is always limited, so it needs to be focussed on things that are of concern, lest he/she gets lost in the details.

PDL C-401

This is the place where the optimization seminar is held every tuesday at UW. Today I had my camera in hand, the reason being the speaker - Dmitri Bertsekas.
The camera also served another purpose: The view of UW and beyond from this place is awesome...

A sequencing problem

Found this problem in one of the orkut puzzles community. Though not a real tough problem, I found the solution to be interesting.
The problem is to find the next number in the sequence:

16 , 176 , 552 , 1312 , 2360 , 3504, ?

If you find the solution to the above problem interesting enough, I thought of a similar problem but with added complexity that might be worth trying out..

92, 440, 300, 1309, 728, 1360, ?

Nostalgia

I woke up at 9 pm today (night out the previous day), went through some interesting concepts from the book 'Elementary Probability' by David Stirzaker for about 3 hrs. Remembered that I was hungry and looked out the window to see that it was raining, as it usually does in Seattle. At this moment I was reminded of my life back at IITM where I had done similar crazy things. If this were my hostel room, I just had to cycle another 200 metres to reach gurunath which would have been closing at this moment.
I would have bought the milka cake or a similar cake along with one or two packets of mug noodles (its cold and raining outside, so I figure it would be nice to have something hot).
On the way back, I would have met a friend from Saras proceeding back to his hostel. I start farting with him on some worthless topic and that takes me to his room. I meet two more guys and we start talking about strategies in Quake and AOE and in the next moment we talk about how our 4th year is so different from the other 3 years we have spent in IIT. Muggus during the first two years, many change gears in the 3rd and 4th year, having found a way to beat the system. Now, my friend is in a mood to crash and starts driving junta away from the room.
"Macha, I have to crash da. I have a quiz tomorrow and I don't even know the portion for the quiz. So junta deesh." He says. I look at the time and see that its 4 am now.

I am halfway through my day, another 3 hrs and I would be sleeping comfortably on my bed with the windows wide open and the cool breeze, an after effect of the thunderstorm would linger around in my room. Ah.. that scent. After spending another 2 hrs in my room mugging for the same quiz my friend has no clue about, I decide to take a walk toward the stadium. I have fond memories of the stadium, the place where I spent almost every evening running 10 -15 laps during my 3rd year in the hopes of getting into the inter-iit team. Now, I notice that the day is just breaking out and despite the ground being wet and slushy, the freshness of the mist laden air captures my imagination. I am rooted at the same spot for a few more minutes as I contemplate my existence, my dreams, my victories and my losses. Moments like these make me look at life from an abstract, philosophical angle.
Meanwhile, I realize I am hungry again. I call my friend from Saras. He apparently crashed for 2 hrs and now is mugging for the quiz. We decide to head out to Hot Chips, an eat out just outside IIT. They are just opening up for the day and I order hot idly vada, pongal and filter kaapi. My friend orders masala dosa and coffee.
Nothing like having a full meal before you sleep during the day. We head back to our hostels, my friend to continue his mugging and I to enjoy my sleep for the few hours I can before the quiz.

Snapping back to reality, I realize I have two assigments due tomorrow and I am yet to make progress. Now it's 3 am, and the day has just begun.

The story of a grad student - 1

"I really am floating in indecision. I like that phrase, I bet no one.....". "Bhaaaaaaskar", called out someone interrupting Bhaskar's thought flow and inducing an irritation in him. He was already pained with the way his life and research was headed and wanted to be left alone. But no.. Vani had spotted him proceeding out of the university and there he was waving to her. He waited as she half-hopped, half-walked the steps of the Information systems building and accosted him with a smile. Ah...that smile, it was a little silly but a really warm one at, that he thought. Bhaskar had known Vani for a few months. There were few Indians at the Texas A and M univesity (TAMU) and Indians generally got more friendly with each other here than back in India. "But what I really like about this is that I can...". "Hi...", you look serious, are you thinking about something?
"Hi..yeah", replied Bhaskar.
"So where are you going?", asked Vani
"I am headed to the ave to have lunch. What about you?"replied Bhaskar
"I am also going out there" said Vani.
Bhaskar thought Vani was acting out a bit strange, atleast a bit strange to him. Bhaskar didn't mind female company but he wasn't looking forward to it in a big way either. He had had a few unsuccessful relationships and that had left him cautious and a tad bit bitter. He wanted things to happen naturally and he definitely didn't want to force relationships. I am not despo, I got plenty of time, he thought.

