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math math math a hundred maths one thousand maths

Post by Fond du lac operon » Sat Nov 10, 2012 2:32 am

This topic was split from the discussion of Minnesota Open 2011. --mgmt.

So, um, since I just only saw the set a couple days ago, I'm going to post my (inflation-adjusted) $0.02 on the Feit-Thompson tossup and the more general phenomenon of quizbowl math.

First, full disclosure: I would have totally powered the Feit-Thompson tossup, and because I'm a gigantic nerd I probably would have actually powered it in high school. (I read a lot about group theory instead of having friends.) Yet I agree with basically everyone else that it was too hard for a tossup. Nevertheless, I think it's important to take away the correct lesson from this experience; that lesson is not "avoid all tossups from 20th-century math/stuff that people don't have 'real knowledge' of entirely."

As a math person and a quizbowl player, I'm usually kinda disappointed in the answerline selection for most tournaments. The answerlines tend to be chosen a few basic concepts from analysis ("Fourier/Laplace/Mellin transform"), algebra ("ring," "Chinese remainder theorem," "eigenvalue"), or general topology ("open," "compact"), or else be about long-dead mathematicians -- I'm not sure I've ever heard a tossup on a more recent mathematician than von Neumann. Maybe John Nash, I guess. I'm sure that this is a pretty common experience in fields in which one is "expert" -- e.g., Dargan's annoyance that contemporary poetry almost never comes up. But I think that in the case of math, it can be mitigated somewhat. It's true that you have to be a really hard-core algebraist to have read any part of the proof of Feit-Thompson (I've read part of the proof of the Suzuki CA(?) theorem and even it is exhausting) but this doesn't mean that math people don't have knowledge about Feit-Thompson. Clearly it would be a bad idea to write a tossup on Shin Mochizuki for any tournament (except the forthcoming Alabama Interuniversal* Hard Math Open), but a hard part on the ABC conjecture, for instance, would likely be fine at hard or even regular+ tournaments. Because mathematicians, and math grad students and even the more involved undergrads, tend to know about major breakthroughs and avenues of research in subfields outside their own. Similarly, if you want to reward people for knowing what Feit-Thompson is about, you can probably work it into a tossup on groups or solvable or simple groups -- to be fair, this sort of thing does happen a good bit.

So, if anything, quizbowl should have more acknowledgment of hard math like Feit-Thompson (even beyond stuff like RH and Poincare). But there are far better ways of rewarding knowledge of these things than writing tossups on them.

Okay, this was probably all super-obvious to people like Eric and Jerry and Matt Weiner, and even other folks. But I just want to put it out there, that I personally would love to see all sorts of crazy clues and/or hard parts about, like, Schramm-Loewner evolution and Floer homology, and that it wouldn't take away much if anything from teams without a really strong math player. If nothing else, think that more people understand those things than understand, like, Jacques Lacan, who is a pretty reasonable hard tossup answerline.

*That's a Shin Mochizuki joke -- don't worry if you don't get it.
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Re: Minnesota/Penn Open IV Discussion

Post by Cheynem » Sat Nov 10, 2012 2:46 am

I mean I understand what you're talking about, but this is probably a classic case of "your mileage might vary." I have no idea what Feit Thompson is and the majority of what you posted reads like the transcript of the Supreme Court case Poodle Dee vs. Poodle Doo. I'm not saying it was a bad post because it seems to make sense if you have an understanding of math. On the other hand, I have read Lacan and know a little bit about him, so if you are a humanities person like me I would imagine Lacan is probably the easier answerline.

In general, I agree with your post in the sense that if you want harder things in your field to come up, introducing them as clues or as bonus parts is a good way to do it and that people with knowledge of the fields should do that in the questions they write. I just wanted to temper your last point, which seems to be that "math is easier to understand than some philo/social science" by saying "not necessarily." In the same way, though, I wouldn't throw tossups on thinkers such as Gertrude Himmelfarb on the world either even though I would consider her easier to understand than a lot of math things.
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Re: Minnesota/Penn Open IV Discussion

Post by Fond du lac operon » Sat Nov 10, 2012 3:04 am

To be clear, I wasn't dissing social science people, I was dissing Lacan, who's pretty infamously obscure, isn't he? Maybe I should have said Derrida instead -- then I'd at least have the backing of, like, John Searle. My point is more that just like most quizbowl players don't get Derrida or Lacan knowledge from actually reading a bunch of Derrida or Lacan (because very few of us want to subject ourselves to that -- although maybe I'm overgeneralizing), we shouldn't rule out hard math answers because nobody's read some massively difficult papers.
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Re: Minnesota/Penn Open IV Discussion

Post by Auroni » Sat Nov 10, 2012 3:14 am

I'm pretty sure that the number of math answers that come up is limited because math is probably the single hardest subject (or at least, jointly the hardest subject with computer science) for lay people. And it's also a difficult subject to write for people who are otherwise good writers or editors, so they go with the same old standby answers. If you want to see certain things come up in math, then you are welcome to submit tossups on famous concepts with those things as leadins, or use those things as third parts at hard tournaments.
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Re: Minnesota/Penn Open IV Discussion

