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

Feeding a controversy

An upsetting story has been posted and is making the rounds, in relation to a theoretical evolutionary biology preprint by Hill. I place a very high value on the right to freedom of speech and expression (though I don't believe money is equivalent to either), so I don't like hearing tales of suppression of ideas.

But just because somebody says it doesn't mean it is good science. Last autumn, I had an opportunity to review Hill's article, and found it sourly lacking as a piece of science. With careful neglect, bad science will languish and be forgotten, and that is what I hoped would happen in this case. But the thing has bubbled up again, and as a theoretical biologist, I want to go on the record about nonsensical social Darwinism to stand up for my field, for myself and maybe also for others.

Perhaps the simplest and most damning criticism of the model is that under very common theoretical assumptions, the exact-opposite conclusion would be reached. Hill claims that simple evolutionary dynamics lead to greater trait variation in one gender than another. In contrast with Hill's assumptions, it is generally accepted that a good simple model of evolution is that evolution evolves to maximize mean fitness. Fitness itself may take many forms, but is often modeled as a concave, monotone increasing function of phenotype. It then follows as a trivial consequence of Jensen's inequality that evolution will prefer mating with subpopulations of smaller random trait variation because that leads to higher mean fitness. We can imagine situations where the fitness function is convex instead of concave, but they are odd situations and you'd have to explain why the convexity flips. Such simple considerations are not addressed at all by the preprint, and thus, it is difficult to see how this can be considered a serious piece of scholarship.

As with most bad scholarship, the manuscript interweaves grains of truth with incomplete ideas and incorrect notions. For example, sexual dimorphism is relatively common in the animal kingdom. Examples include the fiddler crab claw and the lions mane. There are also examples of large stable variations within a sex, such as jack (small) and hooknose (large) morphs in male salmon. But there are a variety of explanations for these large stable variations besides the "variability hypothesis". Variability is well known to be a double-edged in evolution. Too much variability can lead to quasispecies collapse in tight fitness landscapes, while too little variability slows evolution and can make it impossible for species to adapt to changing environments.

Here are some other things that looked suspicious to me, before I decided not to waste more time on my critique.