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March 31st, 2020 (Permalink)

When Bad Math Happens to Good People

Title: Humble Pi

Subtitle: A Comedy of Maths Errors

Author: Matt Parker

Date: 2020

Quote: Today's world is built on mathematics: computer programming, finance, engineering…1it's all just math in different guises. So all sorts of seemingly innocuous mathematical mistakes can have bizarre consequences. This book is a collection of my favorite mathematical mistakes of all time. Mistakes like the ones in the following pages aren't just amusing; they're revealing. They briefly pull back the curtain to reveal the mathematics that is normally working unnoticed behind the scenes. … It's only when something goes wrong that we suddenly have a sense of how far mathematics has let us climb―and how long the drop below might be.2

Comment: We just saw earlier this month a mathematical comedy play on national television, albeit cable, and here's a book all about such mistakes in math and their effects. The author, Matt Parker, has written another book on math, which I haven't read, and apparently does stand-up comedy as well, so the book ought to be humorous. I can't seem to find any math credentials for him, but then I can't find any for me, either3.

The mistake from earlier this month involved dividing millions into millions, and people often seem to lose what little mathematical ability they have when faced with numbers whose English names end in "illion". Here's what Parker has to say about it:

As humans, we are not good at judging the size of large numbers. And even when we know that one is bigger than another, we don't appreciate the size of the difference. I had to go on the BBC News in 2012 to explain how big a trillion is. The UK debt had just gone over £1 trillion, and they wheeled me out to explain that that is a big number. Apparently, shouting, "It's really big! Now back to you in the studio," was insufficient, so I had to give an example. I went with my favorite method of comparing big numbers to time. We know a million, a billion, and a trillion are different sizes, but we often don't appreciate the staggering increases between them. A million seconds from now is just shy of eleven days and fourteen hours. Not so bad. I could wait that long. It's within two weeks. A billion seconds is over thirty-one years. A trillion seconds from now is after the year 33,700 CE. Those surprising numbers actually make perfect sense after a moment's thought. Million, billion, and trillion are each a thousand times bigger than each other. A million seconds is roughly a third of a month, so a billion seconds is on the order of 330 (a third of a thousand) months. And if a billion is around 31 years, then of course a trillion is around 31,000 years.2

Not all mathematical mistakes or misunderstandings are comedic; some are tragic. For instance, consider the two trillion dollar stimulus bill recently signed into law which is supposed to fix the damage done to the economy at least partly by the government's own actions. Few seem to have any grasp of just how huge two trillion dollars is, and the United States is already over $23 trillion in debt4. To put it in a little perspective, two trillion dollars is slightly over $6,000 for every person in America, which is how much the current crisis is so far costing you5, and don't be surprised when they come back for more6. Why don't they just cut every American citizen a check for $6,000? That would probably do more to stimulate the economy, as well as make up for the damage done by the coronavirus, than whatever it is they plan to spend two tera-dollars on.

Anyway, here's Parker on why we keep finding ourselves in these mathematical comedies and tragedies:

Our human brains are simply not wired to be good at mathematics out of the box. … All humans are stupid when it comes to learning formal mathematics. … We were not born with any kind of ability to intuitively understand fractions, negative numbers, or the many strange concepts developed by mathematics, but, over time, your brain can slowly learn how to deal with them. … But if those skills cease to be used, the human brain will quickly return to factory settings. … Which makes the amount of mathematics we use in our modern society both incredible and terrifying. As a species, we have learned to explore and exploit mathematics to do things beyond what our brains can process naturally. … When we are operating beyond intuition, we can do the most interesting things, but this is also where we are at our most vulnerable. A simple math mistake can slip by unnoticed but then have terrifying consequences.2

As with all other "New Book" entries, I haven't read the whole book yet, but what I have read was clearly and interestingly written. Moreover, it's a very well-edited and proofread text, and I haven't noticed a single typographical or grammatical error, which is a surprise nowadays. So, as long as you're going to be housebound until the end of April, you might as well do some reading.


  1. Ellipsis in the original.
  2. "Introduction".
  3. Unless you consider logic a branch of math, which some mathematicians do―of course, it's the other way around.
  4. "U.S. Debt Clock", accessed: 3/31/2020.
  5. Stephen Gandel, "How will US pay for $2 trillion stimulus package?", CBS News, 3/30/2020.
  6. Katherine Chiglinsky, "After $2 Trillion Stimulus, a Call for Another U.S. Rescue Fund", The Washington Post, 3/31/2020.

