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June 27th, 2019 (Permalink)

The Big Democratic "Debate", Part 1

The first of two "debates" of candidates for the Democratic party's nomination for president was held last night, and the second part will be tonight. I have some general comments about these so-called debates:

That's the whole forum in a nutshell. I don't mean to criticize the candidates quoted above specifically since none were significantly different. These candidate forums may serve some useful purpose for anyone planning to vote in a Democratic primary, but as a "debate" about substantive political issues they're a waste of two hours.

Given the above, I doubt that I will have anything additional to say about the second forum tonight, since it will probably be more of the same.


  1. Jeremia Kimelman, "Full transcript: 2019 Democratic debate Night One, sortable by topic", NBC News, 6/27/2019
  2. Allan Smith, "NBC announces five moderators for first Democratic debate", NBC News, 6/11/2019

June 22nd, 2019 (Permalink)

Last Visit to the Hilbert Hotel

In our previous visits to the Hilbert Hotel, we saw that even though the infinite hotel was full it could still provide rooms for new customers1. We also learned that The Hilbert Company, Inc., that owns the hotel also owns an infinitely long railroad line and an infinitely long train that runs on it2. What we didn't learn at the time is that the company owns an infinite number of infinitely long trains running on an infinitude of infinitely long tracks.

So, one day an infinite number of such trains pulled up at the hotel each carrying an infinite number of passengers, all desiring a room for the night. As usual, the "No Vacancy" light was lit. The clerk on duty that day was the same one we met previously who knew how to provide new rooms for any finite number of new guests even when the hotel was full. He also had learned from the manager how to accommodate an infinite number of new arrivals from one of the infinitely long trains.

However, how was he to find rooms for an infinite number of guests from an infinite number of trains? Even if he opened up an infinite number of rooms by moving all of the current guests into the even numbered ones, as he had been taught by the manager, the very first train would fill up all the odd numbered rooms. Of course, once the hotel was full again, he could do the same trick a second time, but how could he do it an infinite number of times?

Instead of trying to accommodate the new customers train by train, the clerk thought that maybe he should start with the first passengers in each train. However, he soon realized that this would not work, either: since there were an infinite number of trains, there were an infinite number of first passengers. He would end up filling up the whole hotel with just the first passengers in each train, and then he'd have to repeat the same procedure an infinite number of times.

The clerk didn't want to bother the manager again, so he thought hard for a few minutes. He could once again move all of the current guests into the even-numbered rooms, thus opening up the odd-numbered ones, of which there were an infinite number. But how could he make sure that every one of the new guests received a distinct room? Can you help the clerk solve the puzzle?



  1. See: No Vacancy at the Hilbert Hotel, 4/29/2019
  2. See: Still No Vacancy at the Hilbert Hotel, 5/13/2019

June 12th, 2019 (Permalink)

Wolff's Howlers

Michael Wolff, author of Siege: Trump Under Fire, is himself under fire for factual errors in the new book. Many of the errors singled out for criticism seem minor, but one is a whopper:

In the book, Wolff claimed to possess copies of special counsel Robert Mueller's alleged March 2018 draft indictment of Trump on counts of obstruction of justice. However, Mueller's office has asserted that the documents "do not exist."1

Of course, the fact that Mueller's office denies the existence of the draft isn't dispositive, but given the denial the burden of proof is now on Wolff to substantiate his claim. However, Wolff has so far not produced the alleged draft:

Pressed on his sourcing, and whether he would release copies of the supposed Mueller draft indictment memos he claims to have gotten, Wolff averred2. He couldn’t release copies, he said, because that might expose one of his anonymous “authoritative” sources. “You just have to trust me,” he said.3

Trust is earned, but so is distrust, and I think Wolff has earned the latter. In addition to the non-existent indictment, all or most of Wolff's sources for the book are anonymous except for one: Steve Bannon, who does not inspire confidence, to put it mildly.

Just as we saw with Naomi Wolf's new book last month4, this is not the first time Michael Wolff's reporting has come under siege for factual errors. His previous book, Fire and Fury, was a bestseller but apparently factually-challenged5.

