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September 13th, 2026 (Permalink)

Very Hot Java Jive

Most of the previous entries in this series on the supposed health effects of coffee have been about claims that coffee is good for you, but rarely a study claims that drinking coffee is the opposite1. Here's a recent one.

A study claiming that drinking very hot coffee increases the likelihood of cancer of the esophagus has recently been reported by several news outlets2. However, according to the study in question, the problem is not with coffee itself, but with drinking any very hot liquid, so that hot tea and hot chocolate are included.

The headline claim is that drinking "scalding" hot beverages can triple the risk of esophageal cancer. Tripling the risk certainly sounds bad, but thrice what? It's a meaningless claim if we don't know what the risk of getting the cancer is for those who don't drink very hot beverages: three times zero is still zero.

The tripling claim is a relative risk or risk ratio (RR), that is, the ratio between the people in the study who drank "very hot" drinks and ended up with cancer of the esophagus to those who didn't drank such hot drinks and still got it. The RR tells us that there were three times as many in the former group as in the latter, but how many were in the latter? Before we can evaluate the RR claim, we need to know the absolute risk (AR) of esophageal cancer, that is, the risk of getting it without drinking superheated beverages3.

Cancer of the esophagus appears to be rare, but how rare? I've known more than one person who had cancer, including a couple who died from it, but I've never met anyone with cancer of the esophagus. The only public figure I've ever heard of who had it was Christopher Hitchens, who died all too young from complications of the cancer4. Did Hitchens drink extremely hot coffee or other beverages? I don't know, but he was notorious for smoking cigarettes and drinking copious quantities of alcoholic beverages, presumably cold5. As many of the news articles point out, cigarette smoking and drinking alcohol are higher risks for esophageal cancer than drinking very hot beverages.

Now, I'm not saying there's no risk of getting cancer of the esophagus―obviously, there must be some risk―but if the risk is very low then tripling it will produce a risk that is still low, maybe very low. This is important to know because life is inherently risky, and we need to know just how risky an activity is to rationally decide whether to do it. For instance, skydiving is risky, but apparently it's enough of a thrill for some people that it's worth the risk. Similarly, there may be some people who enjoy drinking scalding hot coffee so much that a tripled risk of cancer is worth it for them; Hitchens, for instance, claimed that smoking and drinking were worth not just risking it, but actually getting cancer.

In these entries on how health claims are reported, I'm usually quite critical of the reporting, but most of the reports on this study were better than usual. Of course, that's a low standard since so many news reports of new studies simply rewrite the press release without asking questions. However, some of these reporters interviewed an expert who was not connected to the study itself, who then pointed out that the absolute risk is less than 1%, and that smoking cigarettes and drinking alcohol are greater risks than drinking very hot drinks. So, the reporters, to their credit, did some actual reporting.

That said, "less than 1%" still sounded rather high to me, since that would mean one out of a hundred people gets esophageal cancer. Actually, "less than 1%" refers to the percentage of cases of cancer that are of the esophagus, but not everybody gets cancer. What we really need to know is the prevalence of esophageal cancer in the population. It turns out that the rates are quite different for men and women, though both rates are below 1%. For men, it's about .76% and, for women, only around .23%6. Putting these two figures together, the prevalence is approximately .5%7, which is indeed less than 1%. Tripling this rate by drinking searing-hot coffee leads to a risk of 1.5% for people in general.

Whether this is enough of a risk to justify letting your coffee cool off a bit longer before drinking it, I'll leave to your judgment.


Notes:

  1. Here is a list of the entries in this series; only the fourth concerns a study claiming coffee could be bad for your health.
    1. Java Jive, 5/21/2012
    2. Java Jive: A Second Cup, 7/14/2017
    3. Java Jive: A Refill, 11/6/2017
    4. Honey, I shrunk my brain!, 7/27/2021
    5. A Tale of Two Headlines, 12/15/2024
    6. Java Jive Headline, 12/12/2025
  2. Here are a few examples, chronologically:
  3. For more on absolute and relative risks, see: Geoffrey C. Kabat, Hyping Health Risks: Environmental Hazards in Daily Life and the Science of Epidemiology (2009), pp. 42-46.
  4. Richard Pallardy, "Christopher Hitchens", Britannica, 8/29/2026.
  5. Jack Mirkinson, "Christopher Hitchens: Despite Cancer, I'd Drink & Smoke Again", HuffPost, 12/6/2017.
  6. "Key Statistics for Esophageal Cancer", American Cancer Society, 1/13/2026.
  7. "Cancer Stat Facts: Esophageal Cancer", National Cancer Institute, accessed: 9/13/2026.

