Jekyll2026-03-27T14:39:17+00:00http://bcmullins.github.io/feed.xmlBrett MullinsResearcher - Data ScientistNew Paper - Fast Private Adaptive Query Answering for Large Data Domains2026-03-25T00:00:00+00:002026-03-25T00:00:00+00:00http://bcmullins.github.io/fast-private-adaptive-queriesI have a new paper out with my colleagues from UMass Amherst and Penn State: Fast Private Adaptive Query Answering for Large Data Domains. Marginals are statistics that capture low-dimensional structure and correlations among sets of attributes in a dataset and are an important building block for differentially private algorithms. In this paper, we focus on answering large workloads of marginals for discrete tabular datasets over large data domains (i.e., many attributes), which is a computational bottleneck for state-of-the-art query answering and synthetic data mechanisms such as AIM. We introduce a new query answering mechanism called AIM+GReM that integrates our GReM-MLE (Gaussian Residual-to-Marginals) reconstruction method with AIM, which yields improved scalability and competitive error on large datasets.
Abstract:
Privately releasing marginals of a tabular dataset is a foundational problem in differential privacy. However, state-of-the-art mechanisms suffer from a computational bottleneck when marginal estimates are reconstructed from noisy measurements. Recently, residual queries were introduced and shown to lead to highly efficient reconstruction in the batch query answering setting. We introduce new techniques to integrate residual queries into state-of-the-art adaptive mechanisms such as AIM. Our contributions include a novel conceptual framework for residual queries using multi-dimensional arrays, lazy updating strategies, and adaptive optimization of the per-round privacy budget allocation. Together these contributions reduce error, improve speed, and simplify residual query operations. We integrate these innovations into a new mechanism (AIM+GReM), which improves AIM by using fast residual-based reconstruction instead of a graphical model approach. Our mechanism is orders of magnitude faster than the original framework and demonstrates competitive error and greatly improved scalability.
Die Fabrik von Loewe & Co (1926) by Gustav Wunderwald]]>New Talk - Measuring Income Mobility under Differential Privacy2026-02-13T00:00:00+00:002026-02-13T00:00:00+00:00http://bcmullins.github.io/private-income-mobility-talkI recently gave a talk at the Privacy and Public Policy Conference on measuring income mobility under differential privacy. This is joint work with Miguel Fuentes that combines techniques from differentially private query answering with methods for measuring mobility in economics. I’ve had this project idea on the backburner for a while, and it was great to finally work on it and share it with the community. Slides for the talk are available below. This project is still a work in progress!
]]>Interesting Articles I’ve Read in 20252026-01-02T00:00:00+00:002026-01-02T00:00:00+00:00http://bcmullins.github.io/interesting-articles-2025Below are some interesting articles I’ve read in 2025. They fall into a few categories: the mathematics of data privacy, popular mathematics, politics, and nineteenth century philosophy. For data privacy, we look at how technical details may be hindering adoption of differential privacy as well as scaling laws for differentially private language models. Next, we look at excellent popular math articles introducing the Collatz conjecture and the Busy Beaver numbers. In politics, we explore paranoid eighteenth century political rhetoric as well as John Maynard Keynes’ reflections on the Liberal party after a disastrous election in 1924. Finally, we look at two philosophical movements in mid-nineteenth century America and an 1875 article on the relation between the verifiability and discoverability of truths.
If you have some thoughts on my list or would like to share yours, send me an email at brettcmullins(at)gmail.com. Enjoy the list!
Setting $\epsilon$ is not the Issue in Differential Privacy
When one hears about a deployment of differential privacy, the usual followup question is “under which privacy budget?” The privacy budget $\epsilon$ refers to the parameter in differential privacy that quantifies how much information from one’s dataset is leaked in the worst case. A smaller $\epsilon$ means stronger privacy guarantees, while a larger $\epsilon$ allows for more accurate results but weaker privacy protection. The early literature on differential privacy often suggested values for $\epsilon$ between 0.01 and 1. However, in practice, many deployments of differential privacy have used much larger values, sometimes exceeding 10 or even 100. In empirical DP research, we often seek to design mechanisms that work well for both large and small privacy budgets and often evaluate them on a grid of values between $\epsilon = 0.01$ and $\epsilon = 100$.
The choice of $\epsilon$ is often viewed as a critical decision in deploying differential privacy; however, reasoning about the privacy loss is difficult, especially for non-technical policymakers and business partners. Cyffers argues that focusing too heavily on the choice of $\epsilon$ can unfairly hinder the adoption of differential privacy. Instead, she contends that this difficulty is inherent to any rigorous privacy risk assessment and that DP simply makes these trade-offs explicit. Moreover, this focus may lead decisionmakers to adopt less rigorous privacy-preserving techniques that are easier to understand but offer weaker (or no) privacy protection other than security by obscurity.
The Dangerous Problem: the century-long struggle to prove the Collatz conjecture
Consider a sequence of natural numbers generated by the following rules: starting with a natural number, if the number is even, divide by two; if the number is odd then multiply by three and add one. Rinse and repeat. An interesting property is that all known cases eventually yield a repeating cycle of $4, 2, 1$. The Collatz conjecture, introduced by Lothar Collatz in 1937, is that this property holds for all natural numbers.
We may find it comforting that the conjecture holds for the first several quintillion numbers (checked using solvers). However, it is possible that the first counterexample is quite large. For example, the Pólya conjecture held up through an exceedingly large number of cases. This problem has an allure to it emanating from its simplicity of presentation but evasion of any solution. Kloc concludes by intimating that this and other such unresolved number theoretic problems are possibly independent of ZFC (the standard axioms of set theory).
This short article is an excellent example of math communication (and in Harper’s of all places)! The writing is engaging and easy to follow yet bursting with context and excitement. In just two pages, Kloc explains the problem, its appeal and resistance to solution, and prospects for solving it. This sort of excitement and energy always reminds me of Language, Truth and Logic by A. J. Ayer, which I read in undergrad and was drawn to like a magnet.
Philosophy of the people: How prairie philosophy democratized thought in 19th-century America
This article describes two midwest philosophic schools in the mid-nineteenth century: the St. Louis Hegelians and the Illinois Platonists.
The St. Louis Hegelians were started by the German immigrant Henry Clay Brokmeyer, who was interested in studying and disseminating the ideas in Hegel’s Science of Logic. William Torrey Harris was a St. Louis teacher who joined Brokmeyer’s circle. Harris served as the editor of their Journal of Speculative Philosophy, the first American philosophy journal, founded in 1867. Harris would later become United States Commissioner of Education and instrumental in modeling American education after the German Bildung model, e.g., by introducing Kindergarten in public education.
In the middle of the nineteenth century, Jacksonville, Illinois was a hotbed for intellectuals, including “literary clubs, feminist and antislavery groups” as well as the newly founded Illinois College. One such group was led by Hiram Kinnaird Jones and focused on the study of Plato, Greek philosophy, and the classics. Similar reading groups quickly spread to neighboring towns. By the final decade of the century, Jones’ club, now called the American Akademe, operated three journals.
Keegin offers these groups as examples when thinking about how philosophy may be practiced in the future. As Philosophy increasingly finds itself on the chopping block at universities, it’s possible that there will be far fewer professional philosophers in the near future. Keegin notes that the current university organization has only existed since the end of the Second World War, so there’s no reason to think it will continue in the current form forever.
Scaling Laws for Differentially Private Language Models
Neural scaling laws are empirical regularities with neural network architectures that describe the relationship between model parameters and model utility. The usual citation here is Kaplan et al. (2020), which finds that model utility depends strongly with a power law relationship on each of dataset size, number of model parameters, and compute budget. These laws can guide model training by suggesting which knobs to turn and are an excellent example of a stylized fact in computer science.
This paper studies how scaling laws change once privacy is introduced to the equation. In particular, the authors compare how compute budget (a combination of batch size, number of model parameters, and number of epochs), data budget (number of observations), and privacy budget affect model utility. To this end, they fit a model to predict validation loss as a proxy for model utility by training several BERT models on a grid of parameter settings and fitting a linear interpolation model to the parameter space. Using this model, they look at what happens when we turn knobs and find that some scaling laws look quite different when privacy is added. For example, for a fixed compute budget, the optimal private model is a few orders of magnitude times smaller than the optimal non-private model. Using these scaling laws as a guide, they trained and released VaultGemma, an open language model with 1.3 billion parameters fully satisfying differential privacy.
Conspiracies in American political rhetoric are not a recent phenomenon, e.g., the Illuminati scare in the late eighteenth century. The Illuminati originated as a small Enlightenment society in Bavaria in 1776 and, a decade later, was formally quashed by the conservative Catholics. Approaching the turn of the century, the Illuminati became a hidden force of lore upending society and the cause, e.g., of the age of revolutions. In the late 1790s, various conservative preachers, including Timothy Dwight, the President of Yale, used the Illuminati to rail against the recent wave of French and Irish immigrants as well as the campaign of future president Thomas Jefferson. This fervor died down in 1799, however.
As with the European witch hunts, in both the Illuminati panic and its later echoes, the real threat came from the counterconspiracy rather than from any conspiracy itself. Imagining themselves at risk of dark powers, Federalist preachers and the press organised in opposition to those powers. The immediate result was a threat not just to those it targeted but to free speech. While this threat passed, the moment left scars that have not faded as readily. As one of the earliest incidents in America’s long history of political invocations of the demonic, the Illuminati scare warns that the danger of demonology is not the demon, but the demonologist who imagines demons to be fought.
Consider a game where two players quickly write down the largest number they can. One may write a number with lots of digits or more compactly using exponentiation. Writing even more compactly, we have the Ackermann function which, given input $n$, applies an order $n$ operation $n$ times. Then $f(1) = 1$, $f(2) = 2+2 = 4$, $f(3) = 3^3 = 27$, $f(4) = 4^{4^{4^4}}$, etc. The order 4 operation is called tetration and applies exponentiation to the fourth power four times. From four onward, this function grows extremely fast. It’s the standard example of a function that’s recursive but not primitive recursive (it grows more quickly than any primitive recursive function).
Aaronson now introduces the Busy Beaver function. The $n$-th Busy Beaver number $BB(n)$ is the maximum number of steps that a Turing machine with $n$ states that halts takes before halting. Note that this is the maximum over all Turing machines with a given number of states that compute a function. Unsurprisingly, $BB$ grows very quickly. Since the Ackermann function is computable, the Busy Beaver function is strictly larger (at least asymptotically). At the time of writing, only up to the fourth Busy Beaver number was known; however, it has since been shown that $BB(5) = 47176870$.
Credit: Kristina Armitage and Nico Roper, Quanta Magazine
It’s important to note that the Busy Beaver function is not computable. Suppose $BB$ was computable. Consider an arbitrary Turing machine $M$ with $n$ states. Then, for any input, we can determine if $M$ will halt by observing that it either has halted or has run for at least $BB(n)$ steps. But the Halting Problem is undecidable! Is it possible to go bigger than the Busy Beaver numbers? Not in the standard model of computation. Hypercomputation refers to problems belonging to point classes of the arithmetic hierarchy beyond $\Delta_1$. These point classes are closed downward under inclusion, so “hyper” Busy Beaver numbers for higher point classes are strictly larger than the Busy Beaver numbers for recursive sets. But, in general, these “hyper” Busy Beaver numbers require a worked out account of hypercomputation to be well-defined.
This is an excellent blog post that introduces the reader to a breadth of ideas while having a lot of heft. I aspire for my writing to approximate this!
Can Truths be Apprehended Which Could Not Have Been Discovered?
Imagine one obtains an idea in some way like from an apple falling on one’s head. Supposing the proposition expressing this idea is true, Greg asks if we could have discovered the proposition through human faculties and empirical evidence irrespective of its content. For propositions that we can verify, he answers in the positive, since the cognitive tools used to verify the proposition are the same used to arrive at it, i.e., verifiability implies discoverability. His evidence for this is a bit shaky so far, but Greg points out that this explains the futility of attempting to verify religious, spooky, or supernatural propositions using rational or empirical methods. Since these ideas are not discoverable by humans - being outside the scope of our cognitive architecture - they are not verifiable.
I thought that Gödel sentences present a counterexample to Greg’s claim, at least within the scope of formal theories, which I wrote about as part of my look back at research from 1875. Gödel’s first incompleteness theorem states that any theory sufficiently strong enough to model arithmetic contains a true sentence that’s not provable, called a Gödel sentence for the theory. The Gödel sentence is verifiable by its construction; however, it’s not provable, i.e., discoverable, from below. A reader noted that Gödel sentences are consistent with Greg’s claim, since a Gödel sentence is only verifiable from a meta-theoretic perspective, i.e., from outside the theory.
The 1924 UK General Election saw a crushing defeat for the Liberal party, who lost 118 of its 158 seats in the House of Commons. This election split the electorate between Labour and Conservatives, a situation that has persisted (mostly) ever since. Foreseeing this, Keynes asks to which of the two parties he should switch his allegiance. On one side, he finds the Conservatives unpalatable whose hard-core is focused on preserving their accumulated power, status, and wealth, even at the expense of new ideas that would benefit everyone. On the other, he calls the hard-core of Labour “the Party of Catastrophe”, who only see the possibility of progress through tearing down existing institutions, even at the expense of new ideas that would benefit everyone.
Keynes sees room for a third party focused on addressing ever-changing economic issues through institutions, which are somewhat insulated from politics. This new Liberal party would need to shed the baggage of its predecessor, which remains mired in nineteenth century policy debates, to focus on economic issues currently facing the voting public, including the increasing role of women in the economy. Rather than forming a new coalition from the ashes of the Liberal party, both left and right parties in the West throughout the twentieth century adopted aspects of Keynes’ technocratic view. This article is prescient today as many Western democracies face similar issues of political polarization and disaffected voters. I read this article as part of my look back at research from 1925.
]]>An Utterly Incomplete Look at Research from 19252025-12-31T00:00:00+00:002025-12-31T00:00:00+00:00http://bcmullins.github.io/research-from-1925Seven years removed from the armistice, 1925 finds the Western intellectual world grappling with reconstruction, not merely of borders and economies but of the conceptual foundations underlying science and the social order. The selections below reflect this theme of rebuilding. Economists theorize about institutional frameworks and the distinction between productive investment and mere speculation. Philosophers return to perennial questions about universals and common sense with renewed rigor. Statisticians formalize the inferential machinery that would come to dominate empirical research.
The Bootleggers (1925) by Edward Hopper
Across several pieces runs a persistent question about international order: which arrangements are most beneficial for the future? Many of these books and articles are not merely retrospective analyses but forward-looking proposals: Root arguing that international institutions represent steps toward lasting peace; Flexner articulating a vision for the modern research university; Pirenne theorizing that the large networks of trade increase social complexity and material prosperity. There is a sense throughout of authors clearing ground and laying foundations for what comes next.
I most enjoyed Frank Ramsey’s Universals and the selections from The Atlantic: Speculation and Investment and A Modern University. While I only included two articles from The Atlantic, several were interesting and the magazine was a joy to read this year. A great example is Confessions of an Automobilist, an amusing take on the perils of buying and owning a car in the 1920s. It’s well worth digging through the archives for more!
