Thinking in polar coordinates: #weareallcartesiansnow

You remember those polar coordinates we did in pre-calc/calc/trig classes? Yeah, it is clearly my desire to revive memories of those days on which we wrote equations as f (r,θ) instead of f (x,y), tried to plug-in values of -2π to 0 to 2π and figured out the direction of a graph, when we moaned and groaned about who would actually use something as pretentious as polar coordinates.

Turns out dart boards are a very straight-forward real-life application of polar coordinates. Each wedge extends from θ to θ+18 and from s to S where s is the radius of the outer bulls eye rings. The double and triple rings also span the same angles, but are characterized by different bounds from the center.

Why am I talking about polar coordinates and dart boards today? Well, due to sheer boredom I started throwing darts recently. It took me a while to get a majority of my throws on the board. I’m doing well now, and I’ve been trying to hit one number consistently. It’s very easy to get carried away throwing darts… the target is well-defined, it’s easy to experiment and improve your throw, and every so often you can hit the target, which is a major motivational factor.

I was trying to hit the double ring on the 17 today. It was way more difficult than I thought it would be. Initially it was difficult to pinpoint why it was so difficult, but I think it all has to do with the fact that we’re not good at dealing with polar coordinates.

Throw a dart randomly and hope it hits a spot in the scoring area. Somewhere along the radius passing through that point lie a few points which are included in the triple ring. If you haven’t already hit your goal of triple ring, you can say, “Ah, I need to throw at the same θ, but just need to change my r up a bit.”

Of course, our first instinct is to not say that… we say “I need to move it x units to the right [or left] and y units down [or up]” and try all kinds of stuff (gravity assist, monocular vision, offering of red jasmines hibiscus flowers and modaks to Ganesh) etc., with the hope that the dart will behave the way we want it to behave. This is perfectly fine. Gravity and initial velocity have an enormous influence on the trajectory of the dart, so we kind of have to isolate the vertical motion of the dart from the horizontal.

Yeah,  dart boards are a straightforward example of polar coordinates, but thinking in polar coordinates is decidedly not straightforward. Polar coordinates are a pretty elegant method to describe some stuff mathematically, but in everyday life it’s going to be really difficult to think of objects as being r units away and θ degrees clockwise/counterclockwise from some other point. To re-iterate the point in my title #weareallcartesiansnow.

So, yeah, it seems way easier to control the horizontal motion of a dart than it is to control the vertical motion. As noted above, there are 3 major factors affecting the trajectory (gravity, initial velocity, initial height; air resistance notwithstanding) whereas the horizontal coordinates are only affected by the initial position and velocity.

Phew, enough intellectualizing about darts. Time to sleep.

–Gautam

EDIT: h and j are very close to each in the English alphabet.

Why did I Ever Sign Up to be an Econ Major Part II

Back in High School, I liked Econ not only because I was good at my AP microeconomics class, but that econ just felt intuitive. It’s not like other classes were not intuitive (mechanics, for instance, was pretty intuitive) but econ somehow seemed to explain why certain behaviors I saw out in the market. I could simply parrot ‘supply and demand’ at pretty much anything and it would explain why   got cheaper over months, why the price of gas rose up, etc.

That was in 2006, when the Dow was at 14,000 something. I remember catching whispers in the air about how things were going to unfold in a couple of years, but there was nothing concrete. Back then I didn’t know of any of the blogs I currently surf, didn’t know of any of the debates that rage on in the intellectual circles/blogosphere, etc.

I took macro economics freshman year of college. In my sophomore year, I took intermediate micro and micro and was introduced to “calculus” in economics. The classes are all well and good, but I thought they were just too easy. How is it that after spending several weeks on Walrasian equilibrium people were still unable to understand what “market clearing” is? and how come people couldn’t figure out the solution to relatively trivial optimization problems?

Given the theme of my previous post, and all the thinking I’ve done over the last day or so, my belief is that many of my classmates lost track of economics once it lost the intuitive appeal.  A bunch of log-linear or Cobb-Douglas production functions provide a poor illustration of how an economy decides to allocate its productive powers, and as I discussed yesterday, it is simply not possible that you’ll find someone who knows that his utility function is the natural log function.