August 30th, 2026 (Permalink)

Roll-Playing

In a foreword to a book about the use of mathematics in magic tricks, Martin Gardner wrote: "You will learn how parity (odd or even) can play a roll in magic as well as provide powerful shortcut proofs.1" How do you a play a roll? If you're a drummer, you can play a drumroll, but what does that have to do with magic tricks? You could play a roll on Halloween, just as some people don costumes as hot dogs or bananas2, in which case you'd be playing the role of a roll. Which brings us, of course, to what Gardner meant to write: parity plays a role in some magic tricks and mathematical proofs. Whether Gardner himself misspelled "role" or the misspelling was introduced later, it was ultimately the responsibility of the book's editor to correct it.

"Role" and "roll" are homophones, that is, words that sound the same but are spelled differently and have different meanings. "Role" is a noun for the act of playing a part in something, such as a play or other performance3: the role of Hamlet, for instance. By extension, it can mean the playing of a part in other types of event or situation: for example, the role of magician in a card trick.

"Roll" is a highly ambiguous word with a long list of distinct but related meanings4. It's even ambiguous in grammatical category, since it can play the role of both a noun and a verb, but its use as a verb seems to be primary. "To roll" is to turn something over, or move something by turning it over. As a noun, a "roll" is an object that either works by turning over―such as a roll of toilet paper―or is made by turning over something―such as a cinnamon roll, which is made by rolling dough into a cylinder and then slicing off an individual roll.

One reason why these two English words are spelled so similarly and, thus, so easily confused, is that they descend from a common ancestor, namely, the Old French word "rolle"5. This word seems to have come into English first as "roll", referring to a roll of parchment, which was the predecessor of the modern paper book. Later, "role", as in "playing a role", came from the use of rolls of paper as promptbooks for the actors' lines in a play.

As with many of the confusable word pairs in this series, the confusion goes primarily one way, namely, "role" is misspelled "roll", which may simply be because the latter is the more familiar word. Misspelling "role" in this way is a common enough mistake that I've seen it before, yet not a single one of the reference books I usually consult mentions it.

If you don't want to play the "roll" of an unlettered person, spell it "role".


Notes:

  1. Persi Diaconis & Ron Graham, Magical Mathematics: The Mathematical Ideas that Animate Great Magic Tricks (2012), p. x.
  2. A quick web-search reveals people dressed as cinnamon rolls, sushi rolls, and Tootsie Rolls, but I don't think that's what Gardner had in mind.
  3. "Role", The Britannica Dictionary, accessed: 8/28/2026.
  4. "Roll", The Britannica Dictionary, accessed: 8/28/2026.
  5. John Ayto, Arcade Dictionary of Word Origins (1991), under "roll".

Poll Watch
August 20th, 2026 (Updated: 8/21/2026) (Permalink)

Straw Polls

Something calling itself "Median Strategies" (MS) put out press releases claiming to have done three different polls: one for the Democratic primary for governor of Wisconsin, another for the contest for the governor of Nevada, and finally one for the race for mayor of Los Angeles1. The last one received the most media attention by claiming that Democrat Karen Bass, incumbent mayor of Los Angeles and candidate for re-election, had a twelve percentage point lead over challenger Nithya Raman. Bass' campaign trumpeted the results before it was revealed that all three polls were hoaxes2.

Political partisans frequently claim that polls whose results they dislike are fake, or at least rigged; for instance, President Trump loves the word "fake", calling news he doesn't like "fake news" and poll results he hates "fake polls"3. While there have been "push polls" in the past, which could be rightly called "fake"4, outright hoaxes have been rare.

Since this news may well lead to a decline of trust in polling, I wondered whether any polling had been done to measure the level of trust. Surprisingly, there was such a poll just last week released by a real pollster as opposed to a fraudster: half of respondents said they don't trust polls, with only 28% saying that they did5. According to the pollster, this result has not significantly changed in the last decade, so the pollster has been polling on this topic for at least that long. Assuming that it keeps asking the same question―and I hope it does―it'll be interesting to see whether the current news leads to a loss of trust.

