On Friday, February 1, I gave a 30-minute talk titled “The Stargate Switch” during NAU’s Friday Afternoon Undergraduate Mathematics Seminar (FAMUS). As the name of the seminar suggests, the target audience for FAMUS is undergraduates. Here is the abstract for my talk.
An episode of Stargate SG-1 features a two-body mind-switching machine which will not work more than once on the same pair of bodies. The plot centers around two disjoint pairs of individuals who swap minds but subsequently wish they could reverse the process. We will discuss the mathematics behind the solution to this problem, as well as some generalizations.
This was my third FAMUS talk of the academic year, but my first of the semester. My first FAMUS talk was titled On an open problem of the symmetric group and my second talk was titled Euler’s characteristic, soccer balls, and golf balls.
In the 1999 episode “Holiday” from season 2 of Stargate SG-1, the character Ma’chello tricks Daniel into swapping minds with him. In an attempt to save Daniel, Jack and Teal’c accidentally swap minds, after which they then discover a limitation: the machine will not work more than once on the same pair of bodies. Physicist Samantha Carter saves the day by improvising a sequence of 4 switches that brings everyone back to normal.
In two recent papers, R. Evans and L. Huang from the University of California, San Diego, study the mathematics behind the Stargate Switch Problem, and generalize the solution to permutations involving $m$ pairs of bodies.
The limitation of the machine in Stargate SG-1 is the same as the one suffered by the mind-switching machine in Futurama’s 2010 episode “The Prisoner of Benda”. However, the Stargate Switch, and Evans and Huang’s generalization, is a special case of the problem posed in Futurama. In the general case, we need to introduce two outsiders to solve the problem. But the Stargate Switch can be solved without the addition of outsiders (as long as we have at least 2 pairs of bodies).
The solution to the dilemma in Futurama is known as the Futurama Theorem and was proved by Ken Keeler, who is one of the show’s writers and has a PhD in applied mathematics. I’ve given a few talks about the Futurama Theorem and if you want to know more, check out my recent blog post located here.
As with my previous talks about the Futurama Theorem, I utilized deck.js to create HTML slides and I used MathJax to typeset all of mathematical notation. One advantage of this approach is that it allows you to view the slides directly in your web browser. You can view the slides by going here. To advance the slides, just use your arrow keys. Also, you can get an overview of the slides by typing “m” or go to a specific slide by typing “g”.
Mathematics & Teaching
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Flagstaff and NAU sit at the base of the San Francisco Peaks, on homelands sacred to Native Americans throughout the region. The Peaks, which includes Humphreys Peak (12,633 feet), the highest point in Arizona, have religious significance to several Native American tribes. In particular, the Peaks form the Diné (Navajo) sacred mountain of the west, called Dook'o'oosłííd, which means "the summit that never melts". The Hopi name for the Peaks is Nuva'tukya'ovi, which translates to "place-of-snow-on-the-very-top". The land in the the area surrounding Flagstaff is the ancestral homeland of the Hopi, Ndee/Nnēē (Western Apache), Yavapai, A:shiwi (Zuni Pueblo), and Diné (Navajo). We honor their past, present, and future generations, who have lived here for millennia and will forever call this place home.