Post by Fond du lac operon » Sat Nov 10, 2012 3:31 am

Tokyo Sex Whale wrote:I'm pretty sure that the number of math answers that come up is limited because math is probably the single hardest subject (or at least, jointly the hardest subject with computer science) for lay people. And it's also a difficult subject to write for people who are otherwise good writers or editors, so they go with the same old standby answers.
I'm not that convinced that it's much harder for lay people to write on than chemistry or hard physics.
If you want to see certain things come up in math, then you are welcome to submit tossups on famous concepts with those things as leadins, or use those things as third parts at hard tournaments.
Well, I'm trying to do this, but since there's a maximum of 0.5/0.5 math per packet and I write a maximum of one packet per tournament, it's slow going. Which is why I wrote a silly manifesto about a silly complaint I have with my silly hobby, because I'd like to convince other math people (and people like Eric who aren't math people per se but are very capable of writing on hard math answerlines) to do the same. And by the way, if people genuinely feel less-qualified to write or edit math and CS, I'd be happy to help them edit those categories at a couple of tournaments a year. Pro bono even.
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Re: Minnesota/Penn Open IV Discussion

Post by Dominator » Sat Nov 10, 2012 8:03 am

I am with you in principle that more math could probably be added and make the game better if it is written in an interesting and accessible way. However, the only reason I would write a tossup on Feit-Thompson is if I wanted to induce my audience to demand a permanent quizbowl ban on math when it goes dead hard. But, Feit-Thompson is MUCH more accessible than SLE (I've seen S talk about it at a conference). If SLE starts coming up as an answer, then people will be rightly pissed off; I would be.
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Re: Minnesota/Penn Open IV Discussion

Post by The King's Flight to the Scots » Sat Nov 10, 2012 11:47 am

Well, I'm trying to do this, but since there's a maximum of 0.5/0.5 math per packet and I write a maximum of one packet per tournament, it's slow going.
This is how it should be, since good, prolific editors will have greater sway over the game than people who submit packets once in a while.
Which is why I wrote a silly manifesto about a silly complaint I have with my silly hobby, because I'd like to convince other math people (and people like Eric who aren't math people per se but are very capable of writing on hard math answerlines) to do the same.
To me, your manifesto reads "I want more hard math questions because I'm totally good at them. For evidence, look at all the obscure named things I can mention." You're going to need a more convincing argument
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Re: Minnesota/Penn Open IV Discussion

Post by Cheynem » Sat Nov 10, 2012 1:31 pm

I've read Lacan, I can't believe no one else in quizbowl has either. Certainly people have read Derrida. Again, your general ideas are okay, but math isn't easier than philosophy (it may be for some people, sure, but I could flip your words around and write something about how some hard philosophy concept should totally come up more often).
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Re: Minnesota/Penn Open IV Discussion

Post by Excelsior (smack) » Sat Nov 10, 2012 2:17 pm

Fond du lac operon wrote:Because mathematicians, and math grad students [know hard things]
How many of these do you think exist in all of quizbowl? I don't know for sure myself, but I'm guessing the number of quizbowl-playing mathematicians + math grad students is maybe around ten; at most, twenty. I don't think I could name a single one in the New England area.
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Re: Minnesota/Penn Open IV Discussion

Post by Fond du lac operon » Sat Nov 10, 2012 2:41 pm

Vernon Lee Bad Marriage, Jr. wrote:To me, your manifesto reads "I want more hard math questions because I'm totally good at them. For evidence, look at all the obscure named things I can mention." You're going to need a more convincing argument
Since I have maybe a 5% chance of going to grad school next year, I don't really have a dog in this fight. I just think there are other people who'd be excited about seeing Feit-Thompson or Schramm-Loewner pop up in a first clue or a third part (not a tossup line, because that is crazy) every once in a while.

Anyway, maybe the argument was bad. I wrote it at like 2 in the morning, I'm not super-committed to its correctness or anything.
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Re: Minnesota/Penn Open IV Discussion

Post by Cheynem » Sat Nov 10, 2012 2:50 pm

I agree that those things would make good clues and bonus parts and would encourage you and other mathematician types to include them in questions you write.
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Re: Minnesota/Penn Open IV Discussion

Post by Auroni » Sat Nov 10, 2012 4:09 pm

Fond du lac operon wrote:I'm not that convinced that it's much harder for lay people to write on than chemistry or hard physics.
I dispute this. Even chemists and physicists whose last math is something like differential equations have a hard time traversing the jargon-laden landscape that is today's math questions above high school difficulty, whereas even some non-scientists have an intuitive idea of how bonds can be made or broken or the fact that subatomic particles exist. It's very difficult for good science editors who haven't taken math classes to understand the clues that they are using for math tossups, leading to a disastrous situation for tossup and bonus conversion if they try to write on your ideas.
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Re: Minnesota/Penn Open IV Discussion

Post by Fond du lac operon » Sat Nov 10, 2012 5:01 pm

Yeah, okay, you're probably right, Auroni. I don't think that all science editors have that problem -- Eric's tossup on Feit-Thompson was pretty damn good, just on something far too hard -- but I'll grant that it's easier to find people who understand chemistry and physics and don't understand hard math than the other way around, and both are easier to find than people who are really good at writing/editing across all science topics.

Anyway, whatever. It's 1 question per packet in a silly game that I'm probably going to play for about six more months; I just thought about tossing it out there that quizbowl players could probably stand, and even enjoy, harder and more relevant math topics in places where those things should go, like, first clues in hard tournaments. If more experienced people don't think that's workable, then maybe it's not workable. Again, I'll do what I can to make it workable, but that's not that much.
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Re: Minnesota/Penn Open IV Discussion

Post by Auroni » Sat Nov 10, 2012 5:08 pm

I think Eric was a math minor, for what it's worth.
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Re: Minnesota/Penn Open IV Discussion

Post by Fond du lac operon » Sat Nov 10, 2012 5:12 pm

So was my dad, but that doesn't mean he could write a good tossup on Feit-Thompson, or anything else. Question writing clearly is somewhat divorced from real knowledge, as can be seen from the fact that I've written history questions that have made it into tournaments, ever in my life.

