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March 31st, 2022 (Permalink)

The Fog of War & Bad Science Reporting

War is the province of uncertainty: three-fourths of those things upon which action in War must be calculated, are hidden more or less in the clouds of great uncertainty. Here, then, above all a fine and penetrating mind is called for, to search out the truth by the tact of its judgement.1

The following article deals primarily with mis- and dis-information about the current war in Ukraine being spread by so-called social media, but some of the tips that it provides can be generalized to any propaganda in war or peace.


  1. Karl von Clausewitz, On War (1832), I.iii, quoted in The Dictionary of War Quotations, edited by Justin Wintle (1989), p. 79. This is apparently the source of the phrase "fog of war" as the German word translated here as "clouds" is sometimes translated by "fog". See: "Fog of War", Oxford Reference, accessed: 3/31/2022.
  2. See, for instance:
  3. For the facts in this and the previous paragraph, see the lengthy bombshell article by Katherine Eban: "“This Shouldn’t Happen”: Inside the Virus-Hunting Nonprofit at the Center of the Lab-Leak Controversy", Vanity Fair, 3/31/2022. This was just published today, so I haven't had time to excerpt it or comment on it. It's very lengthy but also recommended reading.

Disclaimer: I don't necessarily agree with everything in these articles, but I think they're worth reading as a whole. In abridging them, I may have changed the paragraphing and rearranged the order of the excerpts in order to emphasize points.

March 27th, 2022 (Corrected: 4/1/2022) (Permalink)

Credibility Checking, Part 3: Ratios, Rates & Percentages

In Parts 1 & 2, we looked at how to compare and contrast1, and how to divide and conquer in order to check the credibility of factual claims involving big numbers2. The purpose of dividing and conquering is to cut such numbers down to size so that they are easier to understand and evaluate. Another way to cut numbers down to size is to use ratios, rates, or percentages, which is what we'll look at in this part.

First, a short refresher on ratios, rates, and percentages: a mathematical ratio is a relationship between two numbers. For instance, the ratio of one to two can be written 1:2, or as the fraction 1/2. A ratio can also be expressed as a decimal number, so that the ratio 1:2 can be written as .5, which is of course short for 5/10.

A rate is just a type of ratio; for instance, miles per hour (MPH). Sixty MPH is the ratio 60:1, where 60 is the number of miles traveled and 1 represents a single hour in which the miles were traveled. The word "per" plays the same role in English as the colon in a ratio, or the virgule or slash (/) in a fraction.

A percentage is a special type of ratio in which the denominator is always 100―per cent, that is, per a hundred―so that the ratio 1:2 can also be expressed as 50%. 50% means "fifty per a hundred", or 50:100. You can turn any ratio, or fraction, into a percentage by converting it to a decimal number and multiplying by 100.

An Example3

Perhaps the best way to learn how to use ratios in credibility checking is to look closely at an example. In 2009, the Allstate insurance company ran an ad campaign supporting legislation which would have withheld federal highway funds from states that didn't adopt measures intended to reduce the number of car accidents caused by novice drivers4. At the top of one of its ads, Allstate made the following claims:

Last year, nearly 5,000 teens died in car crashes. Making it safer for a teen to be in a war zone than on a highway.5

The justification given for the statistic is in fine print at the bottom of the ad: "Sources: Insurance Institute for Highway Safety Fatality Facts 2006, 2007 (latest data available); Centers for Disease Control and Prevention 2008." Presumably, the data supported the claim of 5,000 teen fatalities "last year", though neither of the fact sheets listed are for 2008. However, the number of fatalities probably changes little from year to year, so 5,000 may have been a good approximation for 2008.

Our purpose here is not to question this particular number, which seems plausible enough, but to examine the comparison of this level of fatalities to those in a war zone. It's a surprising comparison, but that's what makes the ad effective. You're supposed to read it and think: "A teen is safer in a war zone than in a car? I didn't know that!" Then, you're supposed to be motivated sufficiently to support the legislation.

