Friday, September 25, 2020

Surprises when teaching the Hero's Journey

I read Richard Bartle's two-part series on the Hero's Journey (1,2) in 2013 when it was published on his blog. It is a worthwhile read, describing not just the Hero's Journey itself from a technical perspective but also the kinds of mistakes that students make when they try to write stories that follow the pattern. I found this juxtaposition invaluable in helping me understand the Hero's Journey because it exposes the common misconceptions and fallacies.

I have taught my game design seminar every Fall since Bartle's publishing his essay, and I usually reference the series as part of a set of optional assignments. One of the options is to do exactly what Bartle writes about, which is to draft a plot outline that follows the Hero's Journey, and I have only had one or two students do this over the years. The other option I have offered is for students to attempt taking an existing video game that they believe follows the Hero's Journey and have them map the game events to the formula. All of these attempts have failed aside from one that I can remember, but more importantly, they have all led to fruitful conversations on the difference between power fantasy and Hero's Journey. Indeed, as one might expect, almost all the games that students would write about violate the primary climactic definition of the Hero's Journey by having the player defeat a boss rather than atone with the father.

This year, I have had to make significant changes to my game design course. All of the important ideas that would come up in natural conversation around students' presentations have had to shift into more didactic individual experiences or transactional discussion board posts. One of the changes to my module on stories and games was to require students to read Chapter 5 of Koster's Theory of Fun for Game Design, in which he discusses what games aren't—that is, he talks specifically about how games and stories do different things, and that stories can be added to games, but that doesn't make games stories. The other major change was to require students to complete the exercise that Bartle describes in his piece on the Hero's Journey: my students were challenged to create a plot that follows the instantiates that pattern.

Honestly, I was surprised at the results, which I read this morning. I expected that they would by and large do well, given that they had Bartle's writing as a guide. Yet, in keeping with Bartle's implicit prediction—given that he explains all this to his own students, and still they get it wrong—about 80% of the submissions demonstrated significant structural misalignment with the form. 

The errors seemed to fall into two categories, although I am doing this analysis from memory rather than rigorous qualitative analysis. First, there were errors of omission, where a step was not well defined. For example, some students had a Refusal that was not actually a refusal: in some cases, the protagonist had no agency to refuse, and in others, nothing really happened at all. The other category seemed to be errors of identification, where students had what seemed to be elements of the Hero's Journey in the story, but they mislabeled or didn't label them. Indeed, Bartle talks about both error modes in his own posts. 

A common thread among the plot outlines is that they emphasized the external properties of the characters. This may have been simply a result of my asking for an outline and not a story, but I suspect it's representative of how the students thought about their stories. I could see this, for example, in how they basically waved their arms at the Road of Trials. For some, it was just one minor encounter, and for others it was "and then some stuff happened." Only one or two explored what the trials might be in any way that resonated with the actual adventure itself, and none expressed explicitly what character changes these might have made on the protagonist. A similar problem showed up in the Woman as Temptress step: almost everyone had the would-be hero pause, remember their family back home who needs them, and then carry on. There was precious little indication of real internal struggle, where a character feels like they have done enough and could just go back and help.

Another common pattern in the students' submissions was that there was some kind of Big Bad who was causing trouble in the mundane world, and the erstwhile hero had to go get the boon that would allow them to defeat the Big Bad. These stories generally then had a "Father" hastily introduced in the Other World, impressed by the prowess or words of the hero, and handing over the macguffin, which the protagonist then brought back to the Mundane World. The character then proceeded to go on another adventure to go track down the Big Bad in his hideout and beat the snot out of him, thereby saving the world. In my feedback, I tried to point out that it's pretty easy to see that the climax of this story is not when the "father" is impressed, but rather, the defeating of the Big Bad. There was one notable exception, which I thought was going in this direction as the would-be hero returns with a magic sword, but the student made this sword symbolic of a dead kingdom: the people rallied around it, and the people overthrew tyranny. That is, the boon empowered the oppressed, while the Hero showed he was Master of Two Worlds. It was a nice twist.

