"Another approach is to use hysteresis—that is, knowledge of what the collection of sand started as. Equivalent amounts of sand may be called heaps or not based on how they got there. If a large heap (indisputably described as a heap) is slowly diminished, it preserves its "heap status" to a point, even as the actual amount of sand is reduced to a smaller number of grains. The idea is that, for example, let's say 500 grains is a pile and 1,000 grains is a heap. There will be an overlap for these states. So if you are reducing it from a heap to a pile, it is a heap going down until, let's say, 750. At that point you would stop calling it a heap and start calling it a pile. But if you replace one grain, it would not instantly turn back into a heap. When going up it would remain a pile until, say, 900 grains. The numbers picked are arbitrary, the point is that the same amount can be either a heap or a pile depending on what it was before the change. A common use of hysteresis would be the thermostat for air conditioning, the AC is set at 77 °F and it then cools down to just below 77 °F, but does not turn on again instantly at 77.001 °F, it waits until almost 78 °F degrees, to prevent instant change of state over and over again.[4]" (Wikipedia, discussion of the sores paradox.)

This really casts some light on the issue. I think it is hysteresis that generates Rapaire's heapof BS in the first place, and this in turn opens the door to resolving the paradox by administering Xanax to optimize the hysteresis levels.


A