What was the motive for the hoax? MS claimed in its announcement that it was "a short-term social experiment examining how purported polling information could enter and spread through the political information ecosystem without independent verification"6. Every report on this hoax that I've seen seems to take this claim at face value, but that's the same mistake that those who reported on the poll as if it were genuine made. Given that MS has lied about everything else, why should we believe this claim?

Assuming that the claim is true, this "social experiment" had mixed results. The alleged poll of Los Angeles voters received the most media attention probably because the Bass campaign publicized it. So, there was at least some "spread through the political information ecosystem without independent verification" of that one. This led some news media to try to investigate MS, and that seems to have triggered its public confession and the whole hoax only lasted a few weeks. I'm about as cynical about our "political information ecosystem" as anyone, but this is a reassuring result. It's not as easy as you might have thought to get away with hoaxing poll results.

If this was a "social experiment" by a scholar or scholars, one would expect that those responsible would immediately reveal their identities, and a publication of some sort should ensue. There is a recent history of scholarly hoaxes, starting with the Sokal hoax and followed by the so-called "Sokal squared" hoaxes7, but in both cases those involved revealed their identities and explained the points of the hoaxes.

If it wasn't a "social experiment", what was it? Perhaps it was an attempt to influence the elections by injecting hoaxed polling data that might contribute to a "bandwagon effect"8. This might explain why the fake polling numbers for Bass were so lopsidedly in her favor, while contemporaneous polls had the race between her and her opponent closer. As a result, the "poll" was an outlier, thus drawing attention to the formerly unknown "pollster".

I haven't been able to find any information on the hoaxed Nevada poll, but the poll on the Democratic primary for governor in Wisconsin was similarly skewed, showing Francesca Hong with a 23-point lead in a race that she subsequently lost9.

In its last statement, MS claimed: "No individual involved with Median Strategies received compensation or financial benefit from the project, and the project was not funded, commissioned, or directed by any candidate, campaign, political party, PAC, media organization, or other outside entity." Again, why should we believe this disclaimer? Even if true, it doesn't rule out that an individual or individuals involved in it―and, thus, inside entities―wanted to help one or more of the candidates and tried to do so by means of the hoax.

Unfortunately, we'll probably never know the correct explanation of this hoax unless the party or parties behind it are identified.


Update, 8/21/2026: That was fast! When I wrote the above, whoever was behind "Median Strategies" was unknown, but now the perpetrator, a young man, has confessed to making up the polling results with the help of "artificial intelligence". As in the final statement put out by MS, he claims to have simply wanted to see whether hoaxed polling results would be picked up by the news media. As I pointed out above, the stunt was only partially successful. He also claims, as he did in that statement, that he didn't make any money from it, but why should we believe him? The Grauniad tracked him down based on his domain name registration for MS' website, so he didn't do a very good job covering his tracks10.


Notes:

  1. Steve Peoples, Amelia Thomson-Deveaux & Ken Sweet, "What to know about the fake election poll numbers shared and retracted by a mysterious company", Associated Press, 8/18/2026. The following news article is the only one I've found that treated any of the hoaxes as real polls: Justin Choi, "Poll: Spencer Pratt Voters Propel Karen Bass to Double-Digit Lead Over Nithya Raman", California Post, 8/14/2026.
  2. Noah Goldberg, "Poll showing Bass leading Raman by double digits was bogus, company says", Los Angeles Times, 8/18/2026.
  3. Jesus Mesa, "Donald Trump Slams 'Fake Polls' After Worst-Ever Approval Rating", Newsweak, 1/22/2026.
  4. Herbert Asher, Polling and the Public: What Every Citizen Should Know (7th edition, 2007), pp. 156-158.
  5. "Only 28% Trust Political Polls", Rasmussen Reports, 8/13/2026. You have to subscribe to read this entire article, but the first couple of paragraphs give the results cited.
  6. "Median Strategies Polling Discontinued", Median Strategies, accessed: 8/18/2026.
  7. Mike McRae, "A Massive Hoax Involving 20 Fake Culture Studies Papers Just Exploded in Academia", Science Alert, 10/4/2018.
  8. Walter Veit, "What Is the Bandwagon Effect?", Psychology Today, 3/14/2020.
  9. Sean James, "Polling Company Collapses After Giving Francesca Hong a 23-Point Lead in a Race She Lost, Admits to 'Bogus' Data on LA Mayor Karen Bass", Mediaite, 8/18/2026.
  10. Sophie Sullivan, Anna Betts & Sam Levine, "Website behind widely shared fake election polls run by 21-year-old", The Grauniad, 8/20/2026.

