schoolyard subversion

2000-09-26 [< * >]

Time for some feedback on the last episode. First, thanks for the letters of support pouring in. I really appreciate feedback, please keep it coming.

One reader wrote:

don't know about the others, but your biology one is total BS.

To get the facts straight, I decided to go to someone I can trust. I went to Dr. Bruce Litow, good friend and senior lecturer at James Cook University. Here's what he wrote:

I sympathize with the denseness of teachers. Being a teacher I know that I am sometimes dense. However, so far as the matter of surface area to volume goes, the matter is a bit trickier than your report of it.

He, like several others, took issue with my claim that the ratio of surface area to volume is meaningless. This is, of course, not true. In my writing of the article, I simplified several of the issues to prove my point. Of course, now I am paying for it, so I will explain them more fully here. My claim is not that the ratio is meaningless, but that measuring it in this way (with these two unrelated units) does not result in a measurement that is universally meaningful. Instead, it is only meaningful in relation to (and comparison with) other items measured in a similar fashion.

He kindly provided a way to measure such an object without running into such problems:

Now imagine a sphere filled with small marbles. Let the sphere have radius R, but regard R as unit-less. [... A] good case can be made for saying that the number of marbles (a unit-less number) is directly proportional to the sphere's volume. [... We can] imagine that the marbles exit the sphere in an orderly way...We can get rid of R^2 marbles in one `wave', so it will take R such waves to do the job.

In summarizing Dr. Litow's explanation, I have removed several of the technical details. For those who are interested, I have provided the entire email for your perusal. In the end, Dr. Litow concludes:

This provides a physical justification for taking seriously the statement that the area/volume ratio of a sphere is inversely proportional to its radius. As we look at bigger and bigger spheres it will take longer and longer to empty them of marbles.

Once again, thanks to everyone for the feedback and a special thanks to Dr. Litow for his gracious explanation of this phenomena.

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