Thursday, January 31, 2008
Airplane on a treadmill
I created this blog specifically to make this post. It may be the only post I ever write, but since human ignorance is seemingly unbounded, perhaps it won't be.
I thought that today would be a monumental day for this topic. Today, the Mythbusters debuted their long-awaited "Airplane on a treadmill" episode. For years, physics teachers around the world have cringed in horror at heated internet debates concerning a ludicrous thought experiment. Sadly, half of them recoiled in disgust at the correct arguments. Forum posters signed their names with such epithets as "Ph.D. Aerospace Engineer" and "20-year pilot." Somewhat tellingly, these ego-boosters were most often employed by those delivering the wrong answers. Mythbusters finally attempted to end the insanity by performing the experiment themselves.
AND YET...
The debate rages on. Even after being shown seemingly conclusive evidence of the other side's argument, forum-goers from near and far continued to staunchly defend their own theories.
Here and now, the debate will end. I intend this long-winded article to be the definitive answer to the great AOAT conundrum. No further debate is necessary - simply direct the ignorant people to this page, tell them to read it, and let's all get on with answering more intriguing questions, like does P = NP?
For those of you just joining us, "Airplane On A Treadmill" is a thought experiment in physics. Some consider it a litmus test for assessing one's knowledge of airplane physics. In its most basic form, the experiment is worded thusly:
A plane is standing on a large treadmill or conveyor belt. The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the plane take off?
The question suffers from many rewordings that muddle much of the debate about the thought experiment. The basic idea is that there's a plane, on a treadmill, and we're going to run the treadmill backwards in an attempt to stop the plane from taking off. And here, at the very beginning of this explanation, is the definitive answer. There are in fact two correct answers to this question:
-No, the plane can't take off.
-Yes, the plane can take off.
Fooled you! But that's just the point. The experiment is meaningless, and the passionate internet debates more so, if we cannot agree on what is truly meant by the question. But don't worry, I won't pull a Lost on you - I do intend to give a truly airtight answer later on. For now though, we need to debate semantics.
Really, we do.
You see, the AOAT confusion all arises from misses - misconceptions, misinterpretations, and misunderstandings. Consider three rewordings of the question:
1) An airplane is sitting at rest on a very powerful treadmill. You are at the controls of the treadmill, while I am at the controls of the airplane. On some signal, I begin to attempt to take flight in the plane, and you attempt to match my speed to try to keep me stationary. Will the plane take off?
2) An airplane is sitting at rest on a very powerful treadmill. You are at the controls of the treadmill, while I am at the controls of the airplane. On some signal, I throttle up the airplane and you turn on the treadmill, and we conspire by our joint effort to try to keep the plane stationary relative to the ground. Will the plane take off?
3) An airplane is sitting at rest on a very powerful treadmill. You are at the controls of the treadmill, while I am at the controls of the airplane. On some signal, I attempt to take flight in the plane, but you match my speed with the treadmill and keep me stationary relative to the ground. Will the plane take off?
Here are the absolute, 100%, bet-your-life-on-it answers to these rewordings:
Yes.
No.
Whoever asked this question is an idiot.
And that's about all this debate comes down to, folks. If we could all agree on one set of rules for the thought experiment, then we ought to be able to make the explanation of the answer clear. As it stands, normally one side has interpretation (1) in mind, and argues vehemently with someone else who has interpretation (2) in mind, and the whole thing blows up into a senseless squabble.