Hidden Purple Tiger

2009.02.21   prev     next

A few articles ago I faulted Einstein et al. for jumping to the conclusion that if you can’t currently contrive a way to observe X, then X must not exist. Instead, I said, the correct scientific declaration is that we don’t currently know whether or not X exists.

One of the standard counterarguments to my logic goes something like this: “Is there a hidden purple tiger¹ in this room with us?” By posing such a question, the speaker hopes to generate a win-win situation where I must say either “there might be,” in which case I look silly, or “that’s silly,” in which case I look like I have failed to follow my own anti-Einstein logic above.

Fortunately, there’s a third option, and it goes like this:

When Michelson and Morley were about to do their famous experiment — but hadn’t done it yet — what do you think their estimation might have been of the probability that the Earth has a velocity through absolute space? I’m guessing they thought it was pretty high, say 0.9. (I.e. 90%) Then, after doing their experiment and getting the result they did, what did they likely think the odds that Earth has an absolute velocity? Something less than they did before. 0.7 perhaps? 0.5? 0.2? Who knows, but definitely less than their pre-experiment probability.

Now, suppose that some day a few weeks from now, you’re out driving your car on randomly selected country roads, just for the fun of it. As you slow down for a sharp L-turn, you notice a nondescript, windowless building right next to the road. It has a door, and you see that the door looks slightly ajar. You pull over to investigate.

You walk up to the door and are about to open it, when you stop and think. Your mind goes back to the “hidden purple tiger” argument, and you suddenly wonder: Could there be a purple tiger behind this door? Never mind a hidden one — just a real tiger with purple fur. You know there are such things as tigers. And you know that although no tigers have purple fur, it’s certainly possible to dye their fur purple temporarily. So, your best information says there could be a purple tiger in the interior space behind this door.

But what are the odds that there is a purple tiger there? The same information you have about tigers, purple dye, etc., tells you also that the odds of there being a purple tiger behind this door are very, very low. You estimate them at 0.0000000001.

Now you open the door and step inside the doorway for a good look. You see a simple, rectangular room. A metal folding chair stands in one corner, and an open, empty paint bucket sits nearby. A folded plastic tarp lies flat on the floor next to the chair, and a bare light bulb protrudes from the ceiling. You see and hear nothing else. You smell the faint odor of paint.

It doesn’t look like there could possibly be a purple tiger in this room. Even if someone wanted to hide one there, it looks like they couldn’t. Behind the wall? Who knows. But in this room? Doesn’t look possible.

Now what is your estimation of the probability of there being a purple tiger (necessarily hidden) in the room? Considerably lower than it was before. In other words, considerably lower than 0.0000000001.

So while the results of the Michelson-Morley experiment lower the odds of Earth having an absolute velocity from 0.9 to something less than 0.9, looking at a randomly selected room, and seeing that it doesn’t appear to have a purple tiger in it, lowers the odds of there being one from 0.0000000001 to something less than 0.0000000001.

The flaw in the “hidden purple tiger” argument is that it mixes two very different ways to figure out whether something exists: (1) by taking a quick look, and (2) by knowing a lot about the thing you’re looking for and the kind of place where you’re looking for it, and being able to statistically estimate the likelihood that you’re going to see it on this particular occasion, even before looking.

The “hidden purple tiger” argument is intended to take people who say that method (1) doesn’t definitively rule out the existence of something, and make them look as if they have denied the validity of method (2), when they actually haven’t.

¹This is not exactly the same as the “flying sphaghetti monster” argument, which I will address at a later time.