I ran out of time to cover everything I wanted to this year. Two books in particular are worth mentioning. First is R. A. Fisher’s Statistical Methods for Research Workers, a highly influential practical guide for applied statistics; however, I cover a technical paper formalizing statistical notions from Fisher below. Second is Walter Lippmann’s The Phantom Public, which critiques the notion of an informed public capable of self-governance and offers interesting thoughts on social epistemology. If I’ve missed anything interesting from 1925 that you enjoy, shoot an email my way at brettcmullins(at)gmail.com.
The prevailing wisdom regarding financial markets in the early twentieth century is that bonds were investments for the prudent, while stocks were speculation for the gambler. In his book Common Stocks as Long Term Investments (1924), Smith compares stock and bond performance for various 20-year periods over the past century and finds that diversified equity portfolios almost always outperformed high-grade bonds.
At the turn of the twentieth century, stock portfolios started outperforming bonds
This article attacks the distinction between speculation and investment by viewing various financial instruments as different flavors of the same dessert. Investing in a single stock exposes one to idiosyncratic risk that a firm will fail. This can be mitigated by investing in a basket of diverse stocks, where the idiosyncratic risks average out. Bonds, often thought to be the paragon of safety, are exposed to the risk of rising prices with respect to a given currency. While forwards and futures are viewed with suspicion as speculative instruments, they can be used to reduce one’s overall risk level through hedging.
Smith concludes that an investment should be defined by its ability to protect purchasing power and provide a real return, rather than just the type of security. John Maynard Keynes reviewed Smith’s book favorably in The Nation and Athenaeum. This line of work contributed to fueling the 1920s bull market by legitimizing holding common stock.
Law and economics are often viewed as two related but distinct approaches to thinking about aspects of human behavior. While law codifies tried-and-true practices for contracts and other dealings, economics is seen as an abstract science of efficiency. This narrow view of economics, however, trims the field of most of its content, which is situated within various systems of legal and social rules. Commons argues that both law and economics are in the business of codifying good practices and are intertwined insofar as economic innovations influence the law, while legal innovations shift market dynamics.
John R. Commons (1862-1945)
This paper is a concise statement of a line of thought in Commons’ Legal Foundations of Capitalism (1924), which makes a case for an institutional approach to economics. On this view, one cannot understand the economy without understanding the legal working rules that define and shape all market activity at a given time. This contrasts markedly with the law and economics approach developed at the University of Chicago in the 1960s. Rather than using the law to understand the economy, Coase, Posner, and friends use economic principles (like efficiency, utility maximization, and price theory) to explain and evaluate legal rules as a system of incentives designed to achieve economic efficiency.
The Trend of Economics, as seen by Some American Economists
The Trend of Economics (1924) is a collection of essays from a (mostly) new generation of economists seeking to reorient the field along empirical and institutional grounds and free it from the perceived metaphysical baggage of the past. Young views the overall tone as particularly arrogant and the task as premature in seeking to replace the methods and foundations of economics. He reviews the articles in the volume arranged by the strength of their call for change, which ranges widely from Frank Knight’s contention that economics can only be successful as part-science, part-art to Wesley Mitchell’s burn-it-all-down and rebuild along institutional lines.
Mitchell would continue work on business cycles with his 1927 survey
While Young provides insightful commentary, we disagree on several articles. In particular, Young calls William E. Weld’s contribution “unsatisfactory” and not meriting “extended discussion”. However, I found this article refreshing due to Weld’s insistence that causal reasoning ought to become the primary method for the economist as reliable information becomes increasingly available. Young reserves most of his frustration for Wesley Mitchell, whom he regards as having done excellent work on business cycles but threw it all away in favor of Thorstein Veblen’s institutional approach.
This paper takes aim at one of the oldest distinctions in philosophy: that between universals and particulars. This is the distinction between the idea of wisdom and Socrates, i.e., between the property and the thing that satisfies it. On the traditional view, going back to Aristotle and revived by Bertrand Russell, this distinction is fundamental to the structure of reality. Ramsey thinks it spurious, or at least far less fundamental than philosophers have supposed.
Ramsey on a hike, ca. 1925
Ramsey takes a fresh look at subject-predicate propositions such as “Socrates is wise”. The traditional view takes Socrates as the subject (a particular) and wisdom as the predicate (a universal). The asymmetry seems baked into the grammar. But Ramsey observes that we can just as easily write “Wisdom is a characteristic of Socrates,” reversing the apparent logical roles. If the distinction between universal and particular were genuinely metaphysical, we shouldn’t be able to reverse position of terms without changing the meaning. More precisely, Ramsey argues that atomic facts like Socrates being wise can be analyzed with either term as the subject. The fact itself is symmetric; only our notation introduces asymmetry. Philosophers have mistaken a feature of language for a feature of reality.
The paper concludes that the whole framework of subjects and predicates, particulars and universals, has led philosophers astray. But the upshot is not that we need a better logical notation to capture the true structure of facts. Rather, Ramsey argues that we cannot know the forms of atomic propositions at all. This is a more radical conclusion than it might first appear: it cuts against the central ambition of Russell’s logical atomism, which sought to reveal the hidden structure of reality beneath the misleading surface of ordinary language.
During the early twentieth century, British philosophy was heavily under the influence of the idealism of F. H. Bradley and J. M. E. McTaggart, though the two would pass away in 1924 and 1925, respectively. These philosophers argued for an understanding of reality where time, space, and individual objects are ultimately unreal or contradictory. In this article, G. E. Moore starts from common-sense propositions that we all (supposedly) know to be true, e.g., asserting “here is a hand” when looking at one’s hand, and uses them to shift the epistemic burden to idealist and other skeptical positions.
Moore’s strategy is to enumerate a series of common-sense propositions that he claims to know with absolute certainty. These include “There exists at present a living human body, which is my body,” “The earth had existed also for many years before my body was born,” and that other human beings have similar experiences and knowledge. From this epistemological foundation, we can infer metaphysical conclusions about the reality of time, space, and other minds.
Crucially, Moore thought that we can fully understand and know the truth of a statement like “here is a hand” in its ordinary sense, even if we cannot explain the complex metaphysical relationship between our sensory experiences and the physical object itself. He charges that skeptics confuse the two, assuming that because we cannot explain the metaphysics of perception, we do not know the object is there.
This article is the most notable essay from the second volume of Contemporary British Philosophy. While I covered the first volume in full last year, the second is largely more of the same, featuring a heavy dose of idealism, which was reflective of the established British philosophers of the time.
Writing during the frenzy of the Scopes Trial, H. G. Townsend argues that science operates by producing models that act as a “magic veil” between the human mind and the “terrifying chaos of experience,” reducing the complex world into “static forms and desiccated categories”. While this simplification is necessary for the comforts of modern life, which allows a physician, for instance, to diagnose pneumonia rather than confronting the unique agony of an individual illness, Townsend posits that this practice can become a source of obscurantism when the simplified map is mistaken for the territory.
The crux of the issue lies in the gap between scientific inquiry and its popular assimilation. While scientists (hopefully) recognize the scope and limitations of their methods, popular science may present these findings as absolute mirrors of reality. This disconnect leaves the layman in a no man’s land, reasonably mistaking models for fact. The situation creates false expectations about what science can deliver, eroding trust especially when new ideas challenge established beliefs. Townsend finds that this reckless mode of communication is particularly prevalent with new ideas in sociology and psychology, e.g., IQ, and may push the layman toward reactionary alternatives.
Fisher’s broader program sought to refound statistics on new conceptual ground. The nineteenth century approach, inherited from Laplace and developed by statisticians such as Karl Pearson, relied heavily on inverse probability and Bayesian reasoning. Fisher found this unsatisfying and obscured what he saw as the central problem: extracting information from data. His alternative built everything on the likelihood function, which captured what the data said about parameters without requiring prior beliefs. Sufficiency told you when a statistic captured all the information; efficiency told you how close an estimator came to the theoretical optimum; consistency ensured convergence to the truth.
In early 1924, Vladimir Lenin’s illness and subsequent death left the young Soviet Union with a power struggle between Trotsky and Stalin & friends. Both factions sought Lenin’s legacy as a source of legitimation. This book can be seen as part of Trotsky’s campaign to cement his relationship with Lenin and his contributions to the revolution.
The narrative begins in 1902 when Trotsky moves to London to write for the Russian Socialist newspaper Iskra, then managed by Lenin. We’re introduced to this book’s main quirk: characters oscillate between being called by their names and pseudonyms. In one sentence, it will be Vladimir Ilyich; the next it will be Lenin. This convention applies broadly with the activist Vera Zasulich going by three names at one point.
Lenin and Trotsky
Trotsky sketches a varied picture of Lenin. On the one hand, he recounts an amusing trip to the opera in Paris in which he and Lenin traded shoes. Earlier on, Lenin purchased new leather shoes but found the fit unbearable. Trotsky was initially enthused with the trade but endured a painful walk home afterward. On the other, in political and economic matters, Lenin is cold and calculating, justifying his thinking on longtermist grounds.
We move forward in time in midst of the Civil War in 1918. This part offers the most interesting and substantive discussion in the book over whether or not to sign the Treaty of Brest-Litovsk, a peace treaty with the Central Powers withdrawing the Soviet Union from the First World War. Would signing the treaty be abandoning the efforts of laborers elsewhere? To save face, should they wait to sign the treaty until Germany attacks? If so, how much of a sacrifice is reasonable? A whole city? A whole region?
The 1924 UK General Election saw a crushing defeat for the Liberal party, who lost 118 of its 158 seats in the House of Commons. This election split the electorate between Labor and Conservatives, a situation that has persisted (mostly) ever since. Foreseeing this, Keynes asks to which of the two parties he should switch his allegiance. On one side, he finds the Conservatives unpalatable whose hard-core is focused on preserving their accumulated power, status, and wealth, even at the expense of new ideas that would benefit everyone. On the other, he calls the hard-core of Labor “the Party of Catastrophe”, who only see the possibility of progress through tearing down existing institutions, even at the expense of new ideas that would benefit everyone.
Keynes sees room for a third party focused on addressing ever-changing economic issues through institutions, which are somewhat insulated from politics. This new Liberal party would need to shed the baggage of its predecessor, which remains mired in nineteenth century policy debates, to focus on economic issues currently facing the voting public, including the increasing role of women in the economy. Rather than forming a new coalition from the ashes of the Liberal party, both left and right parties in the West throughout the twentieth century adopted aspects of Keynes’ technocratic view. This article is prescient today as many Western democracies face similar issues of political polarization and disaffected voters.
Since the late nineteenth century and given increased impetus by the First World War, diplomats sought a venue for states to arbitrate disputes with the aim of preventing armed conflict. Root, a former US Senator and Secretary of State, posits that the success of such a venue as well as laws and institutions more generally is determined by public opinion. Though public opinion heavily swayed toward ideas of outlawing war, there was no consensus route to accomplish this goal.
The World Court at the Peace Palace in The Hague
Root argues that we should support efforts such as the recently established World Court, even if such an institution isn’t perfect or doesn’t satisfy all of one’s particular asks. Part of the aversion to an arbitration venue as a means to a popular end is simply fear of the unfamiliar. Beginning with a narrow scope, such an institution can prove its worth and expand its scope as needed, legitimating itself over time.
Miscellaneous
Medieval Cities: Their Origins and the Revival of Trade
Pirenne proposes that the shift from Antiquity to the Middle Ages was not caused by the internal decay of Rome or barbarian invasions but by an exogenous shock to trading networks. The Mediterranean functioned as a unified economic system until the Islamic conquests of the seventh and eighth centuries effectively partitioned the sea. The Carolingian era resulted from a land-locked Europe, where the absence of liquidity and long-distance exchange necessitated a retreat into the fragmented, subsistence-based hierarchy of feudalism.
The establishment of trading settlements outside of feudal walls was the locus of change toward a more complex economy. Since merchants required freedom of movement and property rights that feudal law could not support, their growing numbers eventually forced the landed aristocracy to grant charters of freedom. On this view, the medieval city is not an organic outgrowth of the agricultural village, but a distinct institutional innovation driven by the necessities of commerce.
This view that economic connectivity is the primary determinant of societal complexity is known as the Pirenne thesis. Pirenne considers the case of the Varangians (Scandinavians) in the eleventh century, who had a thriving trade network along the Dnieper and Volga rivers, linking the Baltic to Byzantine and Islamic markets. Various conflicts severed these river arteries and catalyzed the area’s regression into a feudal, agrarian state.
This book provides a concrete example of history through the lens of economic forces rather than a political or military narrative. Future work, however, would fail to substantiate Pirenne’s main ideas, particularly with regard to dating the fall in Mediterranean trade with Western Europe.
By the 1920s, American higher education looked remarkably like today’s multiversities and is a far cry from the wild west system of the nineteenth century. Publicly funded high schools offered an avenue to a four year college, after which one may continue on to a professional program or a research degree. This article argues that graduate education, particularly research institutions, ought to be unbundled from undergraduate colleges. To produce both knowledge and researchers, graduate study needs to be nimble and exploratory, allowing for quick pivots to new methods and ideas. Undergraduate education, however, is meant to build character and provide structure as much as it facilitates learning in the lecture hall.
IAS in the 1940s
Flexner views these goals as antithetical and holds that their commingling hinders both enterprises. He recommends unbundling the research institute. While this sounds drastic, their co-location is more historical contingency than not. Putting his words into action, Flexner cofounded the Institute for Advanced Study in 1930 and managed it for a decade, coinciding with the influx of eminent mathematicians and physicists from Europe including Albert Einstein, Kurt Gödel, and John von Neumann.
]]>Interesting Books I’ve Read in 20252025-12-08T00:00:00+00:002025-12-08T00:00:00+00:00http://bcmullins.github.io/interesting-books-2025Below are some interesting books I’ve read in 2025. This year’s list is topically wide-ranging: from the mathematics of data privacy and information theory to the history of economic thought, from early analytic philosophy and contemporary metaphilosophy to weird fiction, and even an early nineteenth-century meditation on the art of eating well. If you have some thoughts on my list or would like to share yours, send me an email at brettcmullins(at)gmail.com. Enjoy the list!
Differential privacy (DP) is a mathematical framework for quantifying privacy risk in data analysis. It provides formal guarantees that any individual’s data does not significantly affect the outcome of an analysis, which allows for protecting privacy while still doing useful things. Analyses include calculating means, medians, and other summary statistics, learning data distributions, and training machine learning models. We satisfy differential privacy by injecting randomness into the data analysis such as adding calibrated noise from a Gaussian distribution.
In 2026, differential privacy turns twenty. While there are a handful of monographs, edited volumes, and other sorts of introductions to differential privacy, a wide-interest invitation to this adolescent field was lacking. Garfinkel’s short book fills this void, being light enough for most to follow but with enough heft to say something interesting.
This book does several things well. It spends a good bit of time developing intuitive examples to describe the sort of privacy protection that DP offers. It provides a history (or mythology) for the field that I haven’t seen written elsewhere, beginning with work of Tore Dalenius on statistical disclosure limitation and Latanya Sweeney on reidentification attacks before the introduction of DP and culminating with the 2020 US Decennial Census, the largest (and most scrutinized) deployment of DP to date. Finally, there is lengthy but helpful discussion navigating through arguments for and against DP.