About 30% of the students gender-swapped characters in the story, one of them swapping all the genders available. None, however, explained why they had done this. In my feedback, I tried to get them to consider the implications of their actions: given a format that you're asked to follow, so that you can learn what it is, your first maneuver is to change the format? In retrospect, I could have introduced shuhari here as a conceptual frame. In my video feedback to the class, I suggested that it had to be hubris to think that you could both modify a format and learn the format at the same time. I tried to explain that those who changed the gender did not try putting the Belly of the Whale before the Refusal of the Call, for example, but that it's the same kind of move, like building a ship while you sail. Perhaps not surprisingly, the students who did such gender-swapping also had other significant and gender-irrelevant problems with following the format. 

In my feedback to the class, which I gave in a rather lengthy video this morning, I encouraged them to think again over what the Hero's Journey is about: that it's about self-actualization, the Jungian integration of the shadow. It's not really about the externalities as much as it is about becoming the Hero. Recording the video, I was struck again by how disempowered I feel as an educator who cannot see the faces of his students, to talk with them, to interact with them. Last Fall, I remember a particular student who sat in the back, tried to look cool, and wrote brilliantly. Sometimes, I would say something provocative, and he would give me a look that made it clear he was uncomfortable and thinking, and then I knew we had to drill into that point. As I mentioned in the video today, the best thing you can be is wrong, because then you have something new to learn.

Thinking back on this, my first time rolling out the assignment, I am left with a question that sounds like a great research topic: Why did it go the way that it did? More specifically, what is hard about following the template? Are there specific parts of it that students misunderstand? Are there parts that they only understand in retrospect and with feedback? Are there qualitative or quantitative differences between the approaches taken that were successful vs. unsuccessful? I have already posted a follow-up to my students offering to mentor anyone who wants to pursue an Honors Thesis or something similar along these lines.

My mind cannot help but try to piece together the puzzle, and I wonder if it's possible that students struggled with the Koster reading and with the Hero's Journey exercise because they don't know any good stories. If someone plays video games throughout their formative years, and then signs up for a course on game design, of course they will think that these are great stories. The problem is, by and large, they are not great stories: they are trite shorthand for stories that can be spliced into game experiences. Is it possible that the type of stories encountered in games do not actually foster empathy the way great novels and short stories do, given that they are generally all power fantasies? Or is this most easily explained by the trouble students have completing any complicated assignment to specification?

Thanks for reading. I've essentially written off the possibility of getting any real research done this semester, but I am grateful to have the occasional opportunity to explore ideas here. Next time, it will probably involve barbarians.

Tuesday, September 15, 2020

A formal proof that placing the Kingdomino castle in an interior cardinal position necessitates holes in the kingdom

The Problem

One of my family's favorite games is Kingdomino. This 2017 Spiel des Jahres winner is a tile-laying game in which each player builds a kingdom, scoring points for clever placement of similar terrain pieces. As of this writing, I have logged 57 plays of this game, making it one of my most played games. We especially like it with the Age of Giants expansion. The game accomplishes the admirable goal that my five-year-old and I can both enjoy it at our own levels. The strategy is interesting, there's an appropriate level of risk-taking, and it's not so cutthroat that a friendly player won't point out a good move to an inexperienced one.

Each player starts with a square castle piece and draws a 2x1 tile each turn. The tile must be placed adjacent to the initial castle or adjacent to another tile such that at least one terrain edge matches. If you cannot play your tile, you discard it. Your kingdom must fit in a 5x5 grid, and there are only enough turns in the game that, if you are never forced to discard a tile, you will exactly fill the 5x5 space.

Sample ending board with castle in the middle
(Image by sethOn on BoardGameGeek)

It does not have to be the case that your castle is in the middle of the 5x5 grid, although in the base game there is a bonus for this. Depending on what tiles you draw and what combinations you seek, the castle can end up in any position.

