The PhD Experience

Yesterday I gave a talk titled "The PhD Experience: Lessons learnt in five and half years." I narrated my personal experiences, thoughts and the lessons I learnt while pursuing a PhD at the Department of Electronic Systems Engineering, Indian Institute of Science. 

The key question that I try to address is, "What are the processes and tasks that get the best out of a researcher?" Considering the researcher as a system, I discuss the inputs (information and experiences), outputs (hardware, software, knowledge) and processes of this system. The presentation is targeted primarily at present and prospective graduate students. However, anybody with an interest in learning and productivity might resonate with aspects of the talk.

Here's the video of the talk [video credits: Abhijit Kshirsagar]

The pdf file of my presentation is available here.

P.S. During the talk, I mentioned the importance of developing verb vocabulary.

The Thesis Whisperer has compiled a useful verb cheat sheet that is available here.

Learning How to Learn

This blog post is a course assignment for the Coursera MOOC titled "Learning How to Learn" taught by Prof Barbara Oakley and Prof Terrance Sejnowski, University of California, San Diego. Here I discuss my ideas and experiences with three of the learning techniques mentioned in the course: (1) Switching between focused and diffuse mode of thinking, (2) Memory: spaced repetition and associations, and (3) Interleaving.

1. Focused and diffuse mode of thinking

The pinball analogy described by Prof Barbara Oakley is a very elegant way of conveying how the focused and diffuse mode of thinking work.

Depiction of focused and diffuse mode of thinking in Prof Barbara Oakley's lecture.

[Source: http://projectfidgetyfingers.blogspot.in/2015/01/how-to-be-creative-switching-between.html]

The importance of playing ping-pong between these two modes in cementing the learning cannot be over-emphasized. Several accomplished people have vouched for it. Prof Arindam Ghosh at the Indian Institute of Science is a renowned scientist in the field of low-temperature nano-electronics. I happened to be team mates with him in the institute cricket team and once did an interview of him where he stressed the importance of playing sports. "Sport rejuvenates the mind. In research or, for that matter, any profession that involves a fair deal of thought, it is very easy to get stuck in a thinking loop. Sports helps break that loop so that you can start your thought process afresh, from a new perspective", he avers. You can read the full interview here.

I've come up with my own analogy to illustrate the importance of switching between the focused and diffuse modes. Picture a fly trying to escape out of a car banging against the glass window. The window is half open but the fly is pushing away at the closed part of the window duped by its transparency. Its trying really hard in its focused approach to get out of the car. But no amount of pushing and buzzing against the glass will solve the fly's problem. What it needs to do is to back away from the glass (akin to going into a relaxed diffuse mode) and come back at it a few inches from where it had approached earlier and voila! It's an open window. The problem is solved, the fly is free.


2. Memory: Spaced Repetition and Associations

I tend to browse and read about a diverse range of subjects. In the process of looking up new information all the time, I might not repeat what I already learnt and hence tend to forget many of the things that I learn. On the contrary, when it comes to identifying plants along with their common and scientific names and their key features, I found that I had a very good memory. The key difference that I noticed was that of spaced repetition. Every time I take a walk in the campus to and from my laboratory, I notice these plants and recall their names while observing them. This routine of recall and spaced repetition helped cement the details of these plants in my mind. I now intend to use the same technique in other aspects of my learning.

Another common problem that I had was to frequently forget where I parked my bicycle possibly because I'm absent minded, not paying attention while I'm parking. Lately, I started leveraging my good plant memory for solving this problem. Every time I park my bicycle, I notice the nearest tree. By building this association, the next time I'm looking for the bike I just have to recall the tree and I find my bike!

3. Interleaving

Prof Barbara Oakley stresses the importance of interleaving one's learning using various techniques and from various perspectives. This helps in gaining a better understanding and in better retention of the material. An interleaving technique that I often use and that has helped me in learning various subjects is what I call "Repeated Classification" of the material. I shall illustrate this technique in the following paragraphs.

Number based classification

After having studied a chapter or several chapters of a book on a subject XYZ, I try to cull out all the numbers mentioned in the text and put them together in a list called "XYZ in numbers." E.g. recently I attended a colloquium by Prof Arnab Rai Choudhuri titled "The mysterious magnetic personality of our sun." I distilled out the numbers he presented at various points of the talk as follows.

The sun in numbers:
Surface temperature of sun = 6000K
Temperature at sunspots = 3000-4500K
Temperature of corona discharge = 1,000,000K
Strength of the sun's poloidal magnetic field = 0.3T
Strength of the magnetic field at sunspots = 10T
Time taken by the sun to complete one rotation about its own axis = 27 days
Time period of the sunspot cycles = 11 years
Time period of the polar magnetic field reversals = 22 years

Time based classification: (when)
Another form of classification is based on the historical timeline of events pertaining to a field of study. Systematically listing down the years of occurrence of significant events provides a sense of how a particular field evolved and creates a storyline that makes it easier to grasp the complete picture. Call it the "Timeline of XYZ."

