Austin Contrarian

The picture of irony

The crape myrtle in front of my house:

My blog's reading level

M1EK writes about the same stuff, so out of curiosity I checked his blog:

I guess we're serving different market niches.

Which way is she spinning?

I guess this is an optical illusion.  I can get her to change directions if I squint real hard. (Via Marginal Revolution).

"Let's Make a Deal" vs. "Deal Or No Deal"

One of the legal journals I subscribe to has a piece on "cognitive illusions" that starts out with the Monty Hall "paradox":

You are a contestant on a game show with three doors.  Behind one door is $10,000 cash; behind the other two doors are goats.  The host asks you to choose the door you want, and you select door number one.  The host opens door number three, revealing a goat, and then gives you the opportunity to keep what's behind door number one or switch to door number two.  What do you do? 

Most attorneys [and some mathematicians -- AC] would answer that the decision makes no difference, because there is a 50-50 chance that the cash is behind door number one.  That answer is wrong.  From the moment you chose door number one, you had a one-third chance of having selected the door with the cash behind it.  The other two doors, combined, had a two-thirds chance of hiding the cash.  When it is revealed that door number three does not have the cash, then door number two, alone, has a two-thirds probability of hiding the cash.  Thus, when given the choice, you should always switch doors, because you are twice as likely to win the game.

The writer then says the same principle applies to "Deal or No Deal."  The contestant picks one of 26 briefcases.  One of the 26 has $1 million in it.  "As more and more unpicked briefcases are opened without revealing the $1 million, the contestant believes that the odds he or she picked the right briefcase at the start must be increasing, resulting in the rejection of increasingly high-dollar 'deals.'  In fact, the exact opposite is true:  the odds are increasing -- [up to 25/26] -- that one of the unpicked and unopened briefcases actually contains the $1 million, and the contestant will be left with very little." 

This particular cognitive illusion is indeed deceptive because I think the author is wrong.  He's not wrong about the Monty Hall paradox.  That's right, but he leaves out the critical assumption, which is what trips up most people the first time they hear this: For the sake of suspense, Monty Hall never opens the door with the money. 

The author is wrong about "Deal or No Deal."  Contestants on "Deal or No Deal" pick briefcases at random and (almost always) hit the $1 million.  Suppose a contestant gets down to two briefcases with the $1 million still on the board.  Does he have a 25/26 chance of winning the million if he trades?   If Howie had been picking briefcases, and we knew that Howie would never pick the $1 million briefcase, then yes.  If the contestant had been picking at random, then no.

Update: I've done a more rigorous analysis using Bayes' theorem.

Milk

From dairy to market.

h/t Coyote Blog.

This is pretty wild.

A new study (via Steven Levitt) says the relative length of someone's ring and index fingers predicts whether that person will score better on the math or verbal section of the SAT.  Someone with a longer ring finger is likely to have better math and spatial skills than verbal skills.  Someone with a longer index finger is likely to be more verbal.  There's apparently a biological reason why this should be true.  People with longer ring fingers were exposed to more testerone in the womb, while people with longer index fingers were exposed to more estrogen.  Exposure to different hormones causes the brain to develop differently.

This is consistent with the three-person sample in my household.  My wife's index finger is much longer than her ring finger, and she is much more verbal than mathematical.  My ring finger is much longer than my index finger, and I'm probably more mathematical than verbal.  (I always got higher scores on the math sections of the SAT and GRE, although the math and verbal percentiles were usually the same.  Oh, and I spent three years in math grad school.)  My 16-month-old has a longer ring than index finger.  He's been kind of slow to talk, but he was trying to assemble his nebulizer at one year.

Just out of curiosity, do this blog's readers mainly have long index fingers  or long ring fingers?

Very, very expensive farmland (updated)

A new idea for allowing NYC residents to grow produce locally (h/t Robin MaroneyMoroney/WSJ Informed Reader):

High-rise city farms could allow city dwellers to eat local produce as the population of the countryside dwindles, reports U.S. News & World Report. Columbia University parasitology professor Dickson Despommier, came up with the concept with his students while investigating ways to make third-world agriculture less prone to the parasites that can enter the food chain when human waste is used as fertilizer. His “vertical farm” would work around the year without pollutants or parasites. He estimates 150 farms, 30-stories each, could feed all of New York City. It would water the plants with some of the 1.4 billion gallons of water that New Yorkers pour down the drain. The plants would be grown without soil, suspended in water or a nutrient-packed solution. Lots of windows and solar panels would bring in light. Fish would be kept in tanks and poultry in small pens. Several New York companies, including International Business Machines Corp., have shown interest in building a vertical farm, said Mr. Despommier, who predicts one will be in business in 10 years.

A 30-story building means steel-and-concrete construction, especially if each floor will be loaded up with plants and elaborate irrigation systems.  Around here, that kind of building costs $300+ per square foot, without the fancy finish-out.  Equivalent high-rises in NYC go for $1,000+ per square foot.  That would be the market price -- or opportunity cost -- of one square foot of this "urban farmland."

Let's see.  There are 43,560 square feet in an acre.  That means this "urban farmland" would cost between $13 million and $43 million per acre.  I don't know exactly how productive this super-duper advanced hydroponics system would be, but I doubt it's 4,000-14,000 times as productive as $3,000/acre farmland in Indiana.  That locally-grown broccoli had better taste really, really good.

Update:  There's a lively discussion of vertical farming over at Slashdot.  Some people actually think this will make sense for New York when gas gets real expensive.

I'm always surprised that people don't have a better sense of relative magnitudes.  If you assume that an acre of hydroponic "land" can support 10 people per year (a generous estimate), then 8,000 acres could support 80,000 people per year -- or 1% of New York City's population.

8,000 acres is roughly 348 million square feet, which, coincidentally, is almost exactly the size of Manhattan's entire inventory of office space.  So to meet just 1% of NYC's annual food needs, you would have to find space in NYC to duplicate one of the planet's great concentrations of skyscrapers.

Out in the heartland, where space isn't as valuable, they're more likely to measure land in square miles than square feet.  8,000 acres there isn't 348 million square feet; it is just 12.5 square miles -- a tiny corner of an average county. 

I'm apparently too pessimistic, though.  The vertical farm people claim you can feed 50,000 people per year with just 13 million square feet of floor space.  This extrapolates to 21 million square feet for 80,000 people.  As best I can tell, they get there by assuming that hydroponic techniques will yield 10 to 100 times as much as dirt farming.  (Someone should tell the farmers.)

Fine.  So we really need just 21 million square feet to feed 1% of NYC's population for one year.  No sweat.  That's just eight Empire State Buildings.  And, for another 792 Empire State Buildings, we could feed the other 99% as well.