I thought this was a beautiful video.  The ambiance from the music fit the scene perfectly.  I also love the perspective on the skyscrapers.  I wish I knew more about the places it references.  Someday I wouldn’t mind getting the chance to wander through Tokyo like this.

I used to watch a lot of basketball in elementary school and middle school. Back then in the early 2000s, besides the fact that I had a whole lot more time, it felt like a different sort of game. Jordan was retired, but there was a feeling that the game was about the fundamentals–dribbling, passing, shooting, defense, teamwork. When I look at NBA games now, the game appears to revolve around superstars trampling over everyone else with moves that look good in 10 second clips. It seems like there used to be so much more respect for the game of basketball by the players. Even today, when you hear Jordan talk about basketball, he always refers to “the game” as something more than “a game.” I’m sure the coaches and players always remind themselves to uphold this sort of respect, but it sure seems like a different game today.

Street-Fighting Mathematics

This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.)

This course is designed to teach you a flexible attitude toward problem solving. I’ve divided the attitude into six skills or tools. There are others, and more detail on each, but life is short and these six make a decent toolkit.

…and sounds like it’s a decent class to boot.

I had this little piece written by Paul Krugman bookmarked for a while, and I took some time to read it today.  The most salient part of the piece for me was his “Rules for Research.”  Here are some insightful passages, along with my thoughts:

“I am a strong believer in the importance of models, which are to our minds what spear-throwers were to stone age arms: they greatly extend the power and range of our insight.”

I’ve heard time and again that some of the most contributions to economics involve the formalization of ideas from other disciplines.  For example, Gary Becker opened a new frontier to economics by studying the economics of discrimination.  Krugman’s advocation of “listening to gentiles” acknowledges this but also illustrates the importance of translating what is knowledge from other disciplines into the language of economics.  By creating these economic models, we extend our understanding of the subject by setting our assumptions in a clear manner and studying the full implications.

“If a new set of assumptions seems to yield a valuable set of insights, then never mind if they seem strange.”

I’ve always been quick to criticize material I’ve learned that makes insane assumptions–that all goods are normal, that only one factor of production is used in production, etc….  I was ok with some of the other assumptions of economics such as utility maximization and perfect competition because they at the very least resembled reality.  But really what is important is that these assumptions help build a model that illustrates mechanisms at work in reality.  People often criticize the notion of adding assumptions to perfect a model.  But if they hint at what’s actually going on in reality, maybe it’s worthwhile to study these models.

Fortunately, there is a strategy that does double duty: it both helps you keep control of your own insights, and makes those insights accessible to others. The strategy is: always try to express your ideas in the simplest possible model. The act of stripping down to this minimalist model will force you to get to the essence of what you are trying to say (and will also make obvious to you those situations in which you actually have nothing to say). And this minimalist model will then be easy to explain to other economists as well.

The idea of expressing complex social phenomena in simple terms has always been one that attracted me to economics.  As Krugman says, it is simplicity that allows us to develop an understanding of these phenomena and communicate these ideas to others.

Here’s the Neyman-Pearson Lemma:  Suppose the likelihood ratio test with critical value has significance level  and power . Then any test with significance level or smaller has power less than .

So suppose we sample from some population with some distribution and have some hypothesis about what the parameters are for that distribution.  Then we want to devise some test to figure out when to accept our hypothesis and when to reject.  By controlling for type I error, we’ve found THE test that has the least probability of committing type II error.

Thus, in figuring out the distribution for some random phenomenon, we’ve devised a rather simple test and found that it has the least probability of accepting some hypothesis when it’s false for some specified probability of rejecting that hypothesis when it’s true!

Stringing together stories about people’s struggle to overcome time and circumstance, this beautiful work inched closer to my heart with each passing moment.

