It seems to me that trying to decide on sand pile/not a pile involves two distinct parts. One is external to us (the sand) whilst the other (deciding if the grains form a pile) is inside us and is akin to a belief-system. The pile 'belief' is sticky, so to speak, so if you saw a pile yesterday you'd be more likely to see a pile today even though grains had been removed. Each new person viewing the pile would decide afresh and individually about the sand. Beliefs linger, so each new person viewing the grains would be more likely, when seeing the grains shortly afterwards, to stick to their original decision.
Put another way it's like seeing Jesus in a piece of toast. If you are from another planet you probably see toast (sand) but not Jesus (pile). A person might see Jesus in the toast long after the toast had been toasted a bit more to even out the browning, because what has been seen cannot be unseen (i.e. beliefs are sticky). Coming from the other direction a person seeing a piece of toast fully browned might miss a portrait of Jesus (or Robert Browning) that is revealed bit by bit.
Also, an A doesn't much resemble a D, but a B is a lot like a D with a very tight belt on (or perhaps a female D).
*shakes her fist and scowls as she tries to think about something else*