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The Red-Ball-In-The-Box Fallacy

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.

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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?

25 thoughts on “The Red-Ball-In-The-Box Fallacy Leave a comment

  1. Were you musing on uncertainty (Heisenberg), a paradox (Schrodinger), or willfulness (much of human behavior)?

  2. You’re sure it’s something epistemological and not something simpler like people eliminating “outliers” (essentially saying they’re not “in the box” any more) in their studies?

  3. I guess you could always fall back on the butler-did-it cliche.

    If the red ball is so much bigger and the box is finite I would think the red ball would be the equivalent of an 800 pound gorilla in the room. OTOH, I was once working in a room the size of a typical bathroom and a screwdriver rolled off the bench onto the floor. I never found it.

    Everybody knows a sheet is not a halyard and neither is a stay — in Annapolis anyway. Nothing like coiling up with a good rope after a day’s hard work. But then, hanging around with ropes can be detrimental to your health.

  4. Let’s examine some of the previous topics: trends in timelines, brain scans, the O’s health care plan, …

    my guess is: trends or papers that ‘prove’ obvious fallacies.

  5. From a statistical point of view once you put twenty dirty white balls in the box, the probability of drawing the red ball out of the box (one draw) is less than 5%, so “scientifically” there are no red balls in the box.

  6. This reminds me of “There… Are… Four… Lights!”

    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.

    Give me an example of a truth that’s often incorrectly denied.

  7. “To a first approximation, all the objects in the box are white”?

    Where does that 800lb gorilla sleep, by the way?

  8. Our “sense” for determining color- especially red- does not and cannot work “flawlessly”. We cannot “know” a red ball exists unless we are given at a minimum information on the light source used to “sense” the ball.

    One example is familiar to scuba divers- the color red disappears at about 15 feet depth, yellow is gone by 50 and green by 70feet.

    Is the ball red at 20 feet? Is the ball round at 6000 meters?

    The same effect can be produced while remaining dry by restricting the wavelengths of an artificial light source.

    Since people do not see the entire electromagnetic spectrum -color for us is a perception that changes with both the physics of the object and the environment in which it is found. Importantly, color is also a function of the quality of the light receptors in the eye and the brains ability to interpret the signals.time and place. A dog (and some humans) would never see the ball as red.

  9. Ray Bradbury did a short story on something like this, “No Particular Night or Morning,” [from the book, The Illustrated Man] only it involved a guy on a spaceship that began to wonder if activities he couldn’t see or things he could but could never touch/validate were really real. He went insane. That’s what this blog essay seems like — reading something that insane guy would dwell on & write about.

  10. If the ball cannot be seen in it’s entirety, it would have to be removed from the box to determine that is had been in the box. But then it is no longer in the box. As for feeling the ball, can a soccer sized ball ever be felt completely?

    Or is it about the ball being with the marble or in the marbles in the box?

  11. WARNING: Deliberate overly literal interpretation.

    The box is imaginary and there for contains nothing.

  12. Don’t put too much trust in dreams. In a real situation you would need to keep close watch on those others putting in balls to make sure they didn’t palm the red one. If there could be such a possibility, your knowledge is reduced to “there used to be a red ball in the box”. This is a setup for a magic trick. Think rabbits, hats, and lovely assistants. Was that red ball red because of paint or an interior red LED or what? Was that red ball a melting ice cube? Too many assumptions are needed.

  13. “a sheet is not a halliard is not a cable”
    Also, a rope is not a line but a halliard is a halyard. There is wire rope and nylon line. We used to have fun with new sailors aboard ship. We would send them to the bosuns locker for some waterline. Why are you learning this nautical jargon?

  14. Good one Matt. Reminds me of almost every conversation I have ever had with a religious fundamentalist, which is a lot of conversations, since three out of my four brothers-in-law are fundamentalist preachers.

    Fundamentalist. I love that word, as they are usually not fun, and are rarely, if ever, mentalists…

  15. I’m scratching my head looking for some M. Night Shamalan type ‘twist’…

    Maybe this is it:

    – Red is just a perception– it’s not a real thing. Many people can be looking at the same ball, but not all of them will see a red ball. So far so good?

    – Changing the color of light hitting the ball would change it’s ‘color’ as well. Would a red ball still be a red ball if it reflected no light? No– It _was_ red, but a new observer would see a black ball.

    – You were specific that the marbles were kind of hazy etc… So, adding translucent marbles to the box affects the wave-length of light going in and coming out of the box. So, the more marbles you add, the less red escapes the box.

    – The answer then is that there doesn’t have to be a red ball in the box even though nothing has been physically removed from the box.

    – The question “is there really a red ball in the box” is not the same as “was there ever a red ball in the box?”.

    I’ll shut-up now.

  16. Dream and paint!

    I’ve got it!!! Meng-zi (夢子^_^) is famous for visiting people’s dreams in Taiwan. He must have told Mr. Briggs the following.

    “One shines red when near vermilion
    One gets stained black when near ink.
    Integrity casts a straight shadow.
    Peaceful voce confers loud and clear.”

    (My perfection translation of “故近朱者赤,近墨者黑;聲和則響清,形正则影直。” ~孟子. )

  17. Luis,

    LOL! Fun game. I still haven’t purchased #2. Maybe when it gets a bit cheaper . . .

  18. I assume this an analogy of the proof that all religions are false because there are so many of them, most of which contrict each other on fundamental points, and most of which are patently absurd… or something like that.

  19. 1. A dog would see no ball since they are color blind and red is not percievable in black and white maybe.

    2. Perhaps the see thru white balls change the color of the ball.

    3. Perhaps the white balls influence the shape of the ball.

    4. You never stipulate whether the red ball remained in the box when the friends came along and dropped marbles into it.

  20. “Reminds me of almost every conversation I have ever had with a religious fundamentalist…”

    Odd, reminded me hippies and their endless circle-jerking. As for the topic, it reminded me of Evolutionists and their refusal to see that the degree of complexity of life is so high that natural-selection+mutation would never ever have enough time to do what is attributed to it.

    Simple, and as obvious as… a big old red ball in a box. As for the semi-transparent little balls, those would all the instances of ‘possibility’ devoid of the associated probability thrown about like so many handfuls of night-soil.

    Perhaps the fallacy is that of refusal (?) to think comparatively-objectively. Likely related to why B. Franklin said that reasoning is an art, not a science.

  21. I relate this to the mistakes people make.

    People make basic mistakes all the time… so caught up in the small issues… the little individual things sticking to the central issues become distractions …

    Lost looking at endless details about global warming, and not seeing that it’s not getting hotter… or that the models have never worked.

    So concerned about the “rights” issues of “gay marriage” that people fail to notice that marriage is the human mating pair, and can’t be changed…

    But in the end, they are all failings of perception… the red ball scenario is far too pure to be of practical use as far as I can see.

    One other way we fail like this is when we abandon core principles based on smaller confusions that do not relate in any way to that core principle. Some people stand for individual sovereignty, but because of all the things that national healthcare might give them, they pretend it’s ok to force people to be a part of their healthcare utopian dream. The core principle vanishes.

    Surrounding something with a coating of smaller things that fail to penetrate, is actually a way to measure the central, large object. Where those tiny balls DON’T go, defines where the large one IS.

    I use this idea to find the truth of things when someone speaks… I listen to where their words go… and note carefully the things that they *fail* to say, in order to define the shape of things they are attempting to hide.

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