Mathematics is a fine tool to study economics. I’m kind of glad that people resorted to quantitative approaches, since I’d probably have been turned off if economics only involved making field observations and producing theories to describe the observations. However, by diving into the wreck of equations and optimizations without motivating them, instructors are doing a poor job of reaching out to the people who are generally confused about where these equations and things originated from anyway.

Instead of stressing on the fact that mathematics is a tool for describing some relationships in economics, stressing on making sure people setup optimization problems properly puts the mathematics front and center, leaving the economic framework defenestrated from the students’ perspective. I know this is not the case with me, but I bet there are good portion of students who pass intermediate micro and macro econ (the “gateways” into more econ) being able to solve optimization problems but not having the faintest clue of the implications of the theory that the problems are addressing.

Physics and Engineering departments, for instance, have done a great job of making sure students understand what equations mean; ask an engineer a problem about heat flow, and he’ll immediately tell you the equations he used to solve the problem and the phenomenological description of the equations. Ask people in my finance class about what the CAPM equation is telling you, and you might hardly get 10 responses, no two of which tell you the same thing and none of which are right. I can go so far as saying “It describes the idea that the risk premium associated with a security is a function of the risk premium of holding a market portfolio and a function of the covariance of the security with the market portfolio as a proportion of the variance of the market portfolio.” I hope it’s right; if not, I’ll look like an idiot, but “khuda meherban to gadha pehelvan” always applies.

People in academia these days seem to talk a lot about how models in economics need to change significantly in order to better deal with situations like the financial meltdown (c.f the Economist’s discussion on the same topic.) But nobody ever talks about how dismal the  state of undergrad econ classes are. My colleagues have specifically said that they have gone through 4 years of undergrad without learning absolutely anything beyond Econ 101 and 102. Couple this with the fact that none of the classes are taught by professors*⁺, and you get a student body that has only really seen marginal gains in any knowledge of economics and which is not prepared at all to use their background information to take a stand on particular topics.

Do academicians simply view undergrad as a filter by which the best of undergraduates will be picked out for grad school a and lucrative business jobs, and the remainder see some marginal gains in their incomes due to the possession of a degree? Why is it that during and after recessions, when the popularity of econ majors suddenly starts rising, the University of Minnesota is unable to get any of its faculty to take on some of the excess demand? Do professors just not care about undergraduates? Are they just not worth it? Like I said yesterday, I hope that is not the case, but given the pessimistic outlook you see from me, it might just be wishful thinking.

*This is not exactly true. I have had one course taught by a professor, and it was all right.
⁺I don’t mean to imply that all graduate students who teach classes are terrible. I’ve enjoyed some of the grad students I’ve had, but in general it seems as if undergrad students feel like they’re not getting their money’s worth and generally resign to the fact that instruction is going to be of a relatively lower quality compared to what one would expect of professors.

Are HOV lanes being well utilised?

I am on the SW Transit bus right now, heading home for a while the bus was on the Westbound HOV lane of 394, cruising at 60 or whatever. The thing is: all other non HOV lane occupying vehicles were cruising at 60 mph (if not faster) as well. Pn the other hand, Eastbound 394 was backed up, all the way to St Louis Pk/Golden Valley. So, I immediately asked myself: wouldn’t the HOV lane have been better used for all the EB travelers? Would we WB, public-transit-using folks, have been inconvenienced with using the regular lanes?

There are two ways to answer this, I guess. On the one hand, you can simply ask: what proportion of EB cars would have been eligible to use the HOV lane? If the answe to that would have been 1 in 5, then it surely would have made sense. If the answer had been 1 in 20, it probably wouldn’t lhave made sense. In the latter case it would probably have been better to just open up the 2 lanes for all EB traffic.

However, the situation can be approached another way. When the public planners were designing the HOV lane system, they probably had some data on the distribution of traffic flow. In particular, this data must have told them about the distribution of traffic flow, i.e. the mean rate at different time of the day, the standar deviation, kurtosis, skewness, etc. From this data, (and, of course, comparing the relative flows in each direction) they probably inferred that it is optimal to open up the HOV lanes to WB traffic from, say, 4-7 PM (I don’t know if these are the actual times, but for the sake of argument, let’s assume they are.) All is well and good, right?

