Reviews of three books I’ve read recently.
The Tenant of Wildfell Hall by Anne Bronte
This romance novel from 1848 begins with Gilbert Markham, the male protagonist, telling how he saves a small boy from falling off a high wall. The boy’s mother, the widowed Mrs. Helen Graham, sees him do this; but instead of thanking Gilbert, she treats him coldly and with suspicion. Nevertheless — or perhaps precisely because she treats him so badly — Gilbert falls in love with Mrs. Graham, abandons his previous sweetheart, and pursues this mysterious widow despite her attempts to keep him at arms’ length. So ends the first part of the book. Gilbert manages to portray himself as weak-willed and foolish, and thus not the typical hero of a romance novel.
The second part of the book consists of entries from Helen Graham’s diary, whose real name turns out to be Helen Lawrence Huntington. Helen has given this diary to Gilbert so he can understand her better. In the diary, Helen tells how she fell in love with Arthur Huntingdon, a weak-willed and unscrupulous man. She foolishly marries him. To her astonishment — but not to ours — after their marriage, Arthur reveals himself to be abusive, irrational, domineering, and nasty. Helen puts up with him until she sees that their son is beginning to imitate his father. This she cannot stand, so she flees the marriage with her son, and hides in the country under an assumed name, where she meets Gilbert Markham. So ends the second part. Will her life improve in the third part?
Sadly, the third part of the book is even more depressing than the first two parts. Arthur becomes deathly ill. For no discernible reason, Helen decides she must go and nurse him. He is still abusive, irrational, and nasty, but because of his illness he is less able to be domineering. I suppose this is the one bright spot in the novel: because of Arthur’s illness, Helen is finally able to have some control over him. When Arthur finally dies (none too soon for this reader), Helen is finally able to marry Gilbert. But this is far from a happy ending, because in the course of the novel it has become clear that Gilbert is just as weak and foolish and irrational and selfish as Arthur. At least Gilbert is not intentionally abusive, nasty, or domineering, but that just damns him with faint praise.
The Tenant of Wildfell Hall does not paint a pretty picture of marriage, nor of men. Sadly, this is a far more realistic novel than many conventional romances. I imagine J.D. Vance, who strikes me as abusive, irrational, foolish, and nasty, is not unlike Arthur Huntingdon; but I don’t want to imagine what his marriage is like, any more than I want to know how the marriage of Gilbert and Helen will turn out.
Grim, but worth reading.
Logical Dilemmas: The Life and Work of Kurt Godel by John W. Dawson, Jr.
Stephen Budiansky’s 2021 biography of Kurt Godel got a lot of good press, but I thought it was poorly written. Budiansky clearly had a very limited understanding of Godel’s accomplishments in higher mathematics, mathematical logic, and mathematical physics. As a result, to fill out the biography Budiansky resorted to spending far too much time describing Godel’s cultural milieu on the one hand, and then sensationalizing Godel’s bouts of mental illness on the other hand. I came away from the book feeling that I learned more about Budiansky’s prejudices than I learned about Godel’s intellect and personality.
So I bought a copy of Logical Dilemmas: The Life and Work of Kurt Godel by John W. Dawson, Jr., still the standard academic biography, to see if it gives a more rounded portrait of Godel. Fortunately, it does.
Godel was one of the great intellects of the last century. His accomplishments in logic were simply stunning. His incompleteness theorems proved that within any logically consistent system, the axioms of that system can’t be proven from within that system. This has profound implications for the way we view the world. As Dawson puts it: “Godel’s discoveries have been of utmost importance within mathematics, and there is a growing awareness of the impact they have had on our modern world view.” I suspect that the watered-down pop culture version of postmodernism that tries to make all truth relative can trace part of its ancestry from Godel’s theorems. Godel himself understood the implications of his theories differently; if axioms can’t be proved from within a consistent system, then, he concluded, we must be able to apprehend them directly. That is, Godel thought there was something out there that we can know with apodictic certainty. This is entirely contrary to the pop culture version of postmodernism that tries to teach us that truth is different depending on which social media outlet we follow.