EDIT: There's no real point to this post, I just wanted to diss myself and my family.
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Re: Minnesota/Penn Open IV Discussion

Post by The Ununtiable Twine » Sat Nov 10, 2012 5:38 pm

Vernon Lee Bad Marriage, Jr. wrote: To me, your manifesto reads "I want more hard math questions because I'm totally good at them. For evidence, look at all the obscure named things I can mention." You're going to need a more convincing argument.
Naturally, I have an opinion on the amount of math answerlines in the canon. I think the number of answerlines in the canon should definitely expand with respect to the undergraduate math canon, for sure. There are just way too many things that undergraduates learn that are not given nearly enough attention. Quizbowl also has the habit of ignoring algebraic topology for no real reason whatsoever (even simple things like fundamental groups and homotopy) so naturally people will think that we're just writing about impossible stuff when we write on topics that should relatively easy for a somewhat experienced undergraduate to answer. Ignoring entire accessible subject areas and minimizing what we ask questions on in mathematics (and computer science) does nothing to enhance the game. Some topics are hard for quizbowlers because they are hard topics, and others are hard for quizbowlers because we keep writing about the same few things over and over again, making the other topics that should be accessible seem much harder than they actually are. The game could afford to be more beautiful by expanding into the many more accessible answerlines that the math canon (and CS canon) have to offer. Of course, there are some things that should not be asked about in a tossup below a certain difficulty level by common sense, and others that should not be asked at all unless they are perhaps a hard bonus part at ACF Nationals or an open tournament (Feit-Thompson and Birch/Swinnerton-Dyer conjecture for instance).

I would argue, however, that the tossup on residues that you answered in the final at Nationals could also fit into the regular difficulty canon quite nicely as I learned about things like that when in my undergraduate complex analysis course. I never hear questions about those kind of things in regular difficulty, though. We should be writing about things like complex residues, Legendre symbols, and Galois theory in regular difficulty but instead we get the same rehashed answerlines.
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Re: Minnesota/Penn Open IV Discussion

Post by The Ununtiable Twine » Sat Nov 10, 2012 5:44 pm

Excelsior (smack) wrote:
*That's a Shin Mochizuki joke -- don't worry if you don't get it.
Ha ha indeed I too have heard the phrase "interuniversal Teichmuller theory" does this make me part of the awesome math cabal now
you have been granted temporary membership, it's a fancy thing you can put on your grad school application
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Re: Minnesota/Penn Open IV Discussion

Post by Tower Monarch » Sat Nov 10, 2012 8:00 pm

My jimmies are not rustled enough to join this discussion more than part-way, but I think I agree with the last bit of MattBo's post re: "I want more hard math questions...". In terms of the question that sparked this whole thing, I think that as a tossup answerline that was just short of a completely terrible idea, if only because after taking my graduate Algebra and Number Theory classes this term, I have still only seen that result once in my course and outside readings, and even then WITHOUT A NAME. The solution was already given: write more questions on types of groups like simple, solvable, etc, and write bonuses where maybe the hard part is this theorem. I'd now like to take a second to point out that as someone who has finished a math major and taken only 3 major-level classes in the Film department, I have read significantly more about and by Lacan and Derrida than I ever will on Feit-Thompson unless I decide to focus on Algebra (I likely will not) in grad school. This whole conversation has just made me smile, so I'm thinking the whole "convince other math people" isn't really working out. I'd love to see 1) more math/cs and 2) better-written math/cs, but the rules of good writing and canon-expansion don't just magically disappear when changing categories...

PS: I'm a little sad I couldn't be named as a math person in the New England area.
PPS: The ABC conjecture would make fantastic hard part at a regular difficulty tournament or medium part at some crazier event. Note that despite the fact that I am presenting on algorithms related to that conjecture this Tuesday, I would strongly recommend against tossing it up.
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Re: Minnesota/Penn Open IV Discussion

Post by Muriel Axon » Sat Nov 10, 2012 8:12 pm

The Ununtiable Twine wrote:I would argue, however, that the tossup on residues that you answered in the final at Nationals could also fit into the regular difficulty canon quite nicely as I learned about things like that when in my undergraduate complex analysis course. I never hear questions about those kind of things in regular difficulty, though. We should be writing about things like complex residues, Legendre symbols, and Galois theory in regular difficulty but instead we get the same rehashed answerlines.
As much as I would like to agree with you and Harrison, it is almost certainly true that the vast majority of quiz bowlers do not know what a complex residue or a Galois group is, and tossups going dead is a bad thing. Regular difficulty answer lines in chemistry include things like the van der Waals equation and Diels-Alder, and considering that vastly more people take organic chemistry (and earlier in their college careers) than complex analysis, I don't see how you can really make that comparison.

If there are ways to expand the math canon without writing questions nobody will get, I'd love to see that happen (and you can lead the charge), but I'd rather not we start writing questions about the Nullstellensatz or whatever it is that math majors learn. Harrison actually made a good point when he said "But there are far better ways of rewarding knowledge of these things than writing tossups on them." You can include material on a topic without making it an answer line.

