A partial list of things that cannot be taught:

  • Effortlessness
  • Heroism
  • Subversiveness
  • Resoluteness
  • Commitment
  • Individuality
  • Sympathy
  • Spontaneity

This is not to say that you can't induce people to be some of these things, it's just unclear how they can be taught them without already knowing how. Some teachable things, but difficultly so, include:

  • Detachment
  • Critical Thinking
  • Inner Peace
  • Creativity 
  • Responsibility

The only line I can draw is that the second list seem to be more about ways of thinking, while the first list contains ways of being or feeling. If anyone can draw a better line, or has ways of teaching things on the first list, leave a comment below.

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Nerd Sniped by Nerd Sniping

I got nerd sniped today reading Paul Lockhart’s A Mathematician’s Lament. It’s an excellent rant on the state of mathematics education, but it also contains a short essay on why he finds mathematics fun. It contained this problem:

Do all undirected graphs (of order > 2) contain at least two nodes with the same degree?

Actually, the precise problem that got me is not important (I just wanted to nerd snipe you too). As I was getting coffee and thinking about it though, I wondered if the susceptibility of being nerd sniped is correlated with the breadth of interest. It makes sense that the more things you are interested, the more easily you’d be distracted by a random, sufficiently difficult question. Of course, the “sufficiently difficult” part is hard to measure, but we’ll let that go for now.

But then it occurred to me that all the nerd sniping questions I know are (at least somewhat) logical in nature. I can’t imagine someone being nerd sniped by a history question. For example, I don’t know anything about the causes of World War I, other than that it involved the assassination of Archduke Ferdinand (wow, I even got the name right; I wrote that without checking my sources). But I can’t imagine myself dropping everything to think about this problem. I don’t think this is a lack of interest, either; I can’t even imagine my historian friends doing this. (Yes, I have friends. Shut up.)

I feel the difference is that, for the logic-based questions, it’s not the answer that matters, but the process of getting there. I can tell you the answer to the graph problem: yes (…probably. I haven’t solved it yet). But that answer is not satisfying. It’s like looking at the solution of a solved Sudoku puzzle; the only thing it tells you is that the board can be solved. (For this reason, I think it's pointless to print Sudoku solutions, as long as I trust them to be solvable.) For both the original infinite-grid-of-resistors problem and the graph problem, I want to know how that answer was derived. I might not even believe your answer until you’ve shown me the proof. (By the way, the answer to the resistor problem is 4/pi - 0.5 ohms.)

But that’s not true of the question about World War I. If you tell me (to whatever detail) why WWI occurred, and I would nod and go on my way. I wouldn’t question your explanation (unless it contradicts something I already know), and I wouldn’t question your source of knowledge.

I first thought that this is because the answer is trivially obtainable from, say, Wikipedia; but then, I could also have looked up the proof and be done with it. It’s also not the case that the question about WWI requires a long explanation (eg. it asks “why/how”), while the graph question requires just a binary answer (eg. it asks “do”). I can transform both questions the other way (“Was the assassination of Archduke Ferdinand a factor in starting WWI?” and “Why do all undirected graphs have two nodes with the same degree?”), and the feeling remains the same. Notice, though, that the reworded graph question now presumes an answer, so the new question actually gives more information than the old one.

As I thought more about this, I realized that I get nerd sniped by questions outside of the maths and sciences as well. I’ve nerd sniped someone before with the question, “Is the statement “Unicorns have one horn” true or false?”. I myself have spent entire afternoons thinking about questions from psychology/philosophy, the latest being the nature of vulnerability. Although, if I apply the same reasoning of whether I’d want to know the reasoning behind the answer, I’m not sure if the psychology question is truly a nerd sniper.

Maybe there are also shades of being sniped too. While I wouldn’t think too long on the question of, say, the significance of socks in the Harry Potter series, I can imagine myself disagreeing with someone else’s answer, leading to an afternoon of debate. It’s not as powerful a sniper as the logical questions, and there’s confusion between the appeal of the problem itself with the appeal of a good discussion. I wouldn’t call it nerd sniping for this reason, but it’s still something that would cause me to stop what I’m doing.

I don’t have any answers to my questions about nerd sniping raised here. I am curious whether and how much my mathematical and scientific background has biased me in what I get sniped by. I would love to hear from people in history or anthropology or related subjects, and see if there are questions that get them but don’t get me.