March 28th, 2020 (Permalink)

March Madness

The oldest and strongest emotion of mankind is fear, and the oldest and strongest kind of fear is fear of the unknown.1

I've been puzzling about how to respond to recent events, and whether it's even a good idea to respond at all. Part of our current predicament is the constant media over-attention to the coronavirus pandemic at the expense of all other news, even when there's really nothing new about the disease to report, and I don't want to contribute to that. So, maybe, the best thing to do is to ignore the whole subject.

On the other hand, I can't stop the news media from obsessing about coronavirus, nor President Trump from giving a lengthy news conference every day. So, I did move up my monthly "Recommended Reading" post to try to draw attention to some measured, non-hysterical recent articles. Now, I'm going to discuss in some detail just why I think we over-reacted to this threat.

Just as the proper response to the pandemic is somewhere between inaction and panicked over-reaction, the correct response is for me to neither ignore nor obsess about it, as so many are doing. Hopefully, this entry will fall somewhere in between.

I am not a physician, epidemiologist, or medical scientist of any sort, so I'm not an expert on viruses or epidemics. Moreover, at this point in time, part of the problem we face is uncertainty: even the experts don't know exactly what is going to happen. However, as a logician, there are some logical matters related to the current pandemics of coronavirus and of fear of coronavirus that, hopefully, I can shed some light on.

It should be obvious that at least some of the reaction to the pandemic in the United States is unwarranted. For instance, along with toilet paper, hand sanitizer has been a victim of panic-buying with some stores being cleaned out2, and some news sites providing instructions on how to make your own3. However, washing your hands with soap and water is a better way to prevent the spread of a virus than using hand sanitizer4. Obviously, one reason for this sort of behavior is ignorance, but given the saturation news media coverage of the coronavirus, why are people still ignorant?

It's impossible to be sure exactly what else is contributing to this over-reaction, and this period will be much studied in the near future to figure out how to prevent a re-occurrence. But in the absence of sociological and social psychological studies into what produced the pandemic panic response, I will make some educated guesses about what factors have contributed to it:


  1. H. P. Lovecraft, "Supernatural Horror in Literature", 1934
  2. Jeff Ferrell, "'Panic Buying' blamed for hand sanitizer shortage", KSLA News, 3/4/2020
  3. Boone Ashworth, "How to Make Your Own Hand Sanitizer", Wired, 3/12/2020
  4. "Good luck finding hand sanitizer; CDC says soap is still king", Associated Press, 3/3/2020
  5. Julia Belluz, "80,000 Americans died of the flu last winter. Get your flu shot.", Vox, 12/20/2018
  6. Pien Huang, "How The Novel Coronavirus And The Flu Are Alike…And Different", National Public Radio, 3/20/2020
  7. "Cases in U.S.", Centers for Disease Control and Prevention, accessed: 3/28/2020
  8. Amy McKeever, "Coronavirus is officially a pandemic. Here's why that matters.", National Geographic, 3/11/2020
  9. "What is a pandemic?", World Health Organization, 2/24/2010
  10. Gary D. Friedman, Primer of Epidemiology (2nd edition, 1980), p. 11
  11. "WHO Director-General's opening remarks at the media briefing on COVID-19―3 March 2020", World Health Organization, 3/3/2020
  12. For instance: Jamie Ducharme & Elijah Wolfson, "The WHO Estimated COVID-19 Mortality at 3.4%. That Doesn't Tell the Whole Story", Time, 3/9/2020

March 23rd, 2020 (Permalink)

Book Review: Cold Warriors

Title: Cold Warriors

Subtitle: Writers Who Waged the Literary Cold War

Authors: Duncan White

Date: 2019

Quote: Orwell took [Animal Farm] to [publisher] Jonathan Cape. … The signs were auspicious as…the chief reader of fiction…recommended publication. In May [1944], Orwell met with Cape, who agreed to publish. … On June 19, though, Cape wrote to [Leonard] Moore [Orwell's agent] to tell him he was not going to publish after all. …[T]he real reason for the rejection was…sinister. During negotiations, Cape told Moore that he wanted, "as a matter of policy" to consult a "senior official" at the Ministry of Information. What is remarkable is that this official then followed up with a letter in which he told Cape that publishing Animal Farm would damage relations with the Soviet Union and therefore undermine the war effort. The pressure applied by the official caused Cape to crack. … What Orwell did not know at the time, but came to later suspect, was that there was more going on than weak-willed capitulation to political censorship. The Ministry official who warned Cape against publication was Orwell's old acquaintance…Peter Smollett―or, to give his real name, Hans Peter Smolka. … It is disputed when Smolka first began working for Soviet intelligence. …Smolka…was given the code name "Abo"… Agent Abo's intervention did not kill Animal Farm but delayed its publication, and subsequent impact, by as much as a year.1

