The other day I was strolling through the forest, enjoying a slight breeze and watching the leaves fall.

     I began to see this annual phenomenon in a way I hadn’t before.  Instead of viewing a tree as  losing its leaves, I began to focus on the leaves themselves.  I watched as a leaf ‘let go’ of  the tree that had given it life, from which it had emerged last spring. 

     Since the spring, this leaf had spent its life nourishing that tree–capturing sunlight, converting it to food, and sending it back into the tree.  Along with its thousands of counterparts, the leaf had provided the tree with the food it needs to sustain it through the winter months. 

     Its work now complete, the leaf was no longer receiving chlorophyll from the tree.  The leaf’s green color had disappeared, revealing underneath the autumnal hue of death. 

     Dried and shriveled, the leaf separates from the tree and slowly drifts into the unknown.  And so the leaf falls, taken by gravity, and perhaps diverted a little by a breeze, to its resting place on the forest floor. 

     And there, as the spent leaf slowly decays, it adds life to the soil.–April Moore  

   

     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.