Geet Duggal

A couple of days ago, I had a lunchtime-preoccupation with antennas and electromagnetic induction. We observe a neat phenomenon if you put two wires near each other, and Maxwell stated the phenomenon quite eloquently in his treatise on electromagnetism.  Basically, the instant you change the voltage across one of the wires, the wire next to it (but not touching it) responds with a current that quickly goes away.

By wiggling around the voltage in certain patterns, we can find interesting ways to transmit information back and forth between one another, and through induction we can do this without direct physical contact.  These days it’s easy to take for granted the all the internets sent to us via WiFi and forget about how highly developed an area radio is.

But to get taste of the physical communication, not much is required: basically some power sources and wires. A wire can in fact be practically used as an antenna for certain radio frequencies.

A simple way to check out induction with a laptop is to see if you can transmit a song that usually plays from your speaker through the air and back to yourself.  Since the sound card does both audio input and output as well as the analog-to-digital conversion, a lot of the hairy parts are taken care of for us.

To do this, we need to have the sound output (i.e. from your headphone audio jack) go to a wire.  Next to that wire is another wire that goes into the microphone or “line in” audio jack.  Keep in mind, these are just wires–that’s all.  I just forced myself to part with the headphone that came with my music player and another that I got on an airline flight.

As you can see, the ends of the two headphones lay prostrate next to the two wires connected into the microphone and headphone jacks:

So, now all you have to do is start up some music and record the input with some audio recording program (I used GarageBand since I’m on a Mac):

The green bars towards the middle-right wiggle around while recording indicating that the wire is receiving something.  Doing the same thing without the wires in the line in and out yields no green bars wiggling around.

Because there’s so much power loss, the signal is faint, so I digitally amplified it some in the software.  But horray! I rather shittily transmitted sound back tomyself over air via just two wires.  This, I think, is a neat way to illustrate induction.  Listen for yourself. You’ll need to turn up your volume a bit.

Warning: what follows is a hand-wavy one-sided monologue, continue at your own risk!

It seems that the most appealing and productive way for someone like myself to learn and explore is via solving a somewhat concrete problem that motivates me (e.g. a sampling of the links on the sidebar of this log). Regardless of the fundamental and pure aspects of this motivation, I find that I learn a lot along the way and other interesting problems and doors open–natural extensions to continue doing more interesting work.

So it’s tempting to say, “this is ideally how I should learn: through some form of personally-motivated problem solving,” trusting that this approach will fan out more and more interesting work potentially even covering a lot of ground that I would come across in more artificial, in-order perusals of self-contained texts. Fueling this temptation: since more introductions, review papers, and articles are available online, we may not be as dependent on self-contained texts and can actually tackle a subject at hand (for instance, read the preface here).

While this may be a sensible approach in principle, its limit in scope intuitively ignores two important things which motivate the rest of the entry: (1) like any sport, a push or even nudge of systematic self-contained learning goes a long way in growing more rapidly and increasing competence and (2) in reality abstractions are built and reused in ways that are dependent on one another, so students must take classes on well-defined subjects, professors must teach them, and professionals often end up becoming specialists/experts naturally, or are forced to take “mandatory” training to learn their craft.

Thus, regardless of what’s ideal, simply working for the man may require a more systematic approach to learning material. How this is approached by students seems to be a problem. Most students, for example, may see tough, self-contained classes as a chore or measure of performance, even if aspects of the material interest them. A systematic introduction to a topic meant to fuel thought and cover some potentially very good concrete examples in a breadth of topics in reality just implants the existence of a few keywords, or better-yet, a concept or two. My hunch is this is what the modern teacher/prof settles for in the general student (understandably so, there are often a lot of students per professor).

If I were to have a point (hopefully you don’t assume I need one, especially in a web log entry), it would be something like, “some students either blame themselves too much or not enough; they are either too hard on themselves for not understanding something they find difficult or, equally as bad, assume that something is wrong with the way a class is being taught.” If the systematic learning is approached by the student in less of a pressured or stand-offish way and in more of a, “well, I’m somewhat interested in/required by the man to learn about this, let me be open to the concrete examples and approach them curiously,” then systematic learning may not only prove to be less of a chore and more interesting, but also be a healthy push in an interesting direction.

Keep in mind that I say this as a student benefiting from this attitude for some time, though not nearly long enough.

So as a first-pass exploration into the community structure aspect of complex networks, in particular arXiv, I read-up, then scripted up an exploration on some test citation networks. End result: some marginal progress as expected, but it bought me some increased maturity and satisfaction of concrete play. Also, who doesn’t like to click on nodes and see the communities?

You can see the web page and a TeX-note if you’re interested in killing a few minutes of your time.

Special thanks post-exploration to Aaron Clauset and Michelle Girvan who gave me helpful guidance and suggestions on continuing with this community analysis research after a particularly insightful talk given today. Now finally on to more interesting reading/work on a topic I’ve meant to learn properly for a while.

This note simply tries to get across as accurately and conceptually as possible what a potential energy landscape is. It is part of an inquiry into complex networks and physical structure. The field has quite a bit of activity, and the discussion can be seen as a simple introduction to the topic. It is difficult to find introductions at this level, so it may be of use to others, but mostly I just wrote it to log some progress. Thanks to a friend for his thoughts and I welcome other thoughts and better-yet corrections (though I don’t expect any comments at such an early stage of me web logging).

You can download the PDF directly via this link.