Unnatural Consequences - These are mostly notes to self that I hope are useful to others

Books and more in 2024

These books and plays left an impression on me in 2024, with summaries compiled with the help of Perplexity and ChatGPT.

Books

The Accidental President. Harry S. Truman and the Four Months That Changed the World. A. J. Baime

If not for the decision to drop the two bombs, Truman is the kind of leader that is hard not to respect. He did not want power; he did not want to be president, but when the moment came, he took it seriously and gave it his all.

On serving as Vice President:

The job was “a graveyard of politicians” in Washington parlance, traditionally disparaged by the men who held it. The VP before Truman, Henry Wallace, bragged that he had never had so much time to work on his tennis game. “The Vice President has not much to do,” Truman said, referring to himself as a “political Eunuch.” When asked what he would do with his “spare time,” he answered: “Study history”.

On dropping another A bomb (after the first two on August 6 and August 9!):

General Groves had communicated to the War Department on this day, saying the next bomb would be ready for delivery after August 17 or 18. But now, in the cabinet meeting, Truman said that he was ordering an end to the atomic bombing. He could not stomach the idea of wiping out another 100,000 people, of killing “all those kids,” he said to his cabinet.

Blood Meridian. Cormac McCarthy

Reading this book is a kind of nightmarish out-of-body experience. The language has the signature of a great master—original, unique, and enthralling. The violence is vivid and chilling.

Here is one of the main characters, Jidge Holder, talking about war:

It makes no difference what men think of war, said the judge. War endures. As well ask men what they think of stone. War was always here. Before man was, war waited for him. The ultimate trade awaiting its ultimate practitioner. That is the way it was and will be. That way and not some other way.

This book was so disturbing that I stopped listening to it about halfway through. I think one must be in the right state of mind to consume it entirely. Maybe I will return to it.

Democracy Awakening. Notes on the State of America. Heather Cox Richardson

Richardson is a historian and a professor of history at Boston College and has over 1.7 million subscribers on Substack. For comparison, the New York Times, with close to 6,000 employees, has about 11 million subscribers, and the Washington Post has about 2.5 million subscribers.

America is at a crossroads. A country that once stood as the global symbol of democracy has been teetering on the brink of authoritarianism. How did this happen? Is the fall of democracy in the United States inevitable? And if not, how can we reclaim our democratic principles? This crisis in American democracy crept up on many of us. For generations of Americans, grainy news footage from World War II showing row upon row of Nazi soldiers goose-stepping in military parades tricked us into thinking that the Adolf Hitlers of the world arrive at the head of giant armies. So long as we didn’t see tanks in our streets, we imagined that democracy was secure. But in fact, Hitler’s rise to absolute power began with his consolidation of political influence to win 36.8 percent of the vote in 1932, which he parlayed into a deal to become German chancellor. The absolute dictatorship came afterward.

Some people on the left compare Trump to Hitler. That is a very bad analogy; the circumstances are different, and Trump and Hitler are very different types of characters. When you look at the definition of fascism, however, this administration is starting to check off a lot of the boxes.

Going Infinite, The Rise and Fall of a New Tycoon. Michael Lewis

This a book about a sociopathic child prodigy known as SBF (Sam Bankman Freed), his meteoric rise to fame and fortune as part of the FTX crypto exchange, and its spectacular collapse.

I started reading Lewis, beginning with Lier Poker, a book that was read and quoted by everyone who worked or wanted to work on Wall Street. Since I am fascinated with fraud, particularly when done on a massive scale, I couldn’t pass this up and Lewis did not disappoint. Here is a typical passage.

A guy from Blackstone, the world’s biggest private investment firm, called Sam to say that he thought a valuation of $20 billion was too high—and that Blackstone would invest at a valuation of $15 billion. “Sam said, ‘If you think it is too high, I’ll let you short a billion of our stock at a valuation of twenty billion,’” recalled Ramnik. “The guy said, ‘We don’t short stock.’ And Sam said that if you worked at Jane Street you’d be fired the first week.

Ultimately, the fraud was using customer deposits from the FTX exchange to cover trades at Alameda Research, which is so obviously wrong and illegal that Enron’s Jeffrey Skilling would slap himself silly for working so hard to design much more sophisticated off-balance sheet liability schemes.

It was never clear where Alameda Research stopped and FTX started. Legally separate companies, they were both owned by the same person. They occupied the same big room on the twenty-sixth floor of an office building. They shared the same vista of the forest of high-rises surrounding Victoria Harbor and, twenty miles beyond that, China.

Everything and More. A Compact History of Infinity. By David Foster Wallace

I ran out of DFW’s fiction and essays, and so I turned to this volume to get the great writer’s take on what seems to be his favorite subject — mathematics.

DFW is not a mathematical newb, but he is not a professional mathematician either. No matter. Given his unforgettable writing style and deep fascination with the subject, reading this book is a joy.

In the following, DFW touches on the age-old question of the existence of mathematical objects, meta-questions of existence itself, and some apparently physical phenomena like motion thrown in for good measure.

What exactly do ‘motion’ and ‘existence’ denote? We know that concrete particular things exist, and that sometimes they move. Does motion per se exist? In what way? In what way do abstractions exist? Of course, that last question is itself very abstract. Now you can probably feel the headache starting. There’s a special sort of unease or impatience with stuff like this. Like ‘What exactly is existence?’ or ‘What exactly do we mean when we talk about motion?’ The unease is very distinctive and sets in only at a certain level in the abstraction process—because abstraction proceeds in levels, rather like exponents or dimensions. Let’s say ‘man’ meaning some particular man is Level One. ‘Man’ meaning the species is Level Two. Something like ‘humanity’ or ‘humanness’ is Level Three; now we’re talking about the abstract criteria for something qualifying as human. And so forth. Thinking this way can be dangerous, weird. Thinking abstractly enough about anything … surely we’ve all had the experience of thinking about a word—‘pen,’ say—and of sort of saying the word over and over to ourselves until it ceases to denote; the very strangeness of calling something a pen begins to obtrude on the consciousness in a creepy way, like an epileptic aura.

From Beirut to Jerusalem. Thomas L. Friedman

Friedman was a journalist working in the Middle East in 197os and 1980s and lived in Beirut during the Lebanese civil war.

Of Beirut, Friedman said:

Beirut’s enduring lesson for me was how thin is the veneer of civilization, how easily the ties that bind can unravel, how quickly a society that was known for generations as the Switzerland of the Middle East can break apart into a world of strangers. I have never looked at the world the same since I left Beirut. It was like catching a glimpse of the underside of a rock or the mess of wires and chips that are hidden inside a computer.

On the differences in news coverage:

When Israelis were indirectly involved in the massacre of Palestinians at the Sabra and Shatila refugee camps in Beirut in 1982, the story was front-page news for weeks. When Lebanese Shiites were directly involved in killing Palestinians in the very same camps from 1985 to 1988, it was almost always back-page news—if it was reported at all.

The Maniac. Benjamín Labatut

“The MANIAC” by Benjamín Labatut is a 2023 novel that blends fact and fiction to explore the life of John von Neumann, a brilliant mathematician and polymath. The book is structured as a triptych, beginning with the story of physicist Paul Ehrenfest, centering on von Neumann’s life and work, and concluding with the AI program AlphaGo’s match against Go master Lee Sedol. The novel delves into von Neumann’s numerous contributions to various fields, including game theory, computer science, and artificial intelligence.

Gödel had shown him that if someone succeeded in creating a formal system of axioms that was free of all internal paradoxes and contradictions, it would always be incomplete, because it would contain truths and statements that—while being undeniably true—could never be proven within the laws of that system

Before Gödel, Von Neumann was working on axiomizing mathematics, but the incompleteness theorem had such an impact on him that all of his subsequent work had an applied nature.

All Who Go Do Not Return. Shulem Deen

Published in 2015, the book chronicles Deen’s journey from being a devout member of the Skverer Hasidic sect to losing his faith and ultimately leaving the community.

Deen was raised in the Skverer community, one of the most secluded Hasidic groups in the United States. He married at 18 through an arranged marriage and soon had five children. His first small act of rebellion was turning on a radio, which led to visits to the library and later, the Internet.

As Deen began to question his religious beliefs, he found himself caught between his growing doubts and the fear of being ostracized from the only world he knew. This eventually resulted in him abandoning his community and his faith. The memoir describes the painful consequences of Deen’s departure from the Hasidic community, including the end of his 15-year marriage and the eventual estrangement from his five children.