I understand your point that these things are only hard because nobody asks about them, but I don't buy it - and besides, that could apply to any field. I'm an anthropology major. Nobody in the field talks about applying the concepts of the Apollonian and the Dionysian to the Zuni and Dobu, or even thick description - but as much as I would like to write questions on things that people care about these days (communities of practice? ethnographic reflexivity?) realistically, most of them are just not good options. And it's going to be that way in many fields.
I'm not that convinced that it's much harder for lay people to write on than chemistry or hard physics.
Here's the thing, though - if you know what carbon, hydrogen, oxygen, covalent bonds, and some other basic chemical terms are, you can understand a large chunk of chemistry. But as Mike Cheyne was just saying, literally everything you wrote in your initial post is completely unintelligible to someone who doesn't know much about math, and so is all talk of Lie groups, Cauchy sequences, and differentiable manifolds. Math has a huge repertoire of fundamental concepts, and it's hard to even get an intuition for what they are without having studied them in some depth. I'm a lay person in chemistry, but I can BS my way through writing a chemistry question; it's hard to do the same for math, even though I'm a math minor.
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Re: Minnesota/Penn Open IV Discussion

Post by Cody » Sat Nov 10, 2012 8:16 pm

I think something that is being lost in this kerfuffle is that Harrison explicitly notes that we should not be tossing up harder things. It is a little confusing and does seem like this at first, but towards the end he notes he is referring to bonus parts and clues, not tossup answers. I think, in this respect, that he makes a fine point.
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Re: Minnesota/Penn Open IV Discussion

Post by Fond du lac operon » Sat Nov 10, 2012 8:17 pm

Tower Monarch wrote:Note that despite the fact that I am presenting on algorithms related to that conjecture this Tuesday, I would strongly recommend against tossing it up.
I'm not sure where people get the idea that I'm in favor of tossing up hard math answerlines. I am very much against this. I am in favor of people who know math writing interesting things like ABC as hard parts at hard and maybe even regular tournaments, and trying to put clues about those things early in tossups instead of "can you figure out this formula named after Cauchy." I am also in favor of people who know anthropology sometimes writing things that relate to communities of practice or reflexivity or other things that people care about, although again, these would likely make bad tossups (and I certainly wouldn't get them).

EDIT: Damn you for scooping me, Cody! :razz:
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Re: Minnesota/Penn Open IV Discussion

Post by Tower Monarch » Sat Nov 10, 2012 8:28 pm

The Eighth Viscount of Waaaah wrote:
The Ununtiable Twine wrote:I would argue, however, that the tossup on residues that you answered in the final at Nationals could also fit into the regular difficulty canon quite nicely as I learned about things like that when in my undergraduate complex analysis course. I never hear questions about those kind of things in regular difficulty, though. We should be writing about things like complex residues, Legendre symbols, and Galois theory in regular difficulty but instead we get the same rehashed answerlines.
As much as I would like to agree with you and Harrison, it is almost certainly true that the vast majority of quiz bowlers do not know what a complex residue or a Galois group is, and tossups going dead is a bad thing. Regular difficulty answer lines in chemistry include things like the van der Waals equation and Diels-Alder, and considering that vastly more people take organic chemistry (and earlier in their college careers) than complex analysis, I don't see how you can really make that comparison.

If there are ways to expand the math canon without writing questions nobody will get, I'd love to see that happen (and you can lead the charge), but I'd rather not we start writing questions about the Nullstellensatz or whatever it is that math majors learn. Harrison actually made a good point when he said "But there are far better ways of rewarding knowledge of these things than writing tossups on them." You can include material on a topic without making it an answer line.
Hmm. I think I'm a bit more of a moderate than the two positions stated here. First of all, complex analysis is popping up in high schools, so while it is not as common as orgo, it is as common as any organic chemistry that does not come up in the standard two-term sequence. I've been playing with quizbowl-inexperienced organic chemists for the past year now and for about a third of all orgo tossups, they are sitting there blankly while I answer them right before the giveaway based on stock clues. On the other hand, you can't take an advanced (I guess like 3rd or 4th year UG) engineer or physicist or mathematician and have them miss a question on residues or legendre symbols. Again, though, these should not be tossup answers at anything below regular difficulty and should be used only sparingly in all but Nationals and CO; that's what bonuses are for, where I consider these to be medium parts for most tournaments. It's hard to figure out what kind of canon should exist for a < 1/1 distribution, but don't assume that other subjects like chemistry are any more straightened out.
The Eighth Viscount of Waaaah wrote:
I'm not that convinced that it's much harder for lay people to write on than chemistry or hard physics.
Here's the thing, though - if you know what carbon, hydrogen, oxygen, covalent bonds, and some other basic chemical terms are, you can understand a large chunk of chemistry. But as Mike Cheyne was just saying, literally everything you wrote in your initial post is completely unintelligible to someone who doesn't know much about math, and so is all talk of Lie groups, Cauchy sequences, and differentiable manifolds. Math has a huge repertoire of fundamental concepts, and it's hard to even get an intuition for what they are without having studied them in some depth. I'm a lay person in chemistry, but I can BS my way through writing a chemistry question; it's hard to do the same for math, even though I'm a math minor.
I hope you realize this is unfair rhetorical flourish.... The equivalent to your first sentence is "if you know what derivatives, primes, series, and some other basic mathematical terms are" whereas the chemistry equivalent of your math terms would be "all talk of conjugation, SN2 reactions and Lattice energy". If you BS your way through writing a chemistry question, you'll come out with a mediocre chemistry question. If you BS your way through a math question, you'll get a mediocre math question.
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Re: Minnesota/Penn Open IV Discussion

Post by Tower Monarch » Sat Nov 10, 2012 8:31 pm

Fond du lac operon wrote:
Tower Monarch wrote:Note that despite the fact that I am presenting on algorithms related to that conjecture this Tuesday, I would strongly recommend against tossing it up.
I'm not sure where people get the idea that I'm in favor of tossing up hard math answerlines. I am very much against this. I am in favor of people who know math writing interesting things like ABC as hard parts at hard and maybe even regular tournaments, and trying to put clues about those things early in tossups instead of "can you figure out this formula named after Cauchy." I am also in favor of people who know anthropology sometimes writing things that relate to communities of practice or reflexivity or other things that people care about, although again, these would likely make bad tossups (and I certainly wouldn't get them).

