The Brain Teasers


October 30th, 2014 (Permalink)

A Hallowe'en Costume Contest Puzzle

The four finalists in the All-Hallows' Eve costume contest were traditional costumes:

  1. There was a vampire who looked much like Count Dracula;
  2. A Frankenstein's monster, though more in the Hammer mode than the Karloff;
  3. A person wrapped in white gauze who was either supposed to be a bloody mummy or the victim of a terrible accident;
  4. And, finally, a werewolf-woman.

Three friends who had come to see the contest discussed the finalists:

Alice: I don't know who's going to win, but it sure won't be that pathetic Dracula!

Bob: I think either the mummy or the werewolf will win.

Carol: You're both nuts! It's definitely going to be either the vampire or the Frankenstein monster.

In the event, it turned out that only one of the three friends was right. Which costume won the contest?


October 29th, 2014 (Permalink)

Don't nudge, judge!

This is the fourth and, I expect, last entry on Steven Poole's "Not So Foolish" article―see the Source, below―lest I end up writing more words than are in the article itself. For the three previous entries, see the links below. In this entry, I want to finally discuss what Poole has to say about "nudging", which was a large part of my original motivation for focusing on this article.

Several years ago I wrote a "Book Club" series on Richard Thaler and Cass Sunstein's book Nudge―see links to the entries, below. The book was in the news at the time because Sunstein was an adviser to candidate, then President, Obama and later served for awhile in the administration. For this reason, it was thought that "nudging" was the coming thing, and that we would all be getting elbowed in the ribs by the government during the Obama administration. However, in the intervening six years I've seen little if any evidence of "nudging" done by the federal government. Obamacare, the centerpiece achievement of the current president, doesn't seem very nudgy: it has an individual mandate, not an individual nudge. While certainly paternalistic, Obamacare is not exactly libertarian, though it's more libertarian than a national health service would be.

Now, Sunstein has a new book titled Why Nudge?, based on a lecture series he gave a couple of years ago. One of my disappointments with the first book was its failure, despite having a penultimate chapter dealing with objections to nudging, to deal with what seemed to me to be some obvious counter-arguments. So, I'm curious whether Sunstein, in the new book, will finally get around to addressing these doubts, or at least acknowledging their existence.

Poole's article pleases me partly because he raises some of the same objections as I had, and does so more forcefully. Unfortunately, it arrives too late to nudge Sunstein into addressing these legitimate objections in his new book, but at least it may give greater publicity to them. Here are the main unanswered objections:

I don't want to suggest that Sunstein has no answers to these objections; rather, I'm asserting that up to now he simply has not addressed them at all. Perhaps the new book will remedy this defect.

I'll give Poole the last word:

…[E]ven if we each acted as irrationally as often as the most pessimistic picture implies, that would be no cause to flatten democratic deliberation into the weighted engineering of consumer choices, as nudge politics seeks to do. On the contrary, public reason is our best hope for survival. Even a reasoned argument to the effect that human rationality is fatally compromised is itself an exercise in rationality. Albeit rather a perverse, and…ultimately self-defeating one.

Source: Steven Poole, "Not So Foolish", Aeon Magazine, 9/22/2014

Previous Entries in this Series:

  1. Wink-Wink, Nudge-Nudge, 9/29/2014
  2. The "Linda Problem" Problem, 10/2/2014
  3. The Great Pumpkin, 10/13/2014

Book Club: Nudge:

October 28th, 2014 (Permalink)

Hallowe'en Headline

Grieving Parents Shocked When Dead Son Answers The Door

"The paw!…The monkey's paw!"


October 22nd, 2014 (Permalink)

Check Your Sanity!

A keen sense of proportion is the first skill―and the one most bizarrely neglected―for seeing through numbers. Fortunately, everyone can do it. Often all they have to do is think for themselves.―Michael Blastland & Andrew Dilnot, The Numbers Game

It's time once again to get out your old envelopes or used cocktail napkins, and go figure! A valuable critical thinking skill is to be able to check numerical claims made in the media for plausibility, a process which is sometimes called a "sanity check". You might be surprised at how many won't even stand up to such a check, for the journalists who write media stories are often innumerate or number-phobic. For this reason, don't assume that reporters will check the numbers for you; we've seen many examples in the past―see the Resources, below―where they did not. Also, don't be afraid of the math! To do a sanity check seldom requires any advanced mathematics, and definitely does not require any in this case: if you can add, subtract, multiply, and divide, you can check the sanity of the following number.

The best way to learn how to do such number checks is to see how it's done and work a few yourself. As mentioned, you won't need to learn any new math; you'll just need to learn how to apply what you already know. Here's the number that we want to check for sanity, taken from Michael Blastland and Andrew Dilnot's excellent book The Numbers Game: "In 1997 the British Labour government said it would spend an extra £300 million (about $600 million) over five years to create a million new child care places."