If the Talmud was built on the purported word of God, that word struck you as suspiciously human, with ambiguities and layers of meaning and all the arbitrariness of human language. The very idea of faith suggested something man-made–the idea that we must submit to conviction, rather than simply behold the universe in its natural order.

On the Edge. The Art of Risking Everything. Nate Silver

Published in August 2024, “On the Edge” is an exploration of risk-taking and decision-making in various domains. The book introduces the concept of “The River,” a metaphorical community of risk-takers and analytical thinkers, contrasting it with “The Village,” which represents more conventional, risk-averse mindsets.

Silver delves into multiple areas where calculated risk-taking plays a crucial role, including:

Gambling and poker
Financial markets and Wall Street
Technology startups
Artificial intelligence
Cryptocurrency

Here is Silver quoting George Bernard Shaw.

The reasonable man adapts himself to the world: the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man. —George Bernard Shaw

The Signal and the Noise. Why So Many Predictions Fail – but Some Don’t. Nate Silver

After reading “On the Edge” and liking it, I read Silver’s first book.

“The Signal and the Noise: Why So Many Predictions Fail – but Some Don’t” is an exploration of the art and science of prediction across various fields. Published in 2012, the book examines why many predictions fail and how we can improve our forecasting abilities.

Silver draws on his experience in baseball analytics, poker, and political blogging to analyze prediction methods in diverse areas such as weather forecasting, earthquakes, economics, and terrorism. He argues that while we have access to more data than ever before, distinguishing meaningful information (the signal) from irrelevant or misleading data (the noise) has become increasingly challenging.

Key points of the book include:

The importance of probabilistic thinking and embracing uncertainty in predictions.
The value of the Bayesian approach to probability, updating our prior beliefs after observing evidence.
The dangers of overfitting models to data, leading to false confidence in predictions.
The need for humility and continuous learning in the face of complex systems.

In statistics, the name given to the act of mistaking noise for a signal is overfitting

Indeed it is.

Nine Lives. Aimen Dean

“Nine Lives” is a memoir by Aimen Dean, co-authored with Paul Cruickshank and Tim Lister, detailing Dean’s journey from al-Qaeda operative to MI6 spy. Published in 2018, the book offers a rare insider’s perspective on the world of jihadist organizations and counterterrorism efforts.

Dean, born as Ali, began his journey as a devout Muslim fighting for the Bosnian cause. His experiences in Bosnia, including witnessing atrocities and narrowly escaping death, solidified his commitment to jihad. He later joined al-Qaeda, becoming one of their respected bomb-makers and swearing allegiance to Osama bin Laden.

However, Dean’s faith in al-Qaeda’s mission began to waver. In a pivotal decision, he chose to become a double agent for British intelligence, working undercover within al-Qaeda’s chemical weapons program.

The Strangest Man. The Hidden Life of Paul Dirac, Mystic of the Atom. Graham Farmelo

Paul Dirac was born in 1902 in Bristol to a Swiss father and English mother. His childhood was marked by a difficult family dynamic, with a domineering father who insisted on speaking only French to his children. This led to strained relationships and traumatic experiences for young Paul.

Dirac was a pioneer in quantum mechanics and made contributions to theoretical physics:

Generally considered to have co-discovered quantum mechanics
Married quantum mechanics with special relativity in his theory of the electron
Predicted the existence of antimatter, specifically the anti-electron (positron) in 1931

Dirac was known for his extreme reticence and literal-mindedness, earning him a reputation as “the strangest man” in physics. Despite his reserved nature, he married Manci Balazs (sister of physicist Eugene Wigner) in 1937 and had two daughters.

The book explores Dirac’s lasting impact on physics and his unique approach to scientific research:

Believed in the “religion of mathematical beauty” as a guiding principle in his work
Received the Nobel Prize in Physics in 1933
Considered one of the most influential physicists of the 20th century

Farmelo’s biography provides a detailed account of Dirac’s life against the backdrop of major historical events, including the rise of Nazism and World War II.

Plays

Prayer for the French Republic by Joshua Harmon

The core premise of “Prayer for the French Republic” is about a French-Jewish family grappling with their place in a world where antisemitism persists across generations. It explores the contrast between their ancestors’ survival during World War II and the fears they face in modern France, questioning what it means to feel safe, belong, and carry on their cultural and familial legacy in a society that often feels hostile.

The Night of the Iguana by Tennessee Williams

This play is about a disgraced former clergyman, Reverend Shannon, who seeks refuge at a remote Mexican hotel after a personal and professional breakdown. There, he encounters a group of misfit characters, including the hotel’s earthy owner, Maxine, and a lonely artist, Hannah. Through their interactions, the play explores themes of redemption, human frailty, and the longing for connection, set against the backdrop of a tropical storm that mirrors the characters’ emotional turmoil.

The Hunt by David Farr

“The Hunt” is a play adapted by David Farr from the 2012 Danish film “Jagten” by Thomas Vinterberg and Tobias Lindholm. It tells the story of Lucas, a well-liked schoolteacher in a small Danish town whose life unravels when a young student falsely accuses him of sexual abuse. As the accusation spreads, the tight-knit community descends into mass hysteria, turning against Lucas and blurring the lines between truth and suspicion. Directed by Rupert Goold and featuring Tobias Menzies, the production delves into themes of innocence, trust, and the destructive power of collective fear.

Doubt: a Parable by John Patrick Shanley

The play is set in a Bronx Catholic school in 1964, where Sister Aloysius, the strict and feared principal, suspects Father Flynn, a charismatic priest, of inappropriate conduct with a student. This suspicion sets off an exploration of morality, authority, and the elusive nature of truth as Sister Aloysius confronts Father Flynn, leading both characters and the audience to grapple with their own convictions and uncertainties.

Appropriate by Branden Jacobs-Jenkins

“Appropriate” follows the dysfunctional Lafayette family as they return to a decaying plantation mansion in Arkansas to settle their recently deceased father’s estate. The play is set in the summer of 2011.

As the family gathers, they discover a shocking photo album containing images of lynched Black people among their father’s possessions. This discovery unleashes decades of resentment and forces the family to confront centuries of historical sin.

The play explores themes of legacy, race, and family secrets. It delves into the complexities of family dynamics, with each character bringing their own perspective and baggage to the situation. Toni, for instance, sees herself as a truth-teller and believes she has spent her life caring for others, including her father.

All of Me (The New Group) by Laura Winters

“All of Me” is a romantic comedy play by Laura Winters, presented by The New Group at the Pershing Square Signature Center in New York City. The play, which ran through June 16, 2024, offers a fresh take on the classic rom-com formula by centering on two disabled protagonists who use text-to-speech technology to communicate.

The story follows Lucy (played by Madison Ferris), who uses a motorized scooter, and Alfonso (played by Danny J. Gomez), who uses a motorized wheelchair. They meet outside a hospital and begin a flirtatious exchange, which leads to a budding romance. The play explores their relationship as they navigate personal challenges, family dynamics, and societal expectations.

Uncle Vanya (Lincoln Center) by Anton Chekhov

“Uncle Vanya” is a play that explores themes of disillusionment, unrequited love, and the search for meaning in life. The story centers around Ivan Voynitsky (Vanya), played by Steve Carell, who manages the rural estate of his deceased sister’s husband, Professor Serebryakov. When Serebryakov visits with his new, younger wife Yelena, tensions rise as Vanya’s resentment towards the professor’s selfishness and his own unfulfilled life boil over. Vanya’s declaration of love to Yelena is rebuffed, and his anger culminates in a failed attempt to shoot Serebryakov after the professor suggests selling the estate. Ultimately, the professor and Yelena depart, leaving Vanya and his niece Sonya to return to their monotonous lives, finding solace in the hope of a better afterlife.

I am a big fan of Chechov’s short stories, but this production did not land for me. Maybe it’s because I can’t consume it in English.

Our Class by Tadeusz Slobodzianek

“Our Class” is a powerful play that follows ten Polish classmates—five Jewish and five Catholic—over several decades. The story begins with their childhood friendships but takes a devastating turn as antisemitism and bigotry lead to betrayal and violence. Based on real events, including a 1941 pogrom in a Polish village, the play explores themes of prejudice, cruelty, and the complexities of human relationships. It traces the characters’ lives from innocence to tragedy, examining how ordinary people can become complicit in horrific acts.

Bad Kreyòl by Dominique Morisseau

The story follows Simone, a Haitian-American woman who visits Haiti to stay with her cousin Gigi, who owns a boutique in Port-au-Prince. Their grandmother’s dying wish was for the cousins to rekindle their relationship. As Simone attempts to connect with her roots and engage in social justice efforts, she encounters cultural barriers and misunderstandings that challenge her American perspective.

