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.

There are many undirected graphs (of order > 2) which contain no nodes with the same degree!

ReplyDeleteConnect three nodes in a line, and then connect one end node to itself. The degree sequence is then (3,2,1)

Connect 4 nodes in a line, connect the last two a second time, and then connect the last to itself, making (5,3,2,1)

A better question would be "Do all finite simple graphs contain at least two nodes with the same degree?"