Coming Out of the Dungeon: Mathematics and Role-Playing Games

After hiding it for many years, I have a confession to make. Throughout middle school and high school my friends and I would gather almost every weekend, spending hours using numbers, probability, and optimization to build models that we could use to simulate almost anything. That’s right. My big secret is simple. I was a high school mathematical modeler. Of course, our weekend mathematical models didn’t bear any direct relationship to the models we explored in our mathematics and science classes. You would probably not even recognize our regular gatherings as mathematical exercises. If you looked into the room, you’d see a group of us gathered around a table, scribbling on sheets of paper, rolling dice, eating pizza, and talking about dragons, magical spells, and sword fighting. So while I claim we were engaged in mathematical modeling, I suspect that very few math classes built models like ours. After all, how many math teachers have constructed or had their students construct a mathematical representation of a dragon, a magical spell, or a swordfight? And yet, our role-playing games (RPGs) were very much mathematical models of reality — certainly not the reality of our everyday experience, but a reality nonetheless, one intended to simulate a particular kind of world. Most often for us this was the medieval, high-fantasy world of Dungeons & Dragons (D&D), but we also played games with science fiction or modern-day espionage settings. We learned a lot about math, mythology, medieval history, teamwork, storytelling, and imagination in the process. And, when existing games were inadequate vehicles for our imagination, we modified them or created new ones. In doing so, we learned even more about math. Now that I am a mathematics professor, I find myself reflecting on those days as a “fantasy modeler” and considering various questions. What is the relationship between my two interests of fantasy games and mathematics? Does having been a gamer make me a better mathematician or modeler? Does my mathematical experience make me a better gamer? These different aspects of my life may seem mostly unconnected; indeed, the “nerd” stereotype is associated with both activities, but despite public perception, the community of role-players includes many people who are not scientifically-minded. So we cannot say that role-players like math, or math-lovers role-play, because “that is simply what nerds do.” To get at the deeper question of how mathematics and role-playing are related, we first need to look at the processes of gaming, game designing, and modeling

What\u27s in a Name? The Matrix as an Introduction to Mathematics

In lieu of an abstract, here is the article\u27s first paragraph: In my classes on the nature of scientific thought, I have often used the movie The Matrix to illustrate the nature of evidence and how it shapes the reality we perceive (or think we perceive). As a mathematician, I usually field questions related to the movie whenever the subject of linear algebra arises, since this field is the study of matrices and their properties. So it is natural to ask, why does the movie title reference a mathematical object

What\u27s in a Name? The Matrix as an Introduction to Mathematics

In my classes on the nature of scientific thought, I have often used the movie The Matrix (1999) to illustrate how evidence shapes the reality we perceive (or think we perceive). As a mathematician and self-confessed science fiction fan, I usually field questions related to the movie whenever the subject of linear algebra arises, since this field is the study of matrices and their properties. So it is natural to ask, why does the movie title reference a mathematical object? Of course, there are many possible explanations for this, each of which probably contributed a little to the naming decision. First off, it sounds cool and mysterious. That much is clear, and it may be that this reason is the most heavily weighted of them all. However, a quick look at the definitions of the word reveals deeper possibilities for the meaning of the movie’s title. Consider the following definitions related to different fields of study taken from Wikipedia on January 4, 2010: • Matrix (mathematics), a mathematical object generally represented as an array of numbers. • Matrix (biology), with numerous meanings, often referring to a biological material where specialized structures are formed or embedded. • Matrix (archeology), the soil or sediment surrounding a dig site. • Matrix (geology), the fine grains between larger grains in igneous or sedimentary rocks. • Matrix (chemistry), a continuous solid phase in which particles (atoms, molecules, ions, etc.) are embedded. All of these point to an essential commonality: a matrix is an underlying structure in which other objects are embedded. This is to be expected, I suppose, given that the word is derived from the Latin word referring to the womb — something in which all of us are embedded at the beginning of our existence. And so mathematicians, being the Latin scholars we are, have adapted the term: a mathematical matrix has quantities (usually numbers, but they could be almost anything) embedded in it. A biological matrix has cell components embedded in it. A geological matrix has grains of rock embedded in it. And so on. So a second reason for the cool name is that we are talking, in the movie, about a computer system generating a virtual reality in which human beings are embedded (literally, since they are lying down in pods). Thus, the computer program forms a literal matrix, one that bears an intentional likeness to a womb. However, there are other ways to connect the idea of a matrix to the film’s premise. These explanations operate on a higher level and are explicitly relevant to the mathematical definition of a matrix as well as to the events in the trilogy of Matrix movies. They are related to computer graphics, Markov chains, and network theory. This essay will explore each of these in turn, and discuss their application to either the events in the film’s story-line or to the making of the movie itself