While there are some nits I could pick, this is an excellent introduction to differential privacy aimed at a wide audience and one that I’ve already recommended to students. This book is part of the Essential Knowledge series from MIT Press. Earlier this year, I also enjoyed their introduction to Cryptography (2024).
Jean Anthelme Brillat-Savarin was a French lawyer, politician, and noted gastronome. His part-memoir part-treatise, Physiologie du goût, is a prolegomenon of sorts to the science of gourmandism. One may be tempted to think that this study of food and culture is merely a guide to gluttony. Brillat-Savarin is careful to dispel such notions. The glutton mindlessly consumes to excess, while the gourmand appreciates and enjoys to satisfaction. Far from a handbook to hedonism, this analysis of the art of the gourmand encompasses gastronomy, physical and mental health, and social interaction.
The book is written in short sections loosely divided into themes, mixing technical discussions of the author’s theory of food chemistry with recipes and tales from his eventful life. The writing is often witty and the translation by Anne Drayton is a pleasure to read. I was hooked from the beginning by the list of aphorisms that preface the main text; the best of which reads:
Dessert without cheese is like a pretty woman with only one eye.
In the section on physical and mental health, Brillat-Savarin discusses the importance of diet in maintaining health and longevity. He makes a case for the benefits of a low-carb diet for losing excess weight, becoming one of its first proponents.
There’s an amusing mention of a correlational health outcomes study by Louis-René Villermé from the prior year. This study finds that “good cheer is far from being harmful to health, and that, all things being equal, gourmands live longer than other men.” Elaborating on the methods:
He compared the various classes of society in which good cheer is habitual with those which are poorly fed, covering the entire social scale. He also considered the various quarters of Paris with one another according to their wealth, for it is well known that wide divergencies exist in this respect.
The most interesting section, however, is the discussion of restaurants near the book’s conclusion. Restaurants in the modern sense were a relatively recent innovation, appearing in Paris in the latter half of the eighteenth century and quickly spreading throughout Europe and beyond during the French Empire’s warring efforts. I read this book as part of my project looking back at research from 100, 150, and 200 years ago.
After Adam Smith: A Century of Transformation in Politics and Political Economy
One way to mark the birth of political economy is the publication of Adam Smith’s The Wealth of Nations (1776). When you think of Smith, several ideas might come to mind: the invisible hand, laissez faire, pin factories and the division of labor, the perfectly competitive market, and the butcher, the baker, and the candlestick maker. Though these ideas are often attributed to Smith today, what he meant by them looked rather different in some cases. This book traces the evolution of Smith’s ideas and the path of political economy from their introduction to the close of classical period in the 1870s.
Today, the invisible hand is a metaphor for the market as a self-regulating system and expresses a fundamental principle in modern economics. Smith mentions an invisible hand only once in The Wealth of Nations and once in The Theory of Moral Sentiments (1759) in a sort of throw-away line. The modern incarnation of the idea only gained popularity in the early twentieth century.
In the 1790s, the Scottish philosopher Dugald Stewart reinterpreted Smith’s account of political economy along the lines of a liberal political program. In particular, Stewart argued that The Wealth of Nations “established a science whose laws dictated that in market economies, intervention was not only unnecessary but positively harmful to the wealth of the nation.” In doing so, Stewart deemphasized the theoretical contributions of the first two books to focus on political conclusions. Milgate and Stimson hypothesize that this is why no one seriously grappled with the theory of value until David Ricardo in the 1810s.
I found this book a challenging but rewarding read. Milgate and Stimson cover a broad range of material but manage to be engaging throughout. I found myself learning something interesting in nearly every section.
Philosophical Analysis: Its development between the two World Wars
During the second world war, a curious change quietly happened in British philosophy: the logical approach to language and metaphysics was supplanted by the ordinary language approach. This short book surveys the rise and fall of the logical approach and the many developments in-between. While Urmson is firmly rooted in the ordinary language tradition, he offers a clear and reasonable account of how and why the logical approach came to be.
Idealism dominated philosophical discourse in Britain throughout the late nineteenth and early twentieth centuries. Roughly, idealism views concepts and reality as an integrated whole, to be studied in a top-down way. The logical approach flips this by reducing concepts to aggregations of logically simple atomic facts.
This bottom-up approach built on work formalizing mathematics in a precise logical language such as the typed language of Russell and Whitehead’s Principia Mathematica (1910), the second edition of which appeared in 1925. On this view, atomic facts correspond to sense data, and concepts such as a red table and the present king of France are interpreted as expressing statements in a formal language such as first-order logic. Natural language, then, is an imprecise way of describing the world that can be improved using the tools of analysis.
This leaves several questions open such as how exactly do atomic sentences correspond to facts about the world. Wittgenstein answers that atomic sentences picture facts in the world, something akin to illustrating a particular feature of the world, from which they make sense. The upshot of this is that propositions not picturing facts are nonsense. This includes philosophical propositions, which Wittgenstein was well aware of, and has intrigued philosophers ever since.
Another approach is to eschew the connection between language and metaphysics and analyze language in a formal context such as scientific reasoning. This is the track taken by Rudolf Carnap and some members of the Vienna Circle, where the meaning of a proposition is determined by the atomic sentences that could verify it. This latter view suffered from self-defeating issues as well, since philosophical propositions could not be empirically verified.
Though I’m familiar with early analytic philosophy, I learned quite a bit from this book. It provides one of the most digestible accounts of Wittgenstein’s picture theory. Urmson’s style is engaging even if a bit terse. The book concludes by sketching the ordinary language approach, which takes a more expansive view of language and relegates analysis to one tool among many.
Tales of the Weird: An Uncanny Introduction
Published: 2023
Tales of the Weird is a book series from the British Library reprinting lesser known novels and themed short story collections from weird fiction, broadly construed. For instance, From the Depths and Other Strange Tales of the Sea collects together spooky nautical short stories from the late nineteenth and early twentieth centuries. The current collection is meant to pull from a variety of themes to introduce the reader to the many flavors of weird fiction.
My favorites are William Hope Hodgson’s “The Voice in the Night” (1907), H. P. Lovecraft’s “The Festival” (1925), and Mary Counselman’s “The Three Marked Pennies” (1934). Each of these three stories paints a vivid picture and really stuck in my mind.
Two complaints are worth noting. The biographical sketches at the beginning of each story are both too brief and frequently spoil crucial elements of the plot. The structure would be better served by putting these after the story. The least interesting of the bunch - Vernon Lee’s “Marsyas in Flanders” (1900) - appears first, due to the stories being in chronological order. I recommend any other order than this!
An Introduction to Information Theory: Symbols, Signals and Noise
Information theory is the mathematical study of communication and provides a framework for quantifying information transmission. It has applications all over the place from cryptography to machine learning to data privacy. This book is a highly-readable and wide-ranging introduction to the field. Pierce worked as an engineer at Bell Labs with Claude Shannon during the development of information theory in the mid-twentieth century.
The book begins with an excellent survey of information theory’s early years and provides a wealth of citations to interesting papers (enough to fill a backlog). The core chapters develop mathematical ideas such as source coding and channel coding in a semi-formal yet approachable way. The auxiliary chapters are more topical and lax, ranging from connections between entropy in communication (uncertainty in terms of bits) and entropy in physics (amount of free energy) to speculations on generative models for music composition.
This book feels both ahead of its time and quite dated. I would likely not recommend it as a first stab at information theory; check out David MacKay’s wonderful text instead. This book would be great for someone with some familiarity of these ideas who can appreciate Pierce’s historical anecdotes and speculations while reacquainting themselves with the fundamentals. For a taste, here’s Pierce on AI and thinking machines:
Will computers be able to think? This is a meaningless question unless we say what we mean by to think. Marvin Minsky, a free wheeling mathematician who is much interested in computers and complex machines, proposed the following fable. A man beats everyone else at chess. People say, “How clever, how intelligent, what a marvelous mind he has, what a superb thinker he is.” The man is asked, “How do you play so that you beat everyone?” He says, “I have a set of rules which I use in arriving at my next move.” People are indignant and say, “Why that isn’t thinking at all; it’s just mechanical.”
Minsky’s conclusion is that people tend to regard as thinking only such things as they don’t understand. I go even farther and say that people frequently regard as thinking almost any grammatical jumbling together of “important” words. At times, I’d settle for a useful, problem-solving type of “thinking,” even if it was mechanical. In any event, it seems likely that philosophers and humanists will manage to keep the definition of thinking perpetually applicable to human beings and a step ahead of anything a machine ever manages to do. If this makes them happy, it doesn’t offend me at all. I do think, however, that it is probably impossible to specify a meaning and explicitly defined goal which a man can attain and a computer cannot even including the “imitation game,” proposed by A. M. Turing, a British logician [sic].
A philosophical proposition is a statement regarding the fundamental nature of reality, knowledge, or values that cannot be decided empirically. Think of them as the armchair analog to scientific laws. Two examples in different domains are “murder is impermissible” and “the mind survives the body after death”.
How do we reason about philosophical propositions? With empirical statements, we have observation. In philosophy, however, we often rely on rational intuition. Yet, this is just one method among many that are used to form beliefs about philosophical propositions. Christian revelation or drug-induced mysticism, for instance, may yield radically different beliefs than rational intuition with the above examples.
How are we to decide between these (potentially) conflicting perspectives? This puts us in a pickle, since we cannot rely on rational intuition (or any of the other methods) without fear of circularity or an infinite regress. Hales rescues truth for philosophical propositions by relativizing truth to a perspective. He shows that the relativized notion of truth is consistent and makes it concrete by formalizing it in an S5 modal logic.
While his overall project is persuasive, it is not clear what this relativized notion of truth actually buys us. Much like this NDPR reviewer, I can see what truth relative to a perspective means for moral propositions but much less so for metaphysical propositions such as the mind surviving death. Presumably, the mind either survives or does not. The upshot of this project is that it does allow for legitimate disagreement on philosophical propositions while not giving in to a full-blown relativism.
I came across this book while browsing the philosophy section at the Book Mill in Montague, Mass. I recognized Hales name from his excellent blog and gave his book a shot. Who says a blog can’t drive readers to one’s academic work?!
]]>An Utterly Incomplete Look at Research from 18752025-09-07T00:00:00+00:002025-09-07T00:00:00+00:00http://bcmullins.github.io/research-from-1875The Fortnightly Review was a prominent British periodical in the 1870s, edited by John Morley, publishing articles on a wide range of topics including literature, philosophy, politics, and economics. A quick perusal of the selections below illustrates that the Fortnightly had an excellent year in 1875. Once I started digging in, I found more interesting articles than I had time to read, particularly in the first six issues (January to June). Not only do the topics heavily overlap with those covered in this project, but the articles are generally well-written and often thread the line between academic rigor and popular style. To a modern reader, this means that they are complex enough to have something interesting to say but accessible enough to figure out the context.
Claude Monet, Snow at Argenteuil (1875)
Looking more broadly, we can see two themes from this year’s selections. Several articles probe at the boundary where empirical science ends and metaphysics begins. John Tyndall argues that it is not outside of the scientist’s purview to discuss cosmological questions such as the origin of the universe. William Kingdon Clifford outlines the limits of applying scientific laws to predict both the distant past and remote future. W. R. Greg asks whether there are truths that cannot be discovered through human faculties.
In economics, there is a clear embrace of the subjective theory of value. William Stanley Jevons’ popular account of the institutions facilitating exchange presents the subjective theory of value as the theory of value. George Darwin reconciles John Elliott Cairnes’ cost-of-production theory of value with Jevons’ marginal utility theory. In an odd article, Henry Dunning Macleod argues that political economy is the science of exchange, best analyzed through the subjective theory of value.
This book bills itself as a prolegomenon to Walter Bagehot’s Lombard Street: A Description of the Money Market (1873), one of the first popular books to describe the banking system and liquidity crises; however, it’s much more than that. The first several chapters are a (rather speculative) anthropological look at the origin and nature of money and exchange. Next, we move to a history of coins and currency. Once commerce becomes sufficiently widespread, different forms of currency such as token and representative currencies as well as various bills and bonds are used alongside commodity money, e.g., gold coins, out of convenience. This raises the question of what money is and how liquid an asset must be to be considered money. Similar to what one may find in an introductory economics text today, Jevons notes that there are several notions of money depending on how liquid we want it to be (and we usually want it to be rather liquid).
A 19th-century clearing house in operation
The most interesting part - and the part most worth reading today - describes the banking system through simple examples and introduces the relatively recent innovation of clearing houses, venues for settling checks and other sorts of transactions between banks. While these institutions are depicted as chaotic as the New York Stock Exchange trading floor prior to the millennium, they greased the wheels of the financial system by providing structure and lessening the need to exchange physical currency among banks. Outside of some minor suggestions, Jevons leaves the questions of policy for Bagehot.
Bagehot responds to an idea for an improved standard of value near the conclusion of William Stanley Jevons’ Money and the Mechanism of Exchange (1875). A standard of value is a common unit for measuring the value of goods and services, usually in the form of currency. The conventional wisdom in the nineteenth century was that coined precious metals, often gold or silver, were the appropriate standard of value. Jevons argued that this leads to unnecessary economic volatility because changes in the value of the commodity backing a currency often necessitates price changes with cascading effects, bankrupting some and delivering a fortune to others. Gold, in particular, had been on a price rollercoaster over the prior two centuries.
Jevons’ suggests backing currency by a basket of goods rather than a few precious metals, a precursor to CPI or other price indices. If the goods composing the basket are sufficiently uncorrelated, then the resulting standard of value would be stable. Bagehot finds the idea wholly impractical. Eliminating a common conversion between currencies would impede international trade and particularly harm London since a large portion of international payments flow through the city. Since commodities regularly experience fluctuations in value, it would be difficult to calculate at any time how much the currency was worth, especially for specifying contracts or settling debts. Moreover, standards on the quantity of the basket goods would need to be defined and enforced.
This article seeks to introduce the socialist ideas of Karl Marx to a broader audience. In the 1870s, Marx was overshadowed by Ferdinand Lassalle, who was widely seen as the sole leader of German socialism, though Lassalle died in 1864. Marx’s ideas differed significantly from Lassalle’s. Marx argued that the movement from capitalism toward socialism transcended the state, while Lassalle emphasized the state’s central role in reform. MacDonell offers a critical sketch of Marx’s economic ideas as one of pessimism and protracted misery for the working class followed by extreme optimism for revolution and the future.
MacDonell sought to improve discourse around Marx’s ideas. English economists largely dismiss Marx’s work as “puerile” and based on unreasonable assumptions, while converts adhere to Marx’s teachings beyond all reason. MacDonell thought we shouldn’t throw out the observation that unfettered industry can worsen the lives of the working class along with Marx’s economic theories. This article is particularly timely given the founding of the Socialist Workers’ Party of Germany the same year. The party’s platform, the Gotha Program, sided with Lassalle’s ideas emphasizing the central role of the state, which Marx criticized in his Critique of the Gotha Programme, published later by Fredrick Engels in 1891. Socialism was a thorn in the side of the recently unified German empire; though, it was one concern among many.