August 9th, 2026 (Permalink)

Newsweak Nostradamus

Check out the dueling headlines:

Gas Prices Predicted To Hit Five-Year Low in 20261

Gas Prices on Course To Beat 2022 Record: Which States Are Charging Most?2

Both of these headlines were on articles by the same writer in the same source, Newsweak, about a half-year apart. The first is from early January of this year, prior to the beginning of the current conflict with Iran, and the second is from late last month, months after that conflict had begun. When Newsweak doesn't have any actual news to report, it predicts what the news is going to be.

The actual prognostications reported in these articles are not due to Newsweak itself, but come from the company GasBuddy, which provides information to consumers on gasoline prices3, and when not predicting current prices tries to predict future ones. Such information would be useful if it were correct; for instance, if you knew that the price of gas was going to go up, you could fill up your car prior to an increase, and if you knew it would go down, you could wait until it did to do so.

What's the "five-year low" that the first headline predicted for gas prices this year? According to the article: "Average nationwide gas prices are expected to fall below $3 per gallon this year, according to GasBuddy's predictions―hitting the lowest level since 2020…". According to GasBuddy itself4, the average price of gas for the U.S. was already below $3 per gallon at the time this article was published: it's easy to predict what's already happened.

What's the "2022 Record" that the second headline predicts for the price of gas for the rest of this year? According to the article: "Gas prices in the U.S. are up by more than 30 percent since the start of the Iran war and are likely to reach the highest August level ever next month, according to analysts, surpassing even the record hit in August 2022 when inflation was rampant." So, apparently the record is only for the month of August, which is not nearly as alarming as it would be if it were for the entire year or an all-time record. The nominal price record for the entire year of 2022 was just over five dollars, and the real price record―adjusted for inflation―was set in 20086.

The Newsweak article goes on to say:

Patrick De Haan, head of petroleum analysis at GasBuddy and one of the most prominent experts in the field in the U.S., said on Tuesday that in approximately a week, Americans are "going to see new all-time records set for highest August gas prices ever―even compared to 2022." Considering the national average gas price of $4.08 per gallon then, according to GasBuddy data, De Haan estimated that prices nationwide will reach their "highest level ever for the date" by August 5. In early August 2022, the national average gas price was just above $4; by mid-August, it had fallen to just below $4―the lowest level since early March of that same year.6

According to GasBuddy's own data, the price peaked at about $4.10 a couple of days after this was said, and has been trending downward ever since. On the fifth of this month, the price was $4.05, which might be a penny or two higher than it was on the same date in 2022. Big deal. The current price has already fallen to "just below $4" and we're not even at the middle of the month yet.

The real problem with these prognostications is not that they're wrong, or make a big deal out of nothing much―though they do―but that they simply extrapolate current trends. If the current trend is upward, then they predict that it will keep going up; whereas, if it's currently trending downward, they predict that the trend will continue down. In January, the price of gas was trending downward, so it was predicted to reach a five-year low this year; whereas, since the Iran conflict began, the price has risen, and now it's predicted to beat the 2022 record high. However, the only certainty about current trends is that they won't continue, though when they will change is unpredictable.

I don't blame GasBuddy for not realizing in January of this year that in February we would begin a bombing campaign against Iran that would cause the trend of gas prices to reverse. Perhaps the only person who could have seen that coming was the President, and he may have expected the fighting to end very soon, in which case the impact on gas prices might have been a short spike.

I chose to examine this example not just to pick on Newsweak―that's a bonus―but because it illustrates a larger phenomenon. The future would be predictable if only unpredictable things like wars didn't happen, but things have a way of happening unpredictably. As a result, attempts to predict the future based on current trends are bound to fail eventually. Still, people keep trying: you can count on that.


Notes:

  1. Giulia Carbonaro, "Gas Prices Predicted To Hit Five-Year Low in 2026", Newsweek, 1/7/2026.
  2. Giulia Carbonaro, "Gas Prices on Course To Beat 2022 Record: Which States Are Charging Most?", Newsweek, 7/30/2026.
  3. "About", GasBuddy, accessed: 8/9/2026.
  4. "12 Month Average Retail Price Chart", GasBuddy, accessed: 8/9/2026.
  5. Inflation and "Record-High" Gas Prices, 6/26/2022.
  6. See note 2, above. Paragraphing suppressed.

