The very best way to get ketchup out of the bottle, as was once memorably demonstrated by David Letterman, is to grasp the bottle firmly around the bottom and swing it round and round over your head, like a lariat. Of course, the ketchup will splatter all over the walls, but you asked only how to get it out of the bottle, didn’t you?
There is one method that doesn’t stand a prayer of a chance, yet you see people trying it in restaurants all the time: pounding on the bottom of the bottle. All that does is make Isaac Newton rotate in his crypt at Westminster Abbey.
Sir Isaac taught us (or at least he thought he did) his three laws of motion, the basic laws of mechanics that govern how things move. Had he known about ketchup (which arrived in England only around the time of his death in 1727), he would have stated a fourth law, thus: “He who slammeth ye bottom of ye ketchup bottle doeth naught but drive bottle even more tightly onto ye ketchup.”
Or, since according to Sir Isaac every action hath an equal and opposite reaction, you’re just driving the ketchup more tightly into the bottle, just the opposite of what you want to accomplish.
On the other hand, the Letterman method is legitimately Newtonian because you are applying an outward centrifugal force to both bottle and ketchup, yet restraining the bottle (we hope) while allowing the ketchup to react freely to the outward force. So how would Sir Isaac advise you to de-bottle the sauce without attracting quite so much attention? There are two ways.
First, you can slightly modify the centrifugal force method by holding the bottle horizontally and snapping your wrist downward, so that the tip of the bottle describes a short downward arc, a portion of a circle. As in the Letterman method, the ketchup will experience a centrifugal force outward from the center of the circle and hence outward through the neck of the bottle, a direction which we devoutly hope is toward your plate rather than toward a dinner companion. The latter unfortunate circumstance can result if you begin the arc a trifle too high above the plate.
The second, and safer, Isaac-approved ketchup-removal technique is to give the upside-down bottle a brisk, downward, stabbing-like thrust along its axis, aiming directly at the plate but stopping short at the last possible instant.
In this maneuver, the ketchup inside the bottle will be tricked. It will keep moving toward the plate even though the bottle itself has stopped, just as a driver will move toward the windshield when his car is stopped short by a telephone pole. Or, to paraphrase Sir Isaac, “A body in motion will continue in motion until stopped by a windshield or a french-fried potato.”
If the bottle is new or has been recently refilled (restaurants do that), first loosen the ketchup by rotating a knife blade inside the neck.
The only remaining problem is that, seated at a table, you may not have enough thrusting distance above the plate to carry out a good, swift bottle-stab. So stand up.