Mr Honner

Events with Probability Zero

I just donated this shirt to the Salvation Army. I estimate the probability that I will ever see this shirt again to be zero. In fact, forget estimating: I think the probability that I will see this shirt again is exactly zero.

In fact, I’ll go even further than that: I claim that the probability that anyone who reads this ever sees this shirt is exactly zero. Not .0000000000001. Zero.

Even if there are infinitely many possible scenarios in which this shirt is seen by someone, this number is dwarfed by the infinitude of possible scenarios in total. Thus

moderate infinity ÷ really big infinity = zero

I dropped it off at the Salvation Army in Brooklyn. Let me know if you see it: evidence will be required to claim your prize.

By patrick honner, 16 yearsAugust 25, 2010 ago

Comprehensive Calorie Counting

There’s an interesting op-ed in the NYT about how mathematics is used to put food production and consumption into context:

http://www.nytimes.com/2010/08/20/opinion/20budiansky.html

For example, we can measure food transportation costs in calories (as a calorie is, indeed, a unit of energy), and so we can look at production and transportation costs of certain foods and compare them to the calorie content of the food itself. For example, it takes about 5000 calories to produce a 100-calorie head of lettuce.

The author’s intent is to poke holes in some of the common arguments used by proponents of “eating local”: Transportation costs for most foods are neglible compared to household storage and preparation costs, says the author, thus “eating local” is not an especially eco-friendly strategy. However, the author hilmself makes a number of weak and erroneous arguments, comparing “apples to rocks” in some cases.

The piece offers some interesting mathematical ideas and a good critical reading exercise.

By patrick honner, 16 yearsAugust 24, 2010 ago

Appreciation Geometry

Garden-Variety Fractals

My Mom gave me some clippings of a Christmas Cactus (Chris, pictured at the right), and after taking a while to get accustomed to her new home, Chris is finally starting to grow.

The new leaves sprouting out, smaller but similar to the original, put me in mind of the Mandelbrot set. The bulbs that “grow” out of the Mandelbrot set are perfectly similar to the original, and no matter how much you zoom in, you’ll always see the exact same sort of object.

$plants and fractal$
I can’t say for sure if the leaves of the Christmas Cactus are infinitely self-similar, but it’s close enough for my eyes.

By patrick honner, 16 yearsAugust 23, 2010 ago

Application Geometry

Buckyballs Detected in Space

For the first time, scientists have verified the existence of “buckyballs” in space. Buckyballs are carbon molecules made up of 60 atoms arranged in a soccer-ball like structure

Notice the interlocking pentagons and hexagons. There are 60 vertices in this solid, so how many of each polygon?

Buckyballs are named after Buckminster Fuller, as they resemble the geodesic dome he made famous. Fuller was a creative, prolific man–a futurist–who was never short of whimsical ideas, like using blimps to drop bombs to make holes to plant tree-houses in.

Challenge Geometry

Problem-Solving Under Pressure

Near the end of a long morning building a small table, I encountered the following simple geometry problem: I needed to cut four small rectangles from a square of self-adhesive rubber to serve as the feet of the table’s legs. So I cut the square into four equal strips, lopped off the end of eachand had my feet.

All well and good, but I missed the superior solution that any decent problem solver should have seen immediately:

This solution would have left me with one long rectangular remainder, as opposed to four small square remainders.

After working on the table for a while, I was mentally and physically drained, and I think this affected my ability to see the better solution. I guess it makes sense that being tired [and frustrated!] would negatively impact one’s ability to solve problems.

It’s interesting to think about how our physical, mental, and emotional states can affect our problem-solving abilities. And I think this suggests that problem-solving stamina is something we might want to work on.

By patrick honner, 16 yearsAugust 20, 2010 ago

Events with Probability Zero

Comprehensive Calorie Counting

Garden-Variety Fractals

Buckyballs Detected in Space

Problem-Solving Under Pressure

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