Is this number sane? The question we want to answer is: Is $600 million over five years a large enough amount of money to create a million new child care places, that is, is that amount of funding for day care centers and other child care providers enough to lead to an additional million spots being available for parents who need day care?

How can you answer this question using simple math and what you already know? Most of us do not have experience with large numbers that would allow us to put them into perspective; we lack an intuitive feel for the difference between millions, billions, and trillions. So, one approach to dealing with large numbers is to use math to translate them into smaller numbers that we do have a feel for. Give it a shot, then when you're ready click on "Sanity Check" below to see one way to do it:

Sanity Check

Source: Michael Blastland & Andrew Dilnot, The Numbers Game: The Commonsense Guide to Understanding Numbers in the News, in Politics, and in Life (2009), pp. 12-15


October 21st, 2014 (Permalink)

New Book: Arguing with People

Arguing with People is a new book by philosopher Michael A. Gilbert, also author of How to Win an Argument: Surefire Strategies for Getting Your Point Across. As is suggested by the subtitle of the latter, both appear to focus on practical argumentation.

October 13th, 2014 (Permalink)

The Great Pumpkin

This is the third entry on Steven Poole's "Not So Foolish" article―see the Source, below, and the Resources for the two previous entries. The section of the article that I want to comment on is short, so I suggest reading or re-reading it, but here are the most important parts:

One interesting consequence of a wider definition of ‘rationality’ is that it might make it harder to convict those who disagree with us of stupidity. …Dan M Kahan, a professor of law and psychology, argues that people who reject the established facts about global warming and instead adopt the opinions of their peer group are being perfectly rational in a certain light:
Nothing any ordinary member of the public personally believes about […] global warming will affect the risk that climate changes [sic] poses to her, or to anyone or anything she cares about. […] However, if she forms the wrong position on climate change relative to the one [shared by] people with whom she has a close affinity―and on whose high regard and support she depends on [sic] in myriad ways in her daily life―she could suffer extremely unpleasant consequences, from shunning to the loss of employment. Because the cost to her of making a mistake on the science is zero and the cost of being out of synch with her peers potentially catastrophic, it is indeed individually rational for her to attend to information on climate change in a manner geared to conforming her position to that of others in her cultural group.

I've omitted a paragraph comparing this situation to "the tragedy of the commons", which is a useful exercise if you're familiar with the "tragedy" but probably not otherwise. Also, while that analogy draws a distinction between individual and group rationality, that's not the distinction that I want to call attention to. I think Poole―and possibly Kahan, as well―is confusing two distinct types of individual rationality:

  1. The rationality of a belief: If the woman in the example comes to her belief in the wrong way, then her belief may be irrational. For instance, suppose that she thinks to herself: "My peers all disbelieve in climate change, and they would shun me if I believed in it, therefore I won't believe in it." In other words, the woman forms her disbelief using the appeal to consequences―see the Fallacy, below. The belief itself is not based on adequate or relevant evidence, therefore it is irrational.
  2. The rationality of believing: In contrast, despite the fact that the belief itself is irrational, it may still be rational for the woman to believe it, at least in the narrow, economic sense of "rational".

Perhaps a different example will make the distinction clearer: Let's take as our example of an irrational belief the existence of The Great Pumpkin. Presumably, we can all agree that there is not sufficient credible evidence of its existence, such that to believe in The Great Pumpkin is to believe in something irrational, that is, such a belief is irrational in sense 1, above.

Now, suppose that a rich man were to offer you a million dollars if you believe in The Great Pumpkin. Put aside the objection that you can't believe something by an act of will, which may be true but is beside the point. Also, to answer the objection that no one can see inside your head to tell if you really believe something, let's suppose that the rich man has a "psychoscope" that allows him to read your beliefs. So, in order to get the million dollars, you must really believe in The Great Pumpkin.

Clearly, it would be rational for you to believe in The Great Pumpkin, given that you stand to gain a million dollars and lose very little by so believing. Perhaps you'd be rather embarrassed by believing it, but a million dollars ought to help make up for that: you can cry all the way to the bank, as someone once said. So, it is rational for you to believe in The Great Pumpkin, but the belief itself is still irrational.

In other words, there are at least two different ways that a belief can be rational, and these ways may conflict. In the first way, it is rational to hold the belief because the belief itself―that is, the proposition that is believed―is supported by sufficient evidence. In the second way, it is rational to believe the proposition because of the good or bad consequences that may follow from believing or disbelieving it.

Now, there is no guarantee that these two types of rationality will always go together. There is, of course, no problem when one believes a proposition that is supported by appropriate evidence and expects good consequences from doing so. Similarly, we would all surely condemn believing a proposition for which one has no good evidence, neither expecting good nor fearing bad consequences of believing it.