EDIT: Damn you for scooping me, Cody! :razz:
The problem with internet forums is it is hard to direct different sentences. I overall agree with your stances, but if I don't make clear that I only support ABC conjecture and other things as bonus answers, then some new writer will think tossing it up at the next regular difficulty tournament is a good option. In effect, my post is responding more to what the responses have made your stance out to be, if that makes sense.
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Re: Minnesota/Penn Open IV Discussion

Post by Muriel Axon » Sat Nov 10, 2012 8:45 pm

SirT wrote:I think something that is being lost in this kerfuffle is that Harrison explicitly notes that we should not be tossing up harder things. It is a little confusing and does seem like this at first, but towards the end he notes he is referring to bonus parts and clues, not tossup answers. I think, in this respect, that he makes a fine point.
Yes, I quoted him saying that. Apologies if the "you and Harrison" I addressed my post to threw things off; I agree that Harrison had a good point. On the other hand, Jake was explicitly talking about answer lines for most of his post.
I hope you realize this is unfair rhetorical flourish.... The equivalent to your first sentence is "if you know what derivatives, primes, series, and some other basic mathematical terms are" whereas the chemistry equivalent of your math terms would be "all talk of conjugation, SN2 reactions and Lattice energy".
Right, I agree, although I think you misread my answer. My point was that if you know basic chemical terms, you can come to understand conjugation and SN2 reactions without extensive difficulty. It may still not be easy to write questions of them, but it won't be terribly difficult. But even if you know what primes, series and derivatives are, it will still be pretty hard to understand manifolds, groups, and all that (and write questions on them). It's not that math is especially hard - all subjects are hard - but that math has a large repertoire of fundamental concepts, some of which aren't even introduced until you get to higher classes.

Crucially, I was not trying to understand that knowing about covalent bonds is of the same order of difficulty as knowing what a Cauchy sequence is.
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Re: Minnesota/Penn Open IV Discussion

Post by The Ununtiable Twine » Sat Nov 10, 2012 8:52 pm

Since when have all quizbowlers understood everything they buzz in and write questions on, Shan? People write questions in this part of the canon all the time without knowing what's going on.

EDIT: to be slightly clearer.
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Re: Minnesota/Penn Open IV Discussion

Post by Muriel Axon » Sat Nov 10, 2012 8:55 pm

The Ununtiable Twine wrote:Since when have all quizbowlers understood everything they buzz in on, Shan?
The comment about "understanding" was in the context of writing questions, and it is at least very useful to have some understanding when writing a question on a particular topic, although I will grant that that does not always happen. My point is that for many people, it is probably easier to write a question in chemistry without a deep knowledge in the field than it is in mathematics, regardless of whether one achieves true understanding (and nobody achieves true understanding in a field just by writing quiz bowl questions). This is probably at least true for many "standard" topics in both fields, even if there are some important exceptions. In any case, I would find it highly surprising if a large number of people said they did not find it at least somewhat easier to write chemistry than math.
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Re: Minnesota/Penn Open IV Discussion

Post by Tower Monarch » Sat Nov 10, 2012 9:09 pm

So I started making a list of the Math canon a while back for study purposes, and here is the list of answerlines I made: https://docs.google.com/spreadsheet/ccc ... 2Ync#gid=0 . The first column are things that I could imagine multiple, well-written tossups on with decently-interesting clues. I think anyone who can write a good chemistry tossup should be able to write an equally good tossup on any of these answers. The second column are things I see being tossupable at regular difficulty and above, but will a) not have as high conversion rates as the ideal and b) would admittedly take an informed writer to make a good question out of them. I started making a list of things I've seen tossed up that I don't believe a non-mathematician can write a good question on, but that is a way more subjective list. I think this could be a nice jumping-off point for someone looking to write for a submission but unsure about answer choice.
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Re: Minnesota/Penn Open IV Discussion

Post by The Ununtiable Twine » Sat Nov 10, 2012 9:14 pm

The Eighth Viscount of Waaaah wrote:
The Ununtiable Twine wrote:Since when have all quizbowlers understood everything they buzz in on, Shan?
The comment about "understanding" was in the context of writing questions, and it is at least very useful to have some understanding when writing a question on a particular topic, although I will grant that that does not always happen.

EDIT: In the process of editing to account for Jake's edits...
Yes, and a lot of the topics in the undergraduate math canon are not overly difficult to understand. For example, one uses Legendre symbols to determine when a number is a square modulo some prime. That wasn't that hard to understand, was it? Now take a good number theory textbook and write about the Legendre symbols using something that is written in English and maybe mentions some other mathematicians (like Jacobi's symbol being a generalization of Legendre symbol, for instance). Then look for out-of-textbook sources and find something interesting about it and use it as a leadin. You already have a 6-7 line question - submit it and if your set has a good math/science editor he/she will make some use of your ideas to make a good question.