John Elliott Cairnes is considered one of the last classical political economists and passed away in 1875 soon after this article was published. Darwin seeks to reconcile Cairnes’ understanding of exchange value based on relative costs of production, developed in Cairnes’ Some Leading Principles of Political Economy Newly Expounded (1874), with William Stanley Jevons’ marginal utility theory. Darwin provides a clear, intuitive statement of subjective utility and diminishing marginal utility through examples such as the diamond-water paradox.
An ink portrait of Cairnes from the Online Library of Liberty
Cairnes views exchange value between two commodities as proportional to the ratio of their total costs of production. Darwin observes that this follows as a consequence of Jevons’ system assuming perfect competition, i.e., where prices equal the cost of production. Jevons’ “equation of exchange” shows that the utility maximizing rate of exchange between two commodities - understood as the ratio of their marginal utilities and today called the marginal rate of substitution (MRS) - is equal to the ratio of their prices, a standard result in modern consumer theory.
The dominant conception of classical political economy in the 1870s was “the consumption, distribution, and value of wealth”. Macleod takes issue with this account arguing that past writers varied significantly on their understanding of all four technical terms. Some examples: François Quesnay, whom Macleod regards as the rightful founder of political economy, held that all wealth is agriculture. Adam Smith held that labor determined value in some places and that the market determined value in others. John Stuart Mill is portrayed as hopelessly confused about the meaning of terms.
Macleod prefers a definition he attributes to Richard Whately: “the science of exchange”. This account builds a scientific basis for economics alongside established sciences such as mechanics, the science of motion, and optics, the science of light. Macleod begins the article oddly by claiming that his earlier work started a revolution in economic thought, thereby implicitly equating himself with other revolutionary thinkers such as Newton. I first thought he was taking claim for the marginal revolution; however, Macleod does not view the marginal utility principle as significant in his history of economic thought. Perhaps, he was simply talking about the subjective theory of value instead.
Philosophy
The Scottish Philosophy: Biographical, Expository, and Critical from Hutcheson to Hamilton
The Scottish philosophy refers to an approach to philosophical problems developed in Scotland during the seventeenth and eighteenth centuries. This book is part-encyclopedia, part-narrative history of its development. McCosh advances the idea that the Scottish school is defined by its focus on human psychology, its use of inductive methods, and its connection with the Christian religion.
James McCosh (1811–1894)
Francis Hutcheson is the most important precursor to the story. Writing in the early eighteenth century, Hutcheson develops a moral theory based on the existence of a moral sense or faculty that guides one’s behavior. Next, we’re introduced to our first antagonist: David Hume. Hume argues that if our knowledge of the world is derived from sense experience, then it is not possible to justify general metaphysical principles such as cause and effect, which poses a serious skeptical challenge to empiricist views. Our first protagonist, Thomas Reid, replies that there are basic principles at work in human reasoning and belief formation that account for our knowledge of the world, a view now called common sense Realism. Much subsequent work sought to elucidate these principles of the mind inductively through introspection.
At the turn of the nineteenth century, the common sense school butted heads with the idealist approach developed by Immanuel Kant and others in Germany, our other antagonists. Idealism roughly holds that the metaphysical principles in question are built into how we perceive the world. Our story culminates in William Hamilton who combined ideas from Reid and Kant but was ultimately unsuccessful in McCosh’s estimation. He concludes by positing that metaphysics will have to rapidly integrate the results of the natural sciences to remain relevant and combat idealism. This was particularly relevant during a time of rapid scientific advance and the coming wave of idealism in Britain.
George Thompson, View of Nassau Hall, ca. 1860
While important to establishing the legacy of the Scottish school, I hesitate to recommend this book. The writing is dry in the first third, a bit better in the second, but eventually comes alive in the third. McCosh unfairly handles James Mill to the point of nearly calling him the devil incarnate. Despite being the president of the College of New Jersey (now Princeton University), McCosh barely touches on the Scottish philosophy in America outside of John Witherspoon. Moreover, on McCosh’s telling, everyone including the great skeptic David Hume apparently became a Christian on their death bed.
My copy - the 1966 Georg Olms Verlag printing - has quite the quirk: the font size is inconsistent throughout and can change dramatically between chapters. Roughly, chapter size is proportional to the importance of the subject. Longer chapters on, e.g., Thomas Reid or David Hume have a perfectly nice typesetting. Shorter entries, however, size the font to keep the discussion to just a page or two. In more than one case, this yields extremely small, borderline unreadable text!
Cairnes argues that Herbert Spencer’s account of social evolution is not empirically verified and is based on a flawed analogy between biological and social evolution. Spencer holds that societies evolve in a manner similar to species, with social structures developing from simple to complex forms, coining the phrase “survival of the fittest” to describe this process. In this view, societies spontaneously evolve new social structures to meet changing conditions, the moral of which is to let nature take its course.
Cairnes charges Spencer with running to consider the consequences of this theory before providing ample (or any) justification. Moreover, Spencer’s positivist social theory does not account the early Medieval period, i.e., the Dark Ages, where civilization declined. Cairnes claims that Spencer provides less historical evidence than the positivist Comte, whom was not held in high regard at the time.
Social evolution as a whole has greater theoretical than empirical challenges. There are major disanalogies between the evolution of societies and the evolution of species. In particular, the evolution of societies is the result of human intentions and actions, while the evolution of species is not. Spencer responds in a short comment claiming that Cairnes has mischaracterized his work and holds his preliminary comments in The Study of Sociology (1873) to too high of a standard.
Can Truths be Apprehended Which Could Not Have Been Discovered?
Imagine one obtains an idea or proposition in some way like from an apple falling on one’s head. Supposing the proposition is true, Greg asks if we could have discovered the proposition through human faculties and empirical evidence irrespective of its content. For propositions that we can verify, he answers in the positive, since the cognitive tools used to verify the proposition are the same used to arrive at it, i.e., verifiability implies discoverability. His evidence for this is a bit shaky so far, but Greg points out that this explains the futility of attempting to verify religious, spooky, or supernatural propositions using rational or empirical methods. Since these ideas are not discoverable by humans - being outside the scope of our cognitive architecture - they are not verifiable.
This is an interesting short paper, but is it right? Within the scope of mathematical logic, there’s a counterexample with Gödel’s first incompleteness theorem, which says that any theory sufficiently strong enough to model arithmetic contains a true sentence that’s not provable, called a Gödel sentence for the theory. The Gödel sentence is verifiable by its construction; however, it’s not provable from below.
Outlines Of Cosmic Philosophy (1874) is a broad exposition of evolutionary theory from John Fiske applied to social and philosophical quandaries. In this review, Pollock praises much of the book and its attack upon Comte and the positivists; however, he argues that it falls short with respect to metaphysics. Certain metaphysical entities are classed as “the unknowable”, which Pollock takes to be a holdover from Kant’s antinomies. This notion can also be viewed as an optimistic version of von Hartmann’s unconscious. One thing that’s apparent is that both Pollock and Fiske conflate the theories of social evolution from Herbert Spencer with natural selection regarding speciation. This book seems to be seeing how much mileage one can get out of the natural selection argument.
In the undergraduate calculus sequence, students first encounter integration through the Riemann integral, which calculates the area under a curve of a real-valued bounded function by approximating it with rectangles. In particular, you partition the domain into intervals of length at most $d$ and, for each interval, create a rectangle of width the length of the interval and height a value of the function on the interval. Summing up the areas of the rectangles approximates the area under the curve. If all goes well, as $d \rightarrow 0$, the sum of the areas of the rectangles converges to the desired value.
Example of Riemann Integration
Riemann showed that continuous functions are integrable and they remain integrable if you allow for a finite number of discontinuities. At the other end of the spectrum, consider the function that takes the value 1 on the rationals and 0 on the irrationals. This function is discontinuous everywhere and not integrable i.e. the rectangle approximation will fail to converge. But how discontinuous can a function be and still be integrable?
In this paper, Smith makes progress toward an answer through a counterexample to a proposed solution from the German mathematician Hermann Hankel in 1870. Hankel proposed that a bounded function is integrable if and only if the set of discontinuities is “scattered”. By this, he meant a topological notion of being small, which we now call nowhere dense. Smith’s counterexample is a function with a scattered set of discontinuities yet is not integrable. The part of his construction that causes issues for integrability is that the set of discontinuities has non-zero “size” in the domain. We call this sort of construction a fat Cantor set.
Smith’s construction foreshadows the development of measure theory in the first decade of the twentieth century, which offered a rigorous notion of “size”. In 1907, Giuseppe Vitali and Henri Lebesgue independently proved that a bounded function is Riemann integrable if and only if the set of discontinuities has measure zero. This differs from Hankel’s result since not all topologically small sets are measure-theoretically small, as evidenced by Smith’s example. These two ways of being small are dual notions that are deeply intertwined.
Following the Franco-Prussian war and the unification of the German Empire, continental Europe found itself in a state of precarious peace. This article updates de Laveleye’s 1873 survey of the relations between European states. de Laveleye thinks that a reasonable observer should expect impending war to result from Germany’s twin chief issues: the Catholic Church and its border with France.
Émile de Laveleye, ca. 1870s
Internally, the unified Germany was divided into a Protestant north and Catholic south. Beyond religious differences among the people, the government sought to stamp out the influence of the Catholic church in state functions, a conflict known as Kulturkampf. To some, the Catholic Church threatened the sovereignty of Germany and could provoke a civil war between the Catholics and Protestants. To complicate matters, the recently annexed Alsace from France is heavily Catholic. de Laveleye views the border between France and Germany, the Rhineland, as an open invitation to further hostilities. France desires to avenge its defeat and reclaim its lost territory. At the same time, Germany may desire expansion; however, it is externally checked by a likely coalition of Catholic states.
Thomas Hare was a nineteenth century political reformer who sought to solve political problems through the systematic redesign of institutions, particularly with respect to electoral reform. He advocated for a ranked style of proportional voting system, now called single transferable vote, which he believed would give a voice to those with unpopular but important opinions, including both intellectual elites and minorities. In particular, Hare’s scheme would eliminate local constituencies in favor of nationwide voting. As to the disfunction of the current system, Hare points to the case of William Gladstone, who, as a popular prime minister, in the early 1870s, faced several challenges for his seat in Parliament by weaponized local constituencies.
Illustration of proportional voting
This article responds to Leslie Stephen’s critique of Hare’s proposal from an earlier issue of the Fortnightly Review from the same year. Stephen viewed Hare’s system as an over-engineered and overly complicated piece of “political machinery.” He thought that it placed too much faith in the intricacies of a new voting system to solve fundamental political and social problems stemming from the cognitive limitations of the voting public.
Following the defeat of the liberals in the 1874 UK general election, the popular former Prime Minister William Gladstone retired from leadership in the Liberal Party, leaving somewhat of a power vacuum at the top. Two possible contenders for leadership in the House of Commons were Lord Hartington and William Edward Forster. Morley argues strongly against the latter who has alienated parts of the Liberal party coalition through various sectarian accommodations to the national education system, which Forster helped push through as legislation in 1870.
Morley offers a cynical view of politics:
There are three sorts of men in the world; first those who earnestly care about social improvement. Second, those who don’t believe in it nor care about it, and boldly say that they do not. Third, those who do not care about it, but pretend that they do. The first are the Radicals; the second are the old Tories; the third are the modern Whigs, whether calling themselves Conservatives or Liberals. Political progress varies with the degree of propulsion which the first sort of men are able to exert upon the third sort.
Without Gladstone, Morley views the Liberals as a rudderless coalition with no identifiable direction. This is an interesting time capsule, since Gladstone would soon return from his hiatus and become Prime Minister again once the Liberals regained power in the 1880 general election.
Philosophy of Science
An Answer to the Arguments of Hume, Lecky, and Others Against Miracles
During the latter half of the nineteenth century, scientific consensus increasingly moved toward naturalistic explanations of the world. At the same time, the spiritualism movement was in vogue and built around mediums, seances, and other spooky stuff. In this essay, Wallace argues that the prima facie rejection of “unnatural” explanations is unwarranted by challenging the accounts offered by David Hume and W. E. H. Lecky.
Hume held that it’s never rational to believe in miracles or spiritual happenings since it’s more likely that an observer is mistaken than a law of nature is violated. Wallace contends that Hume’s definition of miracles is so narrow that it excludes the possibility of advancing science by classifying any gap in theory as incredible. While it’s reasonable that testimony on isolated supernatural events is likely in error, some events are well attested such as the powers of mediums during seances at the time.
Lecky argued that the decline of belief in magic and miracles and the increasing secularization of government accompanied the advancement of society. Belief in spiritual events has been a constant since antiquity, and the preference during the past century for naturalistic explanation is an aberration. Wallace suggests one possible explanation for the decline is that the persecution of witches in Europe suppressed the practice of magic until the rise of the spiritualism movement. This perennial account of magic equates the witches of the early modern period with mediums of the day.
Wallace’s arguments for taking spiritualism seriously are ultimately unconvincing. Many tactics employed are reminiscent of those from science skeptics today. An example: we should be open to any alternative account of phenomena, including spooky accounts, since the frontier of science is frequently incorrect and fails to anticipate new findings. This essay is included in Wallace’s On Miracles and Modern Spiritualism: Three Essays (1875).
This paper considers how much scientific reasoning can inform speculation about the beginning and end of the world. Specifically, to what extent can we rewind and fast-forward the known physical laws to tell us about the deep past and deep future? Clifford begins with a lengthy informal description of James Clerk Maxwell’s statistical view of mechanics and the physical world as atoms, homogenous in kind, bouncing around in the ether.
William Kingdon Clifford (1845–1879)
Clifford argues that our laws are local in that we can reason about the past and future to some extent; however, our purview of the past is much shorter than the future due to entropy and the arrow of time. More generally, we have no reason to think that the present physical laws are either necessary or hold eternally in our world. Perhaps, our laws hold today but not in the deep past or future. Or that our laws evolved as part of a system and could have been otherwise. These conclusions throw some kinks in simplistic approaches to grand speculations about the universe.
John Tyndall’s 1874 keynote address to the British Association for the Advancement of Science was met with intense public backlash and criticism. Tyndall advocated for naturalism and painted a picture of naturalistic science as continually in conflict with religion, much to the detriment of our understanding of the natural world. His critics ranged from dismissing his arguments by attributing them to a sour mood to challenging his domain of discourse. It’s the latter argument that I want to focus on.
A caricature of Tyndall from Vanity Fair, 1872
While Tyndall is acknowledged as an expert in physics and the experimental sciences, his critics allege that he overstepped his bounds when speculating about the origins of life and the universe, since these matters are beyond the scope of experimental science. On this view, no results from a lab experiment could ever tell us about the origins of the universe. By advocating for naturalism, Tyndall is wading wholly unprepared into the depths of philosophy and theology.
While Tyndall is largely guilty of this charge, this does not undermine the thrust of his argument. He notes that scientists routinely go beyond the empirical evidence when developing and evaluating scientific theories. Moreover, this sort of inductive reasoning is a reliable guide to understanding the natural world, including its more remote parts. The dispute on this point is really about who gets to claim cosmology and other such areas of inquiry. Should cosmology be informed by our best current theories in physics or should it remain the domain of metaphysical speculation?