I'm less interested in the specifics of Wolff's errors than in what this, taken together with the recent Naomi Wolf blunder, says about the state of the fact-checking of books. According to a Washington Post report about Wolff's previous book:

How did mistakes like these get past a fact-checker? Neither Wolff nor his publisher, Henry Holt, responded to…inquiries about how―or whether―“Fire and Fury” was vetted. Whether is a real question here. In many cases, publishers of nonfiction books such as Wolff's perform little, if any, fact-checking, leaving authors with a choice: pay out of their advances for someone to review their work or skip this pesky step altogether. Wolff thanked three people for fact-checking, in the book's acknowledgments section, but did not describe the scope of their work. “In my experience, publishing houses rarely, if ever, pay for fact-checking,” said Robert Liguori, a freelance fact-checker…. “I can't speak to whether any publishers have their own checking departments, but I have never heard of a major publishing house that has an internal staff to check its books.” Liguori said he has always been hired by careful authors, never by a publisher. Dan Kaufman, who has fact-checked books…told me the same thing.5

So, what happened to all those "editors, copyeditors and proofreaders for each book project"4? It was Naomi Wolf's publisher that boasted of them, but doesn't Henry Holt have any? Not all fact-checking is done by people called "fact-checkers", as Sarah Harrison Smith has written:

Fact checkers are everywhere, though many don't call themselves by that name. Editors, copy editors, writers, and researchers for print, radio, and even television verify facts as part of their jobs. Media that don't employ nominal fact checkers often divide the work of a fact checker among employees who do lots of other things, too.6

For this reason, I don't agree with the following:

Author…Susan Orlean told me that she was “flabbergasted” when she turned in a manuscript for her first book and learned that her publisher did not plan to check her work. But she said she has come to understand that “publishers simply can't do it.” “I mean, to properly fact-check a book basically means re-reporting a book,” she said. “That's how you do it. And a publisher can't do that, so I don't think it's malfeasance on their part or neglect. I think it's just not practical for them to do it, and they're assuming that you've done it.”5

Fact-checking is not the same as reporting, or at least it shouldn't be. Fact-checkers wouldn't be expected to redo all of the reporting that goes into a book such as Wolff's, but to check those things that can be quickly and easily checked. For instance, how hard would it have been to pick up a phone and call Mueller's office about the alleged draft indictment? Presumably, some reporter did just that, which is why the office issued the denial.

All of which raises the question: why didn't Wolff himself make such a call? I suspect that the reason is the obvious one that he didn't want to know. It wouldn't have been impossible or even impractical to check this; it just would have been too risky. The book is currently number four on The New York Times hardcover non-fiction bestseller list7.

Update (7/11/2019): Since I wrote this a month ago, the Jeffrey Epstein case has become a major scandal. According to journalist Vicky Ward:

A few years ago the journalist Michael Wolff wrote a profile of him for New York magazine that was meant to “rehabilitate” Epstein’s image and would tell of all the billionaires who still, secretly, hung out with Epstein. The piece had “fact-checking” issues and never ran. Even so, the notion that it was considered is mind-boggling.8

So, fact-checking issues, again, though I wonder whether the fact that "fact-checking" is in quotes suggests that that was just an excuse for killing the article, with the real reason being something else. Perhaps the following excerpts from an article that did run in New York magazine during the time that Epstein was first being prosecuted can help explain why the "mind-boggling" profile was even considered:

Vanity Fair columnist Michael Wolff met him in the Internet bubble, in the late nineties, when Epstein invited him and a group of scientists and media types to fly to a conference on the West Coast in his beautiful 727. “…[A]fter fifteen to twenty minutes, [Wolff said] Jeffrey arrives. … And he was followed onto the plane by―how shall I say this?―by three teenage girls not his daughters. Not adolescent girls. These are young, 18, 19, 20, who knows?…”9

17, 16, 15, 14, who knows? Continuing:

Soon after, Wolff was invited to tea at the house on East 71st Street. He understood that there was a purpose to the cultivation. Epstein was shifting his view to media…. In 2003, he became a discreet confidant to Wolff during the period when Wolff was involved in a bid for New York Magazine. … “He has never been secretive about the girls,” Wolff says. “At one point, when his troubles began, he was talking to me and said, ‘What can I say, I like young girls.’ I said, ‘Maybe you should say, ‘I like young women.’”9

Let me see if I have this straight: a few years after this Wolff was trying to write a profile for the same magazine to rehabilitate Epstein? Mind-boggling, indeed.

Update (7/14/2019): Yesterday, The New York Times published a lengthy article detailing some of Epstein's attempts to rehabilitate his image after his conviction, and the extent to which those attempts were successful. Wolff is not mentioned in the article, but the following passage is suggestive:

Some of the respect Mr. Epstein…drew on was manufactured…. A writer employed by his foundation churned out the news releases, and Drew Hendricks, the supposed author of a Forbes story calling Mr. Epstein “one of the largest backers of cutting edge science,” conceded in an interview that he was given $600 to post the pre-written article under his own name. (Forbes removed the piece after The New York Times published its article.)10

This passage raises some questions: Was Wolff paid by Epstein to write the article that was supposed to help rehabilitate his reputation? Or was he, like Hendricks, paid simply to put his name on an article written by someone else11? Did New York magazine find out about this and kill the article, using "fact-checking" as an excuse? These are just questions that I don't know the answer to, but if the answer were "yes" to any of them, that would help explain the otherwise "mind-boggling" article.

