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.

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.

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.

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.

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.

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'.