Analysis of Boeing 737 MAX 9 Door Plug Accident

I follow aviation accidents pretty closely. For as long as I can remember, I have been fascinated with air and space travel and the associated risks. I even took a flying lesson at Teterboro airport 15 years ago or so, but I never got a chance to get certified.

The latest Boeing 737 Max 9 accident¹ resulted in no loss of life, but the idea of a door, even a fake door, blowing out mid-flight warrants a little analysis. Some questions come to mind: How could this happen, why it happened, under what conditions (the proximal cause), and what could have happened under slightly different conditions? First, a warning: this is not an analysis of how the defect was introduced during manufacturing and assembly; I know nothing about that. This is an analysis of the conditions under which a loose door (I will call that, even though it was technically a door plug) could separate from the fuselage.

The Facts

On January 5, 2024, at 5:00 p.m. local time, Alaska Airlines Flight 1282 took off from Portland International Airport en route to Ontario, California. The sunset was at 5:25 p.m., so it was already fairly dark. When the aircraft reached approximately 16,300 feet (about 5,000 meters), the passengers heard a loud boom as the door blew out from the side of the aircraft.

Everyone on board survived, and the aircraft landed in Portland shortly after, but I am sure most passengers will have a different experience with air travel from that point forward. Many years ago, I was in a much less dangerous but scary landing that did not go as planned (no, not the runway miss with a fly-around, which I experienced twice and is not a big deal), but something more extreme. Since then, I have never been entirely comfortable during unexpected turbulence.

Conditions at 16,300 Feet and Above

The air temperature at this altitude is approximately 0 F (-17 C), and outside air pressure is about 54 kPa (kilo-Paskals) or about 8 PSI (pounds per square inch). For reference, sea-level air pressure is about 101 kPa or 15 PSI. This pressure is the column of air pushing on you as you stand on the ground, and by convention, this gives us yet another unit of pressure — 1 atm (atmosphere). Pressure is related to the number of air molecules available for each breath since the pressure is directly proportional to the density (this comes from the ideal gas law, which I will touch on later). At the cruising altitude of 33,000 feet (about 10,000 meters), the air temperature is about -50 (here, C and F units are close to each other), and air pressure is about 19.3 kPA.

At 8,000 feet and higher, there are not enough air molecules for most people to breathe, so modern aircraft are pressurized (sealed with cabin pressure controlled by the Environmental Control System).

Ideal gas law and what happens during the change in altitude

The fact the door blew out during the ascent was no accident, pardon the pun, and can be explained by the ideal gas law.

$pV = nRT$

The key quantities are Pressure $p$ , Volume $V$ , and Temperature $T$ . The other quantities are constants, so we can write:

$pV \propto T$

From the ideal gas law, pressure is inversely proportional to volume—as pressure decreases, the volume of gas increases, and vice versa. This makes some intuitive sense, as you can imagine what happens when you reduce the volume of a sealed container; the pressure inside goes up and vice versa.

When the pressure outside the sealed container rises, say during a submerging process, the walls experience an inward pressure due to a pressure differential, and when the outside pressure falls, say during an ascent, the wall experiences an outward pressure.

This is why, during a scuba lesson, you are told to keep your mouth open on the ascent so that expanding air doesn’t damage your lungs. For the same reason, when a flight attendant hands you a bag of chips at 30,000 feet, the bag appears inflated².

This outward pressure on the fuselage caused the blowout, and we will now try to estimate how much pressure it took for the door to separate.

Computing the pressure on the fuselage

As a statistician, it always blows my mind how much we can learn from n=1 “experiments” if we are willing to bring some background knowledge, the ideal gas law in this case, to bear on the problem. Physicists would not be impressed, as to them, this is par for the course.

Anyway, back to our problem. To make the calculations, we need to make a couple of key assumptions, namely the pressure outside the aircraft as it climbs and the pressure inside the cabin. The drop in atmospheric pressure with altitude is well-known and follows an exponential decay according to the Barometric formula. This is the blue line in the following diagram.

The green and red horizontal bard indicate my error in assuming gradual cabin pressurization. The dashed line represents the altitude at the time of the accident.

The second assumption we need is the pressure inside the cabin. First, I assume that the target inside pressure is equivalent to about 6,000 feet (1,800 meters), which is at the lower end of the reported range. This type of pressurization balances the passengers’ comfort with the force that the fuselage has to withstand.

Second, I (erroneously) assumed that the pressure is gradually adjusted to reach the target at the cruising altitude of 33,000 feet, the green curve on the above diagram. I later learned that the target pressure is typically reached relatively quickly after takeoff and that the cabin pressure was most likely at its target at the time of the accident. This means that my green curve would drop much more quickly and remain flat for the rest of the flight. The green and red vertical bars at the height of the accident represent this error.

To compute the outward pressure on the fuselage (red), we take the difference between the two curves at 16,300 feet, which gives us 26 kPa, assuming the aircraft was pressurized to about 1,800 meters at the time of the accident. (If we incorrectly assume gradual pressurization, the pressure would be about 36 kPa.)

To make this more interpretable, we can compute how much force (in lb or kg-equivalent units) was applied to the door. We will assume the door is nearly rectangular with 72 x 34 inches (183 x 86 cm) dimensions, taken from a 737 manual. To compute the weight in pounds:

$W = P \cdot A \cdot 2.2/g$

P is the pressure in kPa, A is the area in square meters, and g is the gravitation constant. This turns out to be about 9,400 lb (4,300 kg), which I rounded to 9,000 lb in the diagram. At the cruising altitude of 10,000 meters, the weight on the door would be approximately 19,000 lb (~ 8,600 kg).

Conclusions

When the aircraft finally landed, the passengers were treated to the following view of the airfield.

The calculations can make us appreciate how much force every 1.6 square meters of fuselage must withstand, so constructing a well-pressurized cabin is an impressive engineering achievement, while forgetting to put a few screws into the door plug during a final assembly is a massive management oversight.

One can imagine a situation where the door was a bit more secure than it was (but still not fully installed) and that the separation would have happened at 33,000 feet instead of at 16,000. What then? I am not sure what the immediate depressurization at that altitude would do to a human body (if your mouth and nose are closed, your lungs may rupture; you may also suffer from decompression sickness; if you don’t put on the oxygen mask, you will suffocate), much less if the pilots could descend fast enough to avoid hypothermia and other pleasantries.

Up or Down

In June 2023, a submersible operated by OceanGate imploded near the remains of the Titanic. The Titanic is located at 12,500 feet (3,800 meters) under the sea, and the pressure at that depth is about 38,000 kPa, 380 times more than at the surface (~ 380 atmospheres). When the implosion was originally detected, the Coast Guard undertook a massive search and rescue operation. The rescue part was a fool’s errand — at this pressure, the passengers were instantly disintegrated.

In 2019 and 2020, the 737 Max was involved in two accidents relating to the angle of attack sensors. ↩︎
Why should the bag inflate inside the plane? That’s a good question, and this should be the clue that the cabin’s pressure is not kept at sea level but adjusted downward as the plane climbs. ↩︎

Books 2023

The following is a list of books that made an impression on me in 2023. I listen to most non-technical books on Audible and read technical content on paper or my iPad.

The Trial, Franz Kafka (1925)

Franz Kafka wrote The Trial in 1914 and 1915, and it was published in 1925, according to Wikipedia. This famous work was particularly interesting to me, having grown up under a totalitarian regime. I wanted to read it for a long time, and I am glad I did, but it was an infuriating experience, as I am sure the author intended. The next level in this book is not that a citizen is unable to defend himself against the charges brought by the state; in this, there is nothing unusual as evident, for example, by the current trials under Putin and many before and after him, but rather that the protagonist, Joseph K., doesn’t even know what he is charged with.

Alan Turing: The Enigma, Andrew Hodges (1983)

Alen Turing was a British mathematician and arguably the first computer scientist. This is a thorough biography starting with Turing’s early life and education at King’s College, Cambridge, where he demonstrated remarkable facility with mathematics.

In his 1936 paper, “On computable numbers with an application to Entscheidungsproblem (decision or decidability problem),” he introduced what we now call a Turing Machine. The neat thing about the Turing Machine is that it is a purely theoretical construct, unlike, say, a Von Newman computer, which is a design of a digital computer. Turing Machine is a mathematical abstraction that can compute anything computable, and in the paper, Turing showed that not all things can be computed. This is a mind-blowingly general result.

Other details include Turing’s work at Bletchley part where he led the effort to crack the Nazi Enigma code (using Bayesian methods). The British government thanked Turing for his work by criminally charging him with “acts of gross indecency” (Turing was gay) and ordering him to undergo chemical castration. Alan Turing committed suicide in 1954 when he was 41.

