Mathematics | Chris Aldrich

A Short Essay on the Relationship of STEM and Racist Ideas

I’ve seen many tweets today with the hashtag #shutdownSTEM. Some of them included some people asking why such a thing would be necessary. What does STEM (science, technology, engineering, and mathematics) have to do with racism they ask?

I find myself seeing some immediate and excellent historical examples in Dr. Ibram X. Kendi‘s book Stamped from the Beginning. In chapter nine of the book he discusses the variety and flavors of racism espoused by Thomas Jefferson in his book Notes on the State of Virginia (1785), which would become the most consumed American nonfiction book until well into the mid-nineteenth century.

Shortly afterward Samuel Stanhope Smith countered portions of Jefferson’s racist ideas in the 1787 annual oration to the august American Philosophical Society. This annual lecture was already one of the most heralded scholarly lectures in America and was attended by the wealthy and elite leaders and thinkers in the country. The lecture would be published as the influential Essay on the Causes of Variety of Complexion and Figure in the Human Species.

While Smith used the lecture to attack the abhorrent racist idea of polygenesis, he did espouse a wide array of other racist tropes including assimilationist climate theory. Dr. Kendi specifically notes that he may have picked up this idea from James Bowdoin’s opening oration of the newly established American Academy of Arts and Sciences in Boston on May 4, 1780.

To quote Dr. Kendi:

Samuel Stanhope Smith joined those preeminent intellectuals in Boston’s American Academy of Arts and Sciences and Philadelphia’s American Philosophical Society in attacking polygenesists, in reviving climate theory in America. His scholarly defense of scripture was quickly printed in Philadelphia, in London, and in Lord Kames’s back-yard, Edinburgh. By the time he sat down in Princeton’s presidential chair in 1795, he had amassed an international scholarly reputation.

So in just a few pages Kendi lays out some serious evidence of the direct spread of a wide variety of racist ideas by not only by the academic elite, but the leaders of multiple influential universities and scientific and philosophical institutions in America. The reverberating echos of these wrongs are still haunting us today. They still need to be addressed and righted. We need to use our moral alembic and distill these racist ideas out of science in America.

Lest one wonder about the influence of Samuel Stanhope Smith’s essay, I’ll note that Noah Webster cited Smith directly in Webster’s 1828 Dictionary in the definition of philosophy. The citation was from Smith’s second edition of his Essay on the Causes of Variety of Complexion and Figure in the Human Species (1810). The quote as given: “True religion, and true philosophy must ultimately arrive at the same principle.”

We’re obviously still seeking both true religion and true philosophy.

While you’re thinking about #shutdownSTEM on June 10th and long thereafter, I recommend you spend some time sitting with the ideas that have been handed down to us and question them closely, for this is what science and philosophy are all about. If you find you can’t do that hard work–and it is hard, then perhaps read a bit of Dr. Kendi’s excellent and ardent text Stamped from the Beginning.

Watched Who cares about topology? (Inscribed rectangle problem) by 3Blue1Brown from YouTube

An unsolved conjecture, and a clever topological solution to a weaker version of the question.

No doubt many have already seen that Springer has released about 500 books for free during the COVID-19 pandemic. According to Springer, these textbooks will be available free of charge until at least the end of July.

A bit of Googling will reveal people who’ve already written some code to quickly download them all in bulk as well. I’m happy with doing things manually as there’s only a handful of the 8GB of textbooks I’m interested in.

Browsing through, I’ll note a few that look interesting and which foodies like my friend Jeremy Cherfas may enjoy. (Though I suspect he’s likely read them already, but just in case…)

Food Analysis, ed. S. Suzanne Nielsen
Food Analysis Laboratory Manual by S. Suzanne Nielsen
Brewing Science: A Multidisciplinary Approach by Michael Mosher and Kenneth Trantham
Food Fraud Prevention: Introduction, Implementation, and Management by John W. Spink

Bookmarked At the Interface of Algebra and Statistics by Tai-Danae Bradley (arXiv.org)

This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals recover classical marginal probabilities. In general, these reduced densities will have rank higher than one, and their eigenvalues and eigenvectors will contain extra information that encodes subsystem interactions governed by statistics. We decode this information, and show it is akin to conditional probability, and then investigate the extent to which the eigenvectors capture "concepts" inherent in the original joint distribution. The theory is then illustrated with an experiment that exploits these ideas. Turning to a more theoretical application, we also discuss a preliminary framework for modeling entailment and concept hierarchy in natural language, namely, by representing expressions in the language as densities. Finally, initial inspiration for this thesis comes from formal concept analysis, which finds many striking parallels with the linear algebra. The parallels are not coincidental, and a common blueprint is found in category theory. We close with an exposition on free (co)completions and how the free-forgetful adjunctions in which they arise strongly suggest that in certain categorical contexts, the "fixed points" of a morphism with its adjoint encode interesting information.