Week 234: On Nicknames and Functions
An extended digression on shower thoughts.
The idea for this came to me in a drought and I'm when I'm done writing this I'm going to have a nice long shower.
As you probably know from previous versions of this, I live out in the country. It's not as country as it used to be as housing plans have crawled up the road towards me, but it's still pretty rural. As such I live on top of a hill, at the end of a road, at the end of a phone line, at the end of a gas line, and well away from city water. This doesn't usually come into play, but about once every year, I have to get a truck full of water and reload my well's tank because we've had two months without a lot of rain. This was where we stood last Wednesday night, and though my coyote tank was filled up, the pressure on the line was not good, and we were getting just a trickle.
I had to call a well specialist, and as they came around Thursday and then again on Friday with an air compressor (to fill the pressure tank and level out the flow to the house) I was stuck in the basement with little to do, but look around the boxes which were stored in that area. I knew a couple of them were my old books which I had picked through previously, but I discovered there was another layer of books there. That was where I found these:
Names and Nicknames of Places and Things
Oxford Dictionary of Nicknames
I had been looking for these for a while for purposes of including something in the book, and I needed these as source material to demonstrate the original abstract shower thought about this. It has seemed like a genius idea on many mornings as I steam-heated my back, but faded as I toweled off, and was barely a thought by the time I had gotten in front of a keyboard. The former was one of the first books I ever bought for writing, while the other was a pickup that I remembered could be useful at some point in training Seton. After some polish, will be going in the book. I'd attempted this discussion of orderly information before in here, but now that I have a coherent example, I can truly make it work.
[For purposes of our discussion assume that somewhere earlier in the book, there is a table of information about US States, two of the columns there are State Capitals and State Nicknames.]
Orderly information vs disordered information
When we discussed preparing for television by having the data on states, capitals and nicknames close at hand for the team, we were covering our expectation that the last clue if the state was the answer would be either the capital or a nickname. That's because these are the most orderly data we can ascribe to a state. Every state has one, and so if you are creating an answer with a state as an answer, its capital will be considered to put in as the last clue. Similarly, if the state capital is the answer being sought, the writer will always consider "capital of" to be an appropriate last clue, and be likely to use it in that position.
[This would be the point where I would consider thinking of the relationship between a clue and the answer as a function. Do I do that? It's worth considering, but for the next note.]
In addition to states and capitals, I listed in that table State Nicknames. State Nicknames exist for all states, and they can be useful as clues to identify the state, but unlike capitals, they're not invertible, a good percentage of states have multiple nicknames, and you can't ask for a particular nickname, unless you couch the clues leading up to it. This means that information is less ordered, and less useful to learn in the purely comparative sense.
[This of course leads to the question: Do I really want to teach injective, surjective, and bijective in a discussion of quiz bowl for high school? I probably have to, but I don't have to be happy about it.]
There's also another quality of some elements of the data, the question that would not be asked because it's not almost reflexive, or gives the answer as part of the question. Asking for the state that has its capital at Indianapolis, for instance, would not be done in a question at any level because you're given everything you need right there. It's almost a Turing Test Trap. No human writer would voluntarily write that clue, unless absolutely forced.
Nations and capitals work most of the time in this, but not always. They fail in this, sometimes because there's more than one capital city for the country, sometimes because there country is small enough that it doesn't have a formal name for the capital or its governmental center, and sometimes there are ambiguities in the name because there are audibly identical (Georgetown vs George Town) or there's simply more than one capital with a common name (Victoria).
Nations and capitals are also unlike states and capitals in that there's a significant portion of the nations which I can feel confident will never be an answer for a television question. These would be the ones which challenge the player in Worldle, or are rarely newsworthy, or otherwise lack middle clues to go along with their capital as the last clue.
The reasoning why something doesn't make it as a clue for an answer can vary, but we can treat it as a deviation from the order in the relationship between the two sets: clues and answers. If we treat that as a function, we can think of the relation applying only to a domain of clues which apply to a range of answers.
This becomes an interesting way to look at the usefulness of a type of clue, and whether you should look up the entire class of clues. For our purposes, consider a table with fewer entries than nations and capitals; let's say the list of cities that hosted World's Fairs and years. If there is a clue indicating that the answer held a World's Fair in year X, there's a significant amount of value in knowing it from the X, but there's also value in simply knowing that a World's Fair was held there. There's value in knowing f(X), but there's also value in knowing f exists, to guide the writer in placing the clue, and the player in their study. The clue now exists to limit the answer to an intersection of ranges in a composition of functions.
The interesting thing here is, if that relationship between clues and answers isn't neat, orderly, unambiguous and uniformly easily knowable, it goes to the end of the question. But when it gets dirty, it can find a place further up in the question. Last clues are last clues because they point to the answer in an orderly fashion, but the fact that the relationship between the clue and answer isn't identifying at all. Interesting uniquely identifying clues map to functions that have a single element in the domain and a single element in its range, and their uniqueness means they can start the question. But the clues in this middle ground, where it's significant that a relationship exists, AND that the relationship is this, become things a player should know to take advantage of question construction.
So how does this apply to our two books above? Well, nicknames are a sort of function between words and geographic locations. It's not of uniform difficulty, it's not a one-to-one or an onto relationship so not invertible, and it could be a pun (which would be almost reflexive), or relating to a location that would never be an answer at the level the writer is working. But the books we have listed are essentially tables where the function f is "X is a nickname of f(X)" and have an index listing f(X)'s range in alphabetical order. For the writer that's enough information to select answers to start with, and populate with middle clues. For players, that's enough to study, or browse a source. It probably wouldn't be as useful as visiting the locations, or studying the individual locations, but it would cut across questions and deliver clues in earlier position than the last clues. It's also worth noting that this is not a method of study that you can get from the internet. It's too broadly defined a category to show up on Wikipedia, and there's not a geographic nicknames site that does everything in one location.
As information becomes less orderly about a class of clues, the clue moves from the end of the question to the beginning.
The less orderly a set of clues and answers is:
- The less likely they are to appear as the last clue of a question.
- The more likely the fact that there exists a clue of that class is significant.
I phrase it as 'less likely' and 'more likely' because there are examples of last-clue-worthy clues in set of clue answer relations, but they're a subset.
The other thing I found in the basement, while waiting for the pressure tank to re-pressurize, was a map I stole from the “bound for the dumpster” pile when my office moved in 2012. Someone had decided to throw away a map of the United States with each county meticulously labeled, and laminated in a plastic perfectly able to repel dry erase markers. The only flaw in this gem was that the bottom strip to anchor it rigidly had broken off about five inches from the right side. As I prepared the letters I had sent on Tuesday morning, I thought about putting that map on my home office wall, and marking out the territory by who controls what leagues in each county. It’s one of those megalomaniacal things I should do if I ever get enough time and energy to do it.
But for now, I’ll just take a shower and go to bed.