My big point is that a lot of the topics in the undergraduate canon for math are not terribly hard to understand. No one is asking anyone to understand the works of Milnor or anything like that. If we're writing about compactness, there's no reason we can't ask about complex integration or slightly advanced arithmetic, but the bottom line is that we don't. If the answerlines that I'm suggesting to include in the canon go dead (and dead tossups are not a good thing), that's more of the quizbowl teams not caring to learn about easy math topics than anything - but with a few growing pains that will go away. People neglect learning things they should know about other areas of the science canon all the time. A lot of these answerlines should already be in the canon anyway and it's an oversight on the community's part that they're not. Any reasonably educated undergraduate in math, physics, or engineering should be able to answer a good bit of them with no problem, and for people in these fields that are accustomed to understanding symbols with magickal powers, it's not as hard as you think.

*add-on: Thanks for providing that list, Cameron, I'll take a look at it.

note: Cameron's opinions regarding his list reflect mine for the most part.
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Minnesota/Penn Open IV Discussion

Post by Muriel Axon » Sat Nov 10, 2012 9:42 pm

Re: Writing questions - Unfortunately, when I write math questions, I don't have you with me to explain things. If I look "Legendre symbols" up on Wikipedia, I find something rather more complicated than what you said, and although by poking around a bit, I can see that it's equivalent to what you wrote, it would be by no means obvious to those who've taken less math than I have. So I'm not really interested in continuing this (off-topic) discussion about the relative difficulty of writing math versus other subjects, but I don't think it's quite as easy as you make it seem. Every subject has its difficulties, but I think many would agree that math is one of the hardest subjects to write well.

As for your second paragraph, the main problem I have with this "quizbowl will learn" attitude is that quizbowl often doesn't learn, and while that's unfortunate, it's something we have to keep in mind while choosing answer lines.

That said, I'm out. I'm sure you and I both have better things to do on a Saturday night than this.
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Re: math math math a hundred maths one thousand maths

Post by Tower Monarch » Sat Nov 10, 2012 10:46 pm

Don't use wikipedia or planetmath or wolfram to write questions. They mix in mundane, trivial statements with cutting edge research that no one can be expected to know. Just open a book on number theory; there are literally dozens of quality ones with the titles "Elementary Number Theory" or "An Introduction to Number Theory". Similarly, something like Dummit and Foote's Algebra, available in every college library I've known, has some really down to earth explanations alongside some solid clues for all things algebra. All of these things are easy for anyone with an affiliation with a college and not difficult for others to locate.

Number Theory: You can write any hs question and Fall level question out of any text titled Elementary or Introduction to, and then the canonical second course (or first advanced course) is Hardy and Wright.
Algebra: Dummit and Foote is ideal, Lang suffers from the problem of being an ideal reference or a high level look at low level material so avoid him
Real Analysis: Folland is readable, Rosenlicht is super cheap and accessible though terse
Complex Analysis: Saff & Sider is super-readable and good for people coming from an Engineering background, Stein & Shakarchi is the Princeton standard for all analysis but it goes into way more depth than is usually needed
Topology: Munkres is the standard and goes into depth but is still considered readable
Discrete: Any intro book is good for low levels and Knuth/Graham's Concrete Mathematics is awesome for lead-ins and higher level topics
Last edited by Tower Monarch on Sat Nov 10, 2012 11:43 pm, edited 1 time in total.
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Re: math math math a hundred maths one thousand maths

Post by The Ununtiable Twine » Sat Nov 10, 2012 11:14 pm

I took the same approach that you just did and looked up the Wittig reaction, and what did I see? I saw bunch of strange diagrams with some jargon that I (as an unknower) take to be unconquerable, probably because I am not knowledgeable about said thing or said field. I understand how you feel even as an understander of many scientific symbols. However, I can't help but notice that there are tons of things in biology and chemistry that are asked about repeatedly in quizbowl that non-biologists/chemists don't understand, myself included. Those things in biology and chemistry seem to be more accepted into the canon than some of the undergraduate math answerlines. Why is this?

There is a good reason as to why the apparent complexity of a Wikipedia math or science article is not a good gauge of difficulty. For example, you could look up Artin-Wedderburn theorem and you don't see a lot of complicated pictures or any crazy equations, but I guarantee you that you shouldn't toss that up anywhere outside of CO, and even then it should probably be a hard bonus part. I realize that a lot of people may not have an idea of what to ask about, but undergraduate math is rather canonical. You can figure out what to ask about by looking in a textbook (as with more standard canonical subjects like physics), or maybe looking at the list that Cameron has provided here. Jerry has argued that physics should be more or less canonical, and I argue that quizbowl math should be more or less canonical for similar reasons. You should look in the undergraduate textbooks for acceptable topics as well. If you don't know which textbooks are intended for undergraduates, you can more often than not look in the introduction and it will basically tell you what the intended audience is supposed to be. For the most part, those answerlines are what we (the members of the "math cabal") are trying to say constitutes a very good, representative canon for regular difficulty math questions.