Now, the notion of a "war zone" is highly vague: Clearly, Ukraine is currently a war zone, but also a much more dangerous place for a teen―or anybody else, for that matter―than driving in America. So, what "war zone" was the basis for comparison? I wrote to Allstate asking for the justification of the claims made in the ad, and received the following reply:

The Washington Post has found that 1,019 total U.S. soldiers were killed in 2007. (This statistic includes soldiers of all ages). In 2007, nearly 5,000 teenagers were killed on U.S. roads, according to the National Highway Traffic Safety Administration. Our goal is to raise awareness that teenagers have the ability to make better decisions and to change their driving habits. We believe we can accomplish this through compelling messages that underscore the very real dangers of teen driving.6

So, Allstate compared the raw number of teens killed on American roads with that of American soldiers killed in Iraq and Afghanistan. Now, it's doubtful whether those countries were still at war in 2007 and thus "war zones"―at best, they were borderline cases. Moreover, even if they were war zones, they were atypically peaceful ones, and thus likely to make war zones appear less dangerous than they really are.

However, even accepting that Iraq and Afghanistan in 2007 were typical war zones, the comparison is questionable for the following reason. The number of American soldiers killed in war zones is partly a function of how many soldiers are there, just as the number of teens killed in car accidents in America is partly determined by the number of teens here who drive. The more of one, the more of the other. There were far more teens in the U.S. than American soldiers in war zones, so it needn't be surprising that more teens died than soldiers.

What should be compared if not the raw numbers? Since the claim has to do with the comparative safety of driving and warfare, we need some measure of safety. Raw numbers of deaths are not a good way to measure the safety of activities, since they are affected by the number of people who take part in the activity. For instance, taking a shower is much safer than skydiving, but the absolute number of people who die while showering is much larger than the number who die skydiving, because many more people shower than skydive, thankfully. We need some way of taking into consideration the fact that there were more teenage drivers than soldiers in Iraq and Afghanistan. Instead of comparing the raw numbers of those who died, a better comparison would be the death rates of the activities, that is, the ratio of those who die doing the activity to the total of those who do it7.

Allstate has given us the raw numbers for teen road deaths and military deaths in 2007. If we express the death rates as fractions, these numbers will be the numerators of the fractions. What we need for the denominators is the number of teen drivers in the U.S. and the number of American soldiers in war zones in 2007. We can safely assume that all American teenagers are drivers, so all that we need is the number of American teens of driving age in 2007. Similarly, we're safe in assuming that only American soldiers serving in Iraq and Afghanistan died in a war zone in 2007.

A Ballpark Estimate

How many American teenagers were of driving age in 2007? It's unlikely if not impossible that you could find statistics to answer this question, but since we don't need a precise number we'll just estimate it. The U.S. population in 2007 was 301 million8, and the average American lifespan was 78 years9. From these two numbers, we can estimate the number of teenagers.

If you think about it, there are roughly equal numbers of people of any given age; for instance, the number of 17 year olds at any given time will be close to the number of 16 year olds. Of course, a few 16 year olds won't make it to 17, but thankfully not many. It's only at the upper ages that this tends to be less true as older people die in larger numbers than the young do. So, the number of 85 year olds may be significantly less than that of 84 year olds. Since we're dealing with teens, we can safely assume that the number of teens of the relevant ages is approximately the same. In most states in America, the legal driving age begins at 16, so there are four relevant years from 16 to 19.

To estimate the number of American teens, all we need to do is divide the total population by the lifespan, then multiply by four. As we've seen, the total population in 2007 was 301 million, and life expectancy was 78 years. So, the approximate number of people of any age was about 3,850,000. Multiplying by four, the number of teenage driving years, we get about 15.5 million teenage drivers.

Death Rates

Back to the example: the reason we wanted an estimate of the number of teen drivers in 2007 was so that we could figure the death rate, that is, the ratio of the number of teens who died in car accidents to the total number of teen drivers. The numerator―5,000―was given to us by the insurance company, and we estimated the denominator as 15.5 million. Thus, the death rate is 5,000/15,500,000 or, expressed as a decimal fraction, .0003, or as a percentage, .03%. In other words, three in ten-thousand teenaged drivers died in 2007 in auto accidents.

Now, the reason we wanted that death rate was to compare it to the rate at which American soldiers died in Iraq or Afghanistan in 2007. Again, the numerator was supplied by Allstate―1,019―so that all we need is to do some quick research to find out how many American soldiers were in those two countries in 2007: the answer is about 177.5 thousand10. Thus, the death rate for American soldiers in war zones in 2007 was 1,019/177,500, or a little less than .006, that is, .6%.