Both Flesh and Not, David Foster Wallace (2012)

This is a collection of essays from my favorite essayist, and it did not disappoint. DFW’s fascination with tennis continues with an essay about Roger Federer, which is the book’s title.

Here is an opening quote:

It’s the finals of the 2005 U.S. Open, Federer serving to Andre Agassi early in the fourth set. There’s a medium-long exchange of groundstrokes, one with the distinctive butterfly shape of today’s power-baseline game, Federer and Agassi yanking each other from side to side, each trying to set up the baseline winner… until suddenly Agassi hits a hard heavy cross-court back hand that pulls Federer way out wide to his ad (= his left) side, and Federer gets to it but slices the stretch backhand short, a couple feet past the service line, which of course is the sort of thing Agassi dines out on, and as Federer’s scramblierfng to reverse and get back to center, Agassi’s moving in to take the short ball on the rise, and he smacks it hard right back into the same ad corner, trying to wrong-foot Federer, which in fact he does—Federer’s still near the corner but running toward the centerline, and the ball’s heading to a point behind him now, where he just was, and there’s no time to turn his body around, and Agassi’s following the shot in to the net at an angle from the backhand side… and what Federer now does is somehow instantly reverse thrust and sort of skip backward three or four steps, impossibly fast, to hit a forehand out of his backhand corner, all his weight moving backward, and the forehand is a topspin screamer down the line past Agassi at net, who lunges for it but the ball’s past him, and it flies straight down the sideline and lands exactly in the deuce corner of Agassi’s side, a winner—Federer’s still dancing backward as it lands.

Wallace loves these near-infinite sentences even in assays (his fiction is full of them) and is one of the few authors who can get away with it.

Another tennis essay in the collection is DEMOCRACY AND COMMERCE AT THE U.S. OPEN. Those who know DFW’s work will recognize his fascination with advertising.

For the mathematically inclined, there is RHETORIC AND THE MATH MELODRAMA. Wallace has an appreciation for mathematics (he was an English and Philosophy major with a particular interest in modal logic). This essay introduced me to G. H. Hardy’s “A Mathematician’s Apology,” which I will discuss later.

The Plot Against America, Philip Roth (2004)

I am pretty sure this book reads differently today, after Trump and the October 7 Hamas massacre, than it did when it came out. The premise is that Charles Lindbergh, a famous American aviator and a purported Nazi sympathizer, becomes president with somewhat obvious consequences, including the rise of anti-semitism, relocation of Jews, and so on. Roth is a master storyteller, and this book is a page-turner. I hear HBO has the miniseries now.

This story reminded me of another famous (Lativian) aviator and a Nazi collaborator, Herberts Cukurs, who earned a well-deserved nickname, the Butcher of Latvia. Mossad agents eventually assassinated Cukurs in Urugvaj, while Lindbergh died on Maui of lymphoma, having designed his own coffin.

Open An Autobiography, Ande Aggasi (2000)

This book is ghost-written by J. R. Moehringer and is the best sports biography I have ever read; it is the only sports biography I have ever read if I am being honest. Moehringer also wrote Phil Night’s Shoe Dog, a gripping story of the founder of Nike.

As DFW often noted, it is hard to imagine what it is like to be number one in the world in anything, much less something as competitive as tennis. Stories about Aggasi’s deranged father alone are worth the price of admission. Nothing was easy for Aggasi, but what he lacked in talent (which was not much), he made up in sheer will and perseverance. I found the book inspiring- it put me in a better mood every time I listened.

Educated A Memoir, Tara Westover (2018)

This is another “I can’t believe she made it” book that is both horrifying and uplifting. You can’t help but root for Tara as she navigates her abusive family, particularly her physically and emotionally abusive brother Shawn (pseudonym).

Einstein His Life and Universe, Walter Isaacson (2007)

I read a few Isaacson biographies, and this one has been on my list for a long time. An ardent pacifist, who at one point believed that young people should refuse military service, Einstein gradually changed his mind observing the rise of Nazis. He worried that the Germans would develop the bomb first and encouraged President Roosevelt to fund the development of nuclear weapons, which eventually led to the Manhattan Project (he did not participate in the project directly).

The eventual Nobel Prize was not for relativity but rather for his work on the photoelectric effect, which improved our understanding of light and made possible future inventions like solar panels and any other devices that convert light into electricity.

Martin Gardner has an amusing essay in his book “Fads and Fallacies in the Name of Science” called “Down with Einstein!” In it, Gardner describes a few of Einstein’s skeptics (haters in modern parlance), some of whom unleashed a tsunami of invectives on the physicist. Here is an example of one attack by Jeremiah J. Callahan, a priest (*) and a student of Euclidean geometry, albeit a not-very-good one:

We certainly cannot consider Einstein as one who shines as a scientific discoverer in the domain of physics, but rather as one who in a fuddled sort of way is merely trying to find some meaning for mathematical formulas in which he himself does not believe too strongly, but which he is hoping against hope somehow to establish…. Einstein has not a logical mind.

(*) Lots of priests contributed to science; my favorite, of course, is Reverend Thomas Bayes.

Lying for Money, Dan Davies (2022)

This was Andrew’s (the Gel-dog, as my friend Arya calls him) recommendation, and you can read his detailed review here. As Andrew points out, the neat thing about this book is how Davies, who is an economist by training, considers fraud to be a necessary consequence of any functioning economy in that there is an optimal level of fraud — too little, and you are spending way too much money on prevention and punishment; too much, and you are losing too much in direct damages.

Case studies include Charles Ponzi, Bernie Madoff, Enron, Nick Leeson and the Collapse of Barings Bank (new to me), The South Sea Bubble, and The Nigerian Email scams.

Travels with Charley in Search of America, John Steinbeck (1962)

This was pure comfort food. Tom Hanks recommended it to me (and thousands of other people who listened to the Marc Maron interview.) I started reading Steinbeck in my 30s when I decided it was time to learn about the American experience from quintessentially American writers.

The book is Steinbeck’s travelogue recorded in the 1950s when the author decided to take a journey across America aboard his truck, which he nicknamed Rocinante (*), and accompanied by his poodle Charlie. During the travels, Steinbeck interacts with ordinary Americans and, among other things, experiences the racial tensions and tropes prevalent at the time.

(*) Rocinante was the name of Don Quixote’s horse.

Nobody’s Fool, Daniel Simons & Christopher Chabris (2023)

This is another one of Andrew’s recommendations. I share Adnrew’s fascination with all kinds of fraud, so I usually take his recommendations on the topic.

The book has many exciting examples, including the famous Princess Card Trick. If you haven’t seen it, it’s worth checking it out. Did you figure it out? Yes, all the original cards were replaced, not just the one you focused on.

Another one is statisticians’ favorite which goes by the name of survivorship bias. During WWII, the army tried to figure out how to retrofit B-17 bombers returning from their missions by looking at the pattern of damages they sustained. Suppose you see the following damage pattern.

On a casual inspection, you may want to retrofit the areas where the bullet holes are, but Abraham Wald realized that that would be a mistake. The reason why we do not observe any bullet holes in the blue areas is because the planes that were hit there did not make it back from their missions, and therefore this is where you should fortify the aircraft.

Here are some observations from their section on our collective lack of excitement for situations when something important is being prevented.

We complain when a medication has side effects or doesn’t resolve our symptoms right away, but we don’t think about the possibility that we might have gotten much sicker without it.

Successful precautions to prevent a catastrophic flood go unheralded, but a failed levee draws public ire.

We respond with accusations when a bridge collapses, but we don’t support the engineers who have documented the need for repairs for decades—much less give any thought to the engineers who have kept all the other bridges standing.

Governments might move mountains to respond to an acute health crisis, but health departments responsible for preventing such crises in the first place are chronically underfunded.

The Hundred Years’ War on Palestine, Rashid Khalidi (2020)

This was a difficult book for me, particularly after October 7, when I decided to read it. Khalidi is a Professor of Modern Arab Studies at Columbia University who has deep familiar roots in the region — his great-great uncle was Yusuf Diya al-Khalidi (1842–1906), a mayor of Jerusalem.

The book examines the formation and development of the state of Israel from the Palestinian perspective, starting from the Balfour Declaration in 1917 to the present day; it does not contain any anti-Semitic tropes (just in case you are wondering). To my knowledge, no one had disputed the historical accounts presented in the book (*), but some (not me) objected to the tone.

When trying to understand the world, I believe it is important to consider all credible perspectives, and this book was an important contribution to my understanding of the Middle East and the long-standing conflicts therein.