Creating Successful Calculus Writing Assignments

I discuss three different writing assignments that I have used in my calculus courses. These assignments are introduced with a discussion of purpose and audience. Defining these qualities of an assignment will ensure that your writing assignments are more successful. The assignments discussed and explored here represent three different purposes: personal, informational and a blend of the two. The audiences for these assignments are diverse and force the students to incorporate particular modes of writing that demonstrate much of their thinking. Assessment of student learning as a result of these assignments is discussed. A fourth writing assignment is developed from a basic idea in order to illustrate the use of purpose and audience to create meaningful assignments

A Mathematician Weighs in on the Evolution Debate

There are a variety of reasons underlying the lack of public acceptance for the theory of evolution in the United States. An overlooked cause is related to problems with the mathematics curriculum in the K-12 setting. In this essay, we examine this relationship and propose changes to the mathematics curriculum that could improve mathematical thinking while also providing a basis for understanding theories, like evolution, that are poorly understood

Using spreadsheets to discover meaning for parameters in nonlinear models

Using spreadsheets one can develop an exploratory environment where mathematics students can develop their own understanding of the relationship between the parameters of commonly encountered families of functions (linear, logarithmic, exponential and power) and a natural interpretation of “rate of change” for those functions. The key to this understanding involves expanding the concept of rate of change to include percent changes. Through the use of the spreadsheet model, students can explore and easily determine which type of change is most natural for a given family of functions. This, in turn, provides a mechanism for interpreting the parameters of the function numerically, rather than graphically, as is common

Matching functions and graphs at multiple levels of Bloom’s revised taxonomy

This paper illustrates the power of Bloom\u27s revised taxonomy for teaching, learning and assessing [3] in aligning our curriculum expectations and our assessment tools in multivariable calculus. The particular assessment tool considered involves a common matching problem to evaluate students\u27 abilities to think about functions from graphical and formulaic representations. Through this analysis we gain additional understanding of why students may have difficulty in performing well on certain activities

Deterministic Republic

This story is an extension of the paper Mathematics and Voter Choice published in this same issue of the Journal of Humanistic Mathematics. It explores what elections and politics might look like from the voter perspective if some of the ideas from the paper were implemented. The story is also an attempt to highlight how mathematics and data science are done, much the way a colleague of mine refers to shows like CSI as recruiting tools that use dramatic pipetting in the labs to show day-to-day science in action. The story is, as you will no doubt see, heavily influenced by watching far too many episodes of the Twilight Zone

Aligning Political Options and Aggregated Personal Opinions on the Issues

Much work has been done in studying how to aggregate voter opinions to decide a fair election. These models presuppose that each voter has a solid understanding of their choices and can express that opinion in the election process. We discuss why this is not always the case. Further, we explore some of the issues that arise when considering the multidimensional nature of both voter preference, with respect to the slate of issues in an election, and the platforms of the various candidates, with respect to the same slate of issues. In light of the complications we encounter and with full apologies to Jonathan Swift, a modest proposal is made for conducting future elections in a way that offers all of the voters a true chance to find a voice