An Illuminating Day

Our student pairs have done great work with our daily blog posts.  Each pair has written three posts, and we hope you have enjoyed their descriptions of our group’s experiences over the past few weeks.  For the final three posts, the professors will take a turn at the keyboard.

We have been remarkably impressed with this group of students.  They are cooperative, inquisitive friendly, and eager to learn.  Their curiosity has led the group to investigate a number of aspects of Walt Disney World.  All students have been involved with collecting data in lots of ways, in analyzing that data, and in the preparation of findings.  In these last three blog posts, we will describe three of the projects that have resulted from their work.  (Don’t worry, we will also tell stories about our experiences on these days, too!)

Single Riders?

One of the things that the group has investigated involves what Disney calls “single rider lines” at some of its most popular attractions.  When a ride has its seats arranged in pairs, then it is often the case that odd-sized parties can be completed by pulling from the single rider line (which is made up of people who don’t mind riding by themselves, or actually, with strangers).  Our students are investigating several issues related to this type of situation (for instance, when it is advantageous to try the single rider line as opposed to the regular line).  The students collected lots of data in a variety of interesting ways -- and this caught the attention of many other park guests.   We were certainly proud of their creativity and their persistence.  Fortunately, their work (which was all perfectly legal) did not get the attention of Disney security!

A Blast of a Day

Today started with a little “probability by the pool” as Dr. Hutson met with a group of students to discuss some of the probability ideas relating to the single rider line project. 

After that, the group loaded up and headed over to Epcot to meet with another Disney cast member -- one that one of our students knew from home.  This cast member had spent a number of years working in the pyrotechnics division of the Illuminations nighttime show at Epcot, and he had arranged for one of the show’s directors to give us a backstage tour of the Illuminations setup area.  We learned a great deal about the complexity of the show’s setup, execution, and take down.  We got some very close up views of the huge globe that is the centerpiece of the show as well as a rare look at the inferno barge that was out of the water for routine maintenance.  We were also treated to a peek inside the show’s control room, which is hidden inside a tower in the Mexico pavilion.  Since photographs are not allowed in backstage areas, this exterior shot of Mexico will have to suffice as a memento of our fun