What could be a good "layman" metaphor for illustrating the difference between uniform and pointwise convergence of function series? I am teaching calculus to engineering undergrads; for many of them, the definitions are way too abstract, and mathematical examples are not that illuminating.
I was thinking about people "converging uniformly" towards the end of their kindergarten time (in at the age of 3, all out at the age of 7, say) and "converging pointwise" towards the graduation from university (some need 5 years, some need 10...). However, it turns out that life is not that simple even in the kindergarten, at least in the country where my university is, and I am looking for a more precise metaphor.
Most of the answers show that my question is a bit too vague. It is definitely not my intention to substitute a mathematical definition by any kind of metaphor, or to start the discussion in the class with such a metaphor, or to use it repeatedly or systematically. I was wondering what can I say en passant when the definitions are already given, the examples are discussed, and this is the third class about uniform convergence, but some people still stare at me with empty faces. For those people, the mathematically rigorous presentation obviously did not work, and they need something that might motivate them to think over once again.