One Last Ratio

Clearly, the chance of an American soldier dying in Iraq or Afghanistan in 2007 was higher than the probability of a teen driver dying in America; in fact, the former was an order of magnitude higher. However, we can use one more ratio to find out how much higher, namely, the ratio between the two death rates: .006/.0003 = 20. So, the chance of being killed as a soldier in a war zone was about twenty times greater than the chance of a teen dying in a car accident. Of course, this is only an estimate, but the difference in rates is so great that there would have to be a large error in the statistics in order to make teen driving more dangerous than a war zone.


In this example, we examined the insurance company's claim that driving is more dangerous for teens than being a soldier in a war zone. To do so, we simply accepted the raw numbers provided by the company, but then compared the rates of soldiers killed in Iraq and Afghanistan with that of teenagers who died in car accidents. The raw numbers gave us the numerators of the rates, while we supplied the denominators based on a ballpark estimate and what could be quickly and easily looked up. The result indicated that the claim was not credible.

Advocates often use raw numbers, especially large ones, to argue that a problem is significant, but raw numbers can be misleading. Is 5,000 teenage drivers dead in a single year a large number? Obviously it's too many, but it's only when we compare the raw number to the total number of teenagers that we can get some perspective on just how dangerous it is to drive while teenaged.


  1. Credibility Checking, Part 1: Compare & Contrast, 1/7/2022.
  2. Credibility Checking, Part 2: Divide & Conquer, 2/4/2022.
  3. This example is adapted from the following entry: The Back of the Envelope, 8/15/2009.
  4. Jon Schmitz, "National standards sought for teen drivers", Pittsburgh Post-Gazette, 4/24/2009.
  5. Ad, Allstate (PDF). Thanks to David Orth for calling this ad to my attention.
  6. E-mail from Allstate, 8/10/2009.
  7. This is not the only, or even the best, way of comparing the mortal danger of an activity, but it is probably the simplest, and is sufficient for our purposes. Other measures take into account the amount of time spent doing the activity; for instance, a shower usually takes longer than a skydive, so a better measure of risk would be the number of deaths per an equal amount of time spent doing the activity. Such a measure would show skydiving is even more dangerous than showering.
  8. "What was the population of the United States of America in 2007?", Wolfram Alpha, accessed: 3/27/2022. This is a very useful source for quickly finding factual information.
  9. "What was the lifespan in the United States of America in 2007?", Wolfram Alpha, accessed: 3/27/2022.
  10. See:

March 20th, 2022 (Permalink)

Who's on First?

You might be surprised to learn that the New Logicians' Club has a softball team, but it's true. Less surprising, perhaps, is that the club has given the team's players unusual nicknames. In honor of Abbott and Costello's famous comedy routine, the team's basemen are known as Who, What, and I Don't Know1.

A friend of mine, who is a new member of the club and an avid softball player, wanted to know more about the team. Specifically, he wanted to know the names of the three basemen. Since I'm not interested in the sport I couldn't answer his question, so I suggested he ask the players themselves. Unfortunately, this happened during a meeting at which the club members were playing the old truth-tellers and liars game2, which is the game where the truth-tellers always tell the truth, and liars always lie. This meeting, however, there was an additional rule: new members of the club were given the task of alternating true statements with false ones.

The three basemen were sitting together at the same table. One was a truth-teller, one a liar, and one was a new member like my friend. However, I didn't know which was which. So, my friend approached the table and asked each who was playing what position. Here are the answers they gave:

Who: "I'm on first. What's on second. I Don't Know is on third."

What: "I'm on first. I Don't Know is on second. Who's on third."

I Don't Know: "Who's on first. I'm on second. What's on third."

Fortunately, my friend was able to determine the line-up from these three answers. Can you?