To be continued....

P.S. I appreciate comments and feedback. So bring them on...

Independent research

It's high time I started looking into this aspect seriously. What really is independent research?
It's simply the maturity to conduct research whose contributions have been assessed to be worthwhile, research which you think is significant enough to warrant publication and research where you have an idea of what the possible data sources are.
This begs the question as to what research is?
Simply stated, research always begins with getting a feel for the chosen field of interest. This is done by reading journal papers and articles in the area of interest. The next step is to identify gaps in the existing literature - either a modeling, methodological or a practical gap or a combinaton of them.
So once you have these gaps, you already have a problem to work on, all you need to do is delineate clearly the objectives of the study and the problem features and you are on a roll.

Now doing research in a new area might require extra reading depending on the methodological quotient of the research area. OR is fairly methodological, transportaion operations is half as much. But then again, there might be a fair amount of data collection issues that need to be dealt in area such as transportation engineering.

All said and done, what one needs is the confidence and the will to do it and that surely will take the person on the path to being an independent and influential researcher.

The need for formalism in math and its consequences or lack thereof

A very interesting lecture delivered at CMU by Gregory Chaitin, who has taken up research in problems that were ailing Math during the early 20th century - Problems in formalism and foundation of math.

Was the invention of the computer a quirk of fate? Was it due to the failure of a mathematical proposition by Hilbert that mathematics can be formalized completely through an artificial language?

Is there randomness in math as is seen in quantum physics, something pure mathematicians despise? Are there problems that will remain unsolved due to the very reason that there is no structure or pattern that the problems' solution fits into..that the answer to the problem is an accidental truth?

How can the following statement be resolved:
Prove statement 1. And statemet 1 is "This statement is unprovable."
You simply cannot prove statement 1.
If statement 1 is provable, then we have proved something which is unprovable and therefore flawed or absurd. If statement 1 is unprovable, we cannot prove statement 1 and that is what statement 1 says - That it cannot be proved!
A mathemetician cannot stand the absurdity that comes along in proving statement 1. So statement 1 is a kind of an unresolved problem in maths. The only thing that can be done to statements such as statement 1 is to understand why they exist. And why they exist, as argued by Gregory chaitin, is because some statements are accidental truths, the truth doesn't have a formal structure or pattern that it fits into and hence cannot be proved. And why is the truth accidental?
Oh, that's because God plays dice.


The lecture also dwells on - How randomness can be measured in a sequence of numbers and what it has got to do with problem size complexity. Note, problem size complexity is analogous to computational complexity. The former doesn't worry about the efficiency of the algorithm and its computational time and is founded in information theory. The latter is a measure of fast and efficient algorithms.

Bikes and phdcomics

Can totally identify with the following two comics - One depicts the commonplaceness of bike thefts and the other the disadvantages of biking with 'normal' pants with possible remedies. Now, if I can get a tape, that would be nice....

The interdisciplinary approach to research

Note: This article reflects my views alone. My views as would also be yours, change with time and hence this article reflects my current understanding of the approach to research.


