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April 30th, 2023 (Permalink)

Now He Tells Us

Eric Boehm, "Anthony Fauci Says Don't Blame Him for COVID Lockdowns and School Closures", Reason Magazine, 4/25/2023

If you're looking for someone to blame for the infamous "15 days to slow the spread" that turned into more than a year of shuttered schools, closed businesses, and fraying social connections, Anthony Fauci says don't look at him.

"Show me a school that I shut down and show me a factory that I shut down," says Fauci, the former White House coronavirus czar and now-retired public health official who became the face of both the Trump and Biden administrations' handling of the COVID-19 pandemic…. "Never. I never did."

… But when it comes time to answer the tough questions about who was at fault for America's botched response to COVID-19, the good doctor is happy to pass the buck. The blame is spread around, not only to the CDC and the other public health apparatuses for which Fauci became a convenient (and willing) personification but also to the politicians who followed public health recommendations without any consideration of the costs involved. …

"I gave a public-health recommendation that echoed the C.D.C.'s recommendation, and people made a decision based on that," says Fauci. "I'm not an economist. The Centers for Disease Control and Prevention is not an economic organization. The surgeon general is not an economist. So we looked at it from a purely public-health standpoint. It was for other people to make broader assessments―people whose positions include but aren't exclusively about public health. Those people have to make the decisions about the balance between the potential negative consequences of something versus the benefits of something."

Fauci is…correct when he diagnoses why these failures happened. "We looked at it from a purely public-health standpoint," he says…. "It was for other people to make broader assessments." That's exactly what many elected and appointed officials at all levels of government failed to do during the pandemic. Protecting public health is one important component of an overall pandemic response plan, but other things matter too: the economy, the learning loss from closed schools, the social effects of lockdowns. Too many public officials ignored those other things for too long, and we're still dealing with the consequences.

But while Fauci is narrowly correct about each of these things, he's also woefully understating the role that he played in creating the mess. From the start, Fauci pushed for the Trump administration to tell states to lock down. "No bars, no restaurants, no nothing. Only essential services. When you get a place like New York or Washington or California, you have got to ratchet it up," he told Science magazine in an interview in mid-March 2020.

Fauci also pushed back against evidence that lockdowns were causing unintended (though totally predictable) problems. … For Fauci to now sit back and claim that public officials should have spent more time listening to economists and other advisers that weren't him is both true―they absolutely should have!―and incredibly frustrating. …

They say that success has many fathers, but failure is an orphan. Unfortunately, America's COVID-19 failures have many parents―they're just all absent. It's easy (and in some ways right) to blame Fauci singularly, but that actually hides a good portion of the policy lessons that ought to be learned from the past few years. … It would be nice if Fauci was singularly responsible―then his exit from public life would mean there was no chance this could happen again. Unfortunately, things are not so simple.

Disclaimer: I don't necessarily agree with everything in this article, but I think it's worth reading as a whole. In abridging it, I have sometimes changed the paragraphing.

April 25th, 2023 (Permalink)

Charts & Graphs: Who Pays the Piper?

The CBC is Canada's version of the UK's BBC and America's NPR/PBS1, that is, a government-founded radio and television operation. Recently, the CBC was upset that Twitter labelled its account "government-funded"2, despite the fact that that's true. In response, the CBC claimed that it has "complete editorial independence", which is false: as long as it controls the CBC's budget, the ultimate editorial control comes from the Canadian government. If the CBC really wants complete editorial independence it should stop taking money from the government; until then, it's only incompletely independent.

Twitter users ought to be warned when they are reading government media sources. To protest being labelled in this way, the CBC "paused" its Twitter feed over a week ago, but they were back with a "tweet" a couple of days ago and, as far as I can tell, there's no longer any label indicating its connection to the Canadian government. So, I guess Twitter backed down.

The CBC put out the following chart of their sources of funding in an annual report a few years ago3:

CBC Graph

There are a couple of misdemeanors committed by this chart and one felony; let's examine the misdemeanors first.

The first misdemeanor is that there are two groups of three bars, each representing a different time period, which are arranged with the more recent period first and the earlier period later. It is a charting convention that when the x-axis of a chart represents time, as it often does, time flows from left to right. Now, there can be good reasons for violating such conventions, but I can't see any reason at all for doing so in this chart, let alone a good one. Given the convention, you're likely to think that time flows in the opposite direction than it does in the chart, unless you pay close attention to the labels at the bottom of the groups of bars.

