New Adaptation of an Old Game

The game of Go is an ancient game first developed in China around 2,500 years ago.  I've been playing around with it for the past couple years, though I must admit I'm not very good at it.

The game is played on a grid, usually 19x19, with black and white pebbles. Each turn, a player places one of his pebbles on one of the grid's intersections.  Each intersection has four adjoining intersections, except for those on the edge of the board, which have three, and the corners, which have two.  These are known as "liberties."  If one of your pebbles or group of pebbles is surrounded by your opponent's pebbles, so that there are no more available liberties, they are "captured" and removed from the game. Ultimately, the game ends when both players agree that it is finished, and a player's total score is computed by subtracting the spaces he does control by the number of his pebbles that were captured. Highest  score wins.

After first being introduced to the game, I began creating variations. One of the first was a three person variation. Pebbles were red, black, and white, and your pieces were captured whenever they were completely surrounded.  I managed to coerce a few of my friends into playing a few games with me. What would usually happen is that two of the players would gang up on whichever player was in the strongest position.  Then, since the strongest player would be quickly reduced, the next strongest player would be the strongest, and the two weaker ones would gang up on him.

The end result was one of the most frustrating games ever played. Each player was at any time either losing or fighting against superior odds.  It did not last long among my group of friends.

Other variations I would experiment with usually involved variations on the board.  By lopping off corners, or by removing the a few parts of the center of the grid, or even by removing all edges by having the board be a globe, I could radically change the strategies and tactics needed to win.  The obvious problem was that such boards were irritating to construct. Most had to be drawn on pieces of papers, and some, like the globe, could not be made at all but a system of coordinates, like longitude and latitude, had to be used.  At this point I realized that using only coordinates, two people could play a game by just shouting positions to each other, like blind chess.

All of this brings us to the day before yesterday, when while thinking about something completely unrelated, I realized how irritating it was to try to envision four spatial dimensions.  I felt that if I had some way to practice it, I could think in higher dimensions more easily.  What I came up with was 4d Go.

The rules for 4d Go and regular Go are exactly the same, except 4d Go has more liberties per intersection.  2d Go has four, 3d Go has six (the original four plus one above and one below), and 4d Go has 8 (the six of 3d Go plus the two above and below 4 dimensionally).

The trouble is, with each additional dimension, the playing space becomes absurdly large.  A typical 19 x 19 board has 361 intersections.  A 3d 19 x 19 x 19 board would have 6859 intersections and a 4d 19 x 19 x 19 x 19 board has 130,321 intersections. Obviously, the size of the space makes it impossible to play mentally, or even realistically.

To simplify this, I shrunk the board considerably to 4 x 4 x 4 x4.  With 256 intersections, the board is still very large, but comprehensible. Still, it is difficult to hold the board in mind, so to practice, I began playing Go mentally on just a 4 x 4 board.  The game is too small to end in anything but a draw, but it is good practice.  Then, I moved on to a 4 x 4 x 4 board which has 64 intersections.  It's a challenge to keep in mind, and I haven't yet fully played it out.  I have, though, found that it can be easily played on  chess board by dividing the board into four quadrants and imagining the quadrants stacked atop one another.

The result is a version of Go which is surprisingly easy to play and which I plan on subjecting my friends to.

This Blog Post about Tautology is a Tautological Blog Post

Tautology: noun the saying of the same thing twice in different words, generally considered to be a fault of style; a needless repetition of an idea, statement, or word This definition and this example are both tautologlies, they both needlessly repeat the same idea.

Tautologies amuse me.  The quirky self-reference of them almost always gives my head a quick spin. and whenever I can, I try to find them.

As part of my daily routine of not doing any work, I tend to spend a lot of time surfing the web.  Very rarely do I actually encounter something amusing or witty (and even more rarely, a good tautology that manages to note itself as one), and, more often than not, most of the things I read just annoy me (upon rereading this sentence, I realized "more often than not, most of the things..." is a tautology itself).  Most of the things that tend to annoy me are pieces that strike me as hypocritical, or hypercritical, or just overly politically correct.

