In India, threshold has a special cultural significance. It is step at the door that separates the inside of the house from the outside. It has a symbolic meaning referring to the limits of a house. In the movie Umbartha (threshold) the woman of the house crosses her set limits and makes a life for herself outside the house despite being married to the man of the house. I guess because of this strong cultural reference threshold has always meant to me to be a limit to a horizontal space rather than a vertical space that can be quantified in terms of upper or lower.