Puzzle
August 2nd, 2026 (Permalink)

Crack the Binary Combination

In previous "Crack the Combination" puzzles*, the combination has always been decimal, that is, the digits in the combination were the ten from 0 to 9. Now, the combination lock you need to open has a binary combination of five of the two binary digits―"bits"―0 and 1. The following are some incorrect combinations:

Clue Combination # of bits correct
1 1 0 0 0 0 1
2 1 0 0 1 0 10
3 0 0 1 1 1 11
4 1 0 0 0 1 10
5 0 0 0 1 0 11

Your mission is to determine the correct combination from the above clues.


* I, II, III, IV, V, VI, VII, VIII, IX, X, XI.


Notes & Quotes
July 31st, 2026 (Permalink)

Sylvia Plath, Vigilante, Caveat Lector & Post-Reality


Notes:

  1. Janet Somerville, "The latest historical fiction books take inspiration from Sylvia Plath, a New York vigilante and Shah of Iran", The Toronto Star, 7/16/2026.
  2. Peter Charles Hoffer, Past Imperfect: Facts, Fictions, Fraud―American History from Bancroft and Parkman to Ambrose, Bellesiles, Ellis, and Goodwin (2007), pp. 225f.
  3. See: How to Lie With Notes 4: Ghost Notes, 1/3/2026.
  4. Mario Pei, Words in Sheep's Clothing (1969), pp. 5f. Paragraphing suppressed.

July 25th, 2026 (Permalink)

100% MORE!

…[T]he problem with ads isn't so much what is said or demonstrated as what we infer from what is said or demonstrated, and the best way to induce false inferences is to sketch alluring pictures and leave out crucial bits of information. … A survey shows that this medication works more quickly. Than what does it work more quickly?1

I recently saw an advertisement for an expensive electric toothbrush that made me wonder whether I should purchase one. My current toothbrush has the advantage that it's cheap, but how good does it clean my teeth? Should I pay over ten times as much for a replacement?

The ad claimed, in large print, that the electric toothbrush would remove "100% more plaque". More than what? This is a dangling comparative2, that is, a comparison missing one of the objects compared. What is the electric toothbrush compared to: does it remove more plaque than the previous model, or than a competing brand, or what?

I should have written that it is a semi-dangling comparative since the ad completed the comparison in smaller print: "vs. a regular manual toothbrush". So, it's being compared to the kind of toothbrush I currently use. Why was the rest of the comparison in small print? The ad writer probably didn't want to draw attention to the fact that the ad was comparing an electric toothbrush to a manual one. Perhaps any electric toothbrush would remove "100% more" plaque than a manual one, in which case I should purchase the cheapest electric one I can find instead of the expensive one advertised.

Now, that explains the semi-dangling comparative and the small print, but what about "100% more": what does that mean? 100% of something is, of course, all of it, so adding 100% more to something increases it by the same amount. Thus, if the electric toothbrush removes 100% more plaque than a manual one, it removes twice as much plaque. Why didn't the ad just say that instead of using a potentially confusing percentage?

Percentages, which are a type of fraction, are generally harder to understand than multiplication, since many people find division and fractions difficult. Unlike percentages, we have frequent experience with multiplication by two, which makes "100% more" more confusing than "twice as much" or "double", though perhaps not 100% more confusing. This is an advantage for the ad writer whose goal is not to write clearly but to sell toothbrushes.

My guess is that the writer wanted to trick the casual peruser of the ad into thinking that "100%" referred to all of the plaque, that is, that the toothbrush would remove 100% of it. The use of the percentage together with the semi-dangling comparative could lead an unwary reader astray, yet the fine print would legally protect the company from a charge of false advertising. It's not a literally false ad, but it's a misleading one.

An important fact about percentages is that they always have a base, that is, a percentage is always a fraction of something, which is called its base. If I tell you that I will have 100% more toothbrushes tomorrow than I have today, how many will I have tomorrow? You can't answer this question without knowing the base, that is, how many brushes I have today. So, when confronted by any claim involving a percentage, one should always ask: what is the base? What is the base of the ad's claim that the electric brush removes 100% more plaque than a manual one?

