December 2010

Paradoxes, Etc

stumpedThis is an engaging, if verbose, article in the NYT about logical paradoxes.

http://opinionator.blogs.nytimes.com/2010/11/28/paradoxical-truth/

There’s not much new ground covered here, but the author touches on some of the classics–the Liar’s Paradox (Is the statement “This sentence is false” true or false?), Zeno’s Paradox (you’ll never get from point A to point B because first you have to get halfway to B, say C, then halfway between C and B, say D, and so on).

The author notes that writers and philosophers love paradoxes.  Students love paradoxes, too.  It’s always enjoyable making a student act out Zeno’s paradox by making them get infinitely close to the board, or arguing about whether there are more even numbers or integers.  And of course, everyone loves arguing about whether .999999999….  really equals 1 .

Another nice feature of this article is that the Comments section itself demonstrates a paradox:  hundreds of people with nothing to say, saying plenty.  It reminds me a lot of being in Philosophy class.

By patrick honner, ago

Sharks, Geometry, and Optimization

Whale SharkSome recent research sheds light on the interesting mathematics of how whale sharks move through the ocean.

Covering vast empty spaces between resources forces the shark to be natural optimizers when it comes to energy usage.  For example, due to its natural negative buoyancy, the shark tends to sink in the ocean, meaning that ascending through the water requires greater energy expenditure.

In order most efficiently move through the water, the shark naturally gravitates to two general kinds of ascents.  According to the article, the two techniques are a low-angle ascent that tends to minimize energy expenditure per unit of ascent, and a steep ascent that tends to maximizes the vertical change per unit energy.

It’s no surprise that nature is full of optimizers.  Making the most of your resources goes a long way to survival!

You can read the full article here.

By patrick honner, ago

Efficient Ticket Hypothesis

ticketsIn a past post, I wondered how a local museum theater could make money showing movies to limited audiences.  Well, here is a step in wrong direction, business-wise, anyway:  the $0.00 ticket.

All kidding aside, Free Fridays are a great way to get people into the museums, and it’s probably pretty good for business overall.  The MoMA was packed with people, and the gift shop–and it’s $40 photobooks and $23 T-shirts–was equally occupied.  An interesting question is then “How much does the museum make on each $0.00 ticket?”

An uninteresting question is “why didn’t the security guard just let me in without a ticket, instead of demanding that I go grab two from a big pile on the front desk and then not collect the tickets from me anyway?”

It was enough to make me consider asking for my money back.

By patrick honner, ago

Sidewalk Mathematics

Apparently these graffiti compasses were showing up outside subway station exits this summer in NYC.

Pi GraffitiIt’s really hard to say what I like most about this:  the fact that it’s functional street art, that it’s mathematical in nature, or that the artist’s handle is I. M. Pi.

By patrick honner, ago
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