Nineteen pieces? Wow. I had to write this twice thanks to Spark and his forum shut down today, but here is my best guess at the rubber band meets blade phenomenom:
I spent some time about a year ago conduction 'rubber-band test' experiments. The main conclusion I came to is the test does not really measure the sharpness of the edge.
Different knives with different shapes and edge geometry cut 3 X 1/4 inch rubber bands into different numbers of pieces. Smaller knives tended to make more pieces than larger knives. Sharper knives tend to cut more pieces than duller knives, but some really sharp knives conistantly made very few pieces.
I began marking the center point of the stretched band (between my thumb and forefingers) so that I could see the relative position of the cuts. I was surprised to find that the cuts made pieces of different length, from tiny to long, and these cuts were not evenly distributed around the center point. There might be many on one side and only two on the other. Reconstructing the rubber band showed many curious patterns. The same blade might cut a band in many different ways.
Although it would take a high speed camera and a sophisticated mechanical device to consistently hold, stretch, and release the rubber bands into the blade to confirm this, I think the rubber band phenomenon has more to due with the mechanical physics of the release of the rubber band than it has to do with the sharpness of the blade, although a dull blade will fail to cut at all, or produce only a few discreet pieces or nicks in longer pieces. Smaller sharp blades will make more cuts than larger sharp blades.
A clue comes from observations about the best way to 'shoot' a rubber band. Personal experience shows that a rubber band will travel the farthest if tensioned on only One arm of the stretched circle compared to stretching both arms 'equally'. The ideal equal tension state is probably very difficult to achieve because of variations in the thickness of the rubber band, and the difficulty of holding and releasing the rubber band in exactly the same way every time. These forces in different vectors along two sides of the direction of motion will tend to cancel each other out, decreasing the overall forward momentum (energy) of the moving rubber band. A rubber band shot from thumb and forefinger but tensioned mostly along only one side of the folded band will travel much farther and with more accuracy than a rubber band shot in the usual manner.
When the band is released from it's stretched (tensioned) position; the two sides of the spring will tend to return to their rest position. This energy is transformed into the energy moving the whole mass of the band forward. If the two sides are unequally tensioned, there will be movement much like waves in the moving band. After it reaches its rest point, the band will begin to fold into segments of different lengths that will overlap as the band approaches the blade. A sharp blade will then cut through the band Many times producing various lengths of cut pieces.
If the blade is very wide (approaches the diameter of the rubber band at rest), it will tend to cut the band in fewer pieces because there is less time for the traveling blade to fold. Try tensioning the rubber band on only one side before releasing into the blade and observe the results. Fewer pieces.
The rubber band test says more about the physics of 'shooting' a rubber band than it has to do with blade sharpness. Although a dull blade will tend to produce few cuts than a sharp one, a very sharp blade of the right dimensions may produce only a single cut. Much more is going on here than the cutting ability of the blade.
I would love to see a super slow motion film of this in action. The rubber band test is fun, astonishes people, and is mystifying, but not really all that hard to understand.
Paracelsus