(*) Dmitry points me to the article by Diana Muir, “A Land without a People for a People without a Land.” In it, she cites some evidence that, contrary to Khalidi’s claim, the use of the slogan was not central to the early Zionist movement.

The Dispossessed, Ursula K. Le Guin (1974)

This was my second book by LeGuin. The first one was The Left Hand of Darkness, which left no impression on me when I read it the first time in college and completely blew my mind when I reread it in 2023. I guess there is a time and place for everything.

The story is set on twin planets Urras and Anarres. Urras is rich and abundant, reminiscent of Earth, with complex societies, including one that mirrors capitalist and patriarchal structures. In contrast, Anarres is a barren world where settlers, inspired by the anarchist teachings of Odo, have created a society without government, private property, or hierarchies.

The protagonist, Shevek, is a brilliant physicist from Anarres. His journey to Urras marks the first time in nearly two centuries that someone from the anarchist society of Anarres visits the capitalist Urras. Shevek’s goal is to complete and share his theory of time, which could revolutionize communication and travel in the universe.
ChatGPT 4

What I love about LeGuin is that the science part of her science fiction is beside the point. I wouldn’t even call it science fiction. She creates alternative worlds where different social, moral, and political structures are explored and developed with consequences that seem logical to LeGuin. The alien planets and peoples are a literary device, but their presence illuminates the presentation.

Infinite Powers How Calculus Reveals the Secrets of the Universe, Steven Strogatz (2019)

I hate certain popular books, particularly those that dumb things down so much there is nothing of substance left or, worse, a completely distorted picture of the subject. The airport bookstore is full of them, and I try to avoid them at all costs. This book is the opposite — it explores integral and differential calculus with some history of the subject sprinkled in; it is neither a textbook nor a purely popular book. There are equations, but they are presented with such clarity and context that I feel like anyone with basic knowledge of high-school math should be able to appreciate the underlying beauty that emerges when you slice things into infinitely many pieces and put them back together. Derivatives, integrals, power series, it’s all there.

A Mathematician’s Apology, G. H. Hardy (1940)

David Foster Wallace recommended this book, and it did not disappoint. It presents the opposite view of mathematics than Strogatz’s Infinite Powers, which I believe is shared by many professional mathematicians. Hardy was interested in pure math, so he found engineering mathematics, like calculus, dull. Moreover, he enjoyed the fact that pure math has no practical utility. In his words:

It is undeniable that a good deal of elementary mathematics—and I use the word ‘elementary’ in the sense in which professional mathematicians use it, in which it includes, for example, a fair working knowledge of the differential and integral calculus—has considerable practical utility. These parts of mathematics are, on the whole, rather dull; they are just the parts which have the least aesthetic value.

He continues:

The ‘real’ mathematics of the ‘real’ mathematicians, the mathematics of Fermat and Euler and Gauss and Abel and Riemann, is almost wholly ‘useless’ (and this is as true of ‘applied’ as of ‘pure’ mathematics). It is not possible to justify the life of any genuine professional mathematician on the ground of the ‘utility’ of his work.

This is an exaggeration, I think. For example, Gauss’s work on error functions is of great practical significance to statisticians, and of course, there is a Riemann integral. Nonetheless, I love Hardy’s mathematical puritanism.

Hardy’s love of pure math was not simply esthetic — he hoped that by practicing pure math, no weapons of war and destruction could be created using his tools. He was a pacificist, you see, a much more ardent one than Einstein.

Other Books

Other notable books that I keep coming back to and picking at are The Road to Reality: A Complete Guide to the Laws of the Universe by Roger Penrose (which got me excited about Complex Analysis), but I never got past Fourier Analysis, Theoretical Minimum by Leonard Susskind (I got through the Lagrangian Mechanics but want to read more), Fads and Falacies by Martin Gardner, Regression and Other Stories by Andrew Gelman et al. (I am reading the Causal Inference chapters), and The History of Statistics: The Measurement of Uncertainty Before 1900, by Stephen Stigler.

Michael Kaufman (1954 – 2023)

Last week, as I was having Thanksgiving dinner with my family, my friend Mitia (a Russian short form for Michael) died after a 6+ year battle with esophageal cancer. His son-in-law called me the next day to let me know. I had been dreading this call for years. I tried to hold back my tears but did not succeed. The last time I spoke to him, about a month ago, he seemed calm and content, joking and cursing in Russian, which we both enjoyed doing. He knew he was dying, but never once did I detect even the slightest hint of self-pity or dread. He was old-school-tough like that.

I met Mitia in my twenties when we both worked for CSC, a technology consulting company. We remained close friends ever since. Over the years, I have gotten to know his family, his wife Helen, and his daughters Liza and Marsha. He talked about them often, and I could feel how much he loved them.

I did not want to go to the funeral; I hate funerals (and weddings), but I felt that I should go out of respect for the family. When I got to the funeral home, his daughter Liza got up to the podium to deliver a eulogy. I immediately felt ashamed for not wanting to come. Being there made me realize just how much he meant to the people who mattered most to him. With Liza’s permission, I am posting it here.

…my father was born in Kiev, the only child of Yuri and Julia. The way he describes his childhood is a mix of wonder and poverty, suspended in the failures and economic realities of communism and extreme anti-semitism. After a stint in the army, having been expelled from engineering school due to being Jewish and over the quota permitted, his parents, grandmother and dog knopka, or pushpin, bought and bribed their way out of the country via the first flight jews were allowed to travel after a train carrying Jewish refugees had been hijacked and bombed only a few weeks prior.

They made their way through Vienna and eventually to Rome, where they would spend months stateless trying to figure out where they, a paperless Jewish family, could go.

On August 26, 1976, a day that has since been celebrated each year as coming to America day, they landed in the US as official refugees – four people, one smuggled dog, scraps of what they could carry, and $100 for all of them. I cannot underscore how difficult the first few years in the US were – it was never a time that was reminisced fondly, and the fear and uncertainty of having no safety net never quite left. They thought they made it when they bought their first loaf of commercial bread, and didn’t have to subsit on the scratch and dent sacks of flour. I would also be remiss without mentioning and acknowledging the Arbeiter and Neugroschel families who were part of the circle that sponsored the whole family. Their kindness and their mitzvahs has never and will not be forgotten.

My father worked at least three jobs while going to school, including as in air conditioning installation, despite two left hands and falling through at least one ceiling. College wasn’t easy, either. Papa nearly failed statistics because he didn’t know the word “die” or “dice” and it wasn’t in his Russian English dictionary. The last time he had asked for a translation of a word not in the dictionary, it had been part of a colorfully obscene vernacular and he wasn’t about to make that mistake again.

He graduated and through some luck, good deeds, networking and grit he landed a job at the then-prestigious Bell Labs as an assistant programmer. He loved his work, and although he was restless in his career, it was clear that he took an immense amount of pride in his achievements, including multiple patents. Everyone started to thrive, but he never quite outran the shadow of where he came from and it would be with him throughout his life.

Within 8 years of arriving in the states, he met and married my mom, and bought his second home – their first together. Within a year I was born and my sister a few years after. If you know anything about my father, he loved his family more than anything – his grandmother, his parents, my mom and his kids. He doted on my mother, and there was no point in their marriage where they weren’t a team, or together. Even a short errand was an opportunity for togetherness. He took immense joy in being a proud parent and grandparent. I sometimes think he loved more fiercely than most because he knew what it was to lose everything, risk everything, and have family be the only thing that survives.

He also loved this country – his adopted country that took him in, allowed him to pursue a fulfilling career, raise his family, put his children through school and live a comfortable life. He loved traveling the country and dreamt of buying an RV and traveling nearly full time. Mostly I think he loved democracy – getting to speak his mind, which he did early and often, without fear of losing his life. He equally loved having the ability to vote with his dollars – he cancelled companies before it was a thing and there was constant whiplash about what companies were on the kaufman list of economic sanctions at any time. We all rejoiced when Dijon mustard made its way back into good graces. Heinz ketchup never did, and that’s where the rest of us drew the line and revolted – we always had two ketchups in the fridge.

There are so many other things that he liked that made him him. He had rules for everything, and superstitions wherever rules fell short, and we often referred to kaufman cockamamie plans that were designed to maximize efficiency only he understood. I would routinely be told, including through adulthood, that I boiled the water for tea “wrong”. At the same time, he had a healthy mistrust of low level laws and minor societal rules, having no problem finding loopholes. Indeed, he taught himself a new route to his home of more than 20 years after being warned for the last time by the new Providence police about rolling through a stop sign in his orange stick shift Volvo coupe. When I asked why he would waste gas and time to go around the block, he acknowledged that he’d never fully stop and the eventual ticket would be more expensive and annoying. I honed my legal skills from a young age being the family letter writer to many a traffic court, as well as corporations that had somehow violated his rules and code.