Spatial classification: (where)
Making a list of places and the associated events is another handy way of classifying. Marking the places on map is even better. This can provide insights on how geographically diverse or concentrated the development of a particular field has been. Call it the "XYZ map."

People based classification: (who)
List down the names of all the people associated with the field of study, preferably along with their significant contributions and quotes. Here's a list of the people who appeared in the 'Learning How to Learn' course lectures and interview videos along with a memorable quote or key take-way from each of them:

Dr Barbara Oakley: "Do not just FOLLOW your passions. Instead, BROADEN your passions."

Dr Terrance Sejnowski: "Unfortunately, there is no instruction manual for the brain."

Dr Robert Bilder: "Disagreeability can spark creativity."

Daphne Gray-Grant: "Do not edit while writing!"

Benny Lewis: "Why children learn language easily is because they are not afraid of making mistakes."

Dr Norman Fortenberry: "Multi-mode input is critical for learning."

Scott Young: "Learn a language by immersing yourself in it."

Amy Alkon: "Fast reading tip: approach a book like a buffet; do not eat everything!"

Dr Robert Gamache: "Study every subject everyday, even if it is for only 10 min"

Dr Keith Devlin: "Switching from one task to another is when one is most likely to fall into the procrastination trap."

Dr Richard Felder: "Don't wait for that 'block of time' to get things done. Do the task in short bursts with whatever time slots are available."

Dr Rebecca Brent: "Give your subconscious an assignment."

John G Maguire: "The secret to good writing is objects, not ideas."

Kalid Azad: "The ADEPT method of learning: Analogy, Diagram, Example, Plain English, Technical Description."

While we looked at questions like how many, how much, when, where and who, several other ways of classification are possible using 'what' based questions. E.g. classifications based on techniques, methods, objectives, products, types, resources etc. There are no limitations to how many different ways you can classify the material and play with it providing various insightful perspectives. It is down to your own imagination. Happy learning!

My experiments with toothpaste - II

In part one, we looked at the ubiquitous tube and arrived at an approximate formula for its volume. We had neglected the effect of the increasing major axis on the volume and had taken it as a constant. Here, we shall try to be more accurate by including this tapering as well in our analysis.

For the elliptical cross section of the tube, let the major axis taper linearly from 2R to 3.14R as you move from the bottom of the tube to the top as shown above. The expression for the semi major axis 'a' at any vertical distance 'x' from the top is given by:

The expression for the semi minor axis 'b' at any vertical distance 'x' from the top is given by:

The volume of the tube can be obtained by the following integration.

Substituting the expressions for 'a' and 'b' and working out the integral we get

which is greater than the result obtained earlier.

Applying the result:

For the toothpaste tube under consideration in part one (R=1.6cm, h=13.8cm), the new formula gives a volume of 66.6 ml. Taking a correction factor of 1.5 to account for the bulging profile as opposed to a triangular one, we get a volume of about 100 ml. The choice of an appropriate correction factor is a matter of debate though. For a net weight of 150 gm, the density of the toothpaste would be 1.5 gm/ml as opposed to the earlier result of 2.5 gm/ml. This new result seems more in agreement with literature which says that typically it's in the range of 1.2-1.6 gm/ml.

Thanks to Raghunandan for pointing out an alternative approach to calculating the density of toothpaste coming from the chemical composition data.

Caveat:

Strictly speaking it is not correct to say that both major axis as well as minor axis taper linearly. Whatever be the values of 'a' and 'b', they have to satisfy the constraint that the perimeter of the ellipse has to equal 2 x pi x R (Since our tube was actually formed by pinching one end of a cylindrical tube). Hence, the moment you say that either 'a' or 'b' tapers linearly, the other has to taper non-linearly. But so far as an approximate calculation is concerned we shall not worry about this constraint.

My experiments with toothpaste - I

Brushing my teeth on a Sunday morning I glanced upon the new toothpaste tube and wondered what's the volume of the paste in it. So many of our daily use pastes and gels - toothpastes, shaving creams, face-washes, ointments and many others - come in this weird shape that I don't have a name for. Let me call it the tube. The mensuration tables we all studied in school gave us the formulae for the volumes of common shapes such as cube, cuboid, sphere, cylinder, cone etc. But they didn't talk about this ubiquitous shape!