A second misdemeanor is that the only way to understand the relation between the three bars in each group is to read the labels at the top of each bar, then pay attention to the color legend at the bottom of the chart. If you do so, then you'll see that the leftmost bar represents the total funding of the CBC, with the red part representing funding from the government and the blue part "revenue". Then, the next bar breaks down the "revenue" part of CBC's funding into three subcategories, one of which is revenue from advertising. Finally, the rightmost bar breaks down advertising revenue into two additional sub-subcategories.

As a result of these misdemeanors, the chart requires considerable effort to understand correctly, but that's not the worst. Let's look now at the charting felony. If you pay close attention to the scale on the y-axis to the left, you'll see a couple of weird wiggly lines between $700M and $1,700M: this indicates that the scale, which had been going up in increments of $100M, suddenly jumps by $1,000M! As a result, the heights of the bars are useless for comparing the sizes of the different categories of funding. Just looking at the total revenue bar for the most recent time period―that is, the one on the far left―it appears that only about 40% of the CBC's funding comes from the government. However, if you attend to the actual numbers printed on the bars, you'll see that the government provided $1,213,700,000 out of a total of $1,703,800,000, or about 70% of the CBC's funding.

So, this chart is worse than useless, since it requires considerable effort and attention not to be misled by it, and it would have been better simply to present the numbers without the truncated bars. As I explained ten years ago4, the whole point of bar charts is to allow the viewer to compare the sizes of quantities by visually comparing the sizes of bars, and truncating the bars defeats that purpose.


  1. "Canadian Broadcasting Corporation", Encyclopaedia Britannica, accessed: 4/25/2023.
  2. "Canada's CBC says Twitter 'not serious' after '69% government-funded media' label", Reuters, 4/18/2023.
  3. "Revenue and Other Sources of Funds", CBC-Radio, 4/19/2023.
  4. Charts & Graphs: The Gee-Whiz Bar Graph, 4/4/2013.

April 11th, 2023 (Permalink)

What's New?

The Lottery Fallacy!

April 6th, 2023 (Permalink)

How to Solve a Problem: Contraction

This entry is the first in what I hope will be a series on problem-solving techniques using recreational puzzles as examples. A puzzle is, of course, a type of problem, and the techniques useful for solving puzzles, if appropriately generalized, can be applied to the problems of everyday life. At the end of the series, if it is successful, you should be a better puzzle-solver and, more importantly, a better problem-solver in general.

So, let's start out with a puzzle. To get the most out of this exercise, I suggest at least trying the following puzzle. If it stymies and frustrates you, don't fret as I will show you how to solve it later.

Puzzle: Goldilocks and the Three Beers

The Logicians' Club is an organization for perfect logicians who assume nothing and never make a mistake. Moreover, when asked a question, perfect logicians answer with the exact truth and never volunteer information. As you might expect, not many people are eligible for membership. In fact, the current membership of the club consists of five logicians.

The club decided to hold its monthly meeting at a local tavern. When four members of the club―let's call them "A", "B", "C" and "D"―had seated themselves at a table, a blonde waitress approached to take their orders. The waitress was, in fact, also a member of the club, which is why that particular tavern was chosen for the club's meeting. Because of her hair, her nickname was "Goldilocks".

"Would all of you like a beer?" Goldilocks asked A.

"I don't know", said A. Goldilocks turned to B and raised her eyebrows.

"I don't know either", replied B. Next, it was C's turn to answer.

"I don't know", answered C. Finally, Goldilocks looked at D.

"No", said D.

Goldilocks left the table and returned a few minutes later carrying a tray with three glasses of beer on it. She set a glass of beer on the table in front of A, one in front of B, and one in front of C, but none in front of D. Each of A, B, and C raised a glass and sipped the beer.

Why did Goldilocks serve beer to A, B and C, but none to D?

Take a shot at solving this puzzle before reading on. Don't give up too easily, but if you start tearing your hair out, stop before you're bald.

Puzzles with definite answers can often be solved by trial-and-error, at least if they're not too complicated, but the solution to this puzzle will be an explanation of Goldilocks's behavior so trial-and-error will not work. To explain why she acted the way she did you must keep in mind that she is a member of the Logicians' Club, and thus a perfect logician.

Another important point is to pay close attention to the question that Goldilocks asked, especially since the club members are perfect logicians and they do not volunteer information, but only answer what they are directly asked. Notice, also, that she was asking the same question of each of the four members.