Whitney contrasts two competing perspectives on the study of language: metaphysical and common sense. The former sees language in purposeful terms, as developing toward a particular end, or as an essential property distinguishing humans from other animals. The latter takes language as it exists and asks empirical questions about its nature and function. Metaphysical views on language tend toward sweeping theories and grand narratives and encapsulate the views of leading theorists of the time such as the philologists Max Müller and Friedrich Schlegel. In contrast, Whitney supports the lay view that language is a tool for communication, shaped by practical needs and social interactions. He argues that language evolves organically as a social institution, influenced by cultural and historical contexts rather than by a predetermined purpose or design.
Whitney became involved in an intense feud with Müller over the origin and evolution of language throughout the 1870s. In the latter half of this article, he frames the dispute as his interlocutor uncharitably interpreting his book Language and the Study of Language (1867) while downplaying his admittedly “polemical” language.
Newcomb discusses the economics of mutual life insurance companies. Life insurance is inherently an interesting (and subtly grim) product to price because, unlike fire insurance, not everyone’s house will burn down. The mutual bit means that the company’s beneficiaries are the policyholders rather than investors/stockholders.
Sketch of Newcomb from the Online Library of Liberty
Newcomb observes that there’s an asymmetry between life insurance contracts and other sorts of financial products: if you miss a payment with life insurance, you “forfeit” all that’s been paid in by no longer being covered. On one view, each payment covers one’s risk of death up through the next payment, and policyholders pay proportional to their risk. On another, the insurance company is more like a savings bank where you make regular deposits and withdraw a fixed amount upon death. Adopting the latter view, Newcomb argues that a policyholder that made regular payments up to some point is owed some compensation when their policy is terminated early, particularly due to non-payment.
He concludes by arguing that insurance could run on a leaner budget if they could get rid of those pesky agents. By the latter half of the nineteenth century, on Newcomb’s view, life insurance had become so ubiquitous - at least among this article’s audience - that agents were no longer necessary to inform the consumer.
]]>An Utterly Incomplete Look at Research from 18252025-04-21T00:00:00+00:002025-04-21T00:00:00+00:00http://bcmullins.github.io/research-from-1825A persistent theme throughout the 1820s is the tension between Enlightenment ideals and conservative reaction. The books and articles discussed below capture various facets of this conflict. William Hazlitt’s collection of essays examines intellectuals from the turn of the century, many of whom became swept up in the Romantic movement and adopted illiberal views. J. C. L. de Sismondi’s survey characterizes international relations in the first quarter of the nineteenth century as a struggle between the forces of liberty and tyranny and is optimistic for the former. Liberal ideas were advancing steadily in education, as seen in Henry Brougham’s pamphlet on Mechanics’ Institutes and adult education and the plans to found additional universities in England outside of Oxford and Cambridge.
The Harbour of Dieppe (1825) by Joseph Turner
Of the bunch below, I most enjoyed Samuel Bailey’s On the Nature, Measures, and Causes of Value and The Philosopher in the Kitchen by Jean Anthelme Brillat-Savarin. The former proffers a subjective theory of value that is far ahead of its time both in content and style, and the latter is a time-capsule of French culture through a treatise on gastronomy.
A common notion one finds in early nineteenth century economics is that commodities have an intrinsic value, determined by the amount of labor required to produce the good, in addition to market value. This book is an extended critique of the labor theories of value developed by David Ricardo and Thomas Malthus and expounded on by Thomas de Quincey.
Rather than an abstract property, Bailey argues that value is a relation between two commodities at a given time defined by their ratio of exchange. The relative value I assign to two goods depends on psychological considerations and may be different than the value that you assign. Moreover, the relative value may vary over time. This view requires comparatively little metaphysical baggage.
Portrait of Samuel Bailey (probably)
Perhaps, instead, the amount of labor required is a good measure of value. Bailey contends that it’s unclear what’s even meant by a measure of value. A charitable view is that some common commodity such as money is a good measure of value, since we can use it as a medium to compare how much one is willing to exchange for a given commodity. This, however, falls short of the objective measure that classical economists desired, since money too can rise in value with respect to other commodities.
Another possibility is that the amount of labor required to produce a commodity is the cause of the value of the commodity. Surely, it’s a cause; however, there’s no reason to think its the cause. Even abstracting away from market conditions, the amount of capital employed in the production of a good ought to be considered as a factor. Importantly, it’s likely not the case that capital is just accumulated labor.
This book is very readable and provides a convincing critique of Ricardo’s labor theory of value. Bailey mentions Robert Torrens’An Essay on the Production of Wealth (1821) as another recent contribution to political economy that avoids the labor theory pitfalls. In addition, Bailey’s work provides the most complete and modern citations of the time, which eases the burden of navigating the literature.
This is an unsigned review of the pseudonymous Piercy Ravenstone’sThoughts on the Funding System and Its Effects (1824). This book critiques England’s method of funding its wars in the late eighteenth and early nineteenth centuries through bond issuance, which Ravenstone alleges is both wasteful and to the benefit of the wealthy at the expense of the masses. The reviewer contends that issuing bonds by the state is more reasonable and cost effective than alternatives.
Assuming the state needs to raise money for a worthy cause such as defending its territory from an invading state, how might this be achieved? If the state doesn’t borrow directly through bonds or similar instruments, it can levy a tax on the public. While this seems like a more reasonable approach, since estates can be taxed proportional to their wealth, several wrinkles emerge. What do we do about estates that are wealthy but illiquid? Have them borrow against their assets? There are efficiencies of scale to be gained by negotiating this as a single borrower as the state would. Funding a war effort diverts capital from other investments; however, removing capital uniformly will have a worse effect on returns than only employing idle capital or capital that was less productively employed.
The reviewer throws around a lot of numbers, and it isn’t always clear where their calculations come from.
Mechanics’ Institutes were established in the early nineteenth century to provide education and training for the working-class, particularly those in the manufacturing. The idea was to communicate the fundamentals of the natural sciences that underlie the processes in which the workers operate. These institutes more generally sought to rectify a glaring deficiency in adult education in Britain.
The Manchester Mechanics' Institute ca. 1825
Henry Brougham was a Whig MP and a vocal advocate for popular education and other liberal causes such as expanding the voting franchise and slavery abolition. In this essay, he argues that providing time and a venue for workers to learn new skills and ideas would benefit the workers, the factories, and the community. On Brougham’s vision, these institutes would be joint ventures, where wealthy benefactors provide the funds for starting up, the factories guarantee the workers have sufficient time and place to meet, and the workers themselves participate and, eventually, govern the institute.
While there was some variation, the general blueprint is for an institute to house a library, hold reading groups, and offer full course lectures. Importantly, though, the institutes sought to fend off partisan dispute by discouraging or even banning books and lectures on theological or political matters. By the time of writing, several Institutes had been founded from London to the industrial north and Scotland. Many of these institutions exist today through lineal descent and form a large part of the higher education in the UK.
Jean Anthelme Brillat-Savarin was a French lawyer, politician, and noted gastronome. His part-memoir part-treatise, Physiologie du goût, is a prolegomena of sorts to the science of gourmandism. One may be tempted to think that this study of food and culture is merely a guide to gluttony. Brillat-Savarin is careful to dispel such notions. The glutton mindlessly consumes to excess, while the gourmand appreciates and enjoys to satisfaction. Far from a handbook to hedonism, this analysis of the art of the gourmand encompasses gastronomy, physical and mental health, and social interaction.
The book is written in short sections loosely divided into themes, mixing technical discussions of the author’s theory of food chemistry with recipes and tales from his eventful life. The writing is often witty and the translation by Anne Drayton is a pleasure to read. I was hooked from the beginning by the list of aphorisms that preface the main text; the best of which reads:
Dessert without cheese is like a pretty woman with only one eye.
In the section on physical and mental health, Brillat-Savarin discusses the importance of diet in maintaining health and longevity. He makes a case for the benefits of a low-carb diet for losing excess weight, becoming one of its first proponents.
There’s an amusing mention of a correlational health outcomes study by Louis-René Villermé from the prior year. This study finds that “good cheer is far from being harmful to health, and that, all things being equal, gourmands live longer than other men.” Elaborating on the methods:
He compared the various classes of society in which good cheer is habitual with those which are poorly fed, covering the entire social scale. He also considered the various quarters of Paris with one another according to their wealth, for it is well known that wide divergencies exist in this respect.
The most interesting section, however, is the discussion of restaurants near the book’s conclusion. Restaurants in the modern sense were a relatively recent innovation, appearing in Paris in the latter half of the eighteenth century and quickly spreading throughout Europe and beyond during the French Empire’s warring efforts.
The conservative reaction to the French Revolution dampened liberal attitudes around the turn of the nineteenth century. This collection of essays captures this milieu through portraits of several prominent British figures, from philosophers to poets to MPs.
Self-portrait circa 1802
Outside of a few characters depicted as the embodiment of tyranny and injustice such the Tory MP Lord Eldon, Hazlitt’s general assessment is that each figure’s early work is superior to their later work due to their abandonment of liberal principles. Hazlitt is particularly critical in this regard to the Lake Poets.
In short bursts, Hazlitt’s style is engaging. The opening salvo sharply critiques Jeremy Bentham’s philosophical project as fantasy and navel-gazing. The discussion of Coleridge’s intellectual adventures demonstrates the breadth of Hazlitt’s interests. The profiles of various MPs give insight into the position of the intellectual in the political realm.
When read together, however, this collection grates on one’s mind. Hazlitt has a tendency to juxtapose figures and ideas as diametric opposites. For example, the article on long-time Edinburgh Review editor Francis Jeffrey contrasts the Whig-friendly Edinburgh Review with the Tory Quarterly Review. All that is right with the world is attributed to the Edinburgh and all the muck given to the Quarterly. To be fair, the Edinburgh Review is the better magazine in my estimation; yet, both are inferior to the Westminster.
Hazlitt can stretch his credibility to the point of becoming an unreliable narrator. The article on Walter Scott criticizes his conservative overtones through romanticizing the past; yet, when comparing Scott with Lord Byron, Hazlitt holds the former to be the greatest moralist of the age and the latter a phony liberal.
I most enjoyed the essays on Walter Scott, William Godwin, Horne Tooke, and James MacKintosh. I knew of Scott as the author of Waverley, the philosopher Godwin only as father to Mary Shelley, but was unaware of the interesting MPs: the jurist Tooke and the Scottish philosopher MacKintosh.
Philosophical Considerations on the Sciences and Savants
Auguste Comte is a often presented as one of the villains in the history of social thought. Similar to Wittgenstein, there is the early Comte and the later Comte. The early Comte is interested in the history of thought and intellectual development and is often associated with the six volume Course of Positive Philosophy (1830-1842). It’s the later Comte associated with the System of Positive Polity (1851-1854) and his religion of humanity that is much reviled.
In this article, Comte introduces his law of three stages and the hierarchy of the sciences. The former holds that human intellectual development passes through three stages: theological, metaphysical, and positive. Theological thought is all encompassing and often anthropomorphized, attributing phenomena to supernatural beings. This mode of thought is rigid and allows little room for change. Metaphysical thought is still spooky but less centralized, allowing for the possibility of change. Positive thought is empirical, scientific, and decentralized and seeks to explain phenomena through general laws.
Comte argues that the sciences can be categorized into a hierarchy beginning with the natural sciences up through the social sciences, similar to other attempts to explain the unity of science. Fields of study in the hierarchy progress from bottom up with some fields being scientific while others are still spooky at a given time. In the early nineteenth century, physics and astronomy attained the status of a positive science, while the moral sciences were still largely theological and metaphysical, being dominated by Medieval theology and eighteenth century Enlightenment thought.
This leads to an interesting critique of encyclopedias and the organization of knowledge. Comte argues that such projects are only feasible once human thought has sufficiently developed; otherwise, two adjacent fields at different stages of development may offer mutually exclusive explanations for the same phenomena.
The article concludes with sketching a history of intellectual development. Early societies were theocracies, typified by Egypt, where there was no distinction between priest, philosopher, and state authority. Ancient Greece represented the transition to metaphysics with the distinction of the philosopher from the priest. This is illustrated by the differing philosophical attitudes of Plato and Aristotle. An antagonism between science and theology developed as they butted heads on social issues. Several attempts to reconcile the two under the auspices of theology e.g. by the Jesuits were at best temporarily successful. What remains is to create a social physics i.e. a positive social science. This, in turn, would lead to a reorganization of society in the hands of technocrats.
Least squares is an estimation method that fits a line to a set of points that minimizes the sum of the squared distances from the points to the line and is a workhorse in statistics and machine learning. This method was introduced by Adrien-Marie Legendre in 1805 as a heuristic to correct for measurement error in astronomical data. Aside from an independent investigation from Robert Adrain in 1808, Carl Gauss and Pierre-Simon Laplace offered the first justifications for least squares in important publications from 1809 and 1810, where Gauss derived the normal distribution and Laplace proved the central limit theorem.
Ivory’s paper offers a few justifications for least squares and frames the problem in terms of reducing error from astronomical observations. Ivory begins by critiquing an approach from the early eighteenth century by Roger Cotes that correctly observed that averaging multiple noisy observations decreases error. The first two justifications are the most clearly developed. The first employs an analogy with levers and fulcrums to represent how each observation is weighted. The second is more reasonable and argues that least squares is principled and minimizes mean squared error.
Ivory received the Copley Medal from the Royal Society in 1814
Ivory is an interesting and tragic historical character. He was a Scottish mathematician of the first order and a chief exponent of the continental approach to analysis and mechanics and one of the first in Britain to use Leibniz’s notation for the differential and integral calculus. Despite receiving several awards from the Royal Society and even being knighted, Ivory was plagued by delusion and paranoia, which limited his contributions and resulted in controversies with other big names of the time.
On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies
Imagine you’re trying to determine whether or not a life insurance policy or an annuity is priced fairly. How might you go about this? A reasonable place to start is collecting data on how long people live and calculating a contingency table or an empirical distribution. Even if this sample is representative, this approach has several drawbacks, e.g., the estimated distribution is discrete and making the distribution more fine-grained comes at the cost of higher variance estimates. Calculating the present value of an instrument from a discrete distribution can be computationally expensive (especially using methods from the early nineteenth century).
An interpolated empirical distribution of mortality rates (log scale) in the US in 2003.
Gompertz proposes a model for the mortality rate at age $x$ ($\mu_x$) that increases exponentially with age, now called the Gompertz Law of Mortality. In symbols, $\mu_x = Bc^x$, where $x$ is age, $B$ is the baseline mortality rate, and $c > 1$ is the acceleration of mortality. Much of the paper shows that the proposed model closely approximates various datasets for adulthood, except at very old age. This model provides several benefits. Being a continuous time model, calculating probabilities is as simple as integrating the mortality rate over the desired age range. Moreover, the estimation problem is reduced to two parameters $B$ and $c$ rather than the full empirical distribution.
While some may view life insurance as a bit of a morbid topic, Gompertz doubles down on the macabre by describing his model of the mortality rate as “a deterioration, or an increased inability to withstand destruction”.
International Relations
A Review of the Efforts and Progress of Nations during the Last Twenty-Five Years
The period from the late eighteenth to the early nineteenth century was the age of revolutions. From Europe to the Americas and Africa, monarchies became less absolute - in some cases even overthrown - and power and wealth became more dispersed.
