I was just reading a book on my Nook tablet ( 1632 by Eric Flint ) where a section of West Virginia was transported to 15th century Germany. In one chapter, they were running telephone lines to another city, reinventing a communications system practically from scratch. The statement was made that they couldn't use trees to run the lines since thy would grow at different rates and so would carry the wires upward at different rates.
I've run into this before when someone was installing lights in a tree but figured that they would have to leave a lot of slack in the power line because the tree would grow, stretching the cable.
The misconception is that trees grow like people, with everything moving up in proportion. Actually new growth is just added to the top (or end of branches). As soon as the question is asked "Do you think that the wood inside the tree actually stretches?" then it becomes clear. Branches don't get any higher in the tree as they age, they just get bigger as the tree adds to height at the top.
A simple thing, but surprising how many people don't think it through.
(Note from David: I've seen the brain-teaser along the lines of: if so-and-so carved his initials in a 20-year-old oak tree, 6 feet from the ground, how far off the ground will the initials be in another 20 years? Trick question!)