Starbear, sorry you are wrong the slides will deploy automatically regardless of height from the ground as long as they are armed ie that the girt bars are attached to the floor also the door power assist will also activate rapidly open the doors, again only if the doors are armed, I am of course assuming the B737 has door power assist as have never worked on them.
Actually Matkat, I am not. I will if required find you chapter and verse but for now I assure you that opening of the door (power assisted or not) merely allows the slide to be withdrawn from its bustle and
fall outwards. This drop then causes a cable (lanyard) to pull a pin and activate the air/nitrogen cylinder to inflate, with assistance of aspirators, the slide itself. It is for this reason the worst thing one can do is to remove a set of steps or airbridge away from an inadvertently "deployed" slide.
The slide needs to drop for full activation.