Science Links

1. When the Revolution Came for Amy Cuddy (Susan Dominus in the NYT)

But since 2015, even as she continued to stride onstage and tell the audiences to face down their fears, Cuddy has been fighting her own anxieties, as fellow academics have subjected her research to exceptionally high levels of public scrutiny. She is far from alone in facing challenges to her work: Since 2011, a methodological reform movement has been rattling the field, raising the possibility that vast amounts of research, even entire subfields, might be unreliable. Up-and-coming social psychologists, armed with new statistical sophistication, picked up the cause of replications, openly questioning the work their colleagues conducted under a now-outdated set of assumptions. The culture in the field, once cordial and collaborative, became openly combative, as scientists adjusted to new norms of public critique while still struggling to adjust to new standards of evidence.

2. When correlations don't imply causation, but something far more screwy! (the Atlantic)
2a. John D. Cook follows up with "negative correlations" induced by success.

3. STEM resources for students from K-PhD, and beyond (PathwaysToScience)

Gauss and Ceres

Car Friedrich Gauss was an intellectual colossus, whose work informed or revolutionized broad and seemingly unrelated swathes of science and math. In computational science, his name is attached to numerous methods for solving equations, integrating functions, and describing probabilities.

Interestingly, perhaps two of his most enduring contributions - Gaussian elimination to solve systems of linear equations, and normal or Gaussian distribution are linked through the fascinating story of how Gauss determined the orbit of Ceres (great read!).

While there is plenty of geometry involved, this example illustrates how multiple observations of the asteroid by astronomers, lead to an over-determined system of equations. Assuming that these measurements were tainted by normal or Gaussian error, Gauss built the resulting "normal equations" and solved for the orbit.

When Ceres was lost to the glare of the sun, he was able to use these calculations to direct astronomers to the part of the sky where they should point their telescopes.

Pascal's Wager

I enjoyed this recent conversation between Julia Galef and Amanda Askell on the nuances of Pascal's wager. According to wikipedia:

Pascal argues that a rational person should live as though God exists and seek to believe in God. If God does actually exist, such a person will have only a finite loss (some pleasures, luxury, etc.), whereas they stand to receive infinite gains (as represented by eternity in Heaven) and avoid infinite losses (eternity in Hell).

I always thought this was something of a tongue-in-cheek argument because "of course" the argument fails the smell test. However, if we take it seriously, we find that it resists simple attempts at tearing it down. This blog post ("Common objections to Pascal's wager") outlines some of the rebuttals. It makes for interesting reading.

One of the things from the podcast that stuck with me was a comment about whether belief in climate change maps neatly onto Pascal's wager. Simplistically, let C be the claim that climate change is true, and ~C be the opposite claim. Let A denote action (taken to avert C), and ~A denote inaction (business as usual).

Then, we have the following four possibilities, A|C (action given climate change), A|~C, ~A|C, and ~A|~C.

A|C = mildly painful

An analogy might be something like an appendectomy. There is a problem (inflamed appendix or climate change), and appropriate corrective action is applied (surgical removal, CO2 reduction).

A|~C = mildly painful

An analogy would be unused insurance. You buy home insurance for a year, and nothing happens. You had to fork over premiums (which is mildly painful), but you accept that as reasonable risk against catastrophe.

~A|C = catastrophe

Piggybacking on the previous analogy, here your house is in flames and you realize you skimped on fire insurance. The external "shock" is bad (climate change or house catching fire), but your "penny-wise but pound-foolish" behavior made a bad situation much much worse.

~A|~C = mildly pleasurable

An analogy (which strikes close to home) might be skipping the annual dental checkup, and finding out nothing is wrong with your teeth. As someone once remarked to me, sometimes "pleasure is simply the absence of pain."

Note that the catastrophic outcome 3 (~A|C), with its "infinities", crowds out the others.

Hence, Pascal might argue that we should believe in both, God and climate change.

Introduce Concepts in Historical Order?

Let me confess: I have read very few scientific classics in the original.

I haven't read the Principia, the Origin of Species, or the Elements.

I had not even read Einstein's 1905 classic on Brownian motion, until a few years ago, even though half of my research is directly or indirectly animated by it.

Ever since I saw this amazing series on complex numbers, I have been wondering whether presenting the historical progression of ideas might be "better" than the standard textbook introduction. Here are some of my observations.

The historical approach (HA) is inherently interesting, because it is about ideas and the people behind them. Stories of humans exploring and pushing boundaries, regardless of domain, are fascinating. These stories often have imperfect people grappling with new ideas, getting confused by their implications, arguing back and forth, improving, and gradually perfecting them over centuries. This happened with classical mechanics, evolution, complex numbers, quantum mechanics, etc.

The standard approach (SA), on the other hand, steers away from messy pasts, leaps of intuition that came seemingly from nowhere, the entertaining bickering, and the trials and errors. It trims away the excess fat of distractions, consolidates different viewpoints, and presents a sanitized account of an idea. It is, without question, the quickest and cleanest way to learn a new concept. This is an extremely desirable feature in university courses, which have a mandate to "cover" a set of concepts, often in limited time.

Perhaps, a good practical compromise is to start with an example rooted in the historical approach to motivate the topic,  and transition to the standard textbook approach to teach the meat of the topic. It might be interesting to conclude once again with a historical perspective, perhaps mixed with a discussion of the current state of art and open questions.

LaTeX: Figure Captions

A minimal working example.