Update (7/16/2019): The fact-checker for Wolff's "mind-boggling" profile of Epstein appears to have been Alex Yablon, who titteringly cheeped:

In a new piece @VickyPJWard reports that New York Magazine was going to run a profile on Epstein by Michael Wolff that was killed out of fact checking concerns. Fun fact: I was the checker who killed it! One of my weirdest fact-checking experiences. Wolff let Epstein dictate the piece. He made some agreement that all fact questions would go through Epstein and only Epstein. In the piece, Wolff reported various powerful men still hung out with Epstein―but gave me no proof. I was not allowed to call them for comment. Not surprisingly, NY Mag's lawyers weren't thrilled about a story that alleged various rich and potentially litigious men socialized with a sexual predator without any proof or calling them for comment. As I recall the editor wasn't even aware Wolff had made this agreement. This is really more of a Michael Wolff story than a Jeffrey Epstein story.12

Yes, which is why I'm interested in it. This seems to answer at least part of one of my questions, namely, did someone other than Wolff write the profile? According to Yablon, Epstein himself dictated it! Of course, this answer raises the follow-up question: did Epstein pay Wolff for "writing" it?

It also appears to be the case, if what Yablon says is true, that the profile was killed for genuine fact-checking reasons, since real fact-checking seems to have been ruled out. However, the article seems to have been the result of a corrupt process, since no reporter should allow the subject of a profile to "dictate" it, nor enter into any agreement along the lines of the one described by Yablon. Surely, fact-checking aside, either of these should have been sufficient reason to kill it.


  1. Christina Zhao, "Michael Wolff Defends New Book From Allegations of Factual Inaccuracies in Heated Interview: 'This Critique is Bulls**t!'", Newsweek, 6/8/2019.
  2. "Averred?" Averred what? The author appears not to know the meaning of this word. "Aver" means "affirm" or "declare", and it's a transitive verb but it lacks an object here. What should the author have written? "Demurred", perhaps, which is intransitive and means "objected", and at least sounds similar to "averred". Otherwise, "declined" or "refused" would seem to be what was meant. See:
    • "Aver", Merriam-Webster, accessed: 6/11/2019.
    • "Demur", Merriam-Webster, 5/17/2019.
  3. Michael Isikoff, "Confronted with multiple errors in his new Trump book, a testy Michael Wolff says, 'You have to trust me'", Yahoo! News, 6/8/2019.
  4. See: Wolf's Howler, 5/31/2019.
  5. Callum Borchers, "How did Michael Wolff's 'Fire and Fury' get past a fact-checker? It’s not clear that the book was vetted.", The Washington Post, 1/9/2018.
  6. Sarah Harrison Smith, The Fact Checker's Bible: A Guide to Getting it Right (2004), p. 11.
  7. "Hardcover Nonfiction", The New York Times, accessed: 6/12/2019.
  8. Vicky Ward, "Jeffrey Epstein's Sick Story Played Out for Years in Plain Sight", The Daily Beast, 7/9/2019.
  9. Philip Weiss, "The Fantasist", New York Magazine, 12/7/2007. Warning: Parental guidance suggested. Not for the squeamish.
  10. Jodi Kantor, Mike McIntire & Vanessa Friedman, "Jeffrey Epstein Was a Sex Offender. The Powerful Welcomed Him Anyway.", The New York Times, 7/13/2019.
  11. For what it's worth, here is that article: Drew Hendricks, "Science Funder Jeffrey Epstein Launches Radical Emotional Software For The Gaming Industry", Forbes, 10/2/2013. This is Bing's cache of the page which is no longer available from Forbes; accessed: 7/14/2019.
  12. "Alex Yablon", Twitter, 7/9/2019.

June 1st, 2019 (Permalink)

Medice, Cura Te Ipsum1

Only the night before, Moran was an unknown 23-year-old student in St. Paul, Minnesota. … Living alone in a new city, she worked at a Chipotle to make ends meet…. That morning, though, she discovered she had become someone else. Strangers were calling her nasty names on social media. Her photo was plastered across internet news sites. A video was circulating online, and she was its villain. In it, she could be seen refusing to serve a group of black men at the restaurant the previous evening.2

The above quote is from an article that tells the story of a woman falsely accused of racism, and the online lynch mob that immediately formed and got her fired. It's a compelling story, and I recommend that you read the whole thing as a cautionary tale. I further recommend that you read it before returning to this entry as I have some criticisms to make of one thing in the article. I will assume that you have done so.

As you've read, the incident reported in the article was another rush to judgment based on a misleading online video, similar to the Covington incident earlier this year3, with similar threats of violence against the victim and her family. As far as I know, no one has yet been actually lynched by one of these mobs, but it's just a matter of time before someone acts on the threats.