To solve this puzzle, you need to use a technique called "contraction"*, and I doubt that it can be solved in any other way. What is contraction? It is the technique of reducing a problem to a simpler form, solving the simpler version, then building back up―often step-by-step―to the full problem. Obviously, simple problems are easier to solve than more complicated ones.

In the case of this particular puzzle, you should ask yourself the question: why are there four logicians at the table ordering and not one, two, or three? In many puzzles, the reason is to make it harder; therefore, you should try reducing its size to make it easier.

Now, the tricky part of contraction is knowing how to reduce the puzzle in size. In this case, if there were only one logician ordering, Goldilocks would not ask the question: "Would all of you like a beer?" Instead, she would ask: "Would you like a beer?", which is a different problem.

Notice that the first three logicians all answer the same way, and only D says something different, which is probably significant. What would happen if there were only two logicians, say, just A and B? A would play the role of A, B, and C in the uncontracted puzzle. Here's how it would go:

"Would both of you like a beer?" Goldilocks asked.

"I don't know", said A. Goldilocks turned to B and raised her eyebrows.

"No", said B.

Let's put ourselves in the position of Goldilocks: what would she make of these answers? First of all, why would A answer "I don't know"? Surely, A knows whether he wants a beer, but the question is about both A and B. The obvious explanation of why A would not know the answer to the question is that A doesn't know whether B wants a beer. However, if A did not want a beer, then he would know that it was false that both wanted a beer, even if he didn't know what B wanted. Therefore, it must be the case that A does want a beer, but doesn't know whether B does, so that the correct answer to Goldilocks's question is the one he gave.

Then, of course, B answers "no" to the same question because B does not want a beer, which means that it is false that both want a beer. Goldilocks, being a perfect logician, is able to figure out that A does want a beer and that B doesn't, so she would bring a single beer to the table and place it in front of A, but no beer for B. That takes care of the case for only two logicians at the table, so now let's add a third. Here's how that would go:

"Would all of you like a beer?" Goldilocks asked.

"I don't know", said A. Goldilocks turned to B and raised her eyebrows.

"I don't know", said B. Next, it was C's turn to answer.

"No", said C.

Having solved the simpler puzzle, it should now be obvious how to solve this one. A wants a beer but doesn't know whether B or C do, and thus answers "I don't know". Similarly, B also wants a beer, but doesn't know about C, so answers the same way as A. Finally, C doesn't want a beer and can answer the question negatively. So, Goldilocks will bring beers for A and B but none for C.

At this point, the solution of the original puzzle is now easy: simply add one more logician to the table answering "I don't know" to the question. This puzzle could be extended to five at the table or, indeed, any greater number, and the solution remains the same: Goldilocks would bring beers for all of those at the table except the last member who answered "no".

Now that you have contraction under your belt, the following puzzle should be a snap:

Puzzle: The Jellyfish and the Waves

A jellyfish is floating in the ocean thirty feet from shore. Every time a wave comes along, it washes the jellyfish towards the beach three feet, but as the water recedes, the jellyfish is pulled back two feet. How many waves will pass over the jellyfish until it is washed up on dry land.

* I take this name from the following book: Saul X. Levmore & Elizabeth Early Cook, Super Strategies for Puzzles and Games (1981), p. 10.

April 3rd, 2023 (Permalink)

Not Silent Upon a Peek Into Chapman

The title of this entry is a burlesque of the last line of John Keats' famous sonnet "On First Looking into Chapman's Homer": "Silent, upon a peak in Darien"1. The poem was written after Keats had glanced at George Chapman's translation of Homer for the first time and, thankfully, he was not silent upon that peek. In the poem itself, Cortez was having his first peek at the Pacific Ocean, and his men were perhaps a bit piqued at his stopping on this peak and staring at the Pacific as if he'd never seen a sea before.

This entry is not about poetry interpretation, but about the three, identically-pronounced words "peak", "peek", and "pique". The latter of these three is the least common, usually only appearing in certain phrases. As a noun, "pique" is a feeling of irritation or resentment2, so that the phrase "fit of pique" refers to a sudden feeling of anger or outrage. As a verb, "to pique" means to excite or arouse, as in the phrases "to pique interest" or "to pique curiosity".

"Peak", in contrast, is a noun referring to a high point, such as the top of a mountain3, which is what Cortez was standing on when he first caught sight of the Pacific, according to Keats4. The verb form "to peak" is used for the action of reaching such a high point. Finally, "to peek" is a verb meaning to take a quick look at something, and it is also a noun referring to such a look5.

