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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.

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?

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.

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.

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.

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?

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?

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?

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.

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:
\[
\frac {\partial T}{\partial t} = a \frac {\partial ^2 T}{\partial x^2} \quad (1)
\]

How Cold is the Ground?

It snowed in Ithaca a few weeks ago. Which sucked. But fortunately, it had been warm for the previous few days, and the ground was still warm so the snow melted fast. Aside from letting me enjoy the absurd arguments against global warming that snow in April birthed, this got me thinking: How cold is the ground throughout the year? At night vs. during the day? And the corollary: How cold is my basement? If I dig a deeper basement, can I save on heating and cooling? (I'm very cheap.)

End of the Earth VII: The Big Freeze

http://tinyurl.com/7rdj996

It is traditional here at The Virtuosi to plot the destruction of the earth. We also are making secret plans for our volcano lair and death ray. However, since it is earth day, we will only share with you the plans for the total doom of the earth, not the cybernetically enhanced guard dogs we're building for our moon base. The plan I reveal today is elegant in its simplicity. I intend to alter the orbit of the earth enough to cause the earth to freeze, thus ending life as we know it.

Earth Day 2012: Escape to the Moon

It is now Earth Day 2012, and, according to the Mayan predictions, The Virtuosi will destroy the earth. In a futile attempt to fight my own mortality, I decided to send something to the Moon. It seems, for a poor graduate student trying to get to the Moon, the most difficult part is the Earth holding me back. So first I'll focus on escaping the Earth's gravitational potential well, and if that's possible, then I'll worry about more technical problems, such as actually hitting the moon. Moreover, in honor of the destructive spirit of The Virtuosi near Earth Day, I'll try to do this in the most Wiley-Coyote-esque way possible.

Money for (almost) Nothing

Five Hundred Mega Dollars, to be precise.
(Image from Wikipedia)

I am not typically interested in lotteries.  They seem silly and I am seriously beginning to question their usefulness in bringing about a good harvest.  But this morning I read in the news that the Mega Millions lottery currently has a world record jackpot up for grabs.  In fact, the jackpot is so big...

Tonight Show Audience:  HOW BIG IS IT?

It is so big that I decided to do a little bit of analysis on the expected returns.  Zing!

Pi storage

Let me share my worst "best idea ever" moment.  Sometime during my undergraduate I thought I had solved all the world's problems.

You see, on this fateful day, my hard drive was full. I hate it when my hard drive fills up, it means I have to go and get rid of some of my stuff.  I hate getting rid of my stuff.  But what can someone do?

And then it hit me, I had the bright idea:

What if we didn't have to store things, what if we could just compute files whenever we wanted them back?

Sounds like an awesome idea, right?  I know.  But how could we compute our files?  Well, as you may know pi is conjectured to be a normal number, meaning its digits are probably random.  We also know that it is irrational, meaning pi never ends....

Calculator Pi

There is a very fast converging algorithm for computing pi that you can do on a desktop calculator.

• Set x = 3
• Now set x = x + sin(x)
• Repeat

This converges ridiculously fast, after 1 step you get 4 digits right, after 2 steps you get 11 correct, in general we find:

A Clarification

As there seems to be some confusion among my fellow Virtuosi, I wanted to point out that Pi day occurs on July 22nd or, in the year 4159, on January 3rd.

Today is in fact Seventh Power Day.

Pi-rithmetic

Fun fact:  pi squared is very close to 10.  How close?  Well, Wolfram Alpha tells me that it is only about 1% off.

I first realized this fact when looking at my slide rule, pictured to the left (click to embiggen), just another reason why slide rules are awesome.

It turns out I use this fact all of the time.  How's that you ask?  Well, I use this fast to enable me to do very quick mental arithmetic.

Moving Pi-ctures

My TV celebrates without me.

Today, as I'm sure you're aware, is Pi Day - a day for the festive consumption of pies and quiet self-reflection.  In the spirit of the holiday, I'd like to present a point for discussion:

Everyone has a great talent for at least one thing.

That this is true for at least some people is seen through even a cursory glance at a history book:  George Washington was really good at leading revolutions, Michelangelo was an outstanding ceiling painter [1], and Batman was the best at solving complex riddles (especially in English, pero especialmente en español).

But I'm certain that this holds for everyone.  What's your talent? Mine, as those of you who read this blog should know very well by now, is certainly not doing physics.  Nope, my talent is watching TV.  Seriously guys, I watch TV like a boss [2].  In light of this talent, I thought I would describe a few instances in which I have seen pi represented (for better or for worse) in TV and movies.