Archive for the ‘Mistake of the Week’ Category

Mistake of the Week: The Unknown Unknown

Wednesday, June 21st, 2006

And how is not this the most reprehensible ignorance, to think that one knows what one does not know? But I, O Athenians! in this, perhaps, differ from most men; and if I should say that I am in any thing wiser than another, it would be in this, that not having a competent knowledge of the things in Hades, I also think that I have not such knowledge.

Shtetl-Optimized’s Mistake of the Week series finally resumes today, with what’s arguably the #1 mistake of all time. This one’s been noted by everyone from Defense Secretary Donald Rumsfeld, to some toga-wearing ancient dude, to the authors of the paper Unskilled and Unaware of It: How Difficulties In Recognizing One’s Own Incompetence Lead to Inflated Self-Assessments.

Rather than give examples of this mistake — where would I start? where would I stop? how often have I made it myself? — I figured it’d be easier to give an example where someone didn’t make it. Today I received an email from a graduate student who had proved a quantum oracle separation, and wanted to know whether or not his result was too trivial to publish. I get fan mail, I get hate mail, I get crank mail, I get referee requests, but this is something I almost never see. After telling the student why his result was, indeed, too trivial to publish, I wrote:

There’s no shame in proving things that are already known, or that follow easily from what is. Everyone does it, the more so when they’re just starting out … The very fact that you cared enough to ask me if your result is trivial bodes well for your proving something nontrivial.

Mistake of the Week: Empathy=Sympathy

Saturday, February 25th, 2006

With this post, I begin an occasional series called Mistake of the Week — in which I’ll explore “obvious” howlers that nevertheless show up in many different contexts, are made by people who should know better, and do real damage in the world. If you like, you can retroactively consider my post But What If? to be part of this series.

(Note that, as in This Week’s Finds by John Baez, the word “week” means there will be at most one installment per week, not at least one.)

This week’s mistake is that empathy — the ability to imagine yourself into someone else’s skin — is basically the same as sympathy. In reality, these concepts are not just subtly different: they’re often directly opposed to each other!

Scam artists, stalkers, abusers, rapists, and serial killers often have tremendous empathy for their victims. If they didn’t, they wouldn’t know how to scope them out, isolate them, and prey on their vulnerabilities. In The Blank Slate, Steven Pinker discusses research showing that attempts to “cure” psychopaths by teaching them empathy can make them even more dangerous.

Of course, the world champions of empathy are the guys with dozens of nicks on their bedposts. It’s precisely because they understand women that they’re able to exploit them for their own enjoyment.

So that was empathy without sympathy. What about sympathy without empathy?

I was in Berkeley on 9/11, and many students I talked to in the weeks afterward thought that America basically deserved it. In their analysis, if the US had only ratified the Kyoto Protocol, increased its aid to the developing world, etc., it would have had nothing to fear from al Qaeda. It struck me that these students had considerable sympathy for the 9/11 hijackers, but no empathy for them. They couldn’t understand Mohammed Atta on his own terms — only through the lens of their own values and beliefs. (Predictably, America’s homegrown fundamentalists showed much greater empathy. They understood immediately what their Islamic counterparts were up to.)

History is full of bad people who achieved their goals because good people failed to empathize with them. “But surely this Mein Kampf must only be bluster, written for internal political purposes. There’s no way Hitler could actually believe what he wrote — he’d have to be a lunatic!”

Alright, it’s too easy to bring up examples that everyone already knows about. So here’s a different one: have you ever heard of a feminist writer named Valerie Solanas? If you haven’t (say, because you were born after the 60’s, like me), then I invite you to take the following empathy quiz.

In 1967, Solanas wrote a booklet called the S.C.U.M. Manifesto (S.C.U.M. stands for “Society for Cutting Up Men”). In it, she argues that the human male is a “walking abortion” and an “emotional cripple,” and calls for eradicating men and creating an all-female society. Any man who resists is to be killed. Once women rule the world, however, the few remaining men will kindly be permitted to “exist out their puny days dropped out on drugs or strutting around in drag or passively watching the high-powered female in action,” or else to “go off to the nearest friendly suicide center where they will be quietly, quickly, and painlessly gassed to death.”