What we have to wonder about, then, are when these types of rationality misalign: Believing something for which one has inadequate evidence because of either good consequences one expects from believing, or bad consequences one fears from disbelieving. This is what's happening in the case of The Great Pumpkin, and that of the woman who doesn't believe in climate change. We needn't dwell on the case of those who persist in believing something for which they have good evidence in the face of threats of bad consequences or offers of rewards for not believing―they have their reward.

To return to Poole, I'm certainly on his side in thinking that we shouldn't be so quick to accuse those we disagree with of stupidity. For one thing, much of the time this is simply incorrect. It may indeed be rational, in the second sense discussed above, for the woman in Poole's example to believe what her peer group believes, or at least "to attend to information…in a manner geared to conforming her position to that of others in her cultural group". However, as far as I can see, this is no objection to the psychological work that Poole is criticizing. Instead, Poole is describing a particular way that people come to hold irrational beliefs, namely, it can be economically rational to believe a proposition that is poorly supported by evidence.

Source: Steven Poole, "Not So Foolish", Aeon Magazine, 9/22/2014


October 8th, 2014 (Permalink)

Wikipedia Watch

Here's a follow-up to last month's entry on Neil DeGrasse Tyson's contextomy of President Bush―see the Resource, below. Wikipediocracy has an instructive article about the controversy on Wikipedia as to whether its biography of Tyson should mention the quote controversy―see the Source, below. Check it out.

As I write this, Wikipedia's biography of Tyson contains no reference at all to the Bush contextomy. One could justify this on the basis that the issue is too unimportant to include in a biography, which is indeed how some of its "editors" have argued against its inclusion on the article's "Talk" page. However, the article manages to mention that Tyson has been portrayed in an issue of Action Comics, as well as having appeared in an episode of The Big Bang Theory. It even notes Tyson's appearance as keynote speaker at "The Amazing Meeting", but without noticing the controversy that resulted from his speech. So, if this is any indication of Wikipedia's standards of significance, it's rather hard to believe that the contextomy just isn't important enough to merit, say, a short paragraph.

However, there's the additional objection that the "editors" are apparently unable to find reliable evidence that a controversy even exists, let alone that Bush was quoted out of context. This, despite the fact that Tyson has now admitted and apologized for misquoting Bush. Apparently, even Tyson himself isn't a sufficiently reliable source about what he said, since he only self-published his apology on his Facebook page! In contrast, we learn from the biography the important fact that Tyson won a gold medal in ballroom dancing while in college, despite there being no source at all cited. By the way, I'm available for remedial instruction in researching and evaluating evidence.

The "Talk" page debate suggests that Wikipedia is in danger of turning into, if it hasn't already become, a kind of Tower of Babel. While this entire issue could have been dealt with in a few sentences, and probably less than a hundred words in the article itself, thousands of words have been exchanged on the "Talk" page arguing back and forth about whether to include those hundred words. All of which suggests that if you must check Wikipedia, then you should also check the "Talk" page of any article you read to see how the sausage got made. You may be amazed by both what was put in and what was left out.

Source: Hersch, with research assistance from Eric Barbour & Andreas Kolbe, "'Our Wikipedia is the Wikipedia who defamed the stars'", Wikipediocracy, 10/5/2014

Resource: The Bushisms Strike Back!, 9/21/2014

Previous Wikipedia Watches: 6/30/2008, 10/22/2008, 1/25/2009, 3/22/2009, 5/16/2009, 7/21/2009, 1/9/2013, 10/24/2013, 5/2/2014, 7/21/2014

October 2nd, 2014 (Permalink)

The "Linda Problem" Problem

This is a sequel to the previous entry on Steven Poole's "Not So Foolish" article―see the end of that entry for a link. Instead of tacking it on as an "update", I've decided to make it a separate entry, since the famous "Linda problem" has interest in its own right.

As part of his criticism of skepticism about human reason, Poole critiques the well-known "Linda problem". His argumentative strategy here seems to be to undermine the claims of cognitive psychologists to have found faults in most people's thinking. In the case of the Linda problem, he argues that the answer often given by people to the problem, which is judged to be erroneous by psychologists, may actually be rational after all.

Poole introduces his criticism of the Linda problem by associating it with a definition of rationality from economics. Now, I think there are good reasons to be doubtful about the economic definition of rationality, which certainly seems too narrow if nothing worse. However, it doesn't appear that the Linda problem―or other pieces of evidence for cognitive errors involving judgments of probability―has anything specifically to do with economic "rationality". It's true that the work of psychologists on cognitive biases has been used to cast doubt on whether people are rational in the narrow economic sense, but the Linda problem suggests that people judge probabilities in ways that conflict with probability theory, which is a much deeper failure of rationality.