Take, for example, this blog post from someone at Princeton:

" Along with these paper advertisements were business card ads for a female freshman running for class president. On the right side is her name, the position she’s running for, and her slogan “Looking to have a good time freshman year?” accompanied by “Don’t be Square, Vote for [redacted]!” On the left side of the business card is a photograph of a shirtless male on top of a shirtless (but bra wearing) female. The picture seems to suggest that they are either about to engage in sex or are already engaging in sex."

"These campaign business cards portrayed sex as something that everyone’s doing, and that you should be, too. Or else you’ll be square."

The piece goes on to bemoan the over-sexualized view of college, and what a shame it is that our hookup culture has taken over so strongly, and isn't this a great example of pluralistic ignorance, where everyone assumes that everyone's hooking up when really the majority are not?

And the piece annoyed me.

It annoyed me first because I thought that was a funny and clever way of getting attention for a completely pointless election, and I rather enjoyed the ad.

It annoyed me even more because it struck me as hypercritical.  I felt the author was reading far too much into a silly little freshman election.

It annoyed me because it seemed overly politically correct.  The author didn't bother to say what she really felt, but clearly implied: that the hookup culture and college sex in general is degrading and inappropriate.  I would have more respect for the author if she had just come out and said it. I would have disagreed with her, but her bluntness would have been refreshing.  However, the last comment on the post was refreshingly scathing and witty:

"What is a “square”? Someone conventional. But on the card, sex is associated with not being a square, with not being conventional. The natural conclusion to draw is that having sex is not considered conventional.

Yet you draw the opposite conclusion, that the card implies that the conventional thing to do is to have sex. Why? Because we all know she didn’t chose the word square for the nuances of its definition, she chose it because it rhymes with her name. What she really meant was something like “loser”. In which case your analysis is less bizarre.

“Loser”, however, is an accurate description of students who fail to attract the opposite sex. Men who attempt to attract women but do not succeed are losing out to other men. They are literally losers with respect to women. Romantic success is, I’m willing to guess, very important to college students, so being a loser with respect to the opposite sex more or less amounts to being a loser, period. So, the candidate’s card is really a tautology: if you aren’t hooking up with the opposite sex, you are, in fact, a loser."

I found that rebuttal absolutely excellent for the following reasons:

1. Early on, the commenter pointed out how silly the entire article was: "Because we all know she didn’t chose the word square for the nuances of its definition, she chose it because it rhymes with her name."  It's a freshman election, no one cares about it now, or ever will again. Creating a brouhaha over it is pathetic.

2. The commenter revealed accidental hypocrisy inherent in the post. "The natural conclusion to draw is that having sex is not considered conventional.

Yet you draw the opposite conclusion"  Almost no one is intentionally hypocritical, which is what makes it so entertaining when you find out someone is a hypocrite.  Now, I'm not saying that the author hooks up and then bemoans the hook up culture on her blog.  The hypocrisy I refer is the far more annoying "matyred minority" variety, where someone is convinced that he or she is making a last righteous stand for some pet cause that the masses have long abandoned.  Here, she is convinced she is one of the few public voices trying to stop the massive onslaught of conversation about sex.  But sex is not considered conventional. Despite its prominence in our society, it still is considered scandalous and taboo. That's the only reason the ad made any waves at all. Far from being the last defendant of public morality, the author is just another random hack.  And, the commenter managed to convey most of that in the two sentences quoted above, the brevity and subtlety of it making it all the more biting.

3.  Finally, the commenter makes a tautology reference.  I love tautology, largely because I accidentally engage in it all the time.

I am a member of that Facebook group and I read XKCD. (comic from Randall Munroe's XKCD #703)

"Men who attempt to attract women but do not succeed are losing out to other men. They are literally losers with respect to women. .... So, the candidate’s card is really a tautology: if you aren’t hooking up with the opposite sex, you are, in fact, a loser."