Solanas is vague about what her female utopia will be like; however, it will definitely be “groovy.” “In a female society,” she writes, “the only Art, the only Culture, will be conceited, kooky, funky females grooving on each other and on everything else in the universe.” There will be no need for a government or even a money system. (Hence, no shoe shopping.) Solanas strikes today’s reader as perhaps too sanguine about technology: after the male scientists have been murdered, she writes, women will be able to build a fully-automated society within weeks, and eliminate death and disease within years.

(Incidentally, curing death is only one way Solanas’s utopia could perpetuate itself after the sperm banks have run dry. Another way, which she doesn’t discuss, is cloning from stem cells.)

In short, the whole thing reads like Rush Limbaugh’s fantasy of what feminists believe. That’s why I was surprised to learn that, far from being universally condemned, the S.C.U.M. Manifesto has been praised by feminist leaders such as Ti-Grace Atkinson, assigned in women’s studies courses, and distributed by government-run women’s shelters in Sweden. What’s going on here? The answer seems to be that, for many readers, Solanas’s “final solution to the male problem” is so outlandish that no one, including Solanas herself, could possibly intend it literally. Instead, her proposal must be interpreted as an ironic critique of patriarchal assumptions, or something like that.

Here, then, is my empathy quiz. Read the S.C.U.M. Manifesto, trying as you do to imagine what it would be like to have written it. Then answer this question: does the author strike you as a clever ironist, or as a sincere psychopath who might actually try to kill someone? You can check your answer here.

But what if?

Thursday, January 5th, 2006

I still owe you Part II of my Darwinism post. But in the meantime, I’d like to pontificate about a fallacy that I’ve seen so often it deserves a name. I’ll call it the But-What-If? Fallacy, after the following joke:

“Let n be an integer…”
“But what if n isn’t an integer?”

The fallacy consists of bringing something up that was specifically defined to be irrelevant. Of course, no one would be silly enough to do that in real life! Except…

  • “I would never want to live in a society where people were always happy. Such a society would be a stifling, conformist dystopia, like in Gattaca or Brave New World.”

Well then, people wouldn’t always be happy, would they?

  • “If quantum mechanics is nonlinear, then P=NP in the physical world.”

This one makes steam emanate from my ears. Let’s repeat three times: P and NP are purely mathematical concepts. As such, the laws of physics can have no bearing on whether or not they are equal.

(Of course, it could be that PA=NPA where A is a “real world oracle.” But if you understood that point, then you’re already way beyond the “P=NP in the physical world” crowd.)


  • “I could never marry a guy I didn’t love, even if he was unfailingly kind, generous, and loyal. I’d never know when he might abandon me.”
  • “You shouldn’t take this drug, even if it will help reduce your anxiety. You can reduce your anxiety just as well without it.”
  • “Sure, a perfect computer simulation of a human being might hold an intelligent conversation. But could it ever write a poem, or laugh at a joke, or fall in love, or…”


Sorry, I sometimes get carried away. In the past, my favored solution to the BWI? Fallacy was forcible re-education camps for everyone who commits it. But lately, I’ve come to think that a softer approach might work.

See, the problem is that most people (even theoretical physicists) have very little experience thinking like mathematicians. By nature, people want to keep coming back to the issues they care about, even when you ask them a hypothetical question that defines those issues away. The key is, first, to identify the real question on the other person’s mind:

Are NP-complete problems hard in the physical world?
Is this guy as kind and generous as he seems?
Will this drug really help reduce my anxiety?
Could a computer that writes decent poetry, laughs at jokes, etc. be built?

You can then point out the difference between this question and the one that was asked. Often, the more abstract question won’t even have occurred to the other person. But once the person understands the abstract question — and why it remains, even after the concrete one has been answered — it’s time to extend your hand. “Welcome to the business.”