  1. If by some misfortune you're unfamiliar with this routine, you can watch a version of it here: "Who's on First", YouTube, 6/23/2015
  2. If by some other misfortune you're not familiar with the truth-tellers and liars game, see:

The Giant Spider Invasion
March 13th, 2022 (Permalink)

The Giant Spider Invasion

Alvy Singer: Honey, there's a spider in your bathroom the size of a Buick.1

Like something out of a cheap 1970s monster movie, or a less cheap '70s Woody Allen comedy, the giant spiders are coming. You may have already seen one or more of the following recent headlines:

Brace for an Invasion of Massive Spiders2

Gulp. Giant Invasive Spider Spreading Throughout the Southeast3

If You Live Here, Watch Out for Giant Spiders Falling From the Sky4

Giant spiders expected to drop from sky across the East Coast this spring5

One sign that COVID-19 is finally over is the news media jumping on a new scare. In addition to normal-sized Russians invading Ukraine, there are giant Japanese spiders invading the United States. In an eerie parallel, the spiders are parachuting into the U.S. from Japan like Russian paratroopers dropping into Ukraine.

If you're experiencing deja vu right now, it's probably because you're old enough to remember the invasion of the murder hornets, which was almost two years ago―in other words, ancient history. As I discussed then6, the news media seem to have a template for these kind of scare stories, whether they're about insects, spiders, or even a disease. A good scare story is made from the following ingredients: invasiveness, size, a spreading epidemic, and the threat of death.

Let's check the giant spiders against this template: Invasive? Check; the spiders are an alien species originally from Asia. Big? Check; they're "giant" and "massive", according to the headlines. Spreading? Check; they've already "taken over" the Southeast and "nothing can be done to stop" them from spreading across the entire East Coast, according to the following report:

Giant spiders have taken over the southeastern United States over the last few years, and new research has found that this invasive species could soon spread across the East Coast. … New research from the University of Georgia found that these spiders could spread even farther—reaching across most of the Eastern Seaboard of the United States. And researchers say nothing can be done to stop the spiders from spreading….7

Just how big are the "giant", "massive" insects known as Joro spiders? Reportedly, the females can be three inches long8, but that's including the legs. That's big for a spider, especially those familiar to people in the eastern part of America, but not as big as a Buick. There are tarantulas in the southwest that dwarf the Japanese invaders. The largest spider in the U.S. is, naturally, from Texas, where everything is bigger, and it can grow to be twice the size of the Joro9. I would recommend that the invaders avoid Texas.

The article below the last headline above claims that the Joros will take over the East Coast this spring:

An invasive species of spider the size of a child's hand is expected to “colonize” the entire East Coast this spring by parachuting down from the sky, researchers at the University of Georgia announced last week. Why it matters: Large Joro spiders—millions of them—are expected to begin “ballooning” up and down the East Coast as early as May. … The Joro spider is native to Japan but began infiltrating the U.S. in 2013, concentrating in the southeast and specifically Georgia…. They fanned out across the state using their webs as tiny, terrifying parachutes to travel with the wind.5

Interestingly, this claim has already been fact-checked and rated "false"10. The study that seems to have started this whole scare only found that the spider's metabolism is such that it might be able to survive in colder temperatures, but whether it will in fact spread north, and if so when, is unknown.

According to the template, the only ingredient missing for a sustainable scare story is fatalities. Unlike the "killer" bees and "murder" hornets, which were responsible for occasional deaths, the spiders appear to be harmless. So far, the hornets have failed to murder anyone in the Northwest, so we haven't heard much about them since the original scare. I expect interest in the spiders will similarly die down when no one dies.

At a time when a genuinely deadly invasion is occurring, it's pathetic that the news media have nothing better to do than write scare stories about harmless spiders no matter how large. But, then, here I am writing a silly entry about these silly scare stories. It's a dirty job but somebody has to do it.