Introduction
When I heard from a friend that the civil engineering department at the University of California Davis encourages its students to take courses from other departments such as Applied Math department, it made a lot of sense to me. Transportation Engineering, a sub-division of Civil Engineering is an application oriented field. But what tools are you going to use for approaching transportation problems? Say I need to design, route and schedule a rail transit network in Seattle, my main goals for such a problem/project would be to capture as much segment of the population as possible, all the while minimizing travel, operation and maintenance costs. It is easy to see that this problem can formulated as an optimization problem where you optimize(minimize or maximize) certain objectives: Say minimize travel costs or cost of design and build or maximize the number of people served. You can also have a multiple objectives that are minimized or maximized simultaneously - Talk about multi-objective optimization and you are talking about a HOT field in Operations Research. You see how Math and Transportation are intricately linked now? How do you expect Transportation Engineers to make effective decisions if the tools(software, analysis tools, etc) they use are not catching up with the developments in Applied Math for instance.

The right approach?
You don't have to look at what's going on in terms of research at the Math department, you wouldn't understand it anyway, not to say anything about applying it to engineering. But how about applied math research, these guys have a solid Math background and they are looking to use this background to solve problems in Engineering.
Now when they start doing that, engineers need to stop doing whatever they are doing and seriously consider how their contribution to research might be enhanced by collaborating with the Applied Math guys. Engineers especially in an application oriented field like Transportation are at an advantage in terms of data, since considerable amount of time is spent in data collection efforts through stated preference surveys, house-hold interviews, etc. Transporataiton engineers also spend a considerable time formulating a problem since a real-world problem isn't that easy to formulate into a known model that can be analysed. On the other hand people in the Math Department need a problem. They start with a problem and analyse it to no end or let's say till they reach the end...the end of the proof to a theorem!
It is a kind of startling realisation that researchers in Math and Engineering streams are looking at the same puzzle at the macroscopic level, but since research is always at the microscopic level, the microcsomic worlds of Mathematicians and Engineers seem different.

The need for collaboration
So we have the problem features, problem formulation and data collection on one side and you have analytical tools, methodologies an problem solving on the other side. But everything here has to do with one word - Problem . That's what's troubling everyone. There seems to be a problem or is there? - the engineers crib. Ha, this problem you have given me is interesting and challenging, is the mathematicans exclamaton.

Piecing together what the Engineers and Mathematicians talk about, it can be seen that collaboration would make more sense since one can combine the methodology and tools from the App Math dept with the experience in data collection and problem formulation from the Engineering side and the results would be: a) Practical since the data being analysed is from the real world b) Have a sound methodological backing c) Pave the path for continuous innovation due to the very nature of such a collaboration.
This kind of thinking, though abstract, in the end, if I may be a tad more idealistic, would lead one to realise that researchers are essentially looking at the same problem that has been split up into a million pieces. And each researcher by looking to solving each individual microscopic, nay nanoscopic piece of the bigger problem, claims to be working on a different problem, but in an abstract reality is piecing together or figuring out the same puzzle. Researchers have already started realising this.

Concluding remarks on approach to research
Collaborations are happening left and right these days, I see transportation and logistics courses offered in the IE department at the Texas A and M university. I see many professors who work in different disciplines such as electrical, transportation and computer science engineering also being responsible for creating inter-disciplinary departments. Math is catching up fast with biology - an idea that would have unthinkable a decade back. After all, when you have a tool/software/algorithm/methodology, you would like to test it on as many fields as possible, wouldn't you? Engineering beckons a person with such a tool! So you see, it all comes back to the fundamentals. What are the fundamental principles that govern the behaviour of our world, what processes are common to many of the engineering systems we see in the world today? When you start looking at these questions, the natural way to approach such problems is through systems engineering. Research in the future, I believe should go the systems way - laying emphasis on the fundamentals and consequently on maths, science and its applications, not starting with an application and somehow looking to bring in math and science in an awkward manner. But the problem here is transportation by itself is a very interesting field with all the policy, implementation and political issues and to ask a person to be conversant with all of these issues and methodological tools and techniques is asking a little too much. Therefore, a better solution would be to take the middle path and integrate as many existing related departments and disciplines at some level that help spur collaborations and promote inter-disciplinary research. The good thing is researchers are flexible to ideas. When the idea is good, it is bound to be implemented, provided the idea is communicated to a wide spectrum of the research community. It's kind of an evolution - An evolution in the way research is done.

