Markov chains are a hundred years and four days old, which brings to mind Using Markov chains to analyze Candy Land. As you may know, you can’t even lose in Candy Land on purpose! The results are entirely determined by the initial shuffle. Since it’s a game for children, this is a shame; I think that at least if you have really little kids, you want to be able to lose on purpose, or at least tilt the odds in their favor. Michael Mauboussin has argued that this is a sign that Candy Land is entirely a game of luck. Okay, Mauboussin didn’t talk about Candy Land specifically, but he argues in Untangling Skill and Luck that
There’s a simple and elegant test of whether there is skill in an activity: ask whether you can lose on purpose. If you can’t lose on purpose, or if it’s really hard, luck likely dominates that activity. If it’s easy to lose on purpose, skill is more important.
As far as I can tell, you can only lose in Candy Land by stacking the deck, which doesn’t really count – if I’m going to play games with my future children and I’m going to let them win, I don’t want to have to resort to stacking the deck. This is mostly because I’m not Persi Diaconis and so any stacking I did would be ruined by my shuffle.
Mauboussin has also argued (following Tom Tango, sabermetrician) that although a shortened season is good enough for the cream to rise to the top in the NBA (like last year), the same isn’t true in the NHL (like this year).
I’ve been a bit slow at posting lately – I moved, got sick, and so on – but here we go again.
Yunfan Tan posts some wonderful time-lapse pictures of plants dying, linking to a paper Allometric scaling of plant life history by Yúria Marbà, Carlos M. Duarte, and Susana Agustí which shows that “both population mortality and population birth rates scale as the −¼ power and plant lifespan as the ¼ power of plant mass across plant species spanning from the tiniest phototrophs to the largest trees. ”
The pictures are nice, but as Cosma Shalizi (blog post, slides from talk) and Michael Mitzenmacher have pointed out, it’s all too easy to think you have a power law when you really don’t.
A new dartboard is in use in the darts world championships currently being held, reports Alex Bellos at his Guardian blog. Because in darts one has to end on a double, parity becomes important – but previous dartboard designs had clusters of odd and even numbers. The design, by David Percy at Salford in the UK, tries to separate odds and evens in addition to separating large and small numbers as much previous work had done; you can read Percy’s Mathematics Today article.
I’m having trouble thinking of other games where such a drastic change to the field of play could be implemented. One possible example might be Scrabble. The dynamics of Scrabble and of its clone Words with Friends have always felt just a little different to me because WWF has a different arrangement of premium squares which make very high-scoring plays possible.
Peter Norvig, On Chomsky and the Two Cultures of Statistical Learning. Also, totally unrelated but by the same author: English Letter Frequency Counts: Mayzner Revisited or ETAOIN SRHLDCU.
In 1979, I. J. Good wrote a summary of A. M. Turing’s Statistical Work in World War II. Despite my interests I often forget about Turing’s statistical work; it’s not as well publicized as his work in logic and theoretical computer science, perhaps because it was classified. (Good says this too.)
John Baez has a series on “rolling circles and balls”: Part 1, Part 2, Part 3, Part 4.
From Geoff Nunberg at Language Log: Is “big data” plural?
Correlation between autism diagnosis and organic food sales.
Visionary Images: The Lost Fractals of Benoit Mandelbrot.
Erica Klarreich writes for the Simons Foundation on Privacy by the Numbers.
Edward Tufte, Are there bellwether electoral districts. (You know the heuristic, right? If the title of a paper is a question, the paper will argue that the answer to that question is no.)
David Auckly, Triangles, Rotation, a Theorem and the Jackpot, on uses (some overkill!) of the Atiyah-Singer Index Theorem.
Vince Knight brings us some analysis of the game shut the box.
Carl Bialik’s column and blog post this week describe a study by Kimmo Eriksson, who used to work in combinatorics and co-authored a little book on integer partitions with George Andrews and is now mostly working in quantitative social science.
The basic conclusion is that if you slip some math into the abstract of a paper, people with Master’s or doctoral degrees in social sciences or humanities training will be more impressed than by the same abstract without the math, but people with the same level of scientific training won’t.
Here’s the paper: Kimmo Eriksson, The nonsense math effect, Judgment and Decision Making, Vol. 7, No. 6., November 2012, pp. 746-749.
Sol LeWitt is a conceptual artist, mostly drawing and scultping very simple geometric forms. Check out a Google Image Search. A retrospective of his wall drawings is on view at Mass MoCA (the Massachusetts Museum of Contemporary Art, in North Adams in the state’s northwestern corner). Don’t rush, it’s on view until 2033.
I’m not going to comment – not being an art critic – but if your brain works like mine you will spend some time looking at these.