Indeed, without considering risk:benefit and ever-present uncertainty, can we really get information about someone's beliefs?
(Here I mean actionable beliefs. The interesting thing about many irrational "beliefs", religious, political, or otherwise, is that very often the beliefs are contentless tribal cheers that have no measurable effect on the believer's behavior. Tellingly, pointing this out or putting the believer in a position that requires an explicit choice based on the belief is seen as offensive; see people's responses to betting.)
Many physics lecturers have done the exercise above with their students, and occasionally people in the rationalist community will post these videos. Here I show you why, if someone moves away from the pendulum, she's not necessarily making a strong statement about her belief in the laws of physics.
I like this demonstration of principle in the sense that the point of beliefs is to make good decisions. If your claimed beliefs don't affect your actions, or you're behaving contrary to your claimed beliefs, you have to ask whether they're really your beliefs, or what good they're doing in your head.
But there is always uncertainty, and the degree of uncertainty, as well as the consequences of a decision, should affect your risk:benefit and your decision. In fact, asking people to behave as if they are absolutely certain shows a poor understanding of Bayesian reasoning! Bad rationalist!
In this case, assuming you believe in the laws of physics, your risk:benefit goes like this. "I want to prove that I believe in the laws of physics. If I don't stand my ground when the pendulum swings back, it will look like I don't; my peers will doubt my belief and my ability to behave according to that belief. Even worse, *I* may doubt it.
"On the other hand, the pendulum hitting me in the face will hurt and may injure me, unlikely though I think it is. And there are reasons this might happen without the laws of physics being violated. There might be something that affects the setup, e.g. an air vent is blowing that is normally not on, and this will accelerate the pendulum enough in its return to make it whack me. My a-hole friends might be playng a joke on me (actually, not unlikely at all). And finally, maybe I *don't* 100% absolutely understand the principle, which is important in situations where I can get injured (this would qualify as not believing, at least in this law of physics).
So your utility equation, to get you to stand still, would look something like:
gain from proving to peers you believe in principle
must be greater than
(embarrassment/pain/injury)*(uncertainty about principle)*(general uncertainty including a-hole friends)
But wait, there's more! If this risk:benefit were all that the nervous system was doing in this situation, what we would see is not people stepping up to the pendulum and then flinching as it swings back. They would say no way Jose right from the start. But flinching is a reflex, and it's very difficult to argue that it's subject to belief in the same way as your decision to participate in the exercise. Case in point, I really am quite certain that contact lenses won't hurt me (I don't wear them normally, just for Halloween costumes) but I have great difficulty keeping my eyes open to put them in. Notice, by the way, that the gentleman in this video closes his eyes and makes jokes revealing anxiety about the process, even after (probably) years of doing this very demonstration.
In all decisions, the likelihood and magnitude of the reward and consequences make a difference, even in something so simple as this. Optimism is a good outlook for modern life where at most you risk social rejection - constantly try to do things that are out of your league, and you'll fail most of the time, but by dumb luck you'll score occasionally. (This is why learning to tolerate failure and rejection is so important.) On the other hand, when you're rock-climbing or flying a plane, the consequences of failure are massive. Then, it pays to be pessimistic. And finally, everyone's utility equations are a little bit different. Why is it so important to get people to swear their loyalty to physics? In my case, in this situation, not that much, and the factor that figures heavily in my decision is concern about the utility function of my a-hole friends.