Wrong. There will always be some outliers. I am willing to bet that if there’s a game at Target field at 6 PM, EB 394 is gonna be more crowded. If any other major route leading into downtown is closed there are probably gonna be more cars on EB 394, etc. The traffic flow rates, as I suggested above, will follow a distribution. On average they will take the mean value, but they might not. I think that might have been the case today, with a lot more cars going EB than going WB.

The immediate question that arises is: is it possible to control the HOV lane direction so that traffic flows are optimized? I think so. We probably have a lot of sensors on that road that give us a good idea of how traffic is flowing an a particular instant. Why don’t we leverage this information when we decide the direction in which traffic flows. It will lead to fewer headaches for those poor people stuck on EB 394.

Of course, I may be wrong about all this… but I really don’t think such is the case.

–Gautam
PS: I have reached home at this point. Happy Diwali to all readers.

Solitude

For whatever reason, I feel lonely. I had a hard time accepting the feeling, but here I am.

It’s not like I’ve been physically alone all the time. I’m in lab for 5-6 hours of the day during which there are many other people milling about. The machine by the information desk in Coffman logs in the hours I spend there. I also attend quizbowl practices for an hour every Tuesday/Thursday. In all these things, though, I feel like I’m lacking a “best friend.” I’d never thought I’d come to such a realization during my undergrad career.

Whenever I do something outside of work, I feel a kind of loneliness starting to kick in. I go running alone; the few hours I spend at my apartment go by mostly without talking to my roommates; any impromptu decision I’ve made to step out has involved me being pretty much alone. It’s not like I’ve not thought about asking people to hang out with me… it’s just that there aren’t all that many people on my contact list who I’d like to hang out with and/or with whom I wouldn’t have an awkward time convincing them to spend their free time with me. Conversely (I guess “naturally” fits just as well,) I get very few calls from people asking to hang out. (Note that I’m not complaining, merely observing. I don’t hate people for not calling and suggesting I spend time with them.)

Throughout, I’ve always been playing defense when it comes to making friends. With any major transition I end up taking a year trying to determine who are good people to hang out with, who share similar aspirations as I do, who’d help me realize my shortcomings and capabilities, and so on. I have met most of my friends through classes I have taken. There certainly are other activities and channels through which I’ve made friends, but the overwhelming majority I’ve initiated contact with have been through classes.

However, (and I realise that this is coming embarrassingly late in my life) I’ve come to the not-so-erudite realization that the critical turnover timescale of friends is smaller than my preferred timescale. By “critical turnover timescale” I mean the amount of time over which the set of people I’m likely to interact with (or have the chance to interact with.)  That is, if I meet someone new right now, there’s a distinct possibility that I will not meet him/her after the end of the ongoing semester. Unless, of course, we become good friends, in which case I do whatever possible to maintain contact.

Sitting on a park bench, or in Bruegger’s Bagels (which I’m doing right now,) isn’t randomly going to facilitate my interaction with a future good friend. I realise I have to be more proactive about this. But, honestly, I haven’t found the time to invest in myself, and it seems too much to meet 10 new people a day in the hopes of making a good friend.

I think I’m doing some things right. I’ve restarted running on a frequent basis, and I’ve been going to the rec with regularity. I’ve been practising my Tabla at least twice every week and I intend to continue. People in the lab have been supportive, and I guess I should just give some time for my SUA job to “blossom.” I’ve no doubt that by the end of the summer, I’ll be a different individual than I was prior to its commencement.

I’ll clarify that I didn’t have any ulterior motive (such as craving attention, or whatever have you) in making this post. I don’t expect anyone to call me in a couple of hours suggesting we hang out/have a good time. I just needed to spend a few minutes thinking of the course life has taken so far, and how my indifference curves should be modified.

Gautam

Why am I such a poor half-asser

The title of the post was originally going to be “Why I AM a poor half-asser” but guess what, I couldn’t half-ass enough reasons to support the titular claim. I mean, let’s be honest: I think I have plenty of “real knowledge” of things that I have encountered in classes, that I have encountered from my readings outside of classes, that I have encountered while talking to “experts,” etc. Yet, every time I make claim or try to summarize someone else’s beliefs/work, I find myself hesitating. I am not sure if I am accurately citing my facts, or if I am accurately representing someone’s position on a topic.