An ink portrait of Sismondi from the Online Library of Liberty
In this review, Sismondi surveys revolutions the world over. He characterizes this period as a conflict between two opposing forces: one pushing in the direction of Enlightenment ideas and greater individual liberty, and the other toward greater concentration of power. The former is the wave emanating from the overthrow of the ancien régime in France, and the latter is the conservative reaction.
Individual political movements run the gamut between these extremes; however, Sismondi identifies some patterns to help make sense of the aftermath. When revolutions come from within and capture the elusive public opinion, they tend to favor greater liberty and enfranchisement. In contrast, revolutions brought about by external actors tend to concentrate power, often in the hands of those same actors. Overall, however, the world is trending toward greater liberty and prosperity.
A review in the North American Review takes issue with some of Sismondi’s claims. Sismondi overplays the success of Enlightenment ideas in France; however, this is understandable, since Sismondi had to get his publication approved by the French censors. On the other hand, Sismondi underplays the success of such adoption elsewhere in Western Europe such as Germany and Italy. Perhaps, this was motivated by national rivalry. While I read Sismondi as relatively optimistic about Enlightenment ideals prevailing, the reviewer is even more so.
This letter to the political writer Anna Doyle Wheeler acts as the preface to Thompson’s Appeal of One Half of the Human Race. Thompson begins the letter by attributing the ideas proffered in the book as the joint product of himself and Wheeler. The core argument is that the position of women in society and the laws restricting their political rights are not only unjust but are suboptimal from an utilitarian perspective. By denying women education, political participation, and economic independence, society is squandering a vast reservoir of talent and potential.
Anna Wheeler c.1825
This book is directly responding to a passage discussing representative democracy in James Mill’s Essay on Government for the Supplement to the Encyclopedia Britannica.
Mill argues that, since subgroups of the population can represent the broader interest of the people, we should not extend political rights to women.
This is a bit baffling to read, since Mill is a radical arguing for liberal reforms, and certainly rubs me the wrong way.
I’m glad a response on this point exists!
While I found it dragged on too long, this opening letter is a strong hook for the remainder of the book.
Since the eleventh century, Oxford and Cambridge were the only universities in England. With rise of the working class during the first industrial revolution, the early nineteenth century saw the founding of Mechanics’ Institutes and mutual improvement societies. In the 1820s and 1830s, several candidates popped up for a third university in England to meet the demand for education. This unsigned article discusses and advertises the founding of London University, now called University College London.
While the two university system may have made sense during the Middle Ages, the author argues that it is no longer the case. As the demand for education increased, Oxford and Cambridge were scarcely able to take on more students. The cost of attendance for room and board, tutors, and religious services were exorbitant and priced out many would-be students, an evergreen complaint. Without competition within England, educational standards had stagnated and not kept up with recent advances in knowledge. Moreover, the author cautions that sending young men far from home during their formative years is a recipe for debauchery.
London seems to be a natural fit for a university. Not only is it home to the Royal Society with its large pool of potential professors, but it has ample hospitals to justify a medical school. The author closes by advising that the proposed university was still raising funds. London University would open the next year in 1826.
]]>Interesting Articles I’ve Read in 20242024-12-31T00:00:00+00:002024-12-31T00:00:00+00:00http://bcmullins.github.io/interesting-articles-2024Below is a collection of interesting articles I’ve read in 2024. Three papers are on differential privacy and adjacent topics. There’s a recent method for differentially private SGD utilizing methods from private query answering, an intuitive watermarking scheme for language models, and a paper from 1986 that proposed $k$-anonymity before it was formalized as a criterion for de-identification. Several papers are on the history of ideas ranging from early twentieth century pragmatism, the synergies and antagonisms between poetry and philosophy, and the relation between periodicals and intellectual progress to the deaths of Analytical Marxism and Effective Altruism.
Lately, I’ve been reading papers in the statistical disclosure literature before differential privacy i.e. before 2006. This short paper introduces what would later be called $k$-anonymity, a criterion of privacy that was/is widely applied especially to government datasets. $k$-anonymity would be formalized in a series of papers by Latanya Sweeney and others in the late 1990s and early 2000s.
For a dataset containing sensitive information about individuals such as Census data, a notion of privacy called de-identification seeks to make it impossible to link a record in the dataset with an individual. Removing personally-identifiable information (PII) from the data may not be sufficient to prevent re-identification, since some records may still be unique or only appear a few times.
Alice de-anonymizing Bob
For example, if Alice knows Bob’s age and zip code, she may be able to identify him in a dataset even if his name has been removed. If Bob’s age and zip code combination is unique, then Bob would be the only 45 year old living in downtown Chicago and Alice could identify him perfectly. If, however, there are only a few people that share Bob’s age and zip code, Alice could still identify Bob with high probability. In the latter case, age and zip code are quasi-identifiers, which Dalenius coins in this paper.
Dalenius sketches a few ways to check if $k$-anonymity is satisfied and considers what to do if it’s not. A dataset is said to be $k$-anonymous for a set of attributes if, for every record in the dataset, there are at least $k-1$ other records that share the same values on the given attributes. In the example above, if the dataset is 2-anonymous, then Bob would not be perfectly identifiable because there would be at least one other record that shares his age and zip code.
If anonymity is not satisfied and privacy is potentially compromised, what should we do with the data? We could throw the records away, but that could have unpredictable downstream effects. We could suppress quasi-identifier attributes in the records. Not only does this inherit the former issue, but imputation could be used to recover the suppressed data. We could “perturb the data”, by which he means something like generating synthetic data. Finally, we could implement an encrypted computation scheme such as homomorphic encryption to compute statistics while not directly exposing the data. Unsurprisingly, these latter two options also run into privacy issues of their own.
One generation has dominated American politics for over 30 years
This article is an interesting time capsule. Published on July 4th of this year, Biden had yet to withdraw from the Presidential race and the attempted assassination of Trump was a week or so away. At the time, Biden and Trump were historically unpopular candidates.
Credit: The Economist
The pair also have in common their decade of birth, the 1940s, one which has dominated US politics over the past thirty years. With the exception of Obama, every president from Clinton onward - as well as many challengers on the opposing ticket - were born in the 1940s. The article points to this generation’s hold on power as a source of political disfunction, rehashing the rhetoric and disputes of the tumultuous late 1960s.
As this generation aged, so did the average age of politicians in the US. While US presidents are getting older on average each election over the past fifty years, the trend for OECD political leaders is slightly downward sloping. Moreover, of these countries, the US has the oldest legislature on average in both upper and lower houses. The Economist explores this in depth with their recent podcast Boom!; however, I haven’t had a chance to listen yet.
Taking Pragmatism Seriously Enough: Toward a Deeper Understanding of the British Debate over Pragmatism, ca. 1900-1910
In the early twentieth century, a leading Idealist philosopher in Britain, F. H. Bradley, posited that he may be a pragmatist after all. Roughly speaking, idealism is a speculative approach to philosophy that studies reality as a whole and often in a top-down fashion. Bradley’s idealism sets such a high bar for knowledge and truth that he thinks it practically unattainable. Rather than give in to skepticism, Bradley adopts a pragmatic view as the best one can do.
F. C. S. Schiller
Braaksma argues that F. C. S. Schiller’s response is instructive for understanding pragmatic thought. Schiller denies that Bradley is a pragmatist because Bradley’s account of truth and knowledge still aims to attain absolute certainty. The pragmatism of Schiller, John Dewey, and William James conceives the aim of thought through an evolutionary and psychological frame “whose main function is helping an organism live”. On this account, pragmatism is less about ends and more about the means of one’s theories of truth and knowledge.
The predominant method for privately training a machine learning model is differentially private stochastic gradient descent (DP-SGD). This method adds Gaussian noise to the bounded gradient at each step with noise calibrated to one’s privacy budget (as well as the bounding details), viewing each gradient measurement as a separate query.
This paper introduces a new method for differentially private SGD that treats gradient measurement as a prefix query on the sequence of gradients. The key observation is that the gradient at each step is a sum of prior gradients. To optimally add noise to the gradient, the authors use a variant of the matrix mechanism, a method for optimally answering linear queries under differential privacy. The matrix mechanism utilizes factorization to allow one to answer a workload of queries with low sensitivity and reconstruct answers to the desired workload with minimal noise.
This approach to differentially private SGD is now called DP-MF for matrix factorization. In addition to vanilla SGD, this framework can accommodate SGD with momentum or any extension that uses a linear function of the gradients. Empirically, this approach to noise addition yields significantly higher accuracy on the test set compared to existing methods.
This is a really cool paper because it shows how improvements in fundamental tasks such as private query answering (which is what I work on) can be applied to make non-trivial advances in other areas.
Cocaine: a cultural history from medical wonder to illicit drug
During the forty year period from 1880 to 1920, cocaine went from an obscure compound to a wonder drug, then, to a controlled substance and the attributed cause of social ills. While cocaine was known as a painkiller and stimulant, Karl Koller, an ophthalmologist and colleague of Sigmund Freud in Vienna, discovered its properties as a local anesthetic in 1884. This finding changed how some surgeries were practiced, since patients were no longer required to be fully sedated.
A typical exercise in a first course in mathematical logic is to prove that propositional logic can be expressed using only two of the typical operators such as $\neg, \lor$ i.e. not and or. In 1913, Henry Sheffer proved that there is a single operator — now called NAND — capable of expressing all of propositional logic given by $A \mid B = \neg A \lor \neg B$ for propositions $A, B$.
In this paper, Schönfinkel proves a similar but deeper result for first-order logic that reduces quantification, variables, and predicates to functions. In this setting, first-order logic can be expressed using three functions: a constant function $K$, a substitution function $S$, and a version of NAND $U$ for quantified predicates. Schönfinkel’s presentation is elegant, powerful, and philosophically reflective.
In the midst of Cold War Rationality in the late 1970s and 1980s, Marxism saw a resurgence in the form of analytical Marxism. This approach offered a critique of capitalism largely grounded in the notion of exploitation with the rigor and toolset of analytic philosophy and microeconomic theory. The problem is that the approach didn’t pan out: results were unconvincing and internal coherence was lacking.
Heath offers a amusing history (and lament) of this Marxist wave. He attributes the hastening of the crash to the competing Rawlsian program. While A Theory of Justice (1971) may seem boring in contrast to the high theory of Marxism, it offered a critique of unfettered capitalism from a liberal direction.
What Rawls had provided, through his effort to “generalize and carry to a higher level of abstraction the familiar theory of the social contract,” was a natural way to derive the commitment to equality, as a normative principle governing the basic institutions of society. Rawlsianism therefore gave frustrated Marxists an opportunity to cut the Gordian knot, by providing them with a normative framework in which they could state directly their critique of capitalism, focusing on the parts that they found most objectionable, without requiring any entanglement in the complex apparatus of Marxist theory.
The philosopher Penelope Maddy has argued that the axioms of set theory are in some sense historically contingent. Hamkins builds on this line of thought by considering a plausible alternative history of calculus, where the continuum hypothesis is taken as an axiom. The continuum hypothesis (CH) states that there is no set whose cardinality (or size) is strictly between that of the integers and the real numbers.
From the standard axioms of set theory (ZFC), CH is independent, meaning that it can be neither proven nor disproven. The consistency of ZFC with CH was proven by Kurt Gödel in 1938, and the consistency of ZFC with $\neg$CH was proven by Paul Cohen in 1963, inventing the technique of forcing along the way. While CH is formally independent of set theory, some hold that it is nonetheless true or that we should reason about a multiverse of set theories.
Newton and Leibniz settling their differences Credit: Joel David Hamkins
The proposed alternate history begins with the development of infinitesimal calculus in the 17th century. Mathematicians were able to develop a rigorous foundation for this calculus in terms of hyperreal numbers. The hyperreals are an extension of the real numbers that include infinitesimals, numbers that are smaller than any positive real number but not zero and fill “every conceivable gap in the numbers”. How does CH enter the picture? In ZFC, the hyperreals are underspecified; however, ZFC+CH implies a unique characterization of the hyperreals. Hamkins argues that this development could have led to the acceptance of CH as a fundamental axiom of set theory.
A general worry about this sort of paper being simultaneously a high-level thought experiment and in the weeds of set theory is that subtly unsound reasoning may sneak in unnoticed. As someone familiar with these topics but not a set theorist, it took some time to digest this paper and verify results that were casually mentioned.
In the late nineteenth century, spiritualism was having a cultural moment, partly as a reaction to rapid progress in the sciences. As part of this progress, evolutionary theory generated much controversy with its (largely) materialist account of life and change. This short article describes an episode in the history of science when evolutionary theory collided with spiritualism in “one of the strangest courtroom cases in Victorian England.”
In 1876, Ray Lankester, Thomas Huxley’s lab assistant and a junior member of Charles Darwin’s circle, sought to debunk a purported psychic. Partly, this was to win the elder Darwin’s favor as Darwin’s brother-in-law, Hensleigh Wedgwood, had recently been swept up in the seance fervor. Lankester and a friend confronted the American psychic Henry Slade during a London event and later brought a complaint against him under “an old law intended to protect the public from traveling palm readers and sleight-of-hand artists.”
The trial was sensational. Lankester nearly botched the debunking by neglecting to identify Slade’s slight-of-hand, provide any substantial evidence, or even consistent testimony. In addition, the proceedings featured a stage magician who demonstrated how Slade could have deceived his audience and testimony on the character of Slade from Alfred Russel Wallace, an avowed spiritualist who also formulated natural selection independently of Darwin in the 1850s. The judgement went against Slade but would later be overturned.
The idea of watermarking a physical image or document to prevent forgery has been around for centuries. For generating watermarked images from a model, this looks something like slightly perturbing the image in a way that’s imperceptible to the human eye but detectable by the model owner. Doing something similar for language models poses a challenge because predicting the next word in a sentence offers dramatically less information to work with than all the pixels across channels in an image.
"A Watermark for Large Language Models" Kirchenbauer et al. (2023)
Over the past three years, several approaches to watermarking language models have been proposed. This paper introduces Green-Red Watermarking, where you randomly divide all tokens in the model’s vocabulary into two sets: green and red. During inference, you slightly increase the probability of choosing a green token. The result is text that’s detectible by the model owner by looking at the ratio of green to red tokens. Other approaches offer different trade-offs between the security of the watermark and the effect on the model’s utility, including using ideas from differential privacy.
On the reciprocal influence of the periodical publications, and the intellectual progress of this country
One way to measure how the intellect of a country changes over time is to look at what’s published in its periodicals. By intellect, Stevenson is not as much talking about scientific advancements as the overall quality of discourse. Looking back at the literature from the 1770s, Stevenson observed a dramatic rise in the quality of articles published in London periodicals over the fifty year period. Is published writing merely a reflection of changing intellect, or does causation go both ways?
Stevenson finds the literature from fifty years prior to be a bit pedestrian with respect to both topics and quality relative to the writing of his day. One driver of this is the notion of a moral convulsion. This is an event that causes radical social upheaval and a reevaluation of one’s moral landscape, which Stevenson compares to a volcano erupting and leaving fertile soil in its wake. During the time period in question, a moral convulsion was brought on by the French Revolution and the resulting turmoil.
