Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

This is a question about probability. The Galton box (or quincunx) uses the physical process of shot moving down a pin-board, to demonstrate central limit theorem, eg:


So I am interested in events with converging probabilities (like a coin toss @ 1/2, or card-guessing @ 1/5) and have found this matrix from a paper by E.G. Boring (Boring, E. G. (1941). Statistical frequencies as dynamic equilibria. Psychological Review, 48(4), 279):


And have a stackoverflow question plotting a related graphic in R:


If we think of the heatmap as depicting the shape of a gradient, it seems to me that it is possible to imagine a physical board that contains the same gradient, such that shot put on it would follow the same path.

So my question is, is there an equivalent of the Galton-box, that would allow a physical demonstration of this (and similar) Boring matrices?

Update: I have found this graphic of a quincunx which reminds me very much of the heatmap: quincunx

share|cite|improve this question

migrated from Mar 5 '13 at 21:56

This question came from our site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.

More on a Galton box: – Qmechanic Mar 6 '13 at 1:36
up vote 1 down vote accepted

I am going to guess that it is not possible without an external means of biasing the "hitrate". What do I mean? Consider this galton board, where the pins are replaced by a switch at each junction:


In the Boring matrix pictured in the OP, the chance of going up (a hit) is 1/6. And the probability of getting a miss (going down) is 5/6. Thus the junction must favour going down more than going up. I can imagine it is possible to have a computerized switching board (but then that isn't very different from the R code that was used to get the heatmap).

Also I can imagine that you could use a gear system that allows through every 6th shot at the junctions. But that wouldn't make each run independent of every other, and thus would again be "cheating".

But I certainly cannot think of a comparable method of biasing the physical passage of a shot (or marble) down a board, that can limit hits and misses at the required pass rate (1/6).

Obviously I could be wrong and there is a physical way of doing this that is comparable to the Galton box.

Update: I am going to change my answer to add that I think that it is possible using something like this (source):


share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.