I was in Austin Texas visiting my nephew Jason. I was also giving a talk at the University. My nephew fixes forklifts for a living and does not care about abstract things. (I'd be as bad at his job as he would be at mine.) He asked me what the talk was on. I think he asked just to be polite but did not really care. Even so, I tried to put it in as concrete terms as possible. My thought process: (1) Don't use n. Use an actual number, say 100. (2) Don't state a theorem. State an easily grasped corollary.
BILL: Picture that there is a 100 by 100 chessboard. Picture that you want to put queens on the diagonal so that every square of the board is either covered or under attack. What is the least number of queens you need for this? (NOTE: I leave it to my readers to prove that, for an n x n chessboard, this is IDENTICAL to finding large 3-free sets, that is, large sets that do not have arithmetic progressions of length 3.)
JASON: That is the dumbest problem I ever heard!. First off, chess is played on an 8x8 board. Secondly, only once while playing chess did I ever get my pawn to the end of the board to get a second queen, never mind getting n-o(n) queens (he didn't put it that way). And thirdly... who cares?
BILL: I don't suppose it would help to tell you that this relates to some deep mathematics of interest.
JASON: Of interest to who?
BILL: Uh... Never mind. (I thought about telling him that better bounds on the VDW numbers could get you $3000 dollars but decided not to.)I usually do better than this with very concrete easily grasped statements. But he doesn't care about this problem. And actually, why should he? (I am sure some of my readers don't care about this problem either.)
But what can stop a skeptik that answers "why?" to your answers?
ReplyDeleteI think that arithmetic progressions sounds more interesting than studying pointless games on a 100x100 "chessboard." On the other hand, it is great that you can state an actual problem so concretely. I can't say why he should care about it, but then I don't care about fixing forklifts either.
ReplyDelete"I care" &em; Luke Skywalker
ReplyDeleteMe: "[Prestigious theorist] is giving an invited talk today. He's a really big name."
ReplyDeleteNon-academic friend: "Cool, what does he do?"
Me: "Well, uh, he's a theorist...so he doesn't really do anything..."
I like Jason.
ReplyDeleteThis equivalence is beautiful. Do we know who invented it?
ReplyDeleteThe reference I have for this problem
ReplyDelete(though I have not checked it) is
@article{diagqueens,
author = "E.J.~Cockayne and S.T.~Hedetniemi",
title = "On the diagonal queens domination problem",
journal = jcta,
volume = "42",
pages = "137-139",
year = "1986"
}
jcta= Journal of Combinatorial Theory Series A.
Queens on the diagonal, or queens on the chessboard?
ReplyDeleteHow many queens are permitted on one square of the chessboard?
ReplyDeleteQueens on the diag, one queen to a square.
ReplyDeletebill g.
that is indeed quite interesting, except for its lack of usefulness
ReplyDeletethere are two major diagonals so the answer is either 1 or 2, right?
ReplyDeletethat is indeed quite interesting, except for its lack of usefulness
ReplyDeleteThis painting is indeed quite interesting, except for its lack of usefulness.
Why do mathematicians have the burden of proving the "usefulness" of their work, while poets, composers, and artists do not?
Clarification: We place queens on
ReplyDeleteONE of the diags and need to
cover or capture EVERY square on the n x n board.
The 8-Queens problem is very different but that problem seems to be what people are thinking of when they hear about placing Queens on a board.
ReplyDeleteThere has to be a concrete example of what solving this 100x100 problem has to do with Jason's real world. I'm sure Jason is impressed by something, whether it be space travel, football, NASCAR, military technology, fine art, whatever. The chessboard problem could be compared to a minefield that must be crossed, a border that must be defended (not crossed), a NASCAR or soccer or football move sequence leading to victory, a series of financial trades leading to wealth, a regulatory rule set blocking abuse, a firewall that can't be defeated, a museum laser security system that prevents theft, a DNA shield that blocks a mutating disease, etc. Maybe there is a forklift problem Jason has encountered that you could solve with chess moves.
ReplyDeleteAs for me, I need to look up "large 3-free sets" to see the mathematical context.
Why is it important to explain to laypersons what we do? let's just keep inside our globes with total disregard to everyone else, just like we've been doing (we mathematitians) for centuries!!
ReplyDeleteThe layperson is usually just too stupid for us.