*also, regarding things that I could be doing, trust me I'm listening to the Alabama fans crying all around me. I'm having a good night.
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Re: math math math a hundred maths one thousand maths

Post by The Kid Who Collects Spider-Man » Sun Nov 11, 2012 3:25 am

Tower Monarch wrote:. . . Dummit. . .
Completely unrelated, but this guy's son (who's a math grad student at Madison) totally played on my ACF Fall team.
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Re: math math math a hundred maths one thousand maths

Post by Tower Monarch » Sun Nov 11, 2012 4:07 am

The Kid Who Collects Spider-Man wrote:
Tower Monarch wrote:. . . Dummit. . .
Completely unrelated, but this guy's son (who's a math grad student at Madison) totally played on my ACF Fall team.
That is so cool. It's the standard book for our Algebra sequence, so when I randomly met some UVM faculty visiting Hanover I asked about them and they immediately knew both authors. It's a great book.
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Re: math math math a hundred maths one thousand maths

Post by deserto » Sun Nov 11, 2012 12:41 pm

The Kid Who Collects Spider-Man wrote:
Tower Monarch wrote:. . . Dummit. . .
Completely unrelated, but this guy's son (who's a math grad student at Madison) totally played on my ACF Fall team.
And his daughter, Krysta, played high school qb for Champlain Valley from 2007 to 2011.
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Re: math math math a hundred maths one thousand maths

Post by kayli » Sun Nov 11, 2012 1:12 pm

So what are the arguments against expansion of math? The two main ones I hear are: 1) math is not accessible, which I think is weak considering that physics and chemistry are equally accessible/inaccessible and 2) it's always been like this and if you want more math then just write more math, which I think is also weak because editors can choose just not to use math questions since math questions probably take effort and time to check and edit.

Are there any other arguments I'm missing here?
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Re: math math math a hundred maths one thousand maths

Post by setht » Sun Nov 11, 2012 2:05 pm

Kooikerhondje wrote:So what are the arguments against expansion of math? The two main ones I hear are: 1) math is not accessible, which I think is weak considering that physics and chemistry are equally accessible/inaccessible and 2) it's always been like this and if you want more math then just write more math, which I think is also weak because editors can choose just not to use math questions since math questions probably take effort and time to check and edit.

Are there any other arguments I'm missing here?
There are more arguments over here if you care to go digging through that thread again.

My response to your characterization of argument 1 is that the major/minor science divide isn't based on "math is hard, let's do string theory," but rather a bunch of factors relating to science education: for instance, low-level (e.g., high school and college intro) bio/chem/physics courses generally introduce many topics that could be used as tossup answers. Low-level math courses don't, assuming people aren't interested in giving more distributional space to pre-calculus stuff.

My response to your response to argument 2 is: so? An editor certainly can cut a math question, but then presumably he/she has to take the time and effort to check some other (minor) science question. If people submit well-written math questions that look like they have a shot at reasonable conversion, a decent editor will let some/all of them in.

I generally like pure math questions as they currently appear in quizbowl--drawn mainly from upper division level material--but I recognize that far fewer people have non-quizbowl exposure to that stuff than to the basics of the major sciences, so I think it's fair to have fewer math questions. If people are serious about increasing the number of math questions, I tend to think that the most underasked area of math (relative to the number of people that actually know something about said area) is applied math: numerical methods, statistics, differential equations, etc.

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Re: math math math a hundred maths one thousand maths

Post by Cody » Sun Nov 11, 2012 4:47 pm

I don't think anyone is talking about expanding math here. (unless you mean expanding the clue space)
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Re: math math math a hundred maths one thousand maths

Post by kayli » Sun Nov 11, 2012 5:43 pm

I'm thinking about a little of both. I feel that clue space in math is more robust than people think. The thing about math is that it builds upon itself a lot so even easy accessible answer lines like "continuity" can have a lot of good clues associated to it that spans many levels of mathematics. I'm not so sure if this is as true for physics and chemistry, but I'm willing to be wrong there.

Anyway, I think it's well known by now that I would like at least .5/.5 math in every set, and I won't rehash my argument for that here. But I'm also curious now as to why chemistry and physics deserve a full 1/1 each. It seems that physics and chemistry tossups in college quizbowl both require as much if not more knowledge of jargon, and I'm not confident that there are more people studying physics and chemistry than mathematics at this point.
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Re: math math math a hundred maths one thousand maths

Post by kayli » Sun Nov 11, 2012 6:07 pm

setht wrote:
Kooikerhondje wrote:So what are the arguments against expansion of math? The two main ones I hear are: 1) math is not accessible, which I think is weak considering that physics and chemistry are equally accessible/inaccessible and 2) it's always been like this and if you want more math then just write more math, which I think is also weak because editors can choose just not to use math questions since math questions probably take effort and time to check and edit.

Are there any other arguments I'm missing here?
There are more arguments over here if you care to go digging through that thread again.

My response to your characterization of argument 1 is that the major/minor science divide isn't based on "math is hard, let's do string theory," but rather a bunch of factors relating to science education: for instance, low-level (e.g., high school and college intro) bio/chem/physics courses generally introduce many topics that could be used as tossup answers. Low-level math courses don't, assuming people aren't interested in giving more distributional space to pre-calculus stuff.
I'm not entirely sure if this is true. First, I don't think giving answer space to pre-calculus stuff is that problematic so long as the clues are built from topics post-pre-calculus, which given the nature of how mathematics is constructed, doesn't seem to be that big of an issue. Second, I think that there's plenty of answer space available for mathematics. If we only use topics from calculus and dead mathematicians, I don't think it's unreasonable to fill .5/.5 a packet with good accessible answer lines. If we allow pre-calculus concepts, then we can include even more (I think if nothing else various iterations of IMSANITY have shown that it's possible to have a lot of math answer lines. Granted, there were a lot of problems, but I don't think those were due to the nature of the answer lines so much as due to the question writing if I remember correctly.).
My response to your response to argument 2 is: so? An editor certainly can cut a math question, but then presumably he/she has to take the time and effort to check some other (minor) science question. If people submit well-written math questions that look like they have a shot at reasonable conversion, a decent editor will let some/all of them in.

