My friend Ginny recently sent me an article that touched on a question that has interested me since high school:  “Is mathematics a discovery or an invention?”

     The article, from The Albuquerque Journal, told about a University of New Mexico scientist who has built a model of Virginia’s Shenandoah River Valley.  Why?  He is hoping to discover what makes Hack’s Law work.

     If you’ve never heard of Hack’s Law, you’re not alone.  I only learned of its existence by reading the article Ginny sent me.  Apparently, John Hack was a U.S. government scientist working during the 1950s.  He discovered that there is a mathematical relationship between the length of a river and the area of its drainage basin. 

     This formula, known, obviously enough, as Hack’s Law, has been tested on river after river, and the math is always the same.  If you know the length of a river, you can use Hack’s Law to determine the size of the river’s drainage basin.

     While I don’t claim to understand the formula called Hack’s Law, I am amazed that a constant  relationship between a river’s length and the size of its drainage basin exists.  I would have guessed that so much variety exists among rivers and drainage basins that such a constant relationship would be impossible.  After all, rivers vary in width and depth, and in the course they take.  Likewise, drainage basins vary in terms of land contours and vegetation.  So how could Hack’s Law hold true for the thousands of rivers to which it has been applied?  

     The fact that Hack’s Law does prove true for rivers all over the world is a wonder to me.  And this wonder reminds me that mathematics may indeed be embedded in nature all around us, to be discovered by us humans. 

    

This entry was posted on Wednesday, November 5th, 2008 at 11:42 am and is filed under Insights and Visions on the State of the Earth. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.