The base, in this case, is the amount of plaque removed by a manual toothbrush, but the ad doesn't tell you what that is. Suppose that a manual toothbrush removes 1% of the plaque on your teeth, then how much would the electric one remove, according to the ad? 2%, which is double the manual one, that is, 100% more. This is an example of a feature of percentages to keep in mind: a large percentage―such as 100%―can represent a small amount if its base is small. 100% of nothing is still nothing, and 100% of very little is not much.

In addition to the base, there's a lot of other information missing from this ad that is needed to evaluate the strength of its argument for purchasing the toothbrush. For instance, how were the two types of toothbrush compared? How much plaque is removed by brushing surely must depend on how long one brushes. Was the amount of plaque removed by the two toothbrushes measured after the same length of time spent brushing? It would seem that this would have to be the case for a fair test, but perhaps an electric toothbrush is just faster than a manual one. If so, you might be able to remove "100% more plaque" with a non-electric toothbrush by brushing twice as long. Would the savings in time be worth the much higher price of the electric brush?

In any case, this is not a review of the electric toothbrush or a recommendation about what to use to clean your teeth―dammit, Jim, I'm a logician, not a dentist. I'm just using the ad's claims as an example of what you need to be on the lookout for in advertising. Ads are trying to sell you something; if not a toothbrush then something else, such as a political candidate. Watch out for dangling comparisons, what's hidden in the fine print, and missing information.

Exercise: Supposing that an electric toothbrush really did remove 100% more plaque than a manual one, what is the largest percentage of plaque that the manual brush could remove?


Notes:

  1. John Allen Paulos, A Mathematician Reads the Newspaper (1995), p. 86.
  2. See: Dangling Comparative, 10/16/2023.

New Book
July 18th, 2026 (Permalink)

Sorry, Wrong Number!

Quote: An individual study is a brick, and it only proves itself when incorporated into a useful structure. Bad bricks either get rejected as not fitting into the structure, or exposed when things built on them collapse. But the Wrong Numbers you'll find in this book do not try to fit into structures, they are used to throw through windows instead. They go direct to the public, claiming the authority of science. But it's cargo-cult science1. It looks like science, with equations and data and references and peer review and jargon, but it was never exposed to critical scrutiny, never cross-checked with related work, never used to build structures of understanding.2

Title: Wrong Number

Subtitle: How to Extract Truth From a Blizzard of Quantitative Disinformation

Author: Aaron Brown

Comment: Brown is a writer who has had an interesting career, including professional poker playing, financial risk management―whatever that is―and teaching mathematics in college3. He's the author or co-author of four previous books, including ones on risk and chance. He also has done a series of short videos with the same title as the new book4. According to Brown:

Almost half the chapters in this book are based on studies I examined for…videos, and include some phrasing and research contributed by the team. Bill Fallon, my editor…, noticed the attention generated by the videos and suggested that Wrong Number was a good theme for a book.5

So, if you like the videos then you may like the book, and vice versa.

Date: 2026

Summary: Judging from the Table of Contents and the first, introductory chapter, the chapters appear to be mostly case studies of bad scientific studies, like the short videos Brown has done. Based on their titles, some of the chapters appear to cover the same topics as do some of the videos, though presumably in greater depth.

The Blurbs: The book is positively blurbed by Philip Tetlock, author of Expert Political Judgment6, despite the fact that there is actually a chapter titled "Philip Tetlock"7! Given that I haven't read the chapter, I don't know whether it is positive or negative about Tetlock, though I'd wager that it's positive given the endorsement. While I don't doubt Tetlock's sincerity, it's an obvious conflict of interest to have a subject of the book endorse it in a blurb, especially without revealing that conflict.

Disclaimer: I haven't read this book yet and, therefore, can neither review nor recommend it, but it looks interesting enough to read and I thought others might also be interested. I may review the book in the near future if I have anything new or interesting to say about it.


Notes:

  1. If you're unfamiliar with "cargo cult science", see: Richard P. Feynman, "Cargo Cult Science", Caltech commencement address, 1974.
  2. And the planes don't land. P. 8. Subsequent citations to only page and chapter numbers are to the New Book.
  3. All information on Brown from: "About the Author", Wiley, accessed: 7/13/2016.
  4. For a list of episodes, see: "Wrong Number with Aaron Brown", YouTube, accessed: 7/14/2016.
  5. P. 9.
  6. Philip Tetlock, Expert Political Judgment: How Good is It? How Can We Know? (2005).
  7. Ch. 24.

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