  1. The illustration is not a photograph of a Joro spider, which is large but not that large. It's a movie poster.
  2. Woody Allen & Marshall Brickman, "Annie Hall" (1977). Joro spiders are not actually the size of a Buick.
  3. Claire Lampen, "Brace for an Invasion of Massive Spiders", The Cut, 3/8/2022.
  4. Meghan Overdeep, "Gulp. Giant Invasive Spider Spreading Throughout the Southeast", Southern Living, 3/7/2022.
  5. Zachary Mack, "If You Live Here, Watch Out for Giant Spiders Falling From the Sky", Best Life, 3/7/2022.
  6. Karri Peifer, "Giant spiders expected to drop from sky across the East Coast this spring", Axios, 3/9/2022.
  7. Invasion of the Murder Hornets, 5/10/2020.
  8. Annalise Knudson, "Experts predict giant Joro spiders could invade the entire East Coast", SILive, 3/8/2022.
  9. Madison Dapcevich, "What We Know About the Giant, Parachuting Spiders ‘Invading’ the East Coast", Snopes, 3/7/2022.
  10. James Crowley, "Massive Tarantula Surprises Unwitting Texas Couple", Newsweek, 6/25/2020.
  11. Megan Loe, Eliana Block & Brielle Ashford, "No, a study on Joro spiders doesn’t say they will colonize the entire East Coast by this spring", KHOU-11, 3/11/2022.

March 6th, 2022 (Permalink)

Did Nostradamus predict the Russian invasion of Ukraine?

Spoiler: No.

At the end of last year, we looked at failed predictions for 2021 ascribed to Nostradamus and, at the end of that entry, I briefly mentioned some predictions for this year attributed to him1. One of those predictions was of World War III, and let's hope that the current war does not develop into a wider one that would merit that moniker, but it mentioned neither Russia nor Ukraine so it was just a generic WW3 prediction. People love to interpret Nostradamus as predicting WW3 and, unfortunately, one of these days they may be right. For instance, thirteen years ago I discussed here a whole book that predicted WW3, supposedly based on Nostradamus' prophecies2. However, that war was supposed to begin around that time and end by 2012.

One test of an alleged prophet is whether he predicted an event before it occurred; after all, the word "prophet" comes from the Greek prefix "pro-", which means "before", and "phetes", meaning "speaker"3. So, a "prophet" is one who "speaks before", yet Nostradamus never seems to have predicted anything before it happened. Instead, his followers always interpret his quatrains as predicting an event after the fact.

Interestingly, Sputnik, a Russian state propaganda outlet4, published an article about Nostradamus' supposed predictions for this year a week before the invasion5, though the article says nothing about it. Also, despite invoking Nostradamus, the predictions in the article have no apparent connection to any of his quatrains.

I've checked several different websites that suggest that Nostradamus predicted the invasion, all of which quote from the same two quatrains:

1st Quatrain: II.ii
La tête bleue fera la tête blanche
Autant de mal que France a fait leur bien:
Mort à l'antenne grand pendu sur la branche,
Quand pris des siens le Roi dira combien.
The blue head will inflict upon the white head
As much evil as France has done them good:
Dead at the sail-yard the great one hung on the branch,
When seized by his own the King will say how much.6

Who are the blue heads and the white heads and what do they have to do with the invasion? Edgar Leoni, from whom I took the above translation, comments: "The meaning of blue and white heads is completely obscure.7" Also, there is no mention of Ukraine, Russia, an invasion, or anything else that seems to be related to it. If this has anything at all to do with an invasion or war, it must be one that involves France, which is the only country named.

Henry Roberts interpreted this quatrain as predicting the killing of Mussolini and the ending of the monarchy in Italy8, which makes about as much sense as seeing the Ukrainian invasion in it. You could pick a quatrain at random and find as good or better match to the invasion as this one, and maybe that's how it was selected.

2nd Quatrain:
Tout alentour de la grande cité,
Seront soldats logés par champs et villes:
Donner l'assaut Paris, Rome incité,
Sur le pont lors sera faite grande pille.
All around the great city
Soldiers will be lodged throughout the fields and towns;
To give the assault Paris, Rome incited,
Then upon the bridge great pillage will be carried out.6

This one is a bit better than the previous one, since it does seem to refer to a war, but there is still nothing about Ukraine or Russia. Instead, the quatrain seems to describe the siege of one of the two cities mentioned, though it's ambiguous as to which is besieging which. In either case, what does this have to do with the current war?

Again, earlier Nostradamians have already interpreted this quatrain as predicting events other than the current one. Roberts writes: "The capture and sacking of Rome by the French Duke of Bourbon is here described8." Oddly enough, this took place in 1527, when Nostradamus was still alive and before The Centuries was first published9. It's a lot easier to predict an event after it has already happened. In contrast, another interpreter, R. W. Welch called it one of "Nostradamus' Greatest Hits", and rated it a "10" on a scale of 1 to 10 for accuracy and "overall impressiveness", for supposedly predicting events that took place during the French Revolution10.