Principles

HHH WFE CLMS DX(C)

Mnemonic: HHH (Triple H) in the World Wrestling Federeation claims to be a part of D - Generation X or DX.

HH - Hard work (doubly emphasised)
H - Humility

W - Will Power
F - Focus
E - Equanimity

C - Clarity in thought
L - Lack of lethargy
M - Meditation
S - Silence

D - Discipline (With special focus on the daily routine and sleep times)
X(C) - Extreme Confidence

Dreamer

I dream a lot. I dream of doing great things. I dream of living life to the fullest. I dream of taking risks without any hesitation if I think its worth my while. I dream of doing some top notch research which involves a lot of math. At the same time, I dream of ramping up my running and biking.. Doing marathons and long-distance cycling. I dream of being in a state where I can do all of these things and even more...that state of mind where you are very clear of what's to be done next..nay, what's do be done now, at this very moment. I dream of being a god in my area of research. I dream...I dream..and I dream.
My dreams will just be dreams as long as I only dream and not act. I realise the great potential in these dreams, but at the same time I realise the importance of being down-to-earth, on the importance of knowing where I stand right now as against where I dream myself to be. Consistency in work is more important than random spurts of good work. That's what a phd is all about...Consistent work in an area that interests' you.
And finally, I dream of being consistent in my work.

VRP

A good site on the web that summarizes the problem features, formulations and solution techniques to the VRP(Vehicle routing problem) and its variants such as VRPTW(with time windows), SVRP(stochastic), VRPPD (both pick-up and delivery), CVRP (capacitated), PVRP (periodic), SDVRP (Split delivery),MDVRP(Multiple depot), etc...
Also a nice bibliography of the algorithms and solution techniques for VRP and its variants can be found here.

Writing a research proposal

I took this seminar course whose aim is basically to give you a set of tools to guide your research and fine tune the way you conduct research. Three take homes I got from this seminar are:
1) When to reference and when not to reference when you write a paper
2) Giving a presentation: What needs to be taken care of, the good and bad of a few case presentations.
3) Research proposal: Writing one effectively.

I will just discuss the third take home. Here's a good article on writing a research proposal. Find a pdf version here.

To summarize the article:
There are two things to writing a research proposal - a) The writing part of it b) The content and structure part of it.

The writing part is similar to writing any document - The document should be coherent, have a flow, should be concise and also be easily understandable to the targetted audience.

The content can be summarized as follows and is very similar to the structure of a thesis:
a) Abstract - What is it that you propose to do in your research summarized briefly in a paragraph.
b) Introduction - i) Should clearly define the objectives of the study or research to be conducted
ii) Should establish the context of the study and its significance and/or contribution practically(application) and theoretically(model/technique development/formulation of the problem, etc).
iii) The main problem features should be described and the scope of the problem clearly delineated.
c) Literature review - Should include all contributions from literature relevant to the problem area. The contributions should not be rambling but should be expressed concisely though effectively.
d) Solution Methodology - Should be described in the context of what is in the literature. Should narrow down a few solution techniques and the pros and cons of this subset of techniques should be briefly described.
e) Data - What data do you think is required for this problem. How are you going to get it(Experiments/data collection, etc).
f) Discussion - Summarize the research briefly. Discuss the pros and cons of the solution methodology adopted, data to be used, etc.

Usually a research proposal is made to obtain grants and funding for the research. So a research proposal should be written in a manner that highlights the significance of the research and its contribution. Hence the emphasis on both the 'writing' and the 'content'.

A case of mistaken identity

I was standing in line at the subway inside the hub(univ food joint and hangout..something like a gurunath+sac+clt in iitm put together in one building) during lunch time. There were around 8-9 people ahead of me and no one behind me. The queue moves ahead and then this guy, who I recognize to be an indian, comes along walking really fast with his head slightly tilted downward and to the left, and joins the queue behind me. A few minutes pass and I wonder where he is from.