…Once you get over how I’ve just nerd sniped all of you, of course.

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Regret and Responsibility

A couple months ago I had a conversation with a friend. In that conversation, I ended up expressing a belief that hurt them, leading to a month of tense interactions. But, we eventually sorted it out, and in the resulting conversation, my friend asked me, “Do you regret saying what you did?” I replied, “I’m sorry that you were hurt, but I don’t feel guilty about saying it.”

The words “sorry” and “regret” have several related meanings. ”Sorry” can be used to express condolence without implying guilt, as in “I’m sorry for your loss.” It can, of course, also be used as an apology, as in “I’m sorry I yelled at you.” Although “regret” can be used in the same manner (”I regret yelling at you yesterday.”), it can also simply express a wish for a different outcome, as in “I regret not getting the chocolate ice cream.” I take my friend’s question to use the apologetic meaning of “regret”.

Let’s assume that hurtful behavior is considered bad by both parties. I posit that when someone (the “perpetrator”) apologizes, they must believe they had somehow wronged the “victim”. The question is, could the perpetrator have hurt the victim without having done the wrong thing?

Here’s an example. It turns out that, in the story at the beginning (which is a true story, by the way), my friend had previously told me that they “would always rather have the truth than ignorance”. So, in our conversation, when they had asked me for my thoughts, I had simply told them what I believed, explicitly as a belief of mine (that is, without implying whether that belief was correct). Of course, they then took it personally, leading to the episode above.

Who was at fault in this scenario? It’s true that my friend was hurt because of what I said, and that I had said what I did intentionally. Intuition suggests that, if that was the full story, I probably did something wrong and should apologize and feel bad.

What throws this intuition off is that my friend had asked what I thought, and that they had stated that they “always” prefer the truth. For past-me, the choice between telling and not telling is obvious: there’s no reason I should withhold what I was thinking. I could argue that, even if I had known that what I said would hurt them, given their preference of truth, I should still have told them. Since I had considered my choice before acting, and since a reasonable person would have done the same, I don’t feel guilty about saying what I believed.

But I could argue the other way. Clearly, I hadn’t fully considered my choice; if I had, I would have realized that my friend’s previous statement was not true. They could have been lying then, or more plausibly, they themselves had not considered all the options before making that statement. That is, while they believed they always prefer the truth, their belief was incorrect. Knowing what I know about human psychology (ie. that people don’t know much about themselves), I should have foreseen that they would be hurt despite their statement, and that should have influenced my decision. I was, in other words, negligent.

The question here is not whether I knew that my friend would be hurt; clearly I didn’t know, which is what caused this problem. The question is whether I should have known that my friend would be hurt, whether I am responsible for having that knowledge, and therefore ultimately responsible for their suffering. But on this question I’m stuck. On one hand, I can’t be telepathic or clairvoyant; there must be a limit to what I can know, and whether my friend had told the truth as they knew it, or had actually told the truth truth, seems to be past this limit. Plus, having to decide between correct and incorrect beliefs for every statement anyone ever makes about themselves seems overly cynical. On the other hand, it is true that people often have incorrect beliefs about themselves, particularly ones that give a more generous picture, in this case, that they are more “rational” than they actually are. Moreover, I know this from reading papers in cognitive bias, and have had enough personal conversations to observe it occurring multiple times.

Personally, I lean towards the position that I should have known, or at least should have doubted the veracity of the statement. At least, I do now that I’ve experienced this whole episode, and I will keep an eye out for these situations in the future. As for the episode itself, I do want to support my friend in their pain, and I do wish something else had happened. In that sense, I’m sorry and I’m regretful, but I still don’t think that I did anything wrong.

EDIT 2013-08-11: It occurred to me that intentionality seems to have nothing to do with regret. Either the perpetrator knew the victim will be hurt, and had therefore deliberately acted to hurt the victim (even if it is the lesser of two evils), or the perpetrator did not know the victim will be hurt, and had therefore chosen as well as they could have. Neither case seems to fit the template of someone who should be regretful, although apologies may be necessary in both cases. This suggests that either regret (or lack thereof) does not depend on intentionality, or the whole concept of regret is faulty.

Regardless, the passages about responsibility still hold, although personally I think both concepts of regret and responsibility are incoherent.

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