Okay, friends, I need your help. One day last year, shortly after I had arrived in Taiwan, I awoke from a fitful, jet-lagged sleep at 2 a.m. with the argument which follows in mind. I arose with enthusiasm and enough sense to know that if I did not jot down some notes the argument would be forever lost. So I opened the blog and wrote a few paragraphs, but I soon tired and quit. I recall telling myself something like, “There. That’s enough. I’ll finish in the morning.”
I also remember how pleased I was with myself for thinking up the red-ball analogy. “That’ll show ’em!” There might have been chuckling. I went back to sleep. Next morning, I had business to attend to, and so did not look at my notes. And then time intruded. You can guess the sequel.
I would just toss it out as the product of a fervid dream, which it very probably is, except that (if I may be allowed) I wrote it so compellingly that I badly want to know what the point of it was. The damn thing ends with a cliffhanger, and I can’t wait to see how I was going to escape.
Can you help? It is obviously epistemological in nature; at that time I was working on some philosophy of probability; and given my state of mind, it is almost certainly a fallacy. But there is a tiny chance real meat exists. The idea is sound enough, though: people often incorrectly deny a thing is true even though they can see it because there exist a vast number of competing hypotheses. But as for the idea I had in mind and of the structure of the proof, who knows?
I am still heavily engaged learning the ropes at my new gig—a sheet is not a halliard is not a cable—so I will be slow answering comments.
In front of you is a large open box, painted white. Inside, you can see clearly a large, bright red ball. The question is: given this evidence, and assuming your brain and senses etc. are working flawlessly, is there a red ball in the box?
This is not a trick question. The answer is yes, there is a red ball in the box. Why ask such a simple, even stupidly obviously question? Well, let’s see.
Suppose some person now comes along and drops in the box a semi-see-through dirty white ball. It is the size of a playground marble, much smaller than the bright red ball, which is as big as a soccer ball. The question is again: given the previous and this new evidence, is there a red ball in the box?
The answer one might give is, “You’re boring me. Of course there is a red ball in the box.” This is the right answer.
But now suppose a second, then a third, then several more friends come along and each of them drops an ugly white marble into the box. Perhaps some of the white marbles differ ever-so-slightly from one another. But in the box they go. Further, none of them can be mistaken for the red ball, not even (because of the vast differences in size) by a blind man.
The box is more than large enough to hold all these items, but not so large that you can’t root around in it and examine its contents in a reasonable amount of time. The question is: given all the stated evidence, is there a red ball in the box?
How much of your patience have I sacrificed asking these damn fool questions? Most of it I imagine, and probably next even of all of it, because I’m going to disappoint you by saying there is no catch, no gotcha. The red ball is still there, it can be found and seen, just as the evidence says it can be.
I’ve presented the question as trivial and not worth asking. And it isn’t. Or at least it wouldn’t be if so many people insisted that the red ball isn’t in the box because there are ugly white balls in it, too.
What’s that? You don’t believe anybody would make such a mistake?