He’d pick someone from the class, tell them he was going to check their performance (like they were a Sales manager), a run a ball through the Quincunx. If the ball landed on the left, that meant they’d underperform, and they got a tongue lashing. If it fell on the right, they got praise. People got angry about the senselessness of it all.
But that was the point. The lesson: if you mandate targets on something that is essentially random and can’t be controlled, you’re going to have a bad time. (And if you react to those random results by changing the process, results get even worse — but that was another class for another day.)
To say it served the purpose would be an understatement. We blew through the CLT and derivation of statistical power in 10 minutes, leaving the other 110 minutes for the students to present research papers. One of the best $35 I’ve ever spent (don’t have the Amazon link handy but there are some great versions there). Highly recommended if you teach.
https://stat.ethz.ch/~stahel/lognormal/bioscience.pdf
It really clarified where a log-normal distribution comes from: the consequence of switching a sum of random variables for a product.
I like the photo because it's a bifurcation point for the viewer: there are two options to resolve what you're seeing:
1. It's fake.
2. It's not fake and "there's something there".
The whole PEAR Lab itself suffers from the same ambiguity: they got consistent positive results, but never so positive that skeptics could be decisively satisfied. (Not including one-off things like the photo of the visiting guys who did produce a dramatic undeniable effect.)
My copy is in storage so I can't post a scan. IIRC the visitors are O'Leary and his son.
It turns out he has a wikipedia entry:
> Brian Todd O'Leary (January 27, 1940 – July 28, 2011)[1] was an American scientist, author, and former NASA astronaut. He was part of NASA Astronaut Group 6, a group of scientist-astronauts chosen with the intention of training for the Apollo Applications Program.
> A remote viewing experience in 1979 and a near-death experience in 1982 initiated O'Leary's departure from orthodox science. After Princeton, O'Leary worked Science Applications International Corporation. He refused to work on military space applications, for which reason he lost his position there in 1987. Beginning in 1987, O'Leary increasingly explored unorthodox ideas, particularly the relationship between consciousness and science, and became widely known for his writings on "the frontiers of science, space, energy and culture".
I've known about the central limit theorem for a long time and was probably taught about it in first year, but I have never managed to sit down and understand how to prove it properly. One side effect of the theorem should be to explain least squares—if I am not mistaken then least squares was invented largely due to the central limit theorem by Gauss.
We can always do least cubes, but that does not provide us (usually) with better results.
I'm not really speaking from expertise here, but I thought least-squares error measurement was based on the fact that the metric is easy to minimize, because taking the derivative of x^2 is easy, whereas taking the derivative of |x| is complicated.
Least cubes doesn't really work conceptually, as it would imply that if an outlier above the fitted curve is bad, then an outlier below the fitted curve is good. That's not what you want.
EDIT: I am a bit suspicious though, since the definition of variance implicitly uses least squares. Maybe someone else can explain this better, but my expectation is that variance and the reason why it also uses squares (and not something else) should follow from some set of first principles.
[1] https://upload.wikimedia.org/wikipedia/commons/d/d2/GaltonBo...
+ The additional perturbations make the situation more random, rather than entirely based on the inconsistencies of the board design.
I demo'd it at a STEM fair and everybody has a great time. It makes a ton of noise and a great visual demo. I even ended up learning a bunch about hopper theory because I had to 3d print a hopper to feed it and it kept jamming.
