The Nonlinear Library LW - The Parable Of The Fallen Pendulum - Part 1 by johnswentworth
Mar 1, 2024
03:18
Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: The Parable Of The Fallen Pendulum - Part 1, published by johnswentworth on March 1, 2024 on LessWrong.
One day a physics professor presents the standard physics 101 material on gravity and Newtonian mechanics: g = 9.8 m/s^2, sled on a ramp, pendulum, yada yada.
Later that week, the class has a lab session. Based on the standard physics 101 material, they calculate that a certain pendulum will have a period of approximately 3.6 seconds.
They then run the experiment: they set up the pendulum, draw it back to the appropriate starting position, and release. Result: the stand holding the pendulum tips over, and the whole thing falls on the floor. Stopwatch in hand, they watch the pendulum sit still on the floor, and time how often it returns to the same position. They conclude that the pendulum has a period of approximately 0.0 seconds.
Being avid LessWrong readers, the students reason: "This Newtonian mechanics theory predicted a period of approximately 3.6 seconds. Various factors we ignored (like e.g. friction) mean that we expect that estimate to be somewhat off, but the uncertainty is nowhere near large enough to predict a period of approximately 0.0 seconds. So this is a large Bayesian update against the Newtonian mechanics model. It is clearly flawed."
The physics professor replies: "No no, Newtonian mechanics still works just fine! We just didn't account for the possibility of the stand tipping over when predicting what would happen. If we go through the math again accounting for the geometry of the stand, we'll see that Newtonian mechanics predicts it will tip over…" (At this point the professor begins to draw a diagram on the board.)
The students intervene: "Hindsight! Look, we all used this 'Newtonian mechanics' theory, and we predicted a period of 3.6 seconds. We did not predict 0.0 seconds, in advance. You did not predict 0.0 seconds, in advance. Theory is supposed to be validated by advance predictions! We're not allowed to go back after-the-fact and revise the theory's supposed prediction. Else how would the theory ever be falsifiable?"
The physics professor replies: "But Newtonian mechanics has been verified by massive numbers of experiments over the years! It's enabled great works of engineering! And, while it does fail in some specific regimes, it consistently works on this kind of system - "
The students again intervene: "Apparently not. Unless you want to tell us that this pendulum on the floor is in fact moving back-and-forth with a period of approximately 3.6 seconds? That the weight of evidence accumulated by scientists and engineers over the years outweighs what we can clearly see with our own eyes, this pendulum sitting still on the floor?"
The physics professor replies: "No, of course not, but clearly we didn't correctly apply the theory to the system at hand-"
The students: "Could the long history of Newtonian mechanics 'consistently working' perhaps involve people rationalizing away cases like this pendulum here, after-the-fact? Deciding, whenever there's a surprising result, that they just didn't correctly apply the theory to the system at hand?"
At this point the physics professor is somewhat at a loss for words.
And now it is your turn! What would you say to the students, or to the professor?
Thanks for listening. To help us out with The Nonlinear Library or to learn more, please visit nonlinear.org
One day a physics professor presents the standard physics 101 material on gravity and Newtonian mechanics: g = 9.8 m/s^2, sled on a ramp, pendulum, yada yada.
Later that week, the class has a lab session. Based on the standard physics 101 material, they calculate that a certain pendulum will have a period of approximately 3.6 seconds.
They then run the experiment: they set up the pendulum, draw it back to the appropriate starting position, and release. Result: the stand holding the pendulum tips over, and the whole thing falls on the floor. Stopwatch in hand, they watch the pendulum sit still on the floor, and time how often it returns to the same position. They conclude that the pendulum has a period of approximately 0.0 seconds.
Being avid LessWrong readers, the students reason: "This Newtonian mechanics theory predicted a period of approximately 3.6 seconds. Various factors we ignored (like e.g. friction) mean that we expect that estimate to be somewhat off, but the uncertainty is nowhere near large enough to predict a period of approximately 0.0 seconds. So this is a large Bayesian update against the Newtonian mechanics model. It is clearly flawed."
The physics professor replies: "No no, Newtonian mechanics still works just fine! We just didn't account for the possibility of the stand tipping over when predicting what would happen. If we go through the math again accounting for the geometry of the stand, we'll see that Newtonian mechanics predicts it will tip over…" (At this point the professor begins to draw a diagram on the board.)
The students intervene: "Hindsight! Look, we all used this 'Newtonian mechanics' theory, and we predicted a period of 3.6 seconds. We did not predict 0.0 seconds, in advance. You did not predict 0.0 seconds, in advance. Theory is supposed to be validated by advance predictions! We're not allowed to go back after-the-fact and revise the theory's supposed prediction. Else how would the theory ever be falsifiable?"
The physics professor replies: "But Newtonian mechanics has been verified by massive numbers of experiments over the years! It's enabled great works of engineering! And, while it does fail in some specific regimes, it consistently works on this kind of system - "
The students again intervene: "Apparently not. Unless you want to tell us that this pendulum on the floor is in fact moving back-and-forth with a period of approximately 3.6 seconds? That the weight of evidence accumulated by scientists and engineers over the years outweighs what we can clearly see with our own eyes, this pendulum sitting still on the floor?"
The physics professor replies: "No, of course not, but clearly we didn't correctly apply the theory to the system at hand-"
The students: "Could the long history of Newtonian mechanics 'consistently working' perhaps involve people rationalizing away cases like this pendulum here, after-the-fact? Deciding, whenever there's a surprising result, that they just didn't correctly apply the theory to the system at hand?"
At this point the physics professor is somewhat at a loss for words.
And now it is your turn! What would you say to the students, or to the professor?
Thanks for listening. To help us out with The Nonlinear Library or to learn more, please visit nonlinear.org