I find it amazing how some people are able to produce “facts” out of thin air. I mean, unless I trust someone’s authority of the subject, I’m always skeptical about these claims and I double-check to make sure people’s claims. For instance, I’ll happily accept a statement Dr. Matthes makes about Semaphorins, but no way am I going to accept a claim some random quizbowler makes about what the De-Haas van Alphven effect. This goes the other way too, though. I won’t hesititate to make some bold(ish) conclusions about how things people claim on Bloomberg TV are wrong, but I’m most likely going to pussyfoot on what exactly the Bell’s Theorem means. I’ve definitely encountered the latter topic much less frequently than the former, but I’ve taken a class on quantum mechanics, too! How then, can it come to pass that I have to spend half an hour researching about Bell’s theorem before being able to explain it?

I probably am afraid of the consequences of making an incorrect claim. Just today, I was looking up some topics for the GRE issues essay. One of the topics presented on the official website was:

“What most human beings really want to attain is not knowledge, but certainty. Gaining real knowledge requires taking risks and keeping the mind open—but most people prefer to be reassured rather than to learn the complex and often unsettling truth about anything.”

This topic is so juicy. Probably the most obvious thing I can think of for this topic is John Kenneth Galbraith’s definition of conventional wisdom. This passage summarizes exactly what this passage is talking about. I still didn’t feel comfortable citing Galbraith because I was afraid I would be misrepresenting his ideas. I’ve only read the Affluent Society once, so I’m not exactly familiar with every passage of the book.

Perhaps this is an indication that I should be more well read? Instead of spending more time on this blog or looking up youtube videos of noted Hindi song from Pukar called “Que Sera Sera,” should I be spending all my useful time reading up Galbraith and Keynes so that when I do cite them, I’m more confident about it?

Maybe I should.

Gautam

Crime!, and Punishment?

So, after a long time, I decided to write a real post. I am restarting blogging. For the last year or so, my “blogging” has consisted of copy/pasting articles or youtube videos; I plan on continuing that, but I think I should do more.

Anyway, so, while I was taking a shit today, I was thinking about the layout of the tiles in the bathroom my suite-mate and I share. It consists of several 1″ x 1″ square  tiles which are either beige or grey. The pattern on the floor is seemingly random, with the half towards the shower consisting more of grey tiles and the half towards the toilet consisting of more beige tiles. As I started looking at it deeper, though, I started recognizing several shapes that usually come up in tetris.

I used to be an avid fan of tetris, when I caught the disease spread by people in Physics, as they thought it was the only wise and sane way in which time allotted in class (ostensibly to finish homework and stuff) could be spent. Soon, I, imitating all the cool people, DOWNLOADED tetris onto my TI-89 TITANIUM (see how much cooler I suddenly was?) and started playing it like another crazy bastard. I think I got the game from a certain I. L., or Mr. I. L. played it on my calculator; whatever the case, I was aggravated to see high scores in the realm of 290,000 (!) which I knew I could never beat. I mean, I knew I. L. was crazy, but exactly to what degree he would take his craziness to, I knew not.

While staring at these tiles, a thought occurred to me. Well, really, it occurred to me earlier when I started writing this post, but whatever. Imagine if this I. L. were to be in the Inferno (note: there are several reasons for I. L. to have this fate, notwithstanding his obsession with certain things and a failure to commit himself to Christ); The following question naturally arises – “what would be the best punishment for this I. L.?” Well, surely, a Mr. S. S. would say “In the month of May, Mr. I. L. would have to enter examination halls and take the AP test for all students simultaneously.” However, that does not satisfy the Hell scholars, because I. L. would be unemployed for 11 months of the year! A miss A. Z. proposes, “OMG, HAVE A (TEDDY)BEAR HUGGING HIM FOR A MINUTE FOLLOWED BY MAULING FOR A MINUTE. THE TISSUE CONTINUOUSLY REGROWS SO HE SUFFERS THAT FATE FOREVER.” However, this being too gory for the author’s taste, is promptly discarded.