How might periodicals influence the public intellect? Unlike books, periodicals often expose the reader to a variety of topics and the occasional gem of an article that might not have been sought out otherwise. In this way, ideas can diffuse through society. There are other avenues as well. As the number of published articles grew, outlets specialized to differentiate their collections and capture a specific audience. The resulting exclusivity increased both the prestige and utility of publishing one’s writing in this format, leading brighter minds to contribute to periodicals.
On this latter point, I couldn’t help but think that today we’ve seen some harmful effects emerge from this process of specialization insofar as the public intellect becomes fractured into echo chambers, cognitive islands, and epistemic bubbles. Regardless, this article lays out a strong case for why one should read periodicals, both then and now, and especially broader interest magazines such as The Atlantic and Harper’s.
This article chronicles the rise of effective altruism from the perspective of a philosopher who had similar aspirations in the 1990s. The cinematic synopsis:
The EA saga is not just a modern fable of corruption by money and fame, told in exaflops of computing power. This is a stranger story of how some small-time philosophers captured some big-bet billionaires, who in turn captured the philosophers—and how the two groups spun themselves into an opulent vortex that has sucked up thousands of bright minds worldwide.
Effective altruism began with the combination of Peter Singer’sshallow pond argument and quantified analyses of the effectiveness of charities in saving lives. Toby Ord is a philosopher who pushed in this direction in the 2000s. In the 2010s came William MacAskill, who was more pitchman than philosopher. An amusing passage:
Let me give a sense of how bad MacAskill’s philosophizing is. Words are the tools of the trade for philosophers, and we’re pretty obsessive about defining them. So you might think that the philosopher of effective altruism could tell us what “altruism” is. MacAskill says, “I want to be clear on what “altruism” means. As I use the term, altruism simply means improving the lives of others.” No competent philosopher could have written that sentence. Their flesh would have melted off and the bones dissolved before their fingers hit the keyboard.
Strong hyping of precise numbers based on weak evidence and lots of hedging and fudging. EAs appoint themselves experts on everything based on a sophomore’s understanding of rationality and the world. And the way they test their reasoning—debating other EAs via blog posts and chatboards—often makes it worse. Here, the basic laws of sociology kick in. With so little feedback from outside, the views that prevail in-group are typically the views that are stated the most confidently by the EA with higher status. EAs rediscovered groupthink.
By the late 2010s, effective altruism adopted parts of longtermism. In some sense, longtermism is EA’s final form:
Longtermism lays bare that the EAs’ method is really a way to maximize on looking clever while minimizing on expertise and accountability.
Importantly, Wenar is not claiming that charity is not effective. Rather, the point is that any sort of intervention has both positive and negative effects. A better approach to charitable giving would be to be as transparent as possible about all known effects.
There is an apparent tension between philosophical and poetic attitudes: philosophy prizes truth to the detriment of beauty, while poetry seeks to stir emotion without regard for reason. This article reflects on the degree to which the poetic strays one from the truth.
An ink portrait of Pigou from the Online Library of Liberty
While poetry cannot do all of the heavy lifting of philosophy, Pigou finds a place for poetry in his view of the epistemic regress. Being a strong foundationalist (as was common at the time), Pigou holds that there are two sorts of beliefs or propositions: those inferentially justified and those immediately justified. The former are the stuff of philosophy, logic, mathematics, and the sciences: the this in this follows from that. The latter can be more ephemeral and is the stuff of metaphysics, foundations, methodology, and moral philosophy.
The poetic mode can provide data to support or frame which beliefs are justified immediately. Another place for poetry concerns how hypotheses or positions are discovered rather than their ultimate logical justification. Philosophers of science refer to these as the context of discovery and the context of justification.
Poetry and Philosophy is an excellent companion to C. P. Snow’sThe Two Cultures (1959), since it provides a model of how the humanities and sciences can be complementary endeavors. I discuss Pigou’s paper in my survey of research from 1924.
]]>An Utterly Incomplete Look at Research from 18242024-12-29T00:00:00+00:002024-12-29T00:00:00+00:00http://bcmullins.github.io/research-from-1824The French Revolution cast a long shadow over early nineteenth century thought. Many of the selections below are concerned with the aftermath of the Revolution and the Napoleonic Wars both economically and intellectually. The pseudonymous Piercy Ravenstone critiques England’s system of public finance and its handling of the massive debt resulting from the wars. John Stuart Mill reviews a debate about the effects of war-time spending on prices. His father, James Mill, offers analyses of government, jurisprudence, freedom of the press, and international law along utilitarian lines for the Encyclopedia Britannica. William Stevenson argues that the moral convulsion among the people caused by the French Revolution opened the door for intellectual progress.
A minor strand of thought is a critique of the Enlightenment project. The philosopher Mary Shepherd argues against David Hume’s empiricist and skeptical account of causation. Alexander Blair critiques encyclopedias as obstructing progress in thought and homogenizing knowledge.
Throughout reading for 1824, I became annoyed with the prolific writer Thomas De Quincey. On the one hand, he presents himself as the unquestioning adherent of the economist David Ricardo. On the other hand, he arrogantly muses on extensions and improvements on Ricardo’s work, in his eulogy no less. I hold out some hope for the future, however, since De Quincey’s analysis of Macbeth from last year was quite good and his autobiographical account of opium addiction is well regarded.
I most enjoyed reading John Ramsay McCulloch’s history of economic thought and William Stevenson’s analysis of periodicals and the public intellect. McCulloch’s short book tells an interesting story and provides context on how an influential classical economist viewed their enterprise. Stevenson’s article studies the interplay between periodicals and intellectual progress, which is not so far off from what I’m doing with this project.
I came across a very interesting book Sketches of the Philosophy of Apparitions by Samuel Hibbert-Ware too late in the year to actually read it in time. This book is one of the first to offer a materialist explanation of ghosts and apparitions as pathologies of the human mind. I will catch up with this and other interesting reading that I initially overlooked in a future post. If I’ve missed anything interesting from 1824 that you enjoy, shoot an email my way at brettcmullins(at)gmail.com.
This short book is regarded as the first history of economic thought from a classical economist but is as much an argument for the field of political economy itself. McCulloch presents economics as approximating a completed science and spends much of the book sketching its development. He begins with the mercantilists who thought about the right things in the wrong way by, among other issues, advocating for restrictive trade policies. Dudley North is credited with turning the tide toward liberal thinking in the late seventeenth century.
An ink portrait of McCulloch from the Online Library of Liberty
Though often confounded with political theory, McCulloch argues that political economy is a distinct field. He defines it as the science of wealth and the laws governing its production, distribution, and consumption. Political economy is indispensable to the legislator from taxation and regulation to trade between states. Doing otherwise is essentially being willfully ignorant.
From North America to the European continent, the late eighteenth and early nineteenth centuries saw Britain continually at war. In the course of funding these efforts, the government accumulated considerable debt and suspended the convertibility of bank notes into gold, generating the so-called bullionist controversy. This short book critiques England’s system of public finance along with its strategies to reduce the debt burden.
Ravenstone argues that government borrowing has the potential to be unjust since the burden of the debt falls on future taxpayers. With debt resulting from the wars, he charges that a great deal was squandered and what wasn’t did not yield sufficient returns. Troubles are compounded by the plan to pay off the debt through introducing a temporary tax tied to debt reduction. Not only is such a fund ripe for abuse, but economic growth is hindered by transferring money to the wealthy that hold bonds. Instead, he recommends reducing spending, taxing the idle classes, and promoting economic growth.
The wealth of a nation should be measured by its productive capacity rather than its accumulated capital. This follows from viewing labor as the ultimate source of value, which was commonly held by classical economists. Both labor and capital are important to economic growth, particularly relevant since this was written during the latter bit of the first industrial revolution. Financing government spending through public debt distorts the market by giving an outsized return to capital and the idle classes that own it.
Prior to the development of political economy in the eighteenth century by Adam Smith and others, public finance was characterized by haphazard and unequal taxation as well as irregular and erratic expenditure. Ludwig Heinrich von Jakob’s tome Die staatsfinanzwissenschaft (1821) argues that taxes ought to be judiciously levied, spending should advance the commonwealth, and government action should be transparent and predictable.
The science of public finance balances justice, expedience, and prudence in funding the state. To this end, von Jacob holds that taxes should primarily be derived from income on both capital and labor. Moving from the domain of theory, this book surveys public finance schemes on the continent and their various follies such as the handling of paper (or inconvertible) money. This is particularly relevant given that the recent Napoleonic Wars left states saddled with debt.
In the aftermath of the Napoleonic Wars, the effects of government policy on the economy were increasingly put under the microscope. The pamphlet Observations on the Effects Produced by Government Expenditure during the Restriction of Cash Payments (1823) by William Blake - but not that William Blake - argues that increased spending during the war and its subsequent decrease after 1815 explains the observed pattern of high prices followed by low prices for goods. In particular, he posits that increased market stimulation led to overproduction and a general glut of goods, which then depressed prices.
In his review, John Stuart Mill sides with economist Thomas Tooke by arguing that other explanations such as seasonal variation in crop yields are sufficient to explain price trends. Mill defends an economic principle called Say’s Law that says roughly that supply creates its own demand, implying that a general glut is impossible. Moreover, Mill argues that not all spending is equal: unproductive war-time spending would not generate the same economic growth as investments in one’s industry.
Dialogues of Three Templars on Political Economy, chiefly in relation to the Principles of Mr. Ricardo
When we think about the value of a good today, we think about its market or exchange value. In the nineteenth century, economists also debated a notion of natural value, which can roughly be thought of as the long-run market value or value as the cost of production. In the Dialogues, De Quincey defends the position that the natural value of a good is the quantity of labor required to produce it or, in his words, “the ground of the value of all things lies in the quantity of labor which produces them”. This is the “one principle in Political Economy, from which all the rest can be deduced”, which he attributes to David Ricardo’s On the Principles of Political Economy and Taxation (1817).
De Quincey’s goal is to refine the presentation of Ricardo’s principles, which he finds to be too abstract and nuanced for the lay reader, and fend off criticism such as from Thomas Malthus. He makes the first clear with the following passage:
For the fact is - that laborers of the Mine (as I am accustomed to call them), or those who dig up the metal of truth, are seldom fitted to be also laborers of the Mint, i.e. to work up the metal for current use.
The dialogues feature three characters: a disciple of Ricardo (himself), a disciple of Malthus, and, loosely speaking, a disciple of Adam Smith. The first interlocutor spends much of the time demolishing the arguments of the others, particularly on the distinction between value being a function of quantity of labor in contrast to the cost of the quantity of labor. This is a better effort from De Quincey but struggles to get out from under his ego.
The eighteenth century philosopher David Hume advanced a skeptical account of causation. Hume was part of the British Empiricists who viewed sense experience - as opposed to reason - as the foundation of knowledge and metaphysics. On Hume’s view, we never observe causation outright; rather, we observe the constant conjunction of events and infer causation as a matter of convention. This leads to the problem of induction, among other issues.
In this book, Mary Shepard argues that Humean causation is hollow and misses the part of causation that makes it central to knowledge. Shepard’s account sees causation as a necessary relation between properties of objects or events. We infer causation by reasoning about the properties of objects. Importantly, some properties that figure into the causal relation will be hidden from the observer (think hidden states in a probabilistic model), thus illustrating the poverty of a strong empiricist view. Along similar lines, Shepard critiques the views on cause and effect from the Humean philosopher Thomas Brown and the English surgeon William Lawrence.
Without a more comprehensive notion of causation, Shepard holds that there is no foundation of “scientific research, of practical knowledge, and of belief in a creating and presiding Deity”. Despite being influential among an elite circle at Cambridge, Shepard’s work was largely forgotten until recently. This book received a reprint from Oxford University Press in late 2024.
On the reciprocal influence of the periodical publications, and the intellectual progress of this country
One way to measure how the intellect of a country changes over time is to look at what’s published in its periodicals. By intellect, Stevenson is not as much talking about scientific advancements as the overall quality of discourse. Looking back at the literature from the 1770s, Stevenson observed a dramatic rise in the quality of articles published in London periodicals over the fifty year period. Is published writing merely a reflection of changing intellect, or does causation go both ways?
Stevenson finds the literature from fifty years prior to be a bit pedestrian with respect to both topics and quality relative to the writing of his day. One driver of this is the notion of a moral convulsion. This is an event that causes radical social upheaval and a reevaluation of one’s moral landscape, which Stevenson compares to a volcano erupting and leaving fertile soil in its wake. During the time period in question, a moral convulsion was brought on by the French Revolution and the resulting turmoil.
How might periodicals influence the public intellect? Unlike books, periodicals often expose the reader to a variety of topics and the occasional gem of an article that might not have been sought out otherwise. In this way, ideas can diffuse through society. There are other avenues as well. As the number of published articles grew, outlets specialized to differentiate their collections and capture a specific audience. The resulting exclusivity increased both the prestige and utility of publishing one’s writing in this format, leading brighter minds to contribute to periodicals.
On this latter point, I couldn’t help but think that today we’ve seen some harmful effects emerge from this process of specialization insofar as the public intellect becomes fractured into echo chambers, cognitive islands, and epistemic bubbles. Regardless, this article lays out a strong case for why one should read periodicals, both then and now, and especially broader interest magazines such as The Atlantic and Harper’s.
Histoire comparée des systèmes de philosophie, considérés relativement aux principes des connaissances humaines (1804) by Joseph Marie de Gérando is an in-depth history of philosophy from the Presocratics to the end of the modern period. This review discusses the first of three volumes upon the release of the second edition, which covers up to the early Renaissance. The reviewer laments that no such survey is available in English and provides translations of several lengthy passages.
Gérando claims to structure his history around the so-called terrible question of how we can know anyone or anything exists. Our reviewer delights in pointing out the numerous deviations from this plan. Overall, Gérando’s chronology is fairly standard and reminded me quite a bit of Bertrand Russell’sA History of Western Philosophy (1946). The greatest divergence from Russell’s account, however, is Gérando’s partiality for Plato over Aristotle:
The manner of Plato is warm and enthusiastic. He thinks with all his soul, and inspires us with emotion even in his coolest moments. The other is always didactic. There is no heat in the light which he throws on the subject. The severest reason presides in all his lessons; he addresses himself to the understanding, and puts us on our guard against any kind of excitement. Plato, in short, is the high priest of philosophy, and the father of his pupils, while Aristotle has the character of a judge and a schoolmaster.
Yet, both advocate a sort of perennialism that attributes the ideas of Plato and Pythagoras to the Egyptians and the Ancient Near East.
Thoughts on some Errors of Opinion in respect to the Advancement and Diffusion of Knowledge
Constructing an encyclopedia by gathering and organizing all knowledge is a strong expression of Enlightenment ideals. By the 1820s, several encyclopedias were available such as Diderot and d’Alembert’sEncyclopédie (1751-1772), several editions of the Encyclopedia Britannica, and the recently published Encyclopaedia Metropolitana (1817-1845). Blair critiques these and other comprehensive projects, arguing that they promote a superficial understanding and homogenizing of information rather than deep knowledge.
Portrait of Blair by Hugh Carter
Blair argues that knowledge is highly personal and can only be advanced through willful acts of researchers that gain mastery in a particular field. He sees knowledge as more resembling know-how rather than know-that. Examples of the former include knowing how to ride a bike or bake a cake, while the latter can be expressed as propositions. Reducing one’s knowledge from the former to the latter sort diminishes it and steamrolls progress. On Blair’s account, increasing intellectual specialization is the key toward progress in the arts and sciences.
