A Budget of Paradoxes, Volume I

The Story

The intellectual journey begins with a historical look at the Royal Society, where the scientific method was in its infancy and often indistinguishable from folklore. The narrative describes a time when men of high standing were as likely to test the "sympathetic powder" of a wound as they were to perform rigorous experiments. From this foundation, the scope expands into a vast, unorganized catalogue of "paradoxers"—men who believe they have solved the unsolvable or overturned the bedrock of physical law. The progression follows no single linear path; instead, it leaps from the bizarre geometric claims of sixteenth-century circle-squarers to the heated, often vitriolic debates surrounding the nature of comets and the movement of the planets.

As the narrative unfolds, it maps the rise and fall of various scientific "idols," from the classical status of Aristotle to the shifting reputation of Francis Bacon. The text documents the persistent, centuries-long obsession with squaring the circle—the impossible task of constructing a square with an area equal to a given circle using only a compass and straightedge. It chronicles how scientific academies, once open to all inquiries, eventually had to institute formal bans on receiving further papers on this subject to preserve their sanity and limited resources. The arc of the work serves as a testament to the stubbornness of human conviction; even when a paradoxer is shown the simple error of their ways, they rarely retreat.

The middle section shifts focus toward the intersection of theological mysticism and mathematical inquiry, examining how numbers have historically been imbued with occult significance. The narrative details how figures like Pietro Bungus used complex numeric codes to assign sinister prophetic meanings to names—most famously, finding the number of the beast (666) within the name of Martin Luther. This thread connects the early modern obsession with numerology to the later, equally misguided attempts by various "philosophers" to rewrite the laws of gravity or tides.

The latter half of the work grows more personal and anecdotal. It moves from the dusty shelves of obscure library collections to the author’s own correspondence, where he fields letters from individuals who believe they have uncovered "truths" denied to the rest of the academic world. These segments reveal the intensity of the paradoxers’ zeal, as they frequently label the mainstream scientific community as "ignorant" or "quacks" for ignoring their supposed breakthroughs. The story eventually circles back to the importance of institutional integrity, warning that if societies do not clearly mark where they have altered the works of the dead, they risk destroying their own credibility. The narrative concludes with a look at the interplay between humor and science, including satirical songs meant to capture the eccentric spirit of the scientific life, before leaving the reader with a collection of exhaustive notes that illuminate the lives of the obscure figures mentioned throughout the journey.

The People

• Augustus De Morgan: The author and narrator, a mathematician who acts as a patient but firm arbiter of logic. He maintains a sense of humor about the eccentricities of others, though he is uncompromising when it comes to the rigor of proof and the necessity of intellectual honesty.
• The Paradoxers: A wide array of self-taught inventors, artists, and mystics who populate the book. They are driven by a fierce, often delusional desire to be recognized for discoveries that contradict established science. They are defined by their inability to accept that their "cracks" in the wall of knowledge are merely misperceptions.
• Petri Bungi (Bungus): A collector of numeric mysteries whose work serves as a primary example of the human tendency to find deep, conspiratorial patterns in random occurrences. He seeks to use mathematics to bolster religious dogma, ultimately revealing the absurdity of forced correlations.
• Arthur Parsey: An artist and one of the book’s central case studies in misapplied effort. He attempts to solve the quadrature of the circle and redefine perspective, illustrating the common paradoxer’s transition from a legitimate field (miniature painting) into a realm of pseudo-scientific fantasy.
• William Frend: A historical figure whose algebra work is discussed for its extreme skepticism. He represents the intellectual tension within the academic community, serving as a foil to those who accept established mathematical results without question.

In Its Own Voice

The author reflects on the nature of scientific institutions and their shift from curious, wide-ranging experimenters to gatekeepers of established knowledge:

The scientific academies are what a spiritualist might call "publishing mediums," and their spirits fall occasionally into writing which looks as if minds in the higher state were not always impervious to nonsense.

He describes the particular type of individual who believes they have unlocked mathematical secrets, noting the irony of their self-styled brilliance:

Hic est poeta quispiam Libenter astra consulens Sibique semper arrogans Negata doctioribus, Senex ubique cogitans Sui frequenter immemor Nec explicare circinum Nec exarare lineas Sciens ut ipse praedicat.

He offers a concise, biting assessment of the paradoxer’s tendency to ignore the standard rules of evidence when it suits their personal theory:

Honor to the speculator who can be put in his proper place by one sentence, be that place where it may.

What It's Really About

At its core, this work is an investigation into the psychology of error. While it masquerades as a historical catalogue of scientific failures—specifically the futile attempts to square the circle or trisect an angle—it is fundamentally a study of why the human mind clings to incorrect ideas even in the face of insurmountable proof. It explores the social friction between the "orthodox" scientific establishment and the "heterodox" amateur who operates outside the academy. The central tension is not between truth and falsehood, but between the method of verification and the desire for revelation.

The book examines the fragility of institutional memory. By documenting how societies, newspapers, and governments interact with pseudoscientific claims, the author reveals that "common knowledge" is often a patchwork of convenience and social pressure rather than purely objective truth. He questions the responsibility of the educated classes to address these paradoxes: should they engage with every absurd claim to refute it, or does such engagement lend an unearned legitimacy to the claimant? He argues for a middle ground where rigor is maintained without cruelty, yet he never hides his disdain for those who weaponize ignorance to attack legitimate scientific progress.

Furthermore, the work acts as a critique of how history is written and remembered. The author frequently points out how scholars, even those considered reliable, often misattribute sources, misread dates, or copy errors from one another until those errors become "fact." He treats bibliography as a detective story, suggesting that the way a book is catalogued or the company it keeps on a shelf can reveal as much about a culture as the text itself. The book is an argument for skepticism not just toward the paradoxers, but toward the experts and institutions that serve as the custodians of our intellectual heritage. It challenges the reader to consider that the history of science is not a steady march toward enlightenment, but a messy, ongoing negotiation with the human desire to be right, regardless of what the math actually says. It asks, finally, what happens to the mind when it decides that its own internal logic is superior to the physical reality of the world.

Why Read It Today

This work is for those who enjoy the intellectual equivalent of a cabinet of curiosities. It is a dense, discursive, and deeply rewarding read for anyone fascinated by the history of ideas, the sociology of science, or the sheer, stubborn eccentricity of the human spirit. If you have ever wondered why some people refuse to accept settled science, or if you enjoy watching a sharp mind dismantle a foolish argument with grace and wit, you will find this volume a constant delight.

Reading it feels like sitting in the study of a Victorian polymath who has spent a lifetime collecting the oddest, most frustrating, and most amusing pamphlets of his age. The prose is warm and conversational, yet it demands a high level of attention. You must be prepared for the author to disappear down rabbit holes of Greek poetry, Latin notes, and obscure bibliographical references that can span pages. The book is not interested in being "accessible" in the modern sense; it assumes you are as curious and as literate as the author himself.

The difficulty lies in its structure—or lack thereof. It is a "budget" of collected pieces, which means the pace is determined by the author’s whims rather than a traditional narrative arc. You will encounter untranslated Latin and Greek, and you will be expected to keep track of a revolving cast of characters ranging from famous astronomers to forgotten shipbuilders. However, the reward is a rare, intimate look at the intellectual life of the nineteenth century. What stays with you after closing the book is not the specific geometry of a failed circle-squaring attempt, but the realization that the tension between objective reality and human ego is a constant in every generation. It is a humbling and often hilarious reminder that for every great discovery, there is a mountain of equally passionate, entirely incorrect attempts at the same goal.