Several great suggestions are advanced. It is proposed that A drunk M from the pair M&M keeps requesting I. L. accompany them in bed, but I. L. never gets the chance to be with the second M alone. An M. W. proposes that I. L. answer infinity line long tossups on I Hope They Serve Beer In Hell which happens over and over again. B. S. and V. S. proposes that I. L. be given a giant pair of boobs, and has to he has to keep hugging forever; Oh, and also, I. L. be given four arms so that he can hug himself BELOW THE WAIST TOO.

The author proposes that I. L. simultaneously plays infinity games of tetris on TI-89, all of which end with 0 points to I. L.’s credit! Following every game, I. L. is forced to assume a look of terror as his button down shirt is torn into infinity piece by a blast caused when several tonnes of sodium react with water, and that shirt is reassembled into two shirts by the Banach-Tarski paradox. I know I am a hateful bastard, but imagine how much satisfaction that would give me! I WOULD ALWAYS BE BEATING I. L. AT HIS OWN GAME!

God bless you I. L. I hope you try your best to avoid all those fates.

G. K.

Rainy day high

many drops fall down
the grass appears very green
no more watering

This is awesome.

Moving

We move tomorrow
This house feels very empty.
Get rid of the junk.

Lot of paper here
And a mess of tangled wires.
Another late night.

–Gautam

Somebody tell me that’s technically right….

Mi Experiancia

De acampar. Es un cuento, no es una historia verdadera.

Cuando tenía 7 años, fui a acampar con mi familia y algunos amigos. Fuimos a un lago muy grande lejos de nuestra casa. Salimos a las 5:00 en la tarde y llegamos al lago a las 8:00. Rápidamente, hicimos nuestras tiendas de campañas y luego, dimos una caminata alrededor del lago. El lago era magnífico y me gustó mucho. Desafortunadamente, el sendero tenía muchas piedras y me caí una vez. A las 11:00 de la noche, buscamos leña. La leña estaba mojada, y usamos muchos fósforos para hacer una fogata. Nos sentamos alrededor de la fogata y contamos muchos cuentos por dos horas. Después, dimos “buenas noche” a los amigos, y volvimos a nuestra tienda. Me acosté a las 7:00. Me bañé en el lago, y el agua era fresca. Comimos frutas para el desayuno. Mi mamá trajo manzanas, naranjas, sandias, cerezas, y piñas. Mis amigos y yo jugamos frisbee, cricket y fútbol. A Mi hermano se le olvidó cerrar una cesta, y las hormigas han atacado las frutas. Afortunadamente, no eran ni hormigas ni moscas en otras cestas. Asamos un pavo grande para el almuerzo, y ¡era delicioso! Nos divertimos en estos días y quiero ir allá otra vez.

To buzz or not to buzz.

‘To be or not to be’ parody I wrote for English Class:

To buzz or not to buzz: that is the question:
Whether ’tis proper in the game to suffer
The consequences of scoring an outrageous neg five,
Or to attack the barrage of easy clues,
And by buzzing, power them. To pause, to restrain–
No more – and by a restraint to say we end
The lament, and the million brain slips
That we are prone to make! ‘Tis a perfection
Devoutly to be hoped. To pause, to restrain–
To restrain – perchance to daydream: ay, there’s the impediment,
For in that reverie what thoughts may come
When we have shrugged off the simplicity of the question
Must make us pause. That is the consideration
That makes of so short a round:
For who would bear the burning pain in the future,
Another easy bonus, the opponent thirtying it,
The coach’s disappointment, the reader’s leisure,
The insolence of team-mates, and the rejection
Only capable of evil the person bears,
When he himself might keep his silence
By delegating it to somebody else? Who would bear the burden
To think hard and have a perfect record,
But that the dread of the easy bonus,
The undiscovered country, from whose bourn
The opponent does return, and scorns at our intelligence,
Makes us rather bear the security of a tenner,
Than pry for a power that we know not of.
Thus thinking makes a coward of us all,
And thus the original determination of twenty powers
Is made weak by the brittleness of thought,
And tossups of great value and honor ,
With this regard their thoughts run awry,
And lose the name of action. — Hark, everybody,
Another tossup! — The figure in my prayers
Be all my negs remembered.

How is it?

Gautam