Sunday, June 23, 2013

Tragedy of Great Power Politics? Modeling International War

Recently I finished reading John Mearsheimer's excellent political science book The Tragedy of Great Power Politics. In this book, Mearscheimer lays out his ``offensive realism'' theory of how countries interact with each other in the world. The book is quite readable and well-thought-out -- I'd recommend it to anyone who has an inkling for political history and geopolitics. However, as I was reading this book, I decided that there was a point of Mearsheimer's argument which could be improved by a little mathematical analysis.


Sunday, January 20, 2013

Re-evaluating the values of the tiles in Scrabble™



Recently I have seen quite a few blog posts written about re-evaluating the points values assigned to the different letter tiles in the Scrabble™ brand Crossword Game.  The premise behind these posts is that the creator and designer of the game assigned point values to the different tiles according to their relative frequencies of occurrence in words in English text, supplemented by information gathered while playtesting the game.  The points assigned to different letters reflected how difficult it was to play those letters: common letters like E, A, and R were assigned 1 point, while rarer letters like J and Q were assigned 8 and 10 points, respectively.  These point values were based on the English lexicon of the late 1930’s.  Now, some 70 years later, that lexicon has changed considerably, having gained many new words (e.g.: EMAIL) and lost a few old ones.  So, if one were to repeat the analysis of the game designer in the present day, would one come to different conclusions regarding how points should be assigned to various letters?

Tuesday, January 1, 2013

The Skeleton Supporting Search Engine Ranking Systems



A lot of the research I’m interested in relates to networks – measuring the properties of networks and figuring out what those properties mean.  While doing some background reading, I stumbled upon some discussion of the algorithm that search engines use to rank search results.  The automatic ranking of the results that come up when you search for something online is a great example of how understanding networks (in this case, the World Wide Web) can be used to turn a very complicated problem into something simple. 

Ranking search results relies on the assumption that there is some underlying pattern to how information is organized on the WWW- there are a few core websites containing the bulk of the sought-after information surrounded by a group of peripheral websites that reference the core.  Recognizing that the WWW is a network representation of how information is organized and using the properties of the network to detect where that information is centered are the key components to figuring out what websites belong at the top of the search page.

Thursday, November 29, 2012

When will the Earth fall into the Sun?


The time I spent making this poster could have been spent doing research.
Since December 2012 is coming up, I thought I'd help the Mayans out with a look at a possible end of the world scenario. (I know, it's not Earth Day yet, but we at the Virtuosi can only go so long without fantasizing about wanton destruction.) As the Earth zips around the Sun, it moves through the heliosphere, which is a collection of charged particles emitted by the Sun. Like any other fluid, this will exert drag on the Earth, slowly causing it to spiral into the Sun. Eventually, it will burn in a blaze of glory, in a bad-action-movie combination of Sunshine meets Armageddon.

Saturday, October 27, 2012

Creating an Earth


A while ago I decided I wanted to create something that looks like the surface of a planet, complete with continents & oceans and all. Since I've only been on a small handful of planets, I decided that I'd approximate this by creating something like the Earth on the computer (without cheating and just copying the real Earth). 

Where should I start? Well, let's see what the facts we know about the Earth tell us about how to create a new planet on the computer.


Saturday, August 4, 2012

A Curious Footprint

Lasers!  Credit: JPL/Caltech
In less than two days, NASA's Mars Science Laboratory (MSL) / Curiosity rover will begin its harrowing descent to the Martian surface.  If everything goes according to the kind-of-crazy-what-the-heck-is-a-sky-crane plan, this process will be referred to as "landing" (otherwise, more crashy/explodey gerunds will no doubt be used).

The MSL mission is run through NASA's Jet Propulsion Laboratory where, by coincidence, I happen to be at the moment.  Now, I'm not working on this project, so I don't have a lot to add that isn't available elsewhere.  BUT I do feel an authority-by-proximity kind of fallacy kicking in, so how about a post why not?


Tuesday, July 24, 2012

A Homemade Viscometer I

Stirring a bowl of honey is much more difficult than stirring a bowl of water. But why? The mass density of the honey is about the same as that of water, so we aren't moving more material. If we were to write out Newton's equation, ma would be about the same, but yet we still need to put in much more force. Why? And can we measure it?


Tuesday, June 26, 2012

Batman, Helicopters, and Center of Mass



A couple weeks ago, I came home after a long day at work looking for a break.  I thought to myself, “What’s more fun than physics? Batman*.”  I sat down to play the latest Batman videogame, in which Batman’s current objective was to use his grappling hook to jump onto an enemy helicopter to steal an electronic MacGuffin.  As awesome as this was, it occurred to me that something was very wrong about the way the helicopter moved while Batman zipped through the air.

See if you can spot it too. (Watch for about 5 seconds after the video starts.  Ignore the commentary.  Note: The grunting noises are the sounds that Batman makes if you shoot him with bullets.)

What occurred to me was this: If the helicopter’s rotors provided enough lift to balance the force of gravity, wouldn’t Batman’s sudden additional weight cause the helicopter to fall out of the sky?  Also, to get lifted up into the air, the helicopter must be pulling up on Batman: shouldn’t Batman also be pulling down on the helicopter?  By how much should we expect to see the helicopter’s altitude change?

Tuesday, June 5, 2012

Tales from the Transit of Venus

Sad Old Sun
Today is the transit of Venus, which, aside from being a totally rad astronomical event, is also the perfect excuse to tell my favorite story of an unlucky Frenchman (I have many).

This is by no means new and, if you've ever taken an astronomy course, you've probably already heard it.  It is perhaps the closest thing Astronomy has to a ghost story, told though the glow of a flashlight on moonless nights to scare the children.

This is the story of Guillaume Le Gentil, a dude that just couldn't catch a break.


Saturday, May 26, 2012

How Cold is the Ground II

Images from Wikipedia

Last week (ok, it was a little more than a few days ago....) I used dimensional analysis to figure out how the ground's temperature changes with time. But although dimensional analysis can give us information about the length scales in the problem, it doesn't tell us what the solution looks like. From dimensional analysis, we don't even know what the solution does at large times and distances. (Although we can usually see the asymptotic behavior directly from the equation.) So let's go ahead and solve the the heat equation exactly:
\[
\frac {\partial T}{\partial t} = a \frac {\partial ^2 T}{\partial x^2} \quad (1)
\]