Before I tell you, you're going to have to demonstrate to me that ping pong balls have any intelligence to properly make a choice; a conundrum that saddles the high majority of the animal kingdom, and even most species of the plant kingdom, if not all. Choice is a matter of intelligent processing of information, and that is not a universal skill. But, I will offer you another exercise:
Santayana, is quoted to have said, “Progress, far from consisting in change, depends on retentiveness. When change is absolute there remains no being to improve, and no direction is set for possible improvement: and when experience is not retained, as among savages, infancy is perpetual. Those who cannot remember the past are condemned to repeat it.”
There’s something else Santayana said relative to theory and ignorance: “Theory helps us bear our ignorance of fact.”
What if you’re a good scientist, but only a passable philosopher? What does it mean?
Suppose you are caught in a whirlpool in the ocean. What do you do to survive? If you haven’t the slightest idea, are you dead, already?
It’s only a theoretical argument. There are at least three theories; no evidence suggests that any of the three is an absolute fact. They are urban myth at best, except that all three begin with a prudent suggestion and, inevitably, this much is fact.
First, remain calm. Fear is a killer. From there, the methods vary. One theory says that being calm must even be a matter of physical relaxation, not just emotional. Remain still, and you will float out of danger.
Another theory says to swim hard with the current, and you will reach the edge and swim out of it.
Still another theory says give it up; your life is forfeit.
Three theories. It is likely that only one of them is fact, but which? Ignorant of fact, we take some solace that somebody has thought it through. But, until proven, they are just theories and that, according to Santayana, is solace enough. But, it is solace and nothing else, or, is it even that? There’s no joy in a negative consequence.
Are we plunged into the whirlpool of Santayana’s philosophy? What if the irony is that either theory returns us to the savagery of perpetual ignorance?
You see, at least my theory of free choice requires intelligence to operate within it. Then Santanyana is right; ignorance is mere savagery. Your theory of determinism requires no intelligence whatsoever, because your ping pong balls will follow a path, surely, but they have no contribution to the course, and that requires no intelligence, either. Between the two theories, I prefer the one that acknowledges intelligence and avoids savagery.