I would never really describe him as happy, or at least not happy go lucky and he lived his life waiting for the other shoe to drop. And yet, he took immense, palpable joy is his particular brand of mishegas and misanthropy. While he was mistrustful of people as a whole, he connected with people on an individual level and there’s hardly a store or a place we’d go where people didn’t greet him by name and he greeted them right back – with a joke about their sports team, family, cars, or something else personal he took the time to remember. He always identified deeply with people who he considered to be hard workers trying to get by for their families.

He loved so many small things that were, in retrospect, much larger. I’d like to share with you some of his great affinities and which are things that will forever remind of us of him.

He drank tea vociferously, and having tea together as a family was our quality time. Tea with breakfast, mid-morning, afternoon, and especially at night for dessert. He took his tea with milk, never sweetened and if it wasn’t dessert, he ate jelly with it, that reminded him of his family’s confitures growing up. His love of dark chocolate and most sweets was well-known, and he ate nightly ice cream nearly year round (there are rules you know). His love of ice cream was directly and inversely correlated with the price; his favorite was the carton on sale. As it turns out, many things tasted better on sale, not least of all fruit and we’d drive for miles to get a better deal of cherries or watermelon in season, and for watermelon, it included a thorough inspection of nearly all the fruit in the pallet.

Papa loved animals and particularly dogs. He was a softie and would stuff his pockets full of dog treats when he was going to the city. He needn’t have, because he was a dog whisperer – they were just drawn to him. He could recount, in detail, stories about each of his dogs and grand dogs, and in truth, we pretty much shared my family’s dog, Mothball, for whom he served as chief apologist.

He also had a soft spot for cars and loved to drive, finding it meditative and later, therapeutic. I have never met anyone else with such encyclopedic knowledge about cars, although he never gave himself permission to get a true performance vehicle. A few months ago we recounted every one of his 20+ cars that he owned or leased here and he could recall every detail. I think his favorite was the gray turbo station wagon that wasn’t labeled as a turbo and with which he took particularly delight in racing at traffic lights. He did not race to lose.

He was a soccer nut, and while Arsenal was his favorite team, and Dynamo Kiev was his home team, he really loved the art of soccer. Watching soccer, in the early days on the Spanish channel, was probably the one thing he did for him. He didn’t care who he watched, as long as the game was good, but he especially enjoyed a later-in-life rivalry between Arsenal and Tottenham with Eric. In a testament to him, he had always wanted to see a world cup match, and had the opportunity to do so in 1994, but gave up a coveted ticket because it was my mom’s birthday, and he couldn’t bear not celebrating on the exact date.

Most of all, we will remember him as being funny and just…wildly inappropriate. His particular brand of sarcasm and bending of societal propriety is inimitable, cancellable, and despite our sometimes-mortified reactions, he somehow got away with the most outlandish things. He was also kind, good natured and loving. At his best, these qualities gelled in a way that is difficult to describe, but is a good part of the reason why we loved him and loved spending time with him, which is all we can really hope for. Now that I’m a parent too, I know he did his job right – to raise the type of children who you want around and who want you around, and really nothing else matters. He loved fiercely and we loved him fiercely right back.

We say in Judaism, Zichrono l’vracha: may his memory be a blessing. So I invite you to join our family – the next time you have a cup of milky tea, blow the car next to you out of the water, enjoy a deeply discounted cup of ice cream, hear an announcer cry GOL, eat the middle cherry of the season when the peak ripeness and lowest cost cross in an axis, snuggle with an animal, and you’re enjoying the moment with family, I hope, for just a second, you think of my father. For his family his blessing is so much more than a memory.
Elizabeth Kaufman Bieber

Woodpecker’s hell

There is a small place in hell where the woodpeckers dwell, they discuss what to say to each other, and while doing it softly they peck at the wood for the woodpeckers dwell in their sorrows.

Once the one who was there for eternity years said the following phrase to another: I would give all my death to the one who remains and the one who can state it concretely, what this argument is that we’re trying to please and the rest will fall in rather neatly.

Can science guide policy?

TLDR: It can guide it but it cannot determine it.

In a recent MedPage Today OpEd “What Does ‘Follow the Science’ Mean, Anyway?“, Vinay Prasad argues that science alone is not sufficient to guide policy and that and that to inform decision making, it needs to be supplemented with an appropriate value system. In his words:

… science will never be sufficient to guide choices and trade-offs. Science cannot make value judgments.

If we replace “guide” with “determine”, I agree and I would like to clarify how a value judgment can be incorporated in the context of probabilistic inference. Probabilities alone are not sufficient to guide decision-making as they generally do not account for the costs and benefits of a set of possible actions. In other words, knowing the probability that it is going to rain is not enough to decide if you should carry an umbrella — you need to weigh that by the cost of the umbrella and by how much you hate getting wet. From this, you can see that it could be perfectly rational for two different people to act differently under the same weather forecast.

Decision theory, a science that is concerned with making rational decisions, has a long literature on how to encode these costs and benefits — economists call these utility functions, and statisticians, being a more pessimistic bunch, call them loss functions (U = -L). There is nothing unscientific about utility functions as we can study how closely they match people’s risk and reward preferences. So given that we can specify a utility function for say a vaccination policy, we can integrate it over our uncertainty (from the probabilistic model that includes Pr(efficacy)) and maximize this function with respect to the set of contemplated actions. This process can then guide policy by choosing the action with the highest utility. See, for example, Lin et al. (1999) which works out a policy recommendation for home radon measurement and remediation.

Of course, there is a caveat. Even assuming you can write down a set of realistic utility functions, a very difficult task in itself, who’s utility should we choose to maximize? This is where science is completely silent. It does not take a lot of imagination to realize that the utilities of any set of individuals, a utility of a corporation, and a utility of a population as a whole, are likely different. They may be similar but they are not the same. It is in that sense that science can not determine policy — the final choice of one utility function from a set of possible utilities must incorporate the most relevant value system in a society where it is to be applied. People must choose that, science can’t help you there.

References

Lin, C.-Y., Gelman, A., Price, P. N., & Krantz, D. H. (1999). Analysis of Local Decisions Using Hierarchical Modeling, Applied to Home Radon Measurement and Remediation (No. 3; pp. 305–337).

Learning Bayes from books and online classes

In 2012 I wrote a couple of posts on how to learn statistics without going to grad school. Re-reading it now, it still seems like pretty good advice, although it’s a bit too machine learning and Coursera heavy for my current tastes. One annoying gap at the time was the lack of online resources for learning Bayesian statistics. This is no longer the case, and so here are my top three resources for learning Bayes.

Richard McElreath from the Max Planck Institute for Evolutionary Anthropology recently published the second edition of Statistical Rethinking. In the book, he builds up to inference from probability and first principles and assumes only a basic background in math. I don’t love the obscure chapter names (makes it hard to figure out what’s inside) but this is the kind of book I wish I had when I was learning statistics. The example code had been ported to lots of languages including Stan, PyMC3, Julia, and more. Richard is currently teaching a class called “Statistical Rethinking: A Bayesian Course” with all the materials including lecture videos available on GitHub. For updated videos, check out his YouTube channel.

Aki Vehtari from Aalto University in Finland released his popular Bayesian Data Analysis course online — you can now take it at your own pace. This course uses the 3rd edition of the Bayesian Data Analysis book, available for free in PDF form. This is probably the most comprehensive Bayesian course on the Internet today — his demos in R and Python, lecture notes, and videos are all excellent. I highly recommend it.

For those of us who learned statistics the wrong way or who want to see the comparison to frequentist methods, see Ben Lambert’s “A Student’s Guide to Bayesian Statistics.” His corresponding YouTube lectures are excellent and I refer to them often.

Although not explicitly focused on Bayesian Inference, Regression and Other Stories by Andrew Gelman, Jenifer Hill, and Aki Vehtari is a great book on how to build up and evaluate common regression models while using Bayesian software (rstanarm package). The book covers Causal Inference, which is an unusual and welcome addition to an applied regression book. The book does not cover hierarchical models which will be covered in the not-yet-released “Applied Regression and Multilevel Models.” All the code examples are available on Aki’s website. Aki also has a list of his favorite statistics books.