Dawson’s book can be tough going. He devotes two chapters to the history of higher mathematics for the century or so before Godel lived. Since I know next to nothing about higher mathematics — my college math is limited to a couple of semesters of calculus, and one semester of mathematical logic — I had to read these chapters two or three times, and even then there were parts I did not follow. But those chapters are absolutely essential if you’re going to have even a limited understanding of Godel’s accomplishments. (Not to slam Budiansky again, but those two chapters in Dawson’s book also showed me how little Budiansky understood about Godel’s accomplishments.) Those two chapters also made me realize how little most of us know about the history of mathematics, which is unfortunate.
Beyond all the mathematics, Dawson’s book gives a full and humane account of Godel’s personal life.
Over the course of his life, Godel had several bouts of mental illness that resulted in his spending time in residential mental hospitals. One of those bouts of mental illness was probably what killed him — he became paranoid that he was being poisoned, ate hardly anything, and essentially died of starvation. Dawson treats Godel’s mental illness with compassion, and makes it clear that for much of his life Godel had reasonably good mental health.
In Dawson’s portrait of him, Godel comes across as a very private person. I’d call him a strong introvert. He could be very social, with the right person. But he preferred to socialize with one person at a time, and he also needed plenty of time to himself. His marriage was quite happy, and he enjoyed his wife’s company. He had a few close friendships, including most notably his friendship with Einstein; at one point, he and Einstein met to talk nearly every day, and Einstein’s death was a real blow to him.
Dawson’s book also gives a full account of Godel’s accomplishments.
While the incompleteness theorems are Godel’s best-known mathematical achievements, Dawson lists other major theorems Godel discovered: the completeness and compactness theorem which “are cornerstones of model theory”; constructible sets which “remain an important focus of research in set theory”; and the consistency proof which is important to intuitionist logic. Dawson concludes: “Godel taught few course, had no disciples, and published relatively little; but his works exemplify Gauss’s motto (“few but ripe”) and have had a pervasive interest.”
Godel also did important work in mathematical physics. He developed a mathematical model consistent with relativity theory showing the universe could be rotating but not expanding. This model has since been disproved by empirical observations, but is nevertheless provocative.
Philosophers have mostly ignored Godel, which is unfortunate. When I took a college course in mathematical logic, the course was cross-listed in the mathematics and philosophy departments, but out of a class of twenty or so I think only two of us were philosophy majors. Godel’s Platonism is a turn-off for most philosophers these days. While I’m a staunch empiricist and materialist myself, I’m also an adherent of Emerson and the Transcendentalists. I’m open to the idea that some of our knowledge comes through direct intuition, or at least there is some ideal truth out there that we can know. I’m not smart enough to figure this out on my own, but I do wonder if Godel’s late-in-life interest in Edmund Husserl’s Cartesian Meditations might have found useful insights in the American pragmatist Charles Saunders Peirce’s notion of the community of inquirers who are able to (in the long term) come close to some kind of ideal truth.
A challenging book, but well worth the effort. Highest recommendation.
Revenge of the Tipping Point by Malcolm Gladwell
Gladwell’s first book, The Tipping Point (2000), tried to reduce diverse social phenomena to epidemiological models. Twenty-five years later, Gladwell decided to write The Revenge of the Tipping Point (2025) ostensibly to revisit the questions he was asking back in 2000 (but also, no doubt, in order to make money; this new book is sure to be a bestseller just like the first one).
I wasn’t convinced by Gladwell’s thesis in his first book — that many social phenomena can be explained wholly and solely in terms of social epidemics. His new book still doesn’t convince me. He offers a lot of good storytelling in the new book, but also far too much of what the science fiction fans call “goshwow” — uncritical admiration of things he thinks are cool. Then, too, over and over again he makes logical leaps that don’t convince me — so, for example, I love Gladwell’s story about how most automobile air pollution comes from just a few top polluters, but then when he makes the logical leap that this is somehow related to epidemiological models, I’m not convinced.
Entertaining bathroom reading, and recommended for that purpose. If you want a serious book about social science or epidemiology, avoid like the plague.