After playing the game a few times, we noticed that sometimes players would be forced to have 1x1 "holes" in their kingdoms. That is, we encountered situations where the 2x1 tiles were not covering the 5x5 space. For a long time, we chalked this up to bad play. We believed there must have been some decision made previously that left the player with the necessity for this hole.

The more we played, though, the more we wondered whether the placement of the castle within the 5x5 grid determined whether there had to be a hole. That is, was it less a matter of "bad placement" and more a mathematical necessity based on the position of the castle. I do not remember now who among us first thought of this nor whether it was noticing a pattern or intuition. Once we brought it up, though, we did some post-game experimentation. Sure enough, our experiments seemed to show us that if the castle ended up in one of the interior cardinal positions, you would end up with a hole you could not fill with a 2x1 tile.

Doomed Castle Positions

We took this as a kind of folk wisdom, but my Computer Science sense was tingling. Experimental evidence that these were doomed positions is one thing, but could I write a proof that these positions inevitably led to holes?

I let this sit on the back burner for some time. I have not written a formal proof since writing my dissertation, since that's just not the kind of Computer Science I do. I wrote a ton of them in graduate school, and I remember the general ideas but not many of the specific techniques. It feels to me that we're dealing with a kind of parity problem, that the Kingdomino problem should map to another, more conveniently solved problem. That's a very Computer Science Grad School perspective, by the way: show that your problem can be transformed into an easier problem, and solve that one instead. The lack of inspiration for a similar problem meant that I didn't make any headway on this problem at all. That is, until this morning.

Even though I had not thought of an elegant mathematical solution to the problem, it struck me last night that I could probably approach the problem via proof by contradiction. This one always felt to me like a sort of cudgel, but it works: assume the thing you want to prove false is true, demonstrate that it leads inexorably to an impossible situation, and conclude that it must be true instead. I sat down this morning with a handful of tiles and made my case.

The Proof

Let's assume for the sake of the proof that if we start with our castle in one of the interior cardinal positions (C2, B3, D3, or C4, as shown above as Doomed Castle Positions) that there exists a tiling that produces a full 5x5 kingdom. 

We can assume without loss of generality that the castle starts in position C4. Every other case is symmetric to this one, and for our purposes, starting in any other position is irrelevant. Keep in mind, of course, that at the time you start the game, the castle is not actually fixed in any cell of the grid: it is the placement of the tiles that determine where in the grid the castle ends up. Still, these are the only cases that are relevant to the claim, so we can take it as given.

Step 1: Castle at C4

The space C5 must be filled with a tile, and that tile must be placed horizontally. Assume without loss of generality that we place it over the spaces B5-C5. This covers any other case because of the symmetry of the board: covering C5-D5 would yield the same topology, mirrored.

For the sake of the proof, we will be ignoring the terrain types on the tiles. After all, our assumption is that there is a 5x5 tiling, and so we can assume the player has access to tiles that make these legal moves within the game. Similarly, the tiles could be played in different sequences, but they will yield the same result. Here, for example, the player could have played a piece at D3-D4 for example, but the fact remains that in order to make a complete tiling, they would have to play at C5, as in this step.

Step 2: Play at B5-C5

The space at A5 can only be covered by a tile that spans A4-A5, so that is our next move.

Step 3: Play at A4-A5

Similarly, B4 can only be covered by a tile covering B3-B4.

Step 4: Play at B3-B4

Continue this idea for the next several steps: play a piece into the most constrained position, where only one placement can satisfy the game rules.

Step 5: Play at A2-A3

Step 6: Play at A1-B1

Step 7: Play at B2-C2

Step 8: Play at C1-D1

Step 9: Play at E1-E2

That gives us enough plays to demonstrate the contradiction. There are now two clear positions that must be covered, but cannot both be covered: D2 and C3. Playing to cover D2 will cover D3, but then no tile can legally be played on C3. Playing to cover C3 will cover D3, but then no legal play can cover D2. 