Review: Cold Warriors is a book about how a large number of writers, and their books, were used for propaganda during the Cold War. Sixteen writers are listed in the chapter titles, and many others are mentioned in passing. Here's how White says he chose them:

One of the biggest challenges of this book was deciding which writers to focus on. Some selections seemed obvious for the indisputable influence they exercised over the Cold War: George Orwell, Arthur Koestler, Boris Pasternak, and Aleksandr Solzhenitsyn, for example. Another criterion for selection was writers who had lived through various stages of the Cold War and therefore could provide a throughline to the book: Graham Greene, Mary McCarthy, and Stephen Spender fit this profile. Others have less space dedicated to them but have compelling, essential stories to tell: Ernest Hemingway and the end of the Second World War; Anna Akhmatova under late Stalinism; Howard Fast during the Red Scare; Richard Wright at the Bandung Conference; John le Carré at the Berlin Wall; Vaclav Havel leading the Velvet Revolution.2

White can write about whomever he wants to, but some of his inclusions as well as omissions puzzle me. For instance, Fast, a once bestselling author of potboiler novels made into movies, is probably little read today. White writes of Fast:

Fast's ability to build tension marked him out as an excellent storyteller, and in Spartacus he deployed an ambitious flashback structure, but the novel slipped too easily into overripe prose and melodrama to be considered a work of serious literary merit. It was Fast's gift as an author to be able to write in a way that carried a broad appeal even if that appeal did not last more than one reading.3

Though I've never read Fast, I found his story in Cold Warriors interesting, but it seemed that it could've been better told in a biography, and perhaps it has been. For an example of a writer who is not included, but arguably should be, consider William F. Buckley, Jr., who was a spy novelist with a personal background in espionage, like Greene and Le Carré. Buckley had much more influence on American foreign policy, especially during the Reagan administration, than either Greene or Le Carré seem to have had on British policy. Reagan's policies probably contributed to the fall of the Soviet Union, and thus to the end of the Cold War. So, Buckley may have had more influence on the course of the Cold War than any writer discussed in this book, with the exceptions of Orwell, Pasternak, and Solzhenitsyn.

I suppose that Buckley could be rejected on literary grounds, but so could Fast. Alternatively, it may be that Buckley's political influence was largely due to his magazine editorship, newspaper columns, and television show, rather than his spy novels. Or, perhaps, White just doesn't like him, but likes Fast. Fair enough, but then we readers should be told that the writers are included for subjective reasons, rather than based on historical influence or literary merit.

As far as I can tell, all the writers selected for inclusion were or are left-wing anti-communists, with the possible exception of Solzhenitsyn. This may explain Buckley's exclusion, as well as that of the most famous spy novelist of all, Ian Fleming. I don't know whether Fleming is read much nowadays, but his character, James Bond, is alive and kicking in the movies. When was the last time a movie was made based on a Mary McCarthy or Howard Fast novel?

This is a very long book, and I could have done with less of some of the minor literary figures such as Fast. For example, an entire chapter is devoted to Gioconda Belli, a Nicaraguan poet whom I'd never heard of before and don't care if I never hear of again. The chapter could easily have been left out without affecting the book's "throughline"; I suggest skipping over it if you've never heard of her.

The book is a series of short biographies of writers, focusing on their political lives, embedded in a literary history of the Cold War. Unfortunately, with some exceptions, if you aren't familiar with and interested in the writers, you probably won't find their stories very interesting. The chapters on Orwell, Koestler, Isaac Babel, Akhmatova, and Solzhenitsyn, are exceptional. I've never read Babel or Akhmatova, and I'm not sure that I want to, but their life stories are fascinating.

At its best, the book reads more like an elaborate spy novel, such as those by John le Carré4, than a scholarly history. At its worst, White gets bogged down in uninteresting and confusing historical details5. He often doesn't seem to know the difference between the telling detail and the useless detail.