Me: "Which department are you from?"
Him: 'Computer science department'
Me: "So are you a Phd student?"
Him: 'No I am teaching'
I bulb for a moment and then.....
Me: "So you... you are an assistant professor?"
Him: 'Yeah'
I am, needless to say, a little embarassed; but what can one do when the professor looks, walks, talks like a grad student. After some more small talk, I go my way.

Fundamentals of Optimization

Here are the lecture notes of the course I just finished. Coming from an engineering background, I found this course to be really tough to start with. The 'toughness' didn't change, only I got used to it. The course was graded entirely based on 8 assignments (one every week), which were more an extension of the notes rather than being a completely new devil. I still don't have the big picture or the take-home from the notes, since this course involved pre-requisites such as Linear Algebra and a good enough exposure (supposedly years!) to elements of analysis and advanced calculus, which I didn't have. So most of my time was spent getting a 'feel' for the subject, including notations, concepts et al - basically the 'language of mathematics'. I am still uncomfortable looking at the level of math in the course, but hopefully with more exposure to these kind of courses and materials, I should begin to understand and enjoy the subject more thoroughly.

This is one of a kind course in that it goes into the fundamentals of the subject. Many people (me included) use the word 'optimization' loosely, but hardly realise that there is a whole theory(as I gleaned from this course) that lays the basis for all the algorithms and optimization techniques being widely used in various engineering, science and health disciplines.

A note on my course-mates: Most of them were studs in the field(grad level math course machi)
who left me amazed on their depth in the subject as was evident from the questions fielded in the class. Through this course, I have been fortunate enough to have the experience of knowing first hand how tough Math can be (I had strange opinions on Math before coming here). I might get away with a 3.7 or 3.8 in the course, but you see these assignments were very instructive and guiding the student onto the methodology and analysis required to solve the problems. Ofcourse, I had to understand the theory before attempting the assignment, but as I said earlier the big picture is still missing. I have the bits and pieces from each of these chapters, only I need to piece them together in the coming future.

As a final note, this course(the last course taught by the prof) was taught by a highly knowledgeable prof who was very precise and exact in his development of subject(something new to me since we engineers make a lot of assumptions whenever we can) and as a result, has sort of aroused my interest in optimization theory. Let's see where I can go from here.

On thinking - Part II

Let me further explore the threads in the previous post by taking up a quote on thinking -

Those who know how to think need no teachers - MKG

I decided to jot down my thoughts as I attempted to understand what this quote really meant:

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What did he mean by this statement? Does he mean there is a way of thinking that is to be known, sort of structured way of thinking that is more conducive to self growth? I have heard that mathematicians have a structured way of thinking through problems. But then, they also solve a lot of problems and hence think a lot. Is thinking, say by questioning a given statement, shredding it to the minutae, and analyzing each minutae and then putting it back again a way of thinking? And if I were to know this way of thinking and apply it in reality, does that amount to knowing how to think? Does he mean independent thinking? Or does he mean those who think often, need no teachers? Or does he mean if you know how to think, as in withdraw from the world, in a calm environment and think..does he mean that? Whatever be the case, the central element here is ‘what is thinking’? And why is it so important?

Can an analogy be drawn between exercising your body and exercising your mind: the more you exercise, the more you can exercise (body or mind). Is getting insights a valid output of thinking (I am assuming here that I know what an insight is..ha!)? Is effective thinking a function of number of insights you arrive at during your thinking process?

How do you quantify the effectiveness of your thinking? I just realized I am thinking, if this is what thinking is. You can have many thoughts that come through your mind, but only a few maybe relevant to what you are thinking about or maybe you just don’t know if they are relevant or not. Can you know if your insight is because of the propagation of such and such a thought? Is thinking a state of mind? Is it a state of higher awareness?