Poole's criticism of the psychologists' interpretation of the Linda problem is in terms of conversational implications of the way the original problem was worded. "Conversational" implications are implications of the fact that something was said, or the way it was said, or in this case of something that was not said, as opposed to implications of what was said. So, in the Linda problem to say that Linda is a bank teller and to say nothing else may be taken as implying that she's not a feminist.

This is a familiar objection, as it was discussed in Massimo Piattelli-Palmarini's book Inevitable Illusions from twenty years ago. For this reason, I won't discuss the objection in detail, as you can read Piattelli-Palmarini's book if you're interested in the details. Anyway, the conjunction "fallacy" is still a mistake in probability theory, and at worst this objection shows that the "fallacy" may be a less common one than the experiments seem to show. It may even be the case that the mistake is not common enough to merit the term "fallacy".

So, let's grant Poole his point about the Linda problem and assume that few if any people actually commit the conjunction fallacy. Even so, the Linda problem is only one small, albeit well-known, piece of evidence in favor of the cognitive psychologists' conclusions, and the conjunction "fallacy" is just one of many supposed cognitive biases and illusions. So, even if we accept Poole's argument on this point, it goes only a small way in undermining the psychologists' case.

Source: Massimo Piattelli-Palmarini, Inevitable Illusions: How Mistakes of Reason Rule Our Minds (1994), pp. 67-68.

Fallacy: The Conjunction Fallacy

September 29th, 2014 (Permalink)

Wink-Wink, Nudge-Nudge

Steven Poole, author of Unspeak, has an excellent article―I almost wish I'd written it!―about cognitive biases and the idea of "nudging" people using them. Read the whole thing: it's rather long but worth it. I have a few reservations, together with some supplementary points that I think are worth making.

One reservation I have is that I'm not at all sure how widespread or intense is the kind of skepticism Poole is arguing against. Certainly, one of the dangers of studying cognitive biases and fallacies is that it may lead to despair, to a feeling that we just can't figure things out so we might as well stop trying. However, Poole gives no evidence that such despair is a common thing. Now, I myself have seen signs of people over-reacting in this way to the findings of cognitive science, but I don't know how common it is.

Poole refers to a supposed "present climate of distrust" of human reason, but all he does is cite a few specific examples of such distrust. I could give a few similar examples myself, but are they representative of the "present climate"? There have always been philosophers who are skeptical about reason in one way or another, for one reason or another. It may be that the only thing that's changed is that cognitive psychology has now become a source of such skepticism. However, it wasn't that long ago that Freudian psychology was considered by some to have shown that people are essentially irrational. Now that Freud is out of favor, skeptics about human reason can cite Kahneman and Tversky.

Of course, such skepticism is unwarranted, and I'm completely on Poole's side in rejecting it. We've known about optical illusions for centuries, but nobody claims that such illusions show that we cannot see. Similarly, the fact that there are cognitive illusions doesn't mean that people cannot reason. Also, while the work by psychologists on cognitive biases is a product of the last few decades, philosophers and logicians have been aware of logical fallacies since the beginnings of philosophy.

Furthermore, skepticism about human reason based on the discoveries of cognitive science―like all forms of extreme skepticism―is in danger of sawing through the limb that supports it. It's through human reason itself that we've discovered the limitations of reason, but if reason doesn't work at least some of the time then we've no basis for belief in those results.

While I'm doubtful that skepticism about reason is as widespread as Poole suggests, I still think that it's worth arguing against―though anyone who is sincerely skeptical ought not to be convinced!

I have some further thoughts provoked by Poole's thought-provoking article, but they'll have to wait until I find time to write an update.

Source: Steven Poole, "Not So Foolish", Aeon Magazine, 9/22/2014


September 21st, 2014 (Permalink)

The Bushisms Strike Back!

With the end of the Bush administration, I was hoping for the end of the "Bushism"―those short quotes of President Bush mangling the English language. Slate made a cottage industry out of them, issuing little books and day-to-day calendars, and there was obviously greater demand than the president could supply. When the magazine couldn't find a real one, it would simply invent one by quoting him out of context. In addition, it seldom linked to the source of the quote, making it difficult for the reader to check the context―and this from an online magazine! Moreover, while repeatedly caught manufacturing Bushisms, it rarely issued corrections.

The current example, however, does not come from Slate, but from the astronomer Neil DeGrasse Tyson. In at least one speech that Tyson has given, he made the following claim:

After the 9/11 attacks, when President George W. Bush, in a speech aimed at distinguishing the U.S. from the Muslim fundamentalists, said, “Our God is the God who named the stars.” The problem is two-thirds of all the stars that have names, have Arabic names. I don't think he knew this. This would confound the point that he was making.