Unfortunately, I don't think I learned much about literary propaganda from this book, except for the interesting fact that the United States used balloons to drop copies of Animal Farm behind the Iron Curtain6. What I'd really like to know, though, is did this sort of thing do any good? Of course, the Soviet Union prohibited the publication of the book, otherwise smuggling in copies would make no sense, but was the book really a danger to the Soviet state, or was its prohibition simply the result of an irrational paranoia? One won't learn the answer to such questions from this book, but perhaps no one knows. White quotes the little-known―at least, in America―Russian writer Yulii Daniel, who was put on trial for anti-Soviet writing:

Daniel himself questioned the whole premise that literature could be used as a weapon in the Cold War. "As regards the harm done to our state," he said, "I do not think a couple of books by us, or even a score of books, could inflict any considerable damage on it."7

Now, Daniel was trying to defend himself and his writing during a show trial, but I think he made a good point. Despite quoting this, White doesn't seem interested in the issue himself. Clearly, both sides in the Cold War acted as though novels and poems could be dangerous things, but were they really? I'd like to believe that Orwell's novels contributed to bringing down the Soviet Union, but I suspect that the main reasons for its decline and fall were economic. White's book, despite its great length, supplies little evidence to think otherwise.

The Cold War was a long and, as evidenced by this book, exceedingly complicated series of events, which leads to a sprawling and sometimes hard to follow work. White does not do a very good job of explaining the complex political background that's necessary for understanding the events related, but then he had his work cut out for him. I lived through the latter half of the Cold War, and I've read a good bit about it since, yet there were times when I was lost trying to follow what was happening in the book. Too much is included and too much is left out.

I found parts of Cold Warriors engrossing, but it could've been more interesting as a whole if it had been shorter, with its cast of characters trimmed down to a more manageable size. Even without cutting out some of the lesser writers, the book would've been significantly shorter and an easier read if White didn't so often get bogged down in petty details. There's a good 500-page book inside these 700 pages.

The book is well-proofread, and I noticed only a few typographical and grammatical errors. However, it could have used a ruthless editing to cut it down to size and shape it into a clearer story. No doubt history is complicated and confusing, but that's no excuse for history books being so.

Recommendation: If you're locked inside your house due to the current mass hysteria outside it and you need something long to read, you could do worse than this book―or you might finally get around to War and Peace. Recommended for those who have read or are interested in one or more of the writers covered, and such readers might skip over chapters dealing with ones that they're less interested in, but what's your hurry? Who knows when you can go out again? Those not already familiar with the history of the Cold War should start elsewhere.


  1. Duncan White, Cold Warriors: Writers Who Waged the Literary Cold War (2019), pp. 212-214. All subsequent page citations are to this book.
  2. P. 12.
  3. P. 324.
  4. Unfortunately, Le Carré's life is much less interesting than his novels.
  5. Here's an egregious paragraph from p. 127:
    …"Etienne" introduced Agelhoff to a playboy by the name of Jacques Mornard, who claimed to have deserted from the Belgian army. Mornard seduced Agelhoff, buying her expensive gifts and taking her to sophisticated restaurants. Mornard was not really Mornard, though―he was Ramon Mercader, a highly trained NKVD agent. Mercader had been recruited at some point in 1936 by Leonid Eitingon, who ran the Barcelona NKVD station during the Spanish Civil War. Eitingon was the lover of Caridad Mercader, a radical Spanish leftist and Ramon's mother, and he arranged for her son, who then commanded a Republican army unit, to receive instruction in guerrilla warfare. Ramon was a keen student and helped train foreigners recruited by the NKVD―including, it is speculated, David Crook, the Englishman who spied on Orwell. In the summer of 1937, Ramon traveled to Moscow, where he received further training.

    Got that? There will be a test later. If you think that this passage is taken out of context, you're right, but it's not much better in context, which is why I marked it as a horrible example.

  6. Pp. 1-3.
  7. P. 514.

Debate Watch
March 17th, 2020 (Permalink)

And Then There Were Suddenly Only Two

Sunday night there was another so-called debate between candidates for the Democratic Party's nomination for president. The previous one had seven contenders1, but only two are left standing: Joe Biden and Bernie Sanders2. Agatha Christie would not have plotted it this way. I have a few procedural comments about the event before getting into a substantive issue:

Now, on to the substantive point. During the forum, Bernie Sanders addressed Joe Biden, asserting: "You have been on the floor of the Senate time and time again talking about the need to cut Social Security, Medicare and veterans programs." Biden then denied it5. This exchange provides an example of a common political fallacy.

At least with respect to Social Security (SS), Sanders here is using the word "cut" in the political doublespeak sense of a smaller than requested, scheduled, or expected increase6. What Biden was talking about was lowering the automatic cost-of-living increases of SS. In other words, these would not have been "cuts" in the usual sense of the word, but lower increases. For this reason, Biden was right to deny that he had called for cuts to SS.