While the subject of withered relationships is quite universal, we all still forget how easily memories and feelings become lost through time.  Pushing viewers to face this steady force permeating our lives, Makoto Shinkai creates a sober portrait of loss in real life.  The bittersweet conclusion reminds us of the realities of life lacking in the dramas we typically see on the screen.

Never forcing viewers onto a revelation, the story allowed me to pull up close to the situations it portrayed. Because it is easy to identify with the characters and their struggles, the story conveys the theme with powerful clarity.  The familiar scenes depicting moments of anxiety, hesitation, and desperation reveals the intense feelings we associate with these situations, driving home the significance of the theme of gradual separation.

Simple, subtle, yet effective, 5 Centimeters Per Second is one of the best films I’ve seen in a while.

When I think of this piece, I always think about the numerous complex processes players have to adjust throughout the piece to get the phrasing just right–dynamics, vibrato speed, tempo, tone, etc…

Vargas’ performance of this piece completely changed this outlook.  He made the piece beautiful with simplicity.  There are no dramatic fluctuations in dynamics.   There is no wild rubato.  In short, there’s nothing over the top.

Instead, everything about his sound appears to flow naturally, allowing the true tune to come out without the the obstruction of faux emotions.  People often criticize some of the old time greats as being too cold with their playing.  Perhaps these people are just not listening for the genuine quality in the greats’ playing.

This show continues to surprise me with its beauty and depth.  After watching episode 24 today, I found the message Aria conveyed to be particularly inspiring.  In a nutshell, Akira (one of the mature professional gondaliers on the show) mentioned the idea of how people tend to attach greater significance on unpleasant memories rather than cheerful ones.

Risk Aversion models suggest the cause of this behavior: many people tend to prefer to prevent loss than risk gains.  But why do people develop these particular preferences?  Isn’t it mysterious for us to develop these particular tastes for risk?  In any case, at some point, preventing loss limits us from tremendous opportunities.  This is what Akira is talking about.  It’s truly curious that people choose to focus on losses rather than gains.  Furthermore, if we let our fear of risk cripple us, we will not be able to experience all sorts of wonders the world will offer.

Tremendous idea, no?

For the record, I sort of feel silly putting this thing in econ terms, but I found it fascinating that this econ idea can be applied to such a general dictum.

I just found this neat little game today.  The best part about it is it’s fully functional in the browser.

It beats any of the other word typing programs you find at Kmart (not sure how accurate that WPM measure is though).  Too bad I don’t know much Japanese.  As it turns out, transcribing lyrics with speed and accuracy requires some command of the language–who knew?  Playing this reminded me of what they tell you when you are learning to speed read (in English).   To read with greater speed and precision you have to focus not on individual words but large “blocks” of texts.  In this case, to type with speed and precision, you have to not focus on individual letters but rather whole words or phrases that are sung.

“Imagination is an essential tool, ’cause what imagination is, is the ability to imagine lots of things.  See, if you can’t imagine things, you only have one choice.  And maybe a good choice but a lot of times it’s not.  If you have imagination you can keep trying things out.  You try this.  ‘Does this work?  Does that work?’  That’s what artists do.  That’s what composers do.  That’s what performers do.”

This was taken from a video called How Does Someone So Young Play So Well? I found this to be a very insightful and powerful idea.  Last time I shared my thoughts on Vengerov’s playing, and this sense of imagination is exactly what I was referring to.  What was most brilliant about his playing was this wonderful understanding of the music fueled by an expansive imagination.  And this idea about the power of imagination illustrates how imagination contributes to such artistry.

In fact, if imagination does allow us to analyze and consider different approaches to problems, I believe this ability would not only drive artists but thinkers of all kinds.  For example, the capacity to consider different approaches to problems is what math requires.  Oftentimes, there are different ways of proving different theorems.  And, when you reach a point when you’re trying to create new ideas and new proofs, you can be sure you will need this same ability that great musicians possess.

I had always considered imagination to be a valuable attribute, but it seems like it’s even more important than I had imagined.