This quote is not taken word-for-word from the speech, but from a page on Tyson's own website―see Source 5, below―but you can watch a video clip from the speech containing the disputed quote―see Source 1, below.

One problem with this quote is that Tyson provides no specific source for it other than a Bush speech after 9/11, which makes it difficult to verify and even harder to refute. In the video clip mentioned previously, he claims that the quote comes from a speech given within a week of 9/11, which narrows things down quite a bit. However, no one seems to have been able to find a source for it in a Bush speech within the time frame Tyson mentions. I've looked for such a speech myself, but haven't found anything even remotely resembling the quote.

However, there is a Bush speech with similar words in it, but it's from about a year-and-a-half after 9/11, and the context was not 9/11 or terrorism but the Columbia space shuttle tragedy in which seven astronauts died:

In the words of the prophet Isaiah, “Lift your eyes and look to the heavens. Who created all these? He who brings out the starry hosts one by one and calls them each by name. Because of his great power and mighty strength, not one of them is missing.” The same Creator who names the stars also knows the names of the seven souls we mourn today. (Source 2, pp. 165-166)

In addition to the fact that no one has been able to find a Bush speech with Tyson's version of the quote, it doesn't sound like a plausible thing that Bush would have said, especially in a speech. Anyone who paid attention to Bush's rhetoric at the time would know that he was careful not to describe the "war on terrorism" as a religious war between Christianity and Islam. Here, for instance, is a section from Bush's first major speech after 9/11, his address before Congress:

The terrorists practice a fringe form of Islamic extremism that has been rejected by Muslim scholars and the vast majority of Muslim clerics―a fringe movement that perverts the peaceful teachings of Islam. … I also want to speak tonight directly to Muslims throughout the world. We respect your faith. It's practiced freely by many millions of Americans, and by millions more in countries that America counts as friends. Its teachings are good and peaceful, and those who commit evil in the name of Allah blaspheme the name of Allah. The terrorists are traitors to their own faith, trying, in effect, to hijack Islam itself. The enemy of America is not our many Muslim friends; it is not our many Arab friends. Our enemy is a radical network of terrorists, and every government that supports them. (Source 2, pp. 66-68)

Now, the fact that no one has so far produced a speech with the challenged quote, and that it sounds implausible, do not prove that Bush did not say it. Perhaps Tyson made a mistake about the time frame of the quote and a later speech will be found with those exact words. However, the evidence is strong enough to shift the onus to Tyson to either point out a source other than the Columbia eulogy, or to admit a mistake. Anyone can make a mistake, and this is a relatively minor one, but refusing to correct the error once it's pointed out would be a major mistake.


  1. "Neil deGrasse Tyson: George Bush and Star Names", YouTube, 3/11/2009
  2. George W. Bush, "Selected Speeches of President George W. Bush: 2001-2008", White House Archives
  3. Sean Davis, "Another Day, Another Quote Fabricated By Neil deGrasse Tyson", The Federalist, 9/16/2014
  4. Hemant Mehta, "If We Can’t Trust Neil deGrasse Tyson, Who Can We Trust?", The Friendly Atheist, 9/17/2014
  5. Neil DeGrasse Tyson, "Politics Quotes", Neil DeGrasse Tyson


Fallacy: Quoting Out of Context

Update (9/23/2014): Unfortunately, as far as I can tell, Tyson has yet to address this issue. Jonathan Adler of The Volokh Conspiracy also has called upon Tyson to deal with the Bush quote as well as some other recent criticisms:

They are the sorts of claims someone of Tyson’s stature should not be making in public lectures unless they are, in fact, true. Politicians are routinely flayed for less―and we know Tyson is much smarter than the average politician. He should not be held to a lower standard. It is possible that all of the claims Tyson has made are accurate…. The various quotes, including that by Bush, may well exist. If so, I would think Tyson can provide citations. If not, Tyson should acknowledge his errors.

Adler also has done a fruitless search for a Bush speech with the quote at issue, but he did find another good example of the type of rhetoric that Bush actually used after 9/11―see Source 1, below, it's quite short.

Sean Davis, who appears to be the original complainant about the quote, has also interviewed some of Bush's speechwriters from the time―see Source 3, below. According to Davis, the speechwriters do not recall any such quote used in a speech from that period, and they pointed out that it was not characteristic of Bush's rhetoric. Davis quotes Ari Fleischer, the former White House press secretary under Bush:

“I never heard him say anything like that and I know that’s not how he thinks,”…. “He would not make a reference to God for the purpose of dividing people. … He often referred to God for the purpose of uniting people from various faiths….”