If you look at the horizontal cross section of a right circular cone, it starts out with a big circle at the bottom and as you move up, the circle becomes smaller and smaller till you finally reach a point. The cross section of the tube also starts out with a circle, but as you move up, one of the two principal axes of the circle starts shrinking (minor axis) while the other starts increasing (major axis). You end up with flatter and flatter ellipses finally reaching a line segment of length 3.14xR when the ellipse is completely flattened out at the top. 

Let us assume that the tube tapers off linearly and hence it should look like a triangle from the side view as shown above. Another simplifying assumption is to neglect the effect of the increasing major axis, hence taking it as a constant. As per this assumption the major axis stays at 2R throughout. In other words, the semi-major axis stays at R throughout. (A more accurate analysis taking into account the tapering of the major axis can be found in part two)

The volume of the elemental ellipse of thickness 'dx' located at a distance 'x' from the top is given by,

We get the total volume of the tube by integrating the above elemental volume for 'x' varying from 0 to h,

That's an intuitively pleasing result because it tells us that the volume of the tube is in between the volume of a cone and that of a cylinder having the same base radius and height.

Applying the result:

For the toothpaste tube I was using, R=1.6 cm and h=13.8 cm which gives a volume of about 55.5 ml as per the formula derived above. Since the tube is brand new, it's likely to have a bulging profile as opposed to the triangular one assumed above. So, the volume would actually be slightly larger than the calculated value. Let's take it as 60 ml. The net weight marked on the tube is 150 gm. Hence the density of the paste is (150 gm)/(60 ml) = 2.5 gm/ml, that's two and a half times the density of water.

No wonder, however small amount of toothpaste you put into water, it's bound to sink!

Energetic consequences of doing things slowly

From charging capacitors to filling up water tanks.

Electrical engineers are familiar with the idea that when you try to charge a capacitor from a step voltage source, only half of the energy coming from the source gets into the capacitor while the other half is dissipated in the circuit resistances and/or lost as radiated electromagnetic energy. In other words, the efficiency is only 50%. Does it always have to happen that way? How can we do better?

The answer lies in shaping the applied voltage. If the rate of rise of the applied voltage is of the order of the time-constant of the circuit, the efficiency is much better than 50%. If it is very slow compared to the time-constant of the circuit, the efficiency approaches 100%. This is proved analytically as well as validated by circuit simulation in this article.

Even if we did not shape the voltage, if the capacitor doesn't have a linear relation between charge and voltage (in other words, it is a non-linear capacitor), the efficiency can still be very different from 50%.

The case of a step current source feeding an inductor is also analogous to the above scenario and gives similar results.

Taking a step back and applying this concept to any other domain (other than electrical engineering) can give some interesting insights. Pumping water into an overhead tank through a pipe having finite resistance (due to friction) is an example of an effort source feeding a potential energy storage element much like a voltage source charging a capacitor. Hence, it will take lesser energy if we were to pump the water slowly (trickle pumping) over several hours rather than doing it fast (gushing water) in fifteen minutes flat!

On a philosophical note, a very nice example is that of a teacher teaching a student. If the teacher goes far too fast beyond the grasping speed of the student, much of the knowledge doesn’t get transferred to the student’s brain.

Sleep Detector Power Saver

I remember umpteen instances when I've seen people leave their lights and/or televisions turned on and fall asleep. While the person is recharging himself his appliances are continuously hogging power all night for no useful purpose at all. Of course the easiest solution to the problem is for people to realize the mistake and be responsible enough to turn off all unwanted utilities when they go to sleep.

But since we still have so many careless people around, there is a potentially huge market for a product that could detect sleep in a person and take action accordingly - switch off lights, TV etc. Sleep detection could be done based on monitoring of one or more of various parameters - heart rate or pulse rate, body movement, body temperature, respiration rate etc. The major challenge in such a product would probably be to identify which among these myriad options would provide the cheapest and the most reliable way to detect sleep. Any answers?

[This post is an elaboration of Problem-3 on the post "Nine Problems Worth Solving"]

Jerky Ride Writing Assistant

Travelling by bus, train or car can be tedious if the journey is long and more so if you are all alone. Many resort to reading in order to pass time. There are times when I felt like writing something when traveling. But because of the jerky nature of the ride, it becomes rather difficult to write anything legibly. It's at times like these that I've often wondered if there could be some device that could be strapped on to my wrist, which would allow me to write normally the way I would in a stationary and jerk-free scenario. It could probably compensate for the jerks by applying precise forces (of the right magnitude and direction) on the hand - some sort of an active noise cancellation!

Another possible solution to the problem is to have some sort of a damper or a shock-absorber structure that keeps my hand and the notebook steady irrespective of vibrations in the vehicle. Any thoughts and/or suggestions from the reader are most welcome.

[This post is an elaboration of Problem-2 on the post "Nine Problems Worth Solving"]