Have you ever been strolling around a dimly lit library at night in an old country manor and felt the eyes from a portrait of a long-dead prior owner following your every move? This short paper seeks to explain this phenomenon as an optical illusion created by the artist. We may think that we can determine the direction a portrait is looking by the shape of the irises of its eyes. The reasoning goes that the closer their gaze is to us the more circular the iris, the farther the more elliptical. This approach fails since humans are quite bad at approximating iris shape!
A famous example from a British World War I recruitment poster
Rather, as Wollaston shows through several examples, the relative position of the iris and other facial cues determine the direction. He demonstrates this by providing several illustrations of the same eyes but with different cues, producing variation in direction. Even if this is so, why do the eyes seem to follow us? So long as we are within a cone of the portrait’s vision, we will interpret it as looking at us. The cone is largest if the face is gazing orthogonal to the painting’s plane and diminishes as the angle of the face approaches a side profile. Of course, there’s also another possibility.
International Relations
Essays for the Supplement to the Encyclopedia Britannica
An ink portrait of Mill from the Online Library of Liberty
In early nineteenth century Britain, the philosophical radicals were a group of thinkers who sought liberal reforms for the political system. Following the work of Jeremy Bentham, they held that government should be based on utilitarian principles, i.e. the best course of action is the one that maximizes the greatest good for the greatest number, and deplored the influence exerted by the aristocracy. Mill was a prominent member of this group and advocated for radical and liberal views in several essays for the Supplement to the fourth, fifth, and sixth editions of the Encyclopedia Britannica. These articles were released piecemeal from 1815 to 1824, and the four entries discussed below were collected into a single volume in 1824.
Essay on Government
How does one structure a government based on utilitarian principles? Both monarchy and aristocracy incentivize a small group to act in favor of their interests and against the majority of people. Though there’s clearly some zero-sum reasoning here, Mill quickly dispatches with these options. Direct democracy, however, is seen as infeasible and too chaotic.
Mill eventually lands on representative democracy with checks on power in the form of term limits. Without such checks, the chosen representatives are yet another form of aristocracy, since their interests are not necessarily aligned with the people. Next, Mill argues that we can restrict enfranchisement to specific subgroups but still represent the interest of the people. Notably, women are excluded! The system Mill describes looks suspiciously like the House of Commons.
Essay on Jurisprudence
The purpose of law is to define individual rights, set out punishment or sanctions for undesirable behavior, and outline rules for the administration of justice. The most important aspect of law is that it should be clearly articulated to inform decision making. That this is held to be of central importance implies that utilitarianism is meant as a descriptive account of decision making as much as a normative account of moral philosophy.
Essay on the Liberty of the Press
Similar to David Ricardo’s view discussed below, Mill holds that a free press is an important safeguard against abuses of government. Without the press, people would not know if an MP was representing their interests, possibly breaking an important feedback loop. Moreover, it’s not possible for a government body to abridge speech without doing so arbitrarily and causing harm.
The notable exceptions to a free press are in cases of libel against individuals. Just like other laws, it’s important to clearly set out what’s meant here and what sanctions one could face. I find it odd though that Mill downplays the danger of the press inciting violence.
Essay on the Law of Nations
While I find Mill to be thinking about the right things mostly in the right way, he paints a rather rosy picture of international cooperation that certainly was not warranted at the time.
Mill begins by applying the approach above by treating nations as people and defining the scope of rights, sanctions, and administration. Compared to the prior cases, his reasoning relies more explicitly on the impartial observer model to resolve disputed rights claims. He considers a case of a river that flows through many states but all want to use the waters to ship goods. The proposed utilitarian solution is that all relevant states should be granted navigation access. On its face, this sketch of a solution is reasonable but hides much of the complexity of what such access entails.
The analogy between nations and people is strained by sanctions, since there is no clear authority analogous to the state. Mill suggests the establishment of a tribunal to adjudicate disputes. While states need not cede their sovereignty to the tribunal, disregarding an unfavorable ruling would cause reputational damage and make it less likely that other states would work with and trust the offending state. This latter point was rushed and neglected to consider situations other than one state pitted against all others such as disagreement among coalitions.
Charles J. Ingersoll gave the annual address to the American Philosophical Society in 1823 on how American ideals are reflected in its social institutions through an extended comparison with European society. This review discusses several points illustrating the breadth of Ingersoll’s address but often circles back to education.
The ideals of representative democracy require an educated citizenry. As such, the United States developed an extensively funded system of public education at all levels by the standards of the time. In much of Europe, however, public education was looked on with suspicion by the ruling class and monarchs in particular. Ingersoll sees a future where American literature and science will displace that of Europe who held a commanding lead. The reviewer, however, thinks that space should be reserved in education for learning Latin and Greek. Not only do ancient languages sharpen the mind, but it allows us to pay reverence to the great writers of the past. This provides an amusing contrast to a writer one generation later who argues that the then-current methods of instruction in the ancient languages dull the mind at the “grindstone”.
At the time, books in the United States were subject to import duties, which Ingersoll sees as a hindrance to the spread and advancement of knowledge. Books were much cheaper to print domestically and copyright law was a bit of a mess i.e. unenforceable, so the duty increases the cost of speciality or antique books without favoring the domestic printing industry. The reviewer closes with a quite justified criticism of Ingersoll’s exuberance for America. In his many comparisons with Europe, Ingersoll finds himself exaggerating the gap between the two into a gulf at the expense of his credibility.
It was commonly held in early nineteenth century Britain that freedom of the press was necessary and sufficient for the good governance of Parliament, though this idea had been quite contentious in the mid-seventeenth century. A free press provides a check on the authority of government:
The press, amongst an enlightened and well-informed people, is a powerful instrument to prevent misrule, because it can quickly organize a formidable opposition to any encroachment on the people’s rights, and, in the present state of information, perhaps there would not be found a minister who would be sufficiently daring to attempt to deprive us of it.
Ricardo holds, however, that, while a free press can be a powerful check on government action, it is a measure that works better in some cases than others, particularly large issues such as ill-motivated wars, sweeping changes to popular policies, etc. A free press can struggle to check incremental policies that are cumulatively detrimental to the public or policies that are sufficiently obscure. Ricardo argues that the only sufficient condition for good governance is mass enfranchisement, to ensure that those elected to the House of Commons represent and are accountable to the people at large.
]]>Interesting Books I’ve Read in 20242024-12-23T00:00:00+00:002024-12-23T00:00:00+00:00http://bcmullins.github.io/interesting-books-2024Below are some interesting books I’ve read in 2024. The bulk of what I’ve been reading is either wrapped up in my research on differential privacy or for my project looking back at research from 100, 150, and 200 years ago. Two of the four recommendations below are from the latter project, but all four are of interest from an historical perspective. Wisdom’s Workshop is a history of the American research university from Medieval times to the present. William Stanley Jevons’ The Principles of Science is a wide-ranging treatment of logic and philosophy of science from 1874 that’s bursting with ideas - some more developed than others. Ballyhoo! is a history of professional wrestling and combat sports from its outlaw roots in the late nineteenth century through the first half of the twentieth century. Finally, John Ramsay McCulloch’s Discourse on Political Economy from 1824 is the first history of economic thought from the era of the classical economists.
Whenever I preorder a book or get it fresh from the press - which isn’t very often - I tend to have a strong reaction. In the case of Jerry Gaus’ posthumous The Open Society & Its Complexities from 2021, I loved how he combined a variety of evidence from anthropology and evolutionary theory with his work on strategic accounts of moral diversity.
After stumbling across Eric Cline’s 1177 B.C. in a bookstore a few years ago and loving it, I eagerly awaited the coming sequel. Once After 1177 B.C. arrived in April of this year, I was left a bit disappointed. This book delivers in terms of continuing the narrative and revisiting old friends; however, Cline’s analysis is much less convincing this time around. He seeks to explain why, following the Late Bronze Age collapse, some civilizations eventually gained in power such as the Assyrians and Cypriots, some floundered such as the Egyptians, and others virtually disappeared such as the Hittites and Mycenaean Greeks. The proposed explanation is social resilience or adaptability, which boils down to redundancy in power structures, personnel, and social bonds. From this, Cline attempts to draw lessons for the world today, which comes off as more dubious than not.
If you have some thoughts on my list or would like to share yours, send me an email at brettcmullins(at)gmail.com. Enjoy the list!
Wisdom’s Workshop: The Rise of the Modern University
Wisdom’s Workshop traces the history of the American research university from the Medieval universities of the twelfth and thirteenth centuries to the sprawling multiversities of today. The narrative begins with a look at Medieval colleges. Of particular note are the horrid conditions of libraries. Before the advent of the printing press, accessing manuscripts was rather difficult for the average scholar. Not only were library hours limited by the available sunlight but the books were frequently chained to the shelves!
Early American universities such as Harvard College imported their structure from Oxford and Cambridge and were created to produce clergy and administrators for the colonies. These schools were small, only maintained a few faculty, and were largely clustered in New England.
The nineteenth century saw the proliferation of schools across the US but within a chaotic and unorganized system. These were largely secondary schools and liberal arts colleges. Graduate study in the modern sense was not present in the early nineteenth century outside of professional studies.
By the middle of the nineteenth century, students desiring research training in state of the art methods and thought studied at German (or nearby) universities. Looking at research in the US and UK at the time, we can clearly see the influence of this arrangement through an interest in both German thought and the virtues of their research-focused system of higher education. By the close of the nineteenth century, however, this system had been imported and adapted to form US graduate programs.
Axtell views the golden age of the research university as roughly from the gilded age to the Second World War. The university consisting of liberal arts undergraduate study and research-focused graduate study was fully formed; however, the universities retained many differences as to what material is taught, how it is delivered, and so on. The funding that flowed into universities during the response to the Great Depression and the war effort was a homogenizing force that standardized curricula and student expectations.
I anticipated a gloomy prediction of the future (along the lines of Brad DeLong’s Slouching Towards Utopia). Axtell, instead, suggests that the university will adapt and survive as it as done in the past. I strongly suggest this book for anyone getting a PhD or in academia more generally to better understand the context of the institution at which they work and study.
The principles of science: a treatise on logic and scientific method
A prominent debate in nineteenth century philosophy of science concerned the role of deduction in scientific reasoning. William Whewell proposed that scientific inference consists of induction to form general laws and deduction to apply or test these laws in particular cases. John Stuart Mill, on the other hand, argued that scientific inference is purely inductive and empirical.
This book develops a wide-ranging account of scientific reasoning, in line with Whewell and unified by what Jevons’ calls the Law of Identity. While the notion of logical identity seems vacuous, it serves as the bedrock for Jevons’ analysis of various topics: logic, arithmetic, probability, induction, and the philosophy of science.
Jevons begins with an odd account of predicate logic, where formulas are constructed from the conjunction of predicates. We can think of a conjunction of predicates as the intersection of the extension of each predicate i.e. the subset of the domain that satisfies all predicates in the conjunction. He introduces operators such as or to join conjunctions into formulas. The accompanying unwieldy system of deduction is equivalent to reasoning about the extension of the formulas, though with a limited set of inference rules. At one point, the existential quantifier is even expressed as a predicate.
Jevons treats induction as the inverse of deduction. He draws an analogy to calculus, arguing that deductive inference, like calculating derivatives, is a more straightforward process than inductive inference, resembling integration. Given that induction with certainty is too epistemologically demanding, he argues that general laws, such as those in natural science, can only be established probabilistically.
A ink portrait of Jevons from the Online Library of Liberty
Jevons gets a lot of milage out of the Law of Identity. In probability, it pops up as the principle of indifference, which says that all possible outcomes should be considered equally likely absent evidence favoring any outcome. This implies an epistemic interpretation of probability, where probabilities represent uncertainty or ignorance.
There’s so much going on in this book that my treatment above just scratches the surface. Jevons’ approach is idiosyncratic but interesting and bursting with ideas. With that being said, I find it difficult to recommend this book in general. I’m surprised, though, that I had never heard of this book before digging it up while planning my look back at 1874.
Ballyhoo!: The Roughhousers, Con Artists, and Wildmen Who Invented Professional Wrestling
From the mid-nineteenth century to the early twentieth, professional sports grew from a bed of chaos into the organized leagues we know and love today. Jon Langmead’s Ballyhoo! tells the story of professional wrestling’s role in this transformation through a series of vignettes built around promoter Jack Curley. In many ways, Curley exemplifies the American dream. He was born to an immigrant family in San Francisco, made his way to Chicago for the World’s Fair, stumbled into the shady world of combat sports promotion, and through several ups and downs rose to the top of his industry. By the end of his life, Curley would rub shoulders with high society in New York and beyond and be mentioned alongside contemporary sports icons Babe Ruth and Jack Dempsey.
Along the way, pro wrestling evolved from outlaw fights and circus shows to sold-out events at Madison Square Garden. Wrestling has an alluring appeal that sets it apart from boxing and team sports: the possibility of a good show every time.
With thousands yelling and stamping their feet, mesmerized by the action in the ring, it represented the unusual alchemy of professional wrestling in its purest form: a bell, a referee, and two grown men dressed in their underwear, starkly lit, captivating a crowd by simulating athletic competition.
Langmead uses sports journalists from the time as a second voice in his narration. As we get to know them, they play the dual role of character and storyteller. Unlike an out-of-time narrator, these journalists capture the raw excitement of the events and engage in inside-baseball intrigue. From a New Yorker article Cauliflower and Pachyderms from 1934, journalist Alva Johnston speculates on audience psychology:
There is a common belief that wrestling matches are fixed…This adds greatly to the interest and partly accounts for the popularity of the sport. Betting men enjoy the added element of uncertainty; cynics appreciate the ugly rumors…The subject of fixing is always interesting; the question is not only whether a match has been fixed but whether it has been fixed securely, and whether somebody may not come along at the last minute and fix it the other way. Then, too, running like an unknown X through all calculation is the possibility that the thing maybe on the level.
The ambiguity of legitimacy and recurrent scandals is partly what makes the history of professional wrestling interesting. From the promoter’s perspective, to maintain popularity it’s best for the paying fan to focus on future cards and not to remember when the last big main event was either a bust or screwy. The long-term outcome of this strategy, however, is that much of the past gets forgotten. Langmead’s contribution is to dig up that past through extensive archival research and weave a gripping story.
A Discourse on the Rise, Progress, Peculiar Objects and Importance of Political Economy
This short book is regarded as the first history of economic thought from a classical economist but is as much an argument for the field of political economy itself. McCulloch presents economics as approximating a completed science and spends much of the book sketching its development. He begins with the mercantilists who thought about the right issues in the wrong way by, among other issues, advocating for restrictive trade policies. Dudley North is credited with turning the tide toward liberal thinking in the late seventeenth century.
An ink portrait of McCulloch from the Online Library of Liberty
Though often confounded with political theory, McCulloch argues that political economy is a distinct field. He defines it as the science of wealth and the laws governing its production, distribution, and consumption. Political economy is indispensable to the legislator from taxation and regulation to trade between states. Doing otherwise is essentially being willfully ignorant.