This is further evidence that the quote is implausible, and the fact that Tyson hasn't cited a legitimate provenance for it suggests that it has none, since he could put a stop to the current criticisms by doing so. Of course, it's in the nature of things that it can't be proven decisively that Bush never uttered those words, or something close to them, in the week or so after 9/11. But the evidence that he didn't is getting stronger every day that Tyson remains silent.


  1. "'Islam is Peace' Says President", The White House Archives, 9/17/2001. This short speech was within Tyson's time frame but my own search failed to find it.
  2. Jonathan H. Adler, "The Volokh Conspiracy: Does Neil deGrasse Tyson make up stories?", The Washington Post, 9/22/2014
  3. Sean Davis, "George W. Bush’s Top Aides: We Don’t Remember That Neil Tyson 9/11 Quote At All", The Federalist, 9/22/2014

Update (9/27/2014): Tyson has now admitted that the Bush quote was taken from the Columbia speech, which makes Tyson's use of it a definite contextomy. Unfortunately, Tyson's admission wasn't quite the "Whoops, I blew it! Sorry, folks!" that I hoped for. A comment on his Facebook page quoted from the Columbia speech: "The same creator who names the stars also knows the names of the seven souls we mourn today" and Tyson replied:

Good to see that the Bush quote was found. Thanks to all who did the searching. I transposed one disaster with another (both occurring within 18 months of one another) in my assigning his quote. Perhaps that's a measure of how upset I was in both cases. The mind is surely the next mysterious universe to be plumbed.

Jonathan Adler of The Volokh Conspiracy critiqued Tyson's comment:

What is really so “mysterious” is why Tyson finds it so difficult to confess error and pretends that Bush’s 2003 remarks were only just-now discovered. As noted in my prior post on this controversy, Sean Davis had pointed to this quote as a potential source from the beginning. Yet if this is the source of the quote, then nearly everything else Tyson claimed about it and its significance is false (as is the account of the quote’s provenance he gave last night). Tyson claims to be a man of science who follows the evidence where it leads. The evidence here clearly shows Tyson screwed up. Whether knowingly or not, he regularly repeated a false account in order to cast aspersions on another public figure. The only proper thing to do is recant and apologize. That is what a person of integrity does.

I don't think it's "mysterious" that Tyson finds it difficult to 'fess up and apologize, but it is disappointing. Like Watergate, the cover-up is worse than the crime.


Update (9/28/2014): Tyson had a Twitter exchange today with psychologist Christopher Chabris, co-author of The Invisible Gorilla, which I mentioned a few years ago―see the Resources, below. Chabris asked Tyson:

Why not say "My apologies to George W. Bush for repeatedly & completely misstating what he meant in that quote about 'our God.'"

Tyson replied:

Thanks. Sure, I plan to say something like that soon. I’m looking for a good medium & occasion.

I'm looking forward to that. I think Tyson ought to apologize just as much to his audience for misleading and disappointing us. None of this, in my view, needs to be a big deal. Correcting errors is like removing a bandage: yank it off in one motion! So far, Tyson has been picking at the thing.

Chabris had a good reply to Tyson:

That's great to hear. Human nature makes admitting one's own mistakes a very hard standard to adhere to, so kudos to you.

Chabris is right about human nature, which is why I was unsurprised by though disappointed in Tyson's behavior. To err is human and to deny one has erred is also human, unfortunately.

By the way, just by coincidence I've been reading Chabris' book The Invisible Gorilla. I started to read it four years ago when it came out, but somehow was distracted away, and I'm just now getting back to it. I've only just started reading it, but so far it's very interesting and I may have some things to say about it in the near future.

Source: Neil deGrasse Tyson, Twitter Exchange with Christopher Chabris, Twitter, 9/28/2014


Update (10/2/2014): Apparently Facebook was the "good medium and occasion" that Tyson was looking for, as he has published a short piece apologizing for the Bush contextomy. Here's the relevant part, though go read the whole thing if you'd like, it's not long―see the Source below:

For a talk I give on the rise and fall of science in human cultural history I occasionally paraphrase President George W. Bush from one of his speeches, remarking that our God is the God who named the stars, and immediately noting that 2/3 of all star-names in the night sky are Arabic. … But I was wrong about when he said it. It appears in his speech after the Columbia Shuttle disaster, eighteen months after September 11th 2001. My bad. And I here publicly apologize to the President for casting his quote in the context of contrasting religions rather than as a poetic reference to the lost souls of Columbia. I have no excuse for this, other than both events―so close to one another―upset me greatly.

Though I still wish that he had apologized for letting us down, I think that this is about as good an apology as we can expect.

