Carving defaces tree and shortens its live, making it vulnerable to disease.

 
Beech tree, American beech, Fagus grandifolia Ehrh. Fagaceae.  I was told pioneers fed hogs beech nuts.  The hogs roamed the eastern forests eating the nuts.  Quite a feat the nuts are housed in a durable husk, then a shell, and then not much nut. Tasty though.

This tree is a modern version of "Newspaper rock" a huge stone covered with Native American graffiti in Utah.

Native American Medicine:  used bark decoction to induce abortions, also used for pulmonary problems.  Leaves were decocted  and poulticed over wounds, sores.  Leaf decoction also used over burns. 

Food: Nuts eaten for treating worms, much the same way pumpkin seeds are eaten.

Squirrels will get to the nuts before you can.  Watch a squirrel in a beech forest she/he may lead you to a cache of hundreds of nuts.  Good luck.

(LOVE CREEK)