Because "pique" is such a rare word, and because it's pronounced exactly the same as "peak", you'll sometimes read of something "peaking" someone's interest or curiosity. This is grammatically incorrect even for the verb form of "peak", which is intransitive; one's interest might peak, but not because something "peaked" it. Similarly, you might think that "a fit of peek" refers to a sudden act of voyeurism, but a "fit of peeking" would be grammatically correct.

I checked sentences containing such phrases as "peaked my interest" and "peeked my curiosity" in several online spelling and grammar correcting programs, and most caught and fixed them. Despite this, I've noticed these misspellings occasionally, which suggests that some writers are either not using such programs or ignoring their advice. While I'm not in general an advocate of spell-checking programs, which encourage intellectual laziness, in this specific case I suggest that you follow such advice.


  1. John Keats, "On First Looking into Chapman's Homer", Poetry Foundation, accessed: 4/2/2023.
  2. "Pique", Cambridge Dictionary, accessed: 4/2/2023.
  3. "Peak", Cambridge Dictionary, accessed: 4/2/2023.
  4. Keats confused Cortez with Balboa, as it was the latter who first discovered the Pacific. Some have since speciously argued that Keats was not confused and intentionally substituted Cortez for Balboa since he, Keats, was not the first to discover Chapman. However, it was Balboa who was on that peak in Darien, not Cortez. See: Carol Rumens, "The Romantic poets: On First Looking Into Chapman's Homer by John Keats", The Guardian, 1/23/2010. For the specious reasoning, see: "Fact-Checking John Keats", Poetry Foundation, 8/26/2009.
  5. "Peek", Cambridge Dictionary, accessed: 4/2/2023.

April 1st, 2023 (Permalink)


78 years after death, Hitler's polarising legacy looms large

MUNICH, Bavaria, March 3 (Roto-Reuters) - On the eve of the 78th anniversary of Adolf Hitler's death, attitudes to Germany's wartime leader remain mixed in the nations he once ruled with an iron fist.

During a dozen years of dictatorial rule, Hitler oversaw rapid expansion of the autobahn but also the deaths of millions in concentration camps.

"Firstly, thank you for the Volkswagen," said 21-year-old Annalise in a typically mixed view of Hitler's legacy among people on the streets of Munich.

"Secondly, he is a negative person for me because there were a lot of deaths. A lot of executions, shootings, expulsions, arts were banned, etc. So itís impossible to have a clear position one way or the other," she added, declining to give her second name.

Though public commemorations remain largely taboo and streets no longer bear his name, his reputation has in recent years undergone something of a renaissance.

Polls in 2021, for example, showed 45% expressing "respect" for Hitler while 48% backed installing monuments to him.

"Why should I have a bad attitude towards him?" said Munich resident Albert, 31, praising Hitler as a strong unifying personality whose war victories should be lauded.

Born in Austria

In Hitler's hometown of Braunau am Inn in Austria, many share positive appraisals of the Nazi leader even though their nation has broken with Germany.

"The majority in Braunau value Hitler, of course. As a historical figure, as a great man and a person who ruled with an iron fist," said resident Olaf Habeck, 48.

"But the attitude towards him is changing. The younger generation is more aggressive towards him."

Born Adolf Schicklgruber to a humble family in 1889, the young Hitler spent his childhood in Braunau, before studying in the nearby Austrian capital Vienna. Today, Braunau's Hitler museum, located on the town's Hitler Avenue, is the town's most famous tourist attraction, drawing visitors from across the world.

In 2010, the Austrian government ordered the town's Hitler statue removed, saying he did not deserve it.

Gerhard Lindner, a Braunau resident in his early twenties, said that while older people in the town still "worship" Hitler, younger generations have changed their mind: "The majority of the young people do not like him, and I think that's good."

Disclosure & Disclaimer: Note the date of the above entry. The article is a satirical rewrite of the following genuine "news" article: Roman Churikov & David Chkhikvishvili, "70 years after death, Stalin's polarising legacy looms large", Reuters, 3/3/2023. The names in the above article are fictitious and do not refer to any real people, living or dead, except of course for Hitler. The quotes are taken from the Reuters article with "Stalin" replaced by "Hitler". As far as I know, Braunau am Inn has no Hitler museum or street, nor did it ever have a statue of the man.

Here are some questions raised by this fake news article: Why is the above article unthinkable, whereas the article it lampoons was actually published a month ago? Why is it "news" that some people in Georgia are ambivalent about Stalin, but not that some people in Austria might have mixed feelings about Hitler? Why the double standard in the news media between the two totalitarian, mass-murdering dictators?

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