You yourself don't care about the 100x100 chessboard! You only care about the n x n chessboard. So you're describing a problem you don't care about to someone who also isn't interested in placing queens on a 100x100 chessboard (not knowing that this is equivalent to determining whether there exists a short program that can print the works of Shakespeare), and hoping that they're generalize it in the way that you're imagining. Because it's only by generalizing/extending it that the problem becomes interesting. But your nephew puts it in context differently than you, and thinks about pawn promotion, strategy, etc.
ReplyDeleteI think it's really important to think about why our work is exciting, and not to be patronizing like some of the other commentators are. In this case, the abstraction of the problem is part of what makes it exciting ("I study the question of how hard it is to solve problems, when we only know how to recognize a correct solution."), and so getting rid of that to make the work understandable also makes it seem pointless.
"Why is it important to educate the layperson?"
ReplyDeleteThis is an excellent question and
was one of the topics of discussion at an NSF sponsored summit I was a co-organizer for last week.
http://www.nsfbirds.org/
I think the short answer is that if we expect the tax-payer (layperson?) to fund our research, then why should we not be obliged to explain to them what we are doing? Of course you might have the viewpoint that they are too stupid to understand our work (actually I do not think that is the case for a majority of people we classify as the "layperson").
I was planning on writing a longer blog entry about the summit when
time permits.
Aram Harrow's answer is right on the money mark point.
ReplyDeleteBeing able to talk to a layperson is critical for any scientist/mathematician. In fact I would argue that if you cannot explain your work to a high school student, you don't fully understand it.
ReplyDeleteNot using n is Step 0. In fact, never use any abbreviation, ever. Mathematical abbreviations and shorthand are to save you from writing, not speaking. It doesn't cost you a great deal of time to say "any number of items" instead of "n items". Do this with experts too, it'll make you sound eloquent.
Second, never just start reciting the problem. That's ridiculous. That's like me coming up to you and rattling off numbers for a few minutes, and then asking you what was the biggest one you heard. You'd spend the entire time wondering why I was saying numbers, and you wouldn't be able to answer the question without having me repeat them. And that's not a hard question -- the choice of presentation is what makes it hard.
People need context first, content second. Always. Taking the last example, if I first say, "I'm going to list off numbers for 3 minutes, and it's important to remember the biggest one," the task is now trivial. You've given the listener a context for understanding what's important.
Another poster asked, "Why do mathematicians have the burden of proving the "usefulness" of their work, while poets, composers, and artists do not?" That's not entirely accurate. You don't have to prove it's useful, you have to prove it's interesting, at least potentially. Everyone knows that a poem about love is (potentially) interesting, because love is interesting. An nxn chessboard with queens is not as obvious.
The nXn Queens problem is interesting for many reasons, but it's best to use an example from everyday life to give context before going in to it. Here's a hypothetical better exchange:
Jason: So what's the talk about?
You: The talk is about a particular detail in my job, do you know what I do?
Jason: Math.
You: Yes, but it's more than that. You can use math to do things quickly that are too hard to do by hand.
Jason: Like what?
You: Like, for example, if I asked you how many different combinations of a Tic-Tac-Toe game are there? You'd probably have to sit down with a pen and start sketching out games and counting them. That's slow. With math, there's a way to figure out the answer much quicker.
Jason: So what's the answer?
You: I don't know it off the top of my head, but that's not the point. The point is the math that figures out the answer, not the specific answer. In fact, once you figure out the math for counting Tic-Tac-Toe combinations, you can work with it until it works for other things, like giant chessboards. The talk I'm giving is about the different kinds of combinations of queens you can have on a giant chessboard.
Jason: Why is that important?
You: Well, once you know the math for handling lots of combinations, you can use it in all sorts of stuff. For example, let's say you owned McDonalds, and you wanted to plop down a dozen new restaurants in a city. There's a bunch of different places you can put them, but you don't want them too close to each other or too far. If you know the math for combinations on giant chessboards, you can use the same math to figure out where's the best place to put your restaurants, and you save a ton of money.
Jason: Oh, I get it. Cool.
I hope that helps, and I'm really glad you're trying to share your work with laypeople. So many technically-minded individuals do not, and I think it collectively contributes to the abysmal understanding of science and math in this country. So thanks for trying to change that.
/soapbox