A collection of grains of rice is a pile if and only if (1) a majority of the rice grains are supported by other grains rather than whatever surface the pile is on and (2) you can get from any grain to any other grain by stepping from grain to grain, each step happening between grains whose surfaces are no further apart than 10% of the diameter of a median rice grain in the pile.
Of course I don’t claim that this is The One True Definition of “pile”, but it kinda annoys me that heaps/piles have been the standard example of fuzziness about number for centuries, and everyone assumes that if you did lay down a somewhat arbitrary definition then it would be of the form “at least N objects”, when in fact I think what fuzzily distinguishes piles from non-piles is something else—you can definitely have a pile with 6 objects in it, and you can definitely have 100 objects of the same type that don’t form a pile—and one can give somewhat-plausible clear-cut definitions with no arbitrary numbers-of-objects in them.
This is mostly a mostly-irrelevant tangent, but it’s maybe worth pointing out explicitly the phenomenon that when you have some notion that you leave undefined it’s possible to be mistaken about what sort of notion it is. If you’re having an argument about piles or heaps then you will likely go astray if you start asking “well, how many grains of rice do we need to have before we definitely have a heap?”. Compare: “how complex does a nervous system have to be before we assign moral significance to the organism whose nervous system it is?” which is fairly clearly wrong in the same sort of way as treating “pile” as purely numerical.
A collection of grains of rice is a pile if and only if (1) a majority of the rice grains are supported by other grains rather than whatever surface the pile is on and (2) you can get from any grain to any other grain by stepping from grain to grain, each step happening between grains whose surfaces are no further apart than 10% of the diameter of a median rice grain in the pile.
Of course I don’t claim that this is The One True Definition of “pile”, but it kinda annoys me that heaps/piles have been the standard example of fuzziness about number for centuries, and everyone assumes that if you did lay down a somewhat arbitrary definition then it would be of the form “at least N objects”, when in fact I think what fuzzily distinguishes piles from non-piles is something else—you can definitely have a pile with 6 objects in it, and you can definitely have 100 objects of the same type that don’t form a pile—and one can give somewhat-plausible clear-cut definitions with no arbitrary numbers-of-objects in them.
This is mostly a mostly-irrelevant tangent, but it’s maybe worth pointing out explicitly the phenomenon that when you have some notion that you leave undefined it’s possible to be mistaken about what sort of notion it is. If you’re having an argument about piles or heaps then you will likely go astray if you start asking “well, how many grains of rice do we need to have before we definitely have a heap?”. Compare: “how complex does a nervous system have to be before we assign moral significance to the organism whose nervous system it is?” which is fairly clearly wrong in the same sort of way as treating “pile” as purely numerical.