Source: Neil deGrasse Tyson, "Partial Anatomy of My Public Talks", Facebook, 9/29/2014

September 18th, 2014 (Permalink)

Letter to the Editor

Letters to the editors of magazines and newspapers often provide brief arguments that are good for exercising your skill in understanding reasoning, and even occasionally spotting a fallacy. So, brush up on your logical skills if you need to―see the Lessons, below―and let's get started. The following letter is taken from the Sunday book review section of The New York Times. First, read through the entire letter―see Source 1, below, it's short―or read the following excerpt, which is most of it:

William Deresiewicz argues in his new book, “Excellent Sheep”…that Ivy League schools graduate narrow, dissatisfied and purposeless students. But his anecdotal accounts do not jibe with my 20 years of experience on the faculty of Stanford University, where the majority of undergrads are happy, passionate and thriving. These amazingly talented and diverse students are working side by side with our faculty to reinvent the world. … Based on his unduly negative outlook, I would guess that Deresiewicz feels he was unfairly denied tenure at Yale. But it is time for him to stop whingeing and get back to the teaching and mentoring that he excels at and loves.―Ben Barres

Just what is Barres trying to argue? As I mentioned, this is a letter to the editor of the book review section of The N. Y. Times, and Barres is responding to a review of the book Excellent Sheep. However, unlike many such letters to the book review, he is not writing to defend the author of the book from criticism. Rather, he is criticizing what he takes to be the author's thesis which, according to the letter's first sentence, is: "Ivy League schools graduate narrow, dissatisfied and purposeless students."

Now, I haven't read Excellent Sheep, so I don't know whether this is an accurate characterization of the book's claims. I also don't know whether Barres has read it or is relying on the review's characterization of it. In any case, there is a possibility that the letter is criticizing an inaccurate version of the book's thesis, in which case it's attacking a straw man.

After stating what he takes to be the book's portrayal of Ivy League students, Barres proceeds in the next two sentences to testify against it based on his own experience as a faculty member of Stanford University. Stanford is not, strictly speaking, a member of the Ivy League, though it is the sort of elite university that Deresiewicz appears to be dealing with in his book. The problem with Barres' testimony is that he is just one person at one elite institution: his testimony is some evidence against the book's claims, but quite weak evidence. Barres' experiences may well be based on an unrepresentative sample of students at elite institutions.

Besides, Barres is just one guy. One person at one school is the smallest sample you can have, so it would be quite a hasty generalization to conclude that the book is wrong based on such a small, possibly biased sample. Barres refers to Deresiewicz' "anecdotal accounts", so perhaps he intends to place his own anecdotal account against Deresiewicz. Given my ignorance of the book, this is another possibility I can't verify or dismiss.

Finally, in the last two sentences of the letter, Barres turns to an ad hominem attack on the author of the book. He engages in some amateur psychoanalysis, suggesting that Deresiewicz is complaining bitterly―"whingeing"―just because he was denied tenure at Yale. This, of course, is also a sneaky way to put Deresiewicz down by alluding to the tenure denial. If turnabout were fair play, one might suggest that Barres is bitter because Yale really is an Ivy League school and he's just envious of Deresiewicz. Given that it seems possible that an untenured professor at Yale, or even at Stanford, could write a good book about Ivy League education, this is a fallacious personal attack.

To sum up, there is one glaring fallacy committed by the letter, namely, the ad hominem at the end. More importantly, the letter's argument is a very weak, anecdotal one at best.


  1. Ben Barres, "Poor Little Lambs", The New York Times Sunday Book Review, 9/5/2014
  2. Dwight Garner, "The Lower Ambitions of Higher Education", The New York Times, 8/12/2014. Another review from The Times, which also claims that Deresiewicz was denied tenure.
  3. Anthony Grafton, "The Enclosure of the American Mind", The New York Times Sunday Book Review, 8/22/2014

10 Brief Lessons in Logic: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10


September 12th, 2014 (Permalink)

The Puzzle of the Four Conspirators

A little over a year ago the police consulted with you about a bank-robbing gang, and thanks to your help the gangsters are doing hard time. Now, a police informant has revealed that another gang is planning a heist. Each robber will have one of four specific jobs: the Brains, the Muscle, the Safecracker, and the Wheelman. Having managed to plant bugs in the room where the four criminals are planning the heist, the police overheard the gang discussing the upcoming job:

  1. Artie was heard saying that Danny was the smartest and so ought to be the Brains.
  2. Benjy argued at length that they ought to hit an armored car instead of a bank.
  3. Charlie loudly insisted that Artie was not strong enough to be the Muscle.
  4. Danny claimed that Benjy was not skilled enough to be the Safecracker.

Later, after the decisions were made, the police heard all but one of the crooks complaining that their recommendations had not been followed. Fittingly, the only member of the gang whose advice had been taken was the man who became the Brains. Also, the conspirators had definitely decided to hit either a bank or an armored car, but the police couldn't tell which.

Can you help the police by determining what job each conspirator has been assigned in the heist, and whether they have decided to rob a bank or an armored car?


