Instead of your mathematical analogue of an asymptotic function, I prefer the physical analogue of a self-reinforcing spiral, doomed for destruction without external intervention. A band-aid solution may work initially if the wound is very limited and healing. If not, a surgery will be required at some point. An anecdote of a qualified hire of an app reader is just that, an anecdote. What happens if every HS senior in America (or the world) applies to Princeton?