This may well have been the last forum for Democratic candidates for the party's nomination in this election cycle, since the Sanders boom seems to have fizzled out. If so, the next one will be between the two party nominees―presumably, Biden and Trump―and will be run by the Commission on Presidential Debates, instead of the DNC. Hopefully, the commission will do a better job than the DNC has done.


  1. Debate Watch: And Then There Were Still Seven, 2/26/2020
  2. Mark Z. Barabak & Melanie Mason, "6 takeaways from the Joe Biden-Bernie Sanders Democratic debate", Los Angeles Times, 3/15/2020
  3. "Tulsi Gabbard rips Dems, DNC for ignoring fact she is still in 2020 presidential race", USA Features, 3/10/2020
  4. Logic Checking the Last Debate, 10/20/2016
  5. "Democratic debate fact check: Examining claims from Joe Biden, Bernie Sanders", Associated Press, 3/15/2020
  6. For a couple of previous examples, see: More is Less, 10/21/2004

Recommended Reading
March 10th, 2020 (Permalink)

The Panic Virus

I usually wait until the end of the month to post these reading lists, but given the current state of borderline mass hysteria on the subject of the new virus spreading around the world, I'm putting up this one earlier than usual. So, if you've barricaded yourself in your house until the news media say it's safe to come out, you might as well read something to pass the time. All of the following readings are from experts of one sort or another.

March 7th, 2020 (Permalink)

Beyond Innumeracy

Former NBC Nightly News anchorman Brian Williams has a show on the MSNBC cable "news" network―who knew? Williams was driven from his anchor chair five years ago1 because of a long history of self-aggrandizing falsehoods2. Apparently, MSNBC is NBC's version of Siberia, where disgraced NBC personnel are sent to die.

Judging from a segment of yesterday's episode, it would seem that Williams' mathematical abilities are as bad as his memory. This has already received a lot of publicity3, so you may have heard about it. In case you haven't, you can watch it here:

In their defense, they were only off by a factor of a million! But this was really beyond ordinary innumeracy; it's innumeracy times a million. I suspect that this was the result of what Douglas Hofstadter calls "number numbness"4, which is the paralyzing effect that large numbers have on some people's brains. Throw in the word "million" and they can no longer divide. How else can you explain the fact that it never struck them that giving a million dollars to each American citizen would equal more than 500 million dollars? A lot more.

It's remarkable that no one caught this mistake before MSNBC aired it. It's not just Williams who was at fault here. There was the original Nitwitter, whose innumerate blurt was shown on screen. Then, there's Mara Gay, the oblivious young woman that Williams is interviewing, who's apparently on the editorial board of The New York Times, which could explain a lot. Also, there must be some writers, editors, and producers behind-the-scenes who should have stopped Williams before he became a public laughingstock. Perhaps all of the above people attended the Costello School of Math, see:

Keep this incident in mind if you're ever tempted to watch MSNBC. You can learn much more from Abbott and Costello movies, though they're not as funny.


  1. "NBC removes Brian Williams from 'Nightly News'", Chicago Tribune, 6/18/2015
  2. Paul Farhi, "NBC News finds Brian Williams embellished at least 11 times: report", Chicago Tribune, 4/25/2015
  3. For instance: Reed Richardson, "Watch MSNBC's Brian Williams and NYT Editorial Board Member Both Fail Basic Math on Bloomberg Ad Spending", Mediaite, 3/6/2020
  4. Douglas R. Hofstadter, "On Number Numbness", Metamagical Themas (1985), pp. 115-135

March 1st, 2020 (Permalink)

Quirks Vs. Anti-Quirks

You've heard of quarks, of course, but you may not have heard of quirks. Quirks are a type of subatomic particle recently discovered by physicists, together with their anti-particles, anti-quirks. Quirks got their name because they're quirky: they're strangely unreactive particles. In contrast, anti-quirks are highly reactive.

Quirks and anti-quirks always collide in pairs. Also, if you put a bunch of quirks or anti-quirks together, they will eventually collide. Whenever two quirks collide, they just bounce off each other and go about their business. When two anti-quirks collide, they annihiliate each other. However, when a quirk and an anti-quirk collide, the quirk is destroyed, but the anti-quirk continues on its merry way.

Quirks, it turns out, are easily made, but it takes massive amounts of energy to create anti-quirks. So far, only 23 anti-quirks have been created, and are kept in 23 magnetic bottles on a shelf in the basement of the Extremely Large Quirk Collider (ELQC). No quirks or anti-quirks can escape from the ELQC; they just bounce around in there colliding with one another.

What would eventually happen if all 23 anti-quirks were released together into the collider with an unknown number of quirks?

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