Finally, I would be remiss not to mention my favorite probability book called “Introduction to Probability” by Joe Blitzstein. The book is available for free in PDF form. Joe has a corresponding class on the EdX platform and his lecture series on YouTube kept me on my spin bike for many morning hours. Another great contribution from team Joe (compiled by William Chen and Joe Blitzstein, with contributions from Sebastian Chiu, Yuan Jiang, Yuqi Hou, and Jessy Hwang) is the probability cheat sheet, currently in its second edition.

What are your favorite Bayesian resources on the Internet? Let us know in the comments.

Brighter days ahead

As the dark and frustrating 2020 is winding down, I feel incredibly optimistic about 2021 and beyond. Part of it is my entrepreneurial nature that requires it and part of it is a number of recent developments that bring me hope and I love drinking hope for breakfast.

A number of recent readouts from SARS-CoV-2 trials, particularly those from Pfizer and Moderna, which use a novel mRNA platform, look efficacious and safe in the short-term. (Long-term safety can not be evaluated in rapid clinical trials but the FDA guidelines provide for long-term, post-licensure, safety monitoring.) As soon as these vaccines are made available to the general public and assuming no major safety issues are surfaced, I am getting vaccinated and resuming my pre-pandemic travel schedule.

In case you missed it, on May 30th we witnessed the first American manned space flight since 2011. I watched it in real-time that Saturday and then many more times with my son Andrei who just loves watching rockets being launched into space. Since then, watching launches on Saturdays became a Novik family tradition. Seeing Andrei’s eyes light up every time we do it, brings me an unreasonable amount of joy.

Two weeks ago I ordered my first Virtual Reality headset — Oculus Quest 2. I don’t love the Facebook login requirement but as a newcomer to the world of VR, I am completely blown away by how easily my senses are fooled and by the near-perfect rendering of 3D worlds. It is clear to me that VR is a major technological trend with ramifications far beyond gaming. I can’t wait to virtually sit in front of my family and friends all over the world and interact with them as if we are in the same room. The technology is not quite there to make the experience realistic but I have little doubt that it’s coming. (As a side note, the game Room in VR is nothing short of amazing.)

During the summer, we made a lot of progress at Generable with fitting large meta-analytic models for oncology drugs, and our abstract was accepted at SITC 2020, an immuno-oncology conference. This is a big deal for us as it represents the first publication outside of statistics journals. Most of the work was done by Jacqueline Buros and Krzysztof Sakrejda and is a culmination of our year-long research collaboration with AstraZeneca.

And if this is not enough, 2021 promises to be a much more sane US Federal Government with adults finally taking over and mitigating the Fifth Risk. No doubt countless problems remain (I don’t want to list them) but I am feeling lucky and optimistic.

Communists and Dictators, Liberals and Conservatives, Left and Right, Right and Wrong

I grew up in the Soviet Union, more precisely in Soviet Latvia. Thanks in part to my dad, I was able to come to the United States in 1989, just before the collapse of the USSR. My dad immigrated to the US in 1978 during the so-called first wave of Jewish immigration.

I attended a relatively typical Soviet high school in Riga; it was creatively called School #87, and it specialized in Physics and Chemistry. Not all schools had a specialization, but this one did. I remember attending organic Chemistry lectures at the local university. I hated organic chemistry. High school was a 2-year affair in the old Soviet Union, so grades 9 and 10. The unwritten rule of the Soviet school system was that when you entered first grade, you became an “October Kid”, referring to the October Bolshevik revolution, and received a little red star to be worn on the lapel of your navy blue uniform jacket. The star had Lenin’s portrait engraved in the middle.

In middle school, you would be promoted to a “Pioneer” which was considered the second stage of your communist journey. You were not asked to join – you simply aged into it. You were given a red, two-pronged tie which looked quite festive atop of a white button-down shirt. I wore mine just like everyone else.

Then came high school. In high school, you were supposed to join the “Komsomol” — a communist youth organization, the last step before the actual party membership. Unlike the Pioneers, Komsomol wanted the appearance of a volunteer organization. You were supposed to ask to join and to my knowledge everyone did. I did not. Now, before you think that I was some kind of Solzhenitsyn or Sakharov, let me assure you that I was not. In the late 80s, Gorbachev’s perestroika, which means rebuilding, was in full force. The iron grip was starting to loosen and people started feeling that they can express themselves freely without facing the wrath of the state. Had these been the 70s, 60s, or before, this act of noncompliance would have gotten me and my family into serious trouble, and I doubt that I would have been so brave.

Even so, I hated the communist party and all it represented. Being raised in an educated household, I was aware of some of the atrocities committed by Soviet dictators and their henchmen against their own citizens, and their hypocritical rhetoric of equality and brotherhood was not lost on me. It was also obvious that a centrally planned economy was a colossal failure. And so when it was time to join the Komsomol, our “class leader”, Polina Kononovna, an ardent communist, insisted that I start getting ready for membership. “No, thank you,” I said. “I don’t feel like am ready.” Eventually, she left me alone. It was a small but important win for me.

When I landed in JFK in September 1989, I was 17 and I met my father essentially for the first time — my parents divorced when I was 3 years old and even though my mother tells me that I saw him a few times before he left for the US, I had very little recollection of our interactions. In 1989, my dad was already a successful physician in New Jersey. Like most immigrants from communist countries like Cuba and the Soviet Union, he is a staunch conservative and a proud Republican. After experiencing the evils of communism first hand, people like my dad recoil at anything that appears to have socialist overtones. Their analysis is quite shallow, to be sure, but who has the time or desire to do a deep-dive on the fundamental differences between American liberals and Russian or Cuban communists? I certainly did not, and so I blindly inherited my dad’s conservative principles without being too political. I did not vote for a long time and when I finally did, it was for George W Bush, a decision that I later regretted.

Over the years I made it a point to learn more about American history and the American political system. The more I learned, the more conflicted I felt. On one hand, unlike the Soviet Union, the American experiment was an incredibly successful enterprise that managed to establish an independent judiciary, a free press and freedom of speech, and at least on paper, a guarantee of equal protection to all its citizens. The level of average economic prosperity was also unprecedented. On the other hand, it does not take too much research to learn about the less flattering history: atrocious treatment of Native Americans by the colonists (e.g. purposely infecting them with smallpox, an act of biological warfare), the history of slavery and racism so potent that it lasts to this day, the civil war, women’s suffrage movement (women were not allowed to vote until 1920; see Elizabeth Cady Stanton and Susan B. Anthony), the internment of Japanese Americans during the second world war (deemed constitutional by the US Supreme Court! see Korematsu v. United States), Vietnam, and Chicago 7, just to name a few.

It turns out that no country is perfect and neither is my beloved US. While living in Russia I learned, then later forgot, and then again remembered that one needs to question what the government, any government is doing to and for its citizens. It now seems obvious to me what Adam Gopnik so eloquently described in his book “A Thousand Small Sanities”: liberal, progressive movement must be diametrically opposed to both the far-right (e.g. Fascism) and the far-left (e.g. Communism). These two movements devolve into totalitarian, oppressive states, and have more in common with each other than with a liberal, progressive agenda, with its respect for humanity, human rights, and human dignity above all else.

During the cold war, the world was under a Communist threat. I think in general, the US overestimated just how far USSR was willing to go — Khrushchev was fully aware and clearly unwilling to participate in the mutually assured destruction during the Cuban Missile Crisis although Castro seemed to be ready to annihilate the world. Today, by any reasonable account, the world is in danger of succumbing to right-wing nationalism, the likes of which we have not seen since the second world war. Unfortunately, American conservative politicians don’t realize how far to the right they are moving and under the direction of Donald Trump keep falling further into the abyss. As I sit here and write these words, Trump is refusing to recognize the legitimacy of the election results, an election that he so clearly lost. I never thought I would witness a coup attempt accompanied by this kind of authoritarian rhetoric from an American president. To see Trump’s playbook, if you can call it that, compare his speeches to other autocrats throughout the world: Erdoğan in Turkey, Orbán in Hungary, Bolsonaro in Brazil, and the list goes on. Their dangerous message is the same: restore the country’s greatness while dispensing with basic democratic institutions, like free elections, for example.

When 2016 arrived and with the benefit of a more rounded education I promised myself that I will participate in the political process and vote in every election. Hilary Clinton was not my favorite candidate but against Trump, she seemed like a no-brainer. When Trump won, I was concerned, but I fully accepted the will of the people (even though he lost the popular vote), and I wished him well hoping that the weight of the office would induce a sense of responsibility in a seemingly irresponsible showman. Alas, this did not happen. In his book “The Fifth Risk”, Michel Lewis described just how badly he mismanaged what was a fairly well-functioning Federal Government, starting with the transition in which he refused to participate. (By Federal Government I mean federal agencies, not the legislative branch which has been in stalemate for many years.) During the 2020 election, my favorite candidate was Andrew Yang, who had some fresh ideas like UBI and did not rely on the old-school Democrat talking points like tax-the-rich. (I mean, sure, tax them, but that’s not going to solve our fundamental problems, not to mention that the rich have a lot of options when it comes to avoiding paying taxes.)

