
Galton Board - bmaeser
https://en.wikipedia.org/wiki/Bean_machine
======
nonfamous
One of my Statistics professors made great use of one of these (he called it a
Quincunx) our my Six Sigma class. It was about management, and how reacting to
processes you can’t control just makes things worse.

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.)

------
apathy
I bought one of these to teach a one-shot class on experimental design and
statistics.

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.

~~~
kkylin
As others said, if you can post a link that would be really great. When I've
taught probability in years past, I always showed students Galton boards on
YouTube, but a real one that doesn't break and doesn't break the budget would
be much better.

~~~
gwern
You can just search Amazon. There's nothing special about a quincunx, they're
simple. Any search query on Amazon, whether 'Galton quincunx' or 'Galton bean
machine' or 'Galton board' will pull up a bunch, I just checked.

------
bacr
There was a log-normal version of the Galton board making the rounds last
month:

[https://stat.ethz.ch/~stahel/lognormal/bioscience.pdf](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.

------
carapace
One of my favorite photos in the world is of the large (wall-sized) Galton
board at the old Princeton Engineering Anomalies Research Lab. There are two
guys, visitors, sitting in front of it and they have just used "psychic
powers" to affect a run and the balls are ridiculously skewed to one side,
just ridiculously, obviously skewed.

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.)

~~~
misterprime
A picture is worth a thousand words. No chance you'd be able to share that
photo here, is there?

~~~
carapace
I managed to remember the book in which the photo is published: "The Second
Coming of Science: An Intimate Report on the New Science" by Brian O'Leary
1992

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".

[https://en.wikipedia.org/wiki/Brian_O'Leary](https://en.wikipedia.org/wiki/Brian_O'Leary)

------
eldavojohn
This was discussed in a really interesting way in the Pearl/MacKenzie book
"The Book of Why" which I heavily recommend for people interested in cause &
effect. Really opened my eyes to a lot of things I had been doing
statistically but never known formally what was going on.
[http://bayes.cs.ucla.edu/WHY/](http://bayes.cs.ucla.edu/WHY/)

------
mrich
I fondly remember when I wrote a Galton board simulation as a computer science
school project. It would show the ball falling down and simulate the coin flip
at each stage, summing up the number of balls that fell into each slot. The
hard thing was it had to run on a 80286. The final version had some nifty
background graphics and advanced drawing routines, written in Pascal and some
inline assembly ;)

------
mikorym
If you vary the size of the opening, am I correct that that just changes the
parameters on the curve?

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.

~~~
thaumasiotes
> if I am not mistaken then least squares was invented largely due to the
> central limit theorem by Gauss

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.

~~~
mtrimpe
[https://www.jessicayung.com/mse-as-maximum-
likelihood/](https://www.jessicayung.com/mse-as-maximum-likelihood/)

------
samch93
Recently a good friend gave me a small Galton board for my birthday and it
stands now on my desk. It is so cool to do a little "simulation" and see the
magic of the central limit theorem. Highly recommended as a gift for any
statistically interested person!

------
HeraldEmbar
Is it really 50% though since more than one ball is falling through at a time?
Wouldn't a steel ball hitting another steel ball affect it's possible path?

~~~
leni536
Notice how the drawn Gaussian doesn't follow the bottom row of binomial
coefficients of the Pascal's triangle[1]. The model that assumes that each
ball independently falls left or right exactly one unit is limited and doesn't
actually describe many real world Galton boards.

[1]
[https://upload.wikimedia.org/wikipedia/commons/d/d2/GaltonBo...](https://upload.wikimedia.org/wikipedia/commons/d/d2/GaltonBoard.png)

------
dekhn
I built several of these from scratch after realizing that pegboard is already
set up in the right pattern and dowel pins fit into peg holes perfectly.

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.

~~~
homonculus1
I forget where I first read about hopper theory but I was fascinated to
discover that so much analysis has been done on the dimensions of such a
simple device. It makes perfect sense in retrospect given all the industrial
and agricultural applications but it's one of those little corners of the
world where you would never guess the pains engineers go to understand and
optimize it.

------
dragontamer
This was my favorite "game" at Chuck E Cheese as a kid. I'm very sad that they
removed these old arcade booths from the modern stores.

------
naringas
interesting intro by Michael from Vsauce

[https://youtu.be/UCmPmkHqHXk](https://youtu.be/UCmPmkHqHXk)

------
chewxy
I saw an actual giant Galton board in the Museum of Maths in New York. It was
very satisfying