September 9th, 2014 (Permalink)

New Book: The Organized Mind

Psychologist Daniel J. Levitin, author of a couple of books on music, has a new book: The Organized Mind: Thinking Straight in the Age of Information Overload. Of course, it's the "thinking straight" part that is most relevant for us. Levitin was a student of the late Amos Tversky (p. xxii), so he should know a lot about how cognitive biases and illusions interfere with straight thinking.

September 5th, 2014 (Permalink)

One "myth" that's not quite dead yet

A few years ago I wrote about a shocking statistical claim: "Up to 300,000 girls between 11 and 17 are lured into the U.S. sex industry annually…." At the time, I searched but failed to discover where this claim originated, or what evidence supported it. Instead, I did a "back-of-the-envelope calculation" (BOTEC) to test its plausibility, since I found the number intuitively implausible―see the Resource, below, for the results. According to an article in The Village Voice―see Source 1, below―that appeared a few months after my original entry but which I just recently discovered:

The "100,000 to 300,000"…―the same number that's found its way into dozens of reputable newspapers―came from two University of Pennsylvania professors, Richard J. Estes and Neil Alan Weiner.

Presumably, the "300,000" in the claim that I wrote about is the high end of this estimated range. Unfortunately, the Voice article doesn't explain exactly where the estimate is supposed to come from, though they do quote from a 2001 report authored by Estes and Weiner (E&W)―see Source 2, below. However, though I haven't read the entire report―it's over 200 pages―I don't see any indication that the 100k-300k estimate is due to E&W or the report's own estimate. Instead, the report gives low, medium, and high estimates of 244,181, 286,506, and 325,575, respectively―for those of you playing along at home, these numbers are over-precise. However, if you were to state them as a range from low to high, you'd probably come up with 250k-350k, rather than 100k-300k. For this reason, it seems unlikely that they are the source for the latter estimate.

The Voice article makes a big deal about the fact that E&W's estimate was of children "at risk" for commercial sexual exploitation rather than those actually being so exploited, which is true but beside the point. If the 100k-300k estimate did not come from E&W, then a clearer example of ignoratio elenchi would be hard to find.

So, where did the 100k-300k estimate come from? Of course, I can't be certain, but the 2001 report says the following:

…[T]he first World Congress Against the Commercial Sexual Exploitation of Children …confirmed that large numbers of prostituted children are to be found in rich countries, including in the U.S. for which the "End Child Prostitution, Child Pornography, and the Trafficking of Children for Sexual Exploitation"…estimated their numbers to be between 100,000 and 300,000…. (P. 4)

The passage cites a 1996 report (p. 215) which I have not been able to find online or elsewhere―if you should happen to know where I can find a copy of this report I would be obliged if you let me know. As a result, it's impossible to check the report's methodology for arriving at this estimate, though the wording indicates that this is not supposed to be an estimate of "at risk" children, but of those actually exploited. If so, and if this is the actual source of the original estimate, then the Voice criticism misses the mark. However, the same report quoted above goes on to say:

One of the principal objectives of the present study was to place some reasonable though tentative parameters around the magnitude of the contemporary CSEC [Commercial Sexual Exploitation of Children] phenomenon in the United States. Previous estimates of the number of such cases ranged from a low of 300,000…to a high of as many as 1,000,000 cases…. Neither estimate, though, was based on empirically-derived evidence, and both assertions have been widely criticized as lacking scientific merit. Thus, the present investigation was initiated in the absence of reliable baseline data against which our own findings could even be compared…. (P. 143)

It's odd that this passage claims that 300k is a "low" estimate given that the previous passage gives a range starting at 100k, and both passages cite the same 1996 report. However, the authors indicate that the earlier estimate was not "empirically-derived" nor such that they were willing to rely on it for baseline data.

Also, it should be noted that none of this affects my earlier critique of the claim that "up to 300,000 girls between 11 and 17 are lured into the U.S. sex industry annually". This claim picks the upper end of the estimated range in order to use the larger, more shocking, number. Moreover, the 1996 estimate, as described by E&W, does not say that this number is added "annually", so presumably it is supposed to be the absolute number of exploited children. This is still an implausible claim, but less so.


  1. Martin Cizmar, Ellis Conklin & Kristen Hinman, "Real Men Get Their Facts Straight", The Village Voice, 6/29/2011
  2. Richard J. Estes & Neil Alan Weiner, "The Commercial Sexual Exploitation of Children in the U.S., Canada and Mexico", 2001 (PDF)

Resource: BOTEC, 2/6/2011

Via: Christina Hoff Sommers, "5 Feminist Myths That Will Not Die", Time, 9/2/2014, Myth 2. Sommers seems to have made the mistake of taking this "myth" uncritically from The Village Voice.

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