Now, in case you are trying to classify me, I am not a Democrat, I do not belong to any political party, but today I think it is important for me to go on record. When in 10 or 20 years from now and with the benefit of perspective, this period in American history is rightly recognized as one the darkest, most fragile moments since the beginning of the republic, I want my kids and my grandkids to know where I stood. I unequivocally reject Trump, Trumpism, and all that it represents. Today’s Republican representatives in Congress (but not the people who voted for them) that stand behind Trump to protect their own skin, afraid of the Twitter mobs that he may unleash on them — I do not wish you any harm but there will be a day of atonement, a judgment day when you will be unable to look your kids and your countrymen in the eye. Your names will forever be marred by your cowardice, your inhumanity, your demagoguery, and your lies, willingly told and repeated. While supporting this regime to the very end, you have sold your country and your democracy short. Shame on you! The kind of nonsense propaganda I hear from you today is comparable to what I heard from Soviet apparatchiks in the 80s and 90s.

To the 70 million Americans that voted for Trump (and to the 5 or 6 of you who will read this blog post), I want to be clear — you are not my enemy and I hope I am not yours. As a rule, I usually refrain from voicing my political opinions on social media, nothing good seems to come of it, but I did have the following Twitter conversation the other day:

I can understand my correspondent’s position but to implicate 70 million people in antisemitism because the guy they voted for is a racist is a bit much. For me personally, it is also a little too close to home. You see, my own Jewish father voted for Trump, twice, I think. What am I supposed to do with that now? He is the same father who helped me immigrate from the Soviet Union, the same father who opened his house to me and supported me, the same father who stayed with me in the hospital when I had my shoulder operation. Am I supposed to reject him just because in a momentary lapse of reason that unfortunately lasted for 4 years, he voted for Trump? Absolutely not! I do not reject him or the 70 million citizens whose concerns were ignored for way too long, legitimate concerns, who, I hope, out of desperation voted for Trump. I do not reject you. I believe you will come around, eventually, to empower representatives that put our country’s interests ahead of their own.

Thanks to Jacki Novik for proofreading and providing helpful comments.

Estimating uncertainty in the Pfizer vaccine effectiveness

On Nov 20, 2020, the New York Times published an article titled: “New Pfizer Results: Coronavirus Vaccine Is Safe and 95% Effective.” Unfortunately, the article does not report the uncertainty in this probability and so we will try to estimate it from data.

Assumptions

n <- 4.4e4  # number of volunteers
r_c <- 162  # number of events in control
r_t <- 8    # number of events in vaccine group

NYT reports a 44 thousand person trial with half of the people going to treatment and half to control. They further report that 162 people developed COVID in the control group and 8 were in the vaccine group.

The Pfizer protocol defines vaccine effectiveness as follows:

$\text{VE} = 1 – \frac{p_{t}}{p_{c}}$ Here $p_{t}$ is infection rate in vaccinated group and $p_{c}$ is the rate in the control group.

Model

Also, let’s assume that we have no prior beliefs about the effectiveness rate and so our model is as follows: $\begin{align} p_{c} \sim \textsf{beta}(1, 1) \\ p_{t} \sim \textsf{beta}(1, 1) \\ y_{c} \sim \textsf{binomial}(n_{c},p_{c}) \\ y_{t} \sim \textsf{binomial}(n_{t},p_{t}) \\ \end{align}$ The treatment effect and $VE$ can be computed directly from this model.

$\begin{align} \text{effect} = p_{t} – p_{c} \\ \text{VE} = 1 – \frac{p_{t}}{p_{c}} \end{align}$

The effect will have a distribution and to get the probability of the effect (this is different from VE), we sum up the negative area under the effect distribution. For this problem, we do not need Stan, but I am including it here to show how easy it is to specify this model, once we write down the math above.

data {
  int<lower=1> r_c; // num events, control
  int<lower=1> r_t; // num events, treatment
  int<lower=1> n_c; // num cases, control
  int<lower=1> n_t; // num cases, treatment
  int<lower=1> a;   // prior a for beta(a, b)
  int<lower=1> b;   // prior b for beta(a, b)
}
parameters {
  real<lower=0, upper=1> p_c; // binomial p for control
  real<lower=0, upper=1> p_t; // binomial p for treatment 
}
model {
  p_c ~ beta(a, b); // prior for control
  p_t ~ beta(a, b); // prior for treatment
  r_c ~ binomial(n_c, p_c); // likelihood for control
  r_t ~ binomial(n_t, p_t); // likelihood for treatment
}
generated quantities {
  real effect   = p_t - p_c;      // treatment effect
  real VE       = 1 - p_t / p_c;  // vaccine effectiveness
  real log_odds = log(p_t / (1 - p_t)) -
                  log(p_c / (1 - p_c));
}

Running the model and plotting the results

Let’s run this model from R and make a few plots.

library(cmdstanr)
library(posterior)
library(ggplot2)

# first we get the data ready for Stan
d <- list(r_c = r_c, r_t = r_t, n_c = n/2, 
          n_t = n/2, a = 1, b = 1) # beta(1,1) -> uniform prior

# compile the model
mod <- cmdstan_model("vaccine.stan")

# fit the model with MCMC
fit <- mod$sample(
  data = d,
  seed = 123,
  chains = 4,
  parallel_chains = 4,
  refresh = 0
)

## Running MCMC with 4 parallel chains...
## 
## Chain 1 finished in 0.2 seconds.
## Chain 2 finished in 0.2 seconds.
## Chain 3 finished in 0.2 seconds.
## Chain 4 finished in 0.2 seconds.
## 
## All 4 chains finished successfully.
## Mean chain execution time: 0.2 seconds.
## Total execution time: 0.3 seconds.

# extract the draws
draws <- fit$draws()

# Convert to data frame
draws <- posterior::as_draws_df(draws)
head(draws)

## # A draws_df: 6 iterations, 1 chains, and 6 variables
##    lp__    p_c     p_t  effect   VE log_odds
## 1 -1041 0.0072 0.00045 -0.0068 0.94     -2.8
## 2 -1041 0.0075 0.00034 -0.0071 0.95     -3.1
## 3 -1044 0.0084 0.00072 -0.0077 0.91     -2.5
## 4 -1043 0.0065 0.00027 -0.0063 0.96     -3.2
## 5 -1043 0.0068 0.00026 -0.0065 0.96     -3.2
## 6 -1042 0.0078 0.00029 -0.0075 0.96     -3.3
## # ... hidden meta-columns {'.chain', '.iteration', '.draw'}

# look at the distribution of the effect
ggplot(draws, aes(x = effect*1e4)) +
  geom_density(fill = "blue", alpha = .2) +
  expand_limits(y = 0) + theme_minimal() +
  xlab("Size of the effect") +
    ggtitle("Reduciton in infections on treatment per 10,000
             people")

# Probability that there is an effect is the negative mass 
# of the effect distribution; more negative favors treatment 
# -- there is no question that there is an effect

round(mean(draws$effect < 0), 2)

## [1] 1

ggplot(draws, aes(x = log_odds)) +
  geom_density(fill = "blue", alpha = .2) +
  expand_limits(y = 0) + theme_minimal() +
  xlab("Log odds") + 
  ggtitle("Log odds of the treatment effect.
More negative, less likely to get infected on treatment")

label_txt <- paste("median =", round(median(draws$VE), 2))
ggplot(draws, aes(x = VE)) +
  geom_density(fill = "blue", alpha = .2) +
  expand_limits(y = 0) + theme_minimal() +
  geom_vline(xintercept = median(draws$VE), size = 0.2) +
  annotate("text", x = 0.958, y = 10, label = label_txt, size = 3) +
  xlab("Vaccine effectiveness") +
  ggtitle("Pfizer study protocol defines VE = 1 - Pt/Pc")

quant <- round(quantile(draws$VE, probs = c(0.05, 0.5, 0.95)), 2)

So if we observe 162 infections in the placebo group and 8 in the vaccinated group, the vaccine could be considered to be about 0.95 effective with the likely effectiveness anywhere between 0.91 and 0.97 which represents the median and the 90% quantile interval. We should insist that reporters produce uncertainty estimates and the reporters, in turn, should insist that companies provide them.