As harrowing as the young woman's story is, in the following passage the article itself does something close to the very thing it is describing. It does so by propagating a false accusation of racism in the following claim: "Critics accuse President Trump of normalizing racism by referring to Mexican immigrants as 'rapists'…". As I pointed out last year4, it's a false accusation based on a contextomy.

Almost as bad as spreading this slander is attributing it to some unnamed "critics". This is a weaselly journalistic technique to introduce by innuendo a charge that the journalist doesn't want to have to defend. I'm sure somebody somewhere has accused Trump at some time or other of this, but it's really the journalist who is saying it and at the same time ducking responsibility. If CNN wants to accuse Trump of calling all Mexicans rapists, it should do so openly and stand by it; if it can't stand by it, because it's false, it shouldn't insinuate it.

It's easy to discover that the Mexican rapists accusation against Trump is bunk as not only Politifact but even Salon debunked it last year4. When CNN complains about Trump calling it "fake news"5, I'd be more sympathetic if it would stop publishing things like this.


  1. "Physician, heal thyself", Latin. See: Eugene Ehrlich, Amo, Amas, Amat and More: How to Use Latin to Your Own Advantage and to the Astonishment of Others (1985). This proverb is cited by Jesus in Luke 4:23.
  2. John Blake, "How an internet mob falsely painted a Chipotle employee as racist", CNN, 5/27/2019.
  3. See: Recommended Reading, 1/30/2019, the last two selections.
  4. Meet the Press, 9/25/2018.
  5. Donovan Slack, "Trump to CNN: 'You are fake news'", USA Today, 1/11/2017.

Solution to Last Visit to the Hilbert Hotel: The clerk already knows from the previous puzzle how to open up an infinite number of rooms for an infinite number of new guests. The problem he's faced with is how to enumerate the new guests so that each one can be assigned a different empty room. Here's how the clerk did it:

First of all, he enumerated the infinite number of trains: starting with the train on the tracks closest to the hotel, which was train number one. Then, train two was the next train over, train three the one beyond train two, and so on.

Secondly, he assigned numbers to each passenger on a train. Starting with the front of the train, the passengers in the first row of seats were numbered, starting in the leftmost seat and preceding to the right1. So, if there were six seats in the first row, those passengers would be passengers one through six, from the leftmost seat to the rightmost one. Then, the second row was enumerated in a similar way, preceding away from the front of the train2.

Each of the passengers was then uniquely identified by two numbers: a train number and a seat number. So, the passenger sitting in the front leftmost seat of the first train was identified by two 1s; let's write them so: 1/1. The passenger next to 1/1 will be 1/2, and so on. In general, the passenger in the nth seat of the mth train is passenger m/n.

Having assigned every passenger a unique pair of numbers, he proceeded to assign them rooms as follows: First, he summed the two numbers in the passenger's identifier, and then assigned rooms in stages by these sums. The lowest such sum is 1 + 1 = 2. Only one passenger had this sum, namely, the first passenger of the first train. So, the clerk assigned passenger 1/1 to the first empty room.

The next sum was 3. Two passengers had this sum: the second passenger on the first train―passenger 1/2―and the first passenger on the second train―passenger 2/1. He assigned these two passengers rooms in order of train numbers, so that 1/2 gets the second empty room and 2/1 gets the third one.

The next sum was 4. Three passengers have this sum: 1/3, 2/2, and 3/1, and they were assigned the fourth, fifth, and sixth empty rooms, in that order. Notice that at each stage there are only a finite number of passengers whose train and seat numbers sum to the same number, and these passengers can be enumerated by train number. This is how the clerk enumerated the infinite number of passengers on the infinitude of trains and assigned each a unique empty room3.


  1. The direction doesn't matter.
  2. The train has no rear since it's infinitely long!
  3. This is essentially a proof that the rational numbers, which can be represented as fractions, are countable. See: "An easy proof that rational numbers are countable", Home School Math (2015), which lives up to its title. If the above solution is unclear, see the diagram on this page.

Disclaimer and Historical Note: These puzzles are works of fiction. Infinite hotels, trains, train tracks, or groups of people do not exist. However, David Hilbert, for whom the hotel is named, was a real person. Hilbert was a mathematician who described an imaginary hotel with an infinite number of rooms which is usually referred to as "Hilbert's hotel"*. The purpose of the thought experiment was to illustrate some of the surprising properties of infinite sets.

*: See: Helge Kragh, "The True (?) Story of Hilbert's Infinite Hotel", Arxiv, accessed: 6/21/2019. An historical discussion of the origin of the infinite hotel in lectures by David Hilbert, who gave the solutions to the first and second puzzles. I don't know where the third thought experiment originated, but it apparently wasn't given by Hilbert himself.

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