So, with one short comment, some random troll on the internet turned some idiotic fluff piece that annoyed me immensely and gave it an amusing and distracting skewering.  I salute you, random troll.  And yes, "random troll" is a tautology.

The TSA is Killing People

Okay, that's not exactly true...

But the TSA, with its new restrictions on travel, is causing more people to die.

This topic came up the other night during a seminar with my Economics advisor and a few other students. We were discussing the new TSA restrictions requiring either pat downs or scans before flights.  There was a lot of debate on invasion of privacy versus the necessity of security, and the conversation had bogged down into an ideological stalemate.

That's when my professor piped up and said, "There's an Introductory Economics reason for why the new restrictions are a bad idea. Can anyone tell me what it is?"

After a few half-hearted attempts, one of the girls in the group asked, "Is it because it increases the marginal cost of flying?"
"That's half of it," our professor encouraged.

An awkward silence fell.  Then one of the boys said excitedly, "It increases the number of cars on the road!"
"Exactly!"

Far more people die from car accidents per 100,000 people driving (it averages about 20 per year) than the number of people who die from planes per 100,000 people flying including all crashes, terrorist attacks, and random heart attacks from joining the mile high club (it's less than .1). That's 200 times the fatality rate.  So,  if the increased cost of being patted down or scanned encouraged 1 million more people each year to drive somewhere instead of flying, an additional 199 people would die.

Sure, the increased security may make it more difficult for terrorists to hijack or bomb planes, but considering the number of people who are killed on airlines by terrorists and the number of people who die in car accidents, it's not worth the lives of 200 people just to save 1.  And that's how the TSA is killing people.

Paradox of Freedom

Ask nearly anyone and they'll tell you that more choices are better.

The more options you have, the more likely that the decision you make will match all of your preferences and be the optimal choice.

But that's not exactly true...

Imagine buying a car. If you're a consumer in, say 1912, there's really only one choice: the Model-T Ford.  So, the decision is easy.  You buy the car, and it's the best possible outcome.

Now imagine buying one today.  There are dozens of options.  After a few weeks of careful consideration and test driving, you find the perfect car: well priced, good gas mileage, looks nice, etc.

You buy it, you drive it off the lot, and get it home, and as you're admiring it in the driveway, you look over to your neighbors, the Joneses, and see that they have also bought a new car, and that Mr. Jones is likewise admiring his new car.

A brief conversation later, and you discover that not only did Mr. Jones buy a better car than you, but he got it for the same price.

As the buyer's remorse hits you, you realize that you did not make the best possible choice, but hey, no biggie, you still have a car that you like, right?  And it sure is better than if your only available choice was the Toyota Camry (unless the car you bought was the Toyota Camry, in which case it is better than if your only available choice was the Ford F-150).

But let's say you're buying a car in a possible future fifty years from now. In this fantastical future, there no longer are car brands or standard vehicles. Instead, every single option is customizable, from the seats to the color to the layout on the inside to the way the body looks, you have never been more free.

You spend three months designing your perfect car on your computer, clicking and dragging everything you could possibly, getting rid of all the unnecessary accoutrements, like seat belts or the windshield, and the morning after you finalize your design, your dream car is delivered to your driveway. NICE.

You get in, begin the drive to work, and as you spill your piping hot morning cup of joe all over your shirt, you reflect on the fact that you had forgotten to include cup holders in your design.

Now, at this point, practically any car with cup holders and that could still drive would have been better. Not only has having unlimited freedom result in you choosing a car you don't particularly like, but it has resulted in you choosing a car that's even worse than the car you would have chosen if you had fewer options.

And here's what worse: you wasted all that time designing that car. In economic terms, think of the cost of the car in both time and money.  Even if you had designed a car that was slightly better for you and slightly less expensive than a Camry, the Camry still would have been a better choice because it only took a week for you to choose the Camry and took months to design the other car.  The increased opportunity cost of designing your own car outweighs the slight benefit of having a slightly better car.  The irony is that having too much free choice can easily result in a less optimal situation.