Step 10: Impossible to Satisfy D2 and C3

We have a contradiction, which proves that our initial claim is false. That is, we claimed that there was a 5x5 tiling, but we have shown that it is not possible. Therefore, there is no possible 5x5 tiling of Kingdomino when the castle piece is in an interior cardinal position. Put another way, if your castle is in an interior cardinal position, you will necessarily have an unfilled hole in your final kingdom.

The Implications

One obvious implication of this is for the strategy of Kingdomino. If you desire a 5x5 tiling, ensure that your castle piece is not in one of the interior cardinal positions. Of course, the game is won by score, and so a savvy player might accept such a position if a tile placement yields adequate rewards, but at least this helps such a player fully understand the costs and benefits.

This proof technique still strikes me as inelegant because it doesn't tell us anything about any other board configuration. That is, if we wanted to show any other case, we would have to demonstrate it tediously in the same way. I suspect there are underlying mathematical principles at play here that I am just not seeing.

Thanks for checking this out. If you have some other insight into the topological qualities of the game, or if you have a story about how your own play group discovered this phenomenon, I'd love to hear about it in the comments.

The Update

After my initial post, I shared a link to this on BoardGameGeek's Kingdomino page. Those forums really are a great place to bounce ideas and inspiration around. Ori Artvalion (@SaltyHorse) posted some insights that lead to a much cleaner formulation. Here's a link directly to Ori's post, and I encourage you to check it out! Ori's observation suggests that there are other board positions that lead to a case as I describe above, just as I suspected but could not formalize. Also, that post pointed me toward the mutilated chessboard problem, which now I have a vague recollection of having encountered in grad school, but that was a lifetime ago.

Friday, September 4, 2020

Initial thoughts on OpenMind in HCI

I am taking a moment this morning to capture a few thoughts about integrating the OpenMind platform into my HCI course. I wrote a bit about the initial decision in my post about the course re-redesign. Yesterday, I read my students' second batch of submissions, and I can say that incorporating this platform may have been one of my better decisions from the summer.

In the first week, the students completed the first module, and I had them write about whether they could identify the use of motivated reasoning or confirmation bias in past project work. Most were able to come up with good examples, a few did not, and a few did something much more interesting. These students responded first by saying they didn't think they saw either one, then they explained lucid and clear examples of using these. That is, even in writing about it, they tried to deny this as if it were shameful, but then admitted to having done it. In my feedback, I tried to point out that the important thing was to recognize it, not to feel bad or shameful about it.

This past week was even more interesting. They completed the second OpenMind module, this one on moral foundations theory. At the same time, they read Norman's Design of Everyday Things presentation on constraints, which includes a taxonomy of logical, semantic, cultural, and physical constraints. I asked them to consider how moral foundations theory influenced cultural constraints of design. I have to admit a certain pride in that question, and the students' responses by and large showed that it was both challenging and thought-provoking. A few students were only able to give very broad, abstract answers, essentially answering the question by restating, or trying to answer the easier question of whether it does rather than how it does. Here, it was an opportunity for me to remind them that human experience is almost all about abstractions and assumptions, while design is all about specifics. Indeed, that is a major theme of Design of Everyday Things' discussion of human behavior. Some of the students were able to come up with excellent insights that related the theories of moral foundations and design. Most noteworthy, however, were the few students who made generalizations about all people based on their own moral foundations. That is, they made claims that all peoples preferred safety or liberty, and I was able to push back on the distinction between how one sees the world versus how the world is.

They will be completing the remaining modules over the next three weeks, and I am eager to see how this trend continues. At the end, I want to talk to them about the holistic experience of completing the OpenMind modules, and maybe at the end of the semester try to come back to it and see if they think it impacted their designs.