2024-02-11: Symbolic algebra and typing

2023-08-01: Population waves

2023-05-18: Math of telephone billing mystery

2023-05-05: Franklin and DNA More information…

2023-04-25: On angle and dimension

2023-02-20: On Leonardo da Vinci and Gravity

2022-04-29: Fabricating Evidence to catch Carmen Sandiego

2022-03-04: Probabilistic law of the excluded middle

2020-05-04: Archimedes and the sphere

2019-05-16: Glow worms return

2019-04-11: Original memetic sin

2019-01-31: The theory of weight

2018-11-06: Origins of telephone network theory

2018-10-24: Modern thought

2018-09-10: Feeding a controversy

2018-06-11: Glow worm distribution

2018-04-23: Outlawing risk

2017-08-22: A rebuttal on the beauty in applying math

2017-04-22: Free googles book library

2016-11-02: In search of Theodore von Karman

2016-09-25: Amath Timeline

2016-02-24: Math errors and risk reporting

2016-02-20: Apple VS FBI

2016-02-19: More Zika may be better than less

2016-02-17: Dependent Non-Commuting Random Variable Systems

2016-01-14: Life at the multifurcation

2015-09-28: AI ain't that smart

2015-06-24: Mathematical Epidemiology citation tree

2015-03-31: Too much STEM is bad

2015-03-24: Dawn of the CRISPR age

2015-02-12: A Comment on How Biased Dispersal can Preclude Competitive Exclusion

2015-02-09: Hamilton's selfish-herd paradox

2015-02-08: Risks and values of microparasite research

2014-11-10: Vaccine mandates and bioethics

2014-10-18: Ebola, travel, president

2014-10-17: Ebola comments

2014-10-12: Ebola numbers

2014-09-23: More stochastic than?

2014-08-17: Feynman's missing method for third-orders?

2014-07-31: CIA spies even on congress

2014-07-16: Rehm on vaccines

2014-06-21: Kurtosis, 4th order diffusion, and wave speed

2014-06-20: Random dispersal speeds invasions

2014-05-06: Preservation of information asymetry in Academia

2014-04-16: Dual numbers are really just calculus infinitessimals

2014-04-14: More on fairer markets

2014-03-18: It's a mad mad mad mad prisoner's dilemma

2014-03-05: Integration techniques: Fourier--Laplace Commutation

2014-02-25: Fiber-bundles for root-polishing in two dimensions

2014-02-17: Is life a simulation or a dream?

2014-01-30: PSU should be infosocialist

2014-01-12: The dark house of math

2014-01-11: Inconsistencies hinder pylab adoption

2013-12-24: Cuvier and the birth of extinction

2013-12-17: Risk Resonance

2013-12-15: The cult of the Levy flight

2013-12-09: 2013 Flu Shots at PSU

2013-12-02: Amazon sucker-punches 60 minutes

2013-11-26: Zombies are REAL, Dr. Tyson!

2013-11-22: Crying wolf over synthetic biology?

2013-11-21: Tilting Drake's Equation

2013-11-18: Why \(1^{\infty} eq 1\)

2013-11-15: Adobe leaks of PSU data + NSA success accounting

2013-11-14: 60 Minutes misreport on Benghazi

2013-11-11: Making fairer trading markets

2013-11-10: L'Hopital's Rule for Multidimensional Systems

2013-11-09: Using infinitessimals in vector calculus

2013-11-08: Functional Calculus

2013-11-03: Elementary mathematical theory of the health poverty trap

2013-11-02: Proof of the circle area formula using elementary methods

Glow worm distribution

I’ve been working on a book for a few years now. I’m always keeping an eye out for good examples and problems I can use as exercises. Often, this means finding a brief reference, then digging into the scientific literature to flesh out the material from its original source. Sometimes, everything parses, and I get a new good example. Other times, the process breaks down.

The other day, I found What does randomness look like, an article from 2012 picked up by WIRED. This article mentioned two things I hadn’t seen before. One was a reference to glow worms making non-random patterns on the roofs of caves.

This seems like a really cool example to show students, so I started digging for the original material. The author credits Steven Pinker’s book “The Better Angels of our Nature” as the source, but no peer reviewed scientific article or data. When I got the book, sure enough I found it on page 205. Sure enough, Pinker gave better references. The example actually comes from a story by Stephen Jay Gould, from the book “Bully for Brontosaurus”. Gould has long been an icon for science writing in my family, so that discovery made me feel warm and fuzzy. The story goes that Gould visited caves in New Zealand, and used evolutionary theory to deduce that the glow worm populations would evolve to be more equally spaced than random. It is a good story, but one that you’d want data to support. And there is the catch. The picture label credited to glow worms is actually not real data – it’s a simulation created by Nobelist Ed Purcell for Gould!

So, there’s the problem. As it seems to stand at the moment, Gould’s hypothesis was just that – a hypothesis. There might be confounding factors like the shape of the cave roof. We really need a careful analysis of real glow worm data to determine if he’s right or not.

I have not checkout out the text of Gould’s article to see if he provides greater detail and references. I have not found any independent support yet for the idea either, although I did find this article which appears to have real glow worm location data available for analysis. Unfortunately, it’s an old scanned version and the image quality might not be good enough to tease out the answer to our question of interest.


This blog post also has another issue with the story telling, as I read it. In contrasting the work of Poisson with that of his contemporary Quetelet, it says Poisson “argued that Quetelet was missing a model for his data.” This seems a problematic statement – I have not had time to read Poisson original work, but in Stigler’s discussion of these works (I’ve found Stigler very authoritative in other contexts), Poisson introduces and promptly abandons his distribution, and never so concisely identifies Quetelet’s shortcomings as missing a “model”. The concept of a model doesn’t really seemed to have leaked into statistics by this point in time.