The Yellow Ball Allegory

Consider a long tube set at an angle. A white ball is held at the high end of the tube. Somewhere inside the tube is a mechanism which paints the ball yellow, but we don't know where this mechanism is located. The white ball is dropped into the tube. When it rolls out the bottom, it is yellow. Q1: Where is the painting mechanism located? Q2: At what point in the tube can we state that the ball is not yellow?

Before reading the following commentary on the yellow ball allegory, please pause for a moment and determine your own solution. See if your solution changes as you read the commentary. And if it does... ask yourself why! And ask yourself which of your solutions, the initial or the final, is the objective solution.

Some believe that the painting mechanism lies at the entrance of the tube, some believe that it lies at the exit. Some believe that it lies somewhere in between, and some of those have quite definite beliefs as to the precise position of that in-between point. But these are just beliefs and cannot be proven.

Some scientists believe that technology can detect yellowness within the tube, thereby establishing the position where yellowness begins. Others argue that the scientists are not detecting yellowness, but some other attribute which all yellow balls exhibit, but which does not guarantee the presence of yellowness. Others argue that yellowness inside the tube is somehow different from yellowness outside. But all of these are also beliefs, and cannot be proven.

My solutions...

Q1: Where is the painting mechanism located?
A1: It must be at the entrance, at the exit, or somewhere in between.

Q2: At what point in the tube can we state that the ball is not yellow?
A2: There is no such point.

Those conclusions aren't very conclusive, are they? But that's all that we can say with certainty. The nonscientific arguments are not acceptable because they have no objective justification. The scientific argument has a better foundation but rests on unproveable assumptions. Note, however, that acceptance of the scientific argument, combined with recognition of the fact that it tends to push the calculated position of the painting mechanism towards the entrance as technology improves, leads to the conclusion that the painting mechanism should be assumed to lie at the entrance, since that is where the experiments lead, and there is no objective reason to think otherwise.

I proposed this thought experiment during a political discussion. You've probably guessed the topic already, though I've tried not to make it explicit, because knowledge of that context colors (pun intended) conclusions to the detriment of logic. Personally and tangentially, this is one of those cases in which I found myself defending a political position which conflicts with my metaphysical position, but in a community of differing metaphysical beliefs, that's the only fair thing to do.