I think the deeper point is along the lines of Wigner's classic "The Unreasonable Effectiveness of Mathematics in the Natural Sciences"
http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_...
It happens to be the case that elementary dimensional analysis is sufficient in the case in hand -- and it often is.
I think the deeper point is along the lines of Wigner's classic "The Unreasonable Effectiveness of Mathematics in the Natural Sciences"
http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_...
It happens to be the case that elementary dimensional analysis is sufficient in the case in hand -- and it often is.