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: Lessons On How To Get Things Right On The First Try, published by johnswentworth on June 19, 2023 on LessWrong.

This post is based on several true stories, from a workshop which John has run a few times over the past year.

John: Welcome to the Ball -> Cup workshop! Your task for today is simple: I’m going to roll this metal ball:

. down this hotwheels ramp:

. and off the edge. Your job is to tell me how far from the bottom of the ramp to place a cup on the floor, such that the ball lands in the cup.

Oh, and you only get one try.

General notes:

I won’t try to be tricky with this exercise.

You are welcome to make whatever measurements you want of the ball, ramp, etc.

You can even do partial runs, e.g. roll the ball down the ramp and stop it at the bottom, or throw the ball through the air.

But you only get one full end-to-end run, and anything too close to an end-to-end run is discouraged. After all, in the AI situation for which the exercise is a metaphor, we don’t know exactly when something might foom; we want elbow room.

That’s it! Good luck, and let me know when you’re ready to give it a shot.

[At this point readers may wish to stop and consider the problem themselves.]

Alison: Let’s get that ball in that cup. It looks like this is probably supposed to be a basic physics kind of problem.but there’s got to be some kind of twist or else why would he be having us do it? Maybe the ball is surprisingly light..or maybe the camera angle is misleading and we are supposed to think of something wacky like that??

The Unnoticed Observer: Muahahaha.

Alison: That seems.hard. I’ll just start with the basic physics thing and if I run out of time before I can consider the wacky stuff, so be it.

So I should probably split this problem into two parts. The part where the ball arcs through the air once off the table is pretty easy.

The Unnoticed: True in this case, but how would you notice if it were false? What evidence have you seen?

Alison: .but the trouble is getting the exact velocity. What information do I have? Well, I can ask whatever I want, so I should be able to get all the parameters I need for the standard equations. Let’s make a shopping list: I want the starting height of the ball on the ramp (from the table), the mass of the ball, the height of the ramp off the table from multiple points along it (to estimate the curvature,) uhhh. oh shit maybe the bendiness matters! That seems really tricky. I’ll look at that first. Hey, John, can you poke the ramp a bit to demonstrate how much it flexes?

John pokes at the ramp and the ramp bends.

Well it did flex, but. it can’t have that much of an effect.

The Unnoticed: False in this case. Such is the danger of guessing without checking.

Alison: Calculating the effect of the ramp’s bendiness seems unreasonably difficult and this workshop is only meant to take an hour or so, so let’s forget that.

The Unnoticed: I am reminded of a parable about a quarter and a streetlight.

Alison: On to curve estimation!

The Unnoticed: Why on earth is she estimating the ramp’s curve anyway?

Alison: .Well I don’t actually know how to do much better than the linear approximation I got from the direct measurements. I guess I can treat part of the ramp as linear and then the end part as part of a circle. That will probably be good enough. Ooh if I take a frame from the video, I can just directly measure what the radius circle with arc of best fit is! Okay now that I’ve got that. Well I guess it’s time to look up how to do these physics problems, guess I’m rustier than I thought. I’ll go do that now.

Arrrgh okay I didn’t need to do any of that curve stuff after all, I just needed to do some potential/kinetic energy calculations (ignoring friction and air resistance etc) and that’s it! I should have figured it wouldn’t be that hard, this is just a workshop ...