Then since you're OK with all smaller numbers being equally "instantaneous", then 1/10^4000 seconds is instantaneous too. Add up enough of those to make a second, and you can conceive of your previously inconceivable number! :)

Of course, that will seem silly. I'm just illustrating I don't think there are any grounds for claiming exponentially large numbers are inconceivable, but exponentially small numbers are somehow conceivable. They're just as far from 1, multiplicatively, no matter which direction you go in.