As usual, neither of these quatrains supplies dates for when the events described are supposed to happen, and they are even bereft of the astrological clues that Nostradamus sometimes provided, making them open-ended and unfalsifiable. So, I predict that the next time a major event occurs, we will again be told that Nostradamus predicted it.


  1. When Prophecy Fails, 2021 Edition, 12/31/2021.
  2. Through the Looking Glass, Darkly, 2/7/2009.
  3. Joseph T. Shipley, Dictionary of Word Origins (1945).
  4. "Sputnik News", Media Bias/Fact Check, 2/25/2022.
  5. "Nostradamus' predictions for 2022 are coming true. What awaits Russia?", Radio Sputnik, 2/16/2022. This is an archived page from the Internet Archive's Wayback Machine. Sputnik's website appears to be unavailable, due presumably to the war.
  6. Edgar Leoni, Nostradamus and His Prophecies (1982).
  7. Leoni, p. 585.
  8. Henry C. Roberts, The Complete Prophecies of Nostradamus (New Revised Edition, 1982).
  9. Tony Bunting, "Sack of Rome", Encyclopaedia Britannica, accessed: 3/5/2022.
  10. R. W. Welch, Comet of Nostradamus: August 2004―Impact! (2001), pp. 45-46 & 177-178.

March 2nd, 2022 (Permalink)

Refute or Deny?

The following recent headline caught my attention:

Browns refute claims that former HC Hue Jackson was incentivized to lose games1

To deny something is simply to claim that it is false―that is, "deny" is a negative version of "claim" or "assert"―whereas, to refute is to prove something false―"refute" is a negative version of "prove" or "establish". If you read the story beneath the above headline, you'll discover that the spokesperson for the Cleveland Browns football team did not, in fact, refute Jackson's claims, but instead merely denied them.

For some reason, headline writers seem to be particularly fond of using "refute" in place of "deny", despite the fact that the latter word is two letters shorter. Have editors stopped trying to keep headlines short?

The use of "refute" to mean "deny" is so common that I've written about it twice before2. Though some books on usage do mention that it is a mistake3, it's now so common that many dictionaries offer "deny" as a possible meaning of "refute"4. However, as is the case with "healthy" and "healthful"5, the distinction between merely denying something and refuting it is one worth preserving. Why use "refute" when we already have the perfectly good word "deny"?

Given that this confusion is now so common that lexicographers are reinforcing rather than discouraging it, you're not likely to suffer any bad consequences from using "refute" to mean "deny". Descriptivist linguists will simply say that languages change and that dictionaries have to keep up with such changes. Of course languages do change, but not all change is for the better. How is losing the distinction between "refute" and "deny" a worthwhile change? What do we gain by it?

The lexicographers have abjured any responsibility to preserve and protect the English language and, by their own admission, they now simply look at how people use it. Even if we accept that "refute" can mean the same thing as "deny", that doesn't mean we have to use it in that sense. Why not use the perfectly serviceable "deny"? Ultimately, the way the language changes, or remains the same, is determined by its users. That means you.

As with many of the other confusions we've looked at in the past6, this one seems to go mainly in one direction: "refute" is used when "deny" is called for. Since they are both English verbs, neither spell-checking nor grammar-checking programs are likely to catch this mistake.


  1. Camryn Justice, "Browns refute claims that former HC Hue Jackson was incentivized to lose games", News 5 Cleveland, 2/5/2022.
  2. For instance:
    • Bill Bryson, Bryson's Dictionary of Troublesome Words (2002), under "Refute".
    • Michael Dummett, Grammar & Style for Examination Candidates and Others (1993), p. 95.
    • Harry Shaw, Dictionary of Problem Words and Expressions (1987), under "Refute".
  3. See the following for a discussion of the extent to which recent dictionary-makers have accepted this linguistic change: "Can ‘refute’ mean ‘deny’?", Grammarphobia, 5/9/2018.
  4. Healthy or Healthful?, 1/26/2022.
  5. In addition to that between "healthy" and "healthful", in the previous note, see:

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