I generally like pure math questions as they currently appear in quizbowl--drawn mainly from upper division level material--but I recognize that far fewer people have non-quizbowl exposure to that stuff than to the basics of the major sciences, so I think it's fair to have fewer math questions. If people are serious about increasing the number of math questions, I tend to think that the most underasked area of math (relative to the number of people that actually know something about said area) is applied math: numerical methods, statistics, differential equations, etc.

-Seth
The problem I see is that editors might not be incentivized to include good math tossups because it's a bit harder to check how good they are. To an extent, this is why we need more people to edit science and edit it well, but also I think it'd be pretty hard to sift through the contents of a math tossup when you could probably more easily check a question of feldspars. I conjecture that this problem would also exist with physics and chemistry except their distributions are set in stone so no matter what you can't avoid the task of editing them. NAQT's very rigid sub-distribution structure with their tournaments helps to avoid this problem precisely by determining beforehand how many of each tossup and bonus will be included in a set, but this is something unique to NAQT. Granted, it'd be much more difficult to implement in packet submission tournaments for every single tossup and bonus, since the questions being written are not centralized. However, that's why we mandate certain distributions.

Basically, what I'm trying to say is that the invisible hand of quizbowl will not always necessarily move towards a fair distribution according to what is put in or what people might want. Establishing a set distribution would help aid in that. (A variable one might work too, but is it possible to say that the number of math questions in a tournament will be proportional to the amount submitted? Seems like too much work)

EDIT: Also, I agree that we should expand math beyond pure math questions, so I guess there's even more answer space there.

EDIT EDIT: I guess I should say that I really like VCU Closed's science distribution for grievances above.
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Re: math math math a hundred maths one thousand maths

Post by Windows ME » Sun Nov 11, 2012 6:58 pm

Organic Chemistry takes something like one or two classes before you can understand EVERY organic chemistry tossup. Non-organic chemistry is taught in high school. Ditto biology. You can literally answer some ACF Nationals Bio tossups off clues learned in high school.

You can take five or six classes worth of math courses that cover different areas and still be completely lost regarding half the math that comes up in quizbowl. A lot of high-level math requires extremely specialized knowledge.

I am speaking as a bio/chem player here who has taken the "five or six" math courses in university. Your argument greatly exaggerates the difficulty of the other sciences relative to math - If our lives depended on it I am betting that you would learn and understand high-level chemistry much faster than I would high-level math - I can solve differential equations and do basic calculus - it sure as hell doesn't help when the 20th tossup on "rings" or "groups" comes up. So what? I don't deserve to get those tossups - but to argue that physics and chemistry are as inaccessible as math is just plain wrong - it doesn't actually take a chemistry major to be competent in it - just someone who has taken an introductory course or two that has taught them the jargon.
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Re: math math math a hundred maths one thousand maths

Post by Cody » Sun Nov 11, 2012 7:11 pm

Quizbowl has been around for a long time. I don't think we've had any problems along the lines what you are talking about. Competent science editors have no problem checking math (and Seth is, of course, correct in his response to Question 2. You should listen to him since he actually has experience editing college tournaments).

I think your opinions would change if you had more experience in college quizbowl.

P.S. The version of math you seem to be advocating is quite boring since it excludes any answer lines above calculus.

P.P.S. This thread was not at all about expanding the number of math questions until now. I cannot believe we are having this argument again.
Last edited by Cody on Sun Nov 11, 2012 7:19 pm, edited 1 time in total.
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Re: math math math a hundred maths one thousand maths

Post by kayli » Sun Nov 11, 2012 7:17 pm

Perhaps then that is a function of math tossups not correctly awarding knowledge. If math tossups require you to know more than 7 courses to understand when other questions require 2 courses of knowledge, then it's probably better to just pare down the extraneous hard math clues and answer lines. Overall however, I think there's great parity between the fundamental concepts of mathematics and the fundamental concepts of other disciplines. The problem you bring up seems to just be a problem of matching tossups to difficulty.

EDIT: I'm not saying to exclude concepts above calculus. In fact, we should include post-calculus tossups so long as the answer line is reasonable and we should definitely include post-calculus clues. My point above was just that even at the very base level we can find a robust selection of answer lines to ask about.

EDIT EDIT: I'll just save quizbowl the pain and will stop discussing this further. Food for thought though.
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Re: math math math a hundred maths one thousand maths

Post by Mewto55555 » Sun Nov 11, 2012 7:43 pm

I think Kay's actually somewhat on the right track here -- I don't know a ton about higher mathematics or math questions in college quizbowl, but there's a tremendous amount of answerspace open which allows for common-link type math questions. Maybe writing lots of math questions for high school has warped my perspective, but I've had great success taking something I think is cool and worth using as a clue and extracting an easy answerline from that (so like, for Feit-Thompson, reading the first sentence of wiki "In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable." tells me that it could very easily be an early clue for "odd numbers" or "groups" -- the former could then very easily turn to things that people with less background in mathematics could answer later).

Right now I'm writing the math for LIST; I know it's not exactly comparable, but if anyone's curious I can show them some of the tossups from this and previous years that I think really exemplify this idea of cool, otherwise-unasked, early clues on gettable answerlines.
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