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Now, you can see my thinking as seen from above is hardly structured and many of the thoughts may not make sense, but the key thing is there are a lot of questions raised. So is thinking just about raising more questions? And how much of thinking is logic?

Analyse this.. You have a question pop up in your mind, say, "What is thinking?". How do you approach this question? You could start with what you know about thinking, past experiences of real deep thought and maybe understand the conditions that lead to such thinking. I don't know what thinking is as of yet, but mimicking these conditions could help me do whatever it is that happens during thinking. But isn't that logic? That's what Neils Bohr had to say: "No, no you're not thinking; you are just being logical."

So if I go by the reductionist approach, there are two processes going on here:
a) Arriving at questions b) Addressing these questions through a systematic reasoning process.
One seems due to thinking and the other to what we broadly call logic. But are they really two disparate entities or do they contribute to each other?
Does thinking add to your logic, that is, does it build your logical skills and does logic help thinking?..I mean, to start with, you either have to have logic or thinking (chicken or egg analogy). Now, what do we mean by logic ?
Logic : a particular method of reasoning or argumentation. Notice that, the definition is built around 'a particular method of reasoning', which is indicative of assumptions used to understand a problem, which may also mean the perspective you bring in to understand the problem. And we discussed earlier that thinking might be a process of broadening the perspective or model with which to view the world. So is logic a convenient or specific contextual meaning of the word 'perspective' and can logic be a measure of how much you think?

In conclusion(to this blog), through my understanding of the thinking process and my model of the world, I get an impression(read: abstraction) that thinking is all to do with going to any level of the model we have of the world and analysing the assumptions therein through logic(which involves all levels of the model we have) and refining it or outright discarding it, if the assumptions don't seem right (how this can happen I don't know, since all the logic we have is based on the assumptions of the model with which we view the world and within this context, everything seems self consistent, except that thinking, which is merely raising questions(or is it?), changes these assumptions! Insight might be a key word here that may need further exploration).

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.

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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...

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.

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

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.

Grad life

I find myself posting more about work than anything else on my running blog! Hence this blog. I am not sure this blog will last, I might change my mind and delete this blog as I see fit, as I have done in the past. But grad life warrants a blog. Peculiar incidents need documentation for the very reason that they are peculiar. Peculiar cycles of occurence in particular need to be stashed away for future remincising and humour.

For instance, over the past 4 months, I believe (and as partly shown by a sleep log), I have gone to sleep at almost all hours of the day(and night). Back during my undergrad days, my usual sleeping time ranged between 1 - 5 am with ocassional flashes of going in accordance with "Early to bed, early to ri...." by sleeping at 10 pm. Many of these 10 pm crashes were due to night outs made the previous night. But that's about the range of my sleeping times during my undergrad: 9pm - 7am.
Come grad life, I started pondering on the definition of life itself. Life as a process of change made more sense now than ever before. I mean there is this whole American culture , invisible social ettiquete et al, that I had to deal with coupled with courses that overwhelmed me not so much by the content as much by the sheer number of assignments.
Add to all this I was never sure when I was going to sleep. But there was a pattern to all this chaos. There would be cycles of regularity in sleep, work, etc and then life would take a plunge into the stochastic realm and all hell would break loose.
Right now my sleep times have stabilized..I mean really stabilized. I am crashing more or less at a time between 10pm and midnight. I am not sure how long this would last but an offshoot of this discipline I have enforced here is that I am beginning to grasp how difficult it is to work beyond 8 hrs in a day. I mean, during my "night out" phase, I believed that I could work as long as possible if a deadline needed to be met. But now, I need to crash by 12 no matter what and I also need to eat, fart, browse and work all in a time span of 17 hrs. Plus as the evening comes along, my thinking plummets, my mind vacillates to no end or better stops functioning and I as such feel miserable. So there, regularity in sleeping times brought out a barrier I never knew existed. Anyway so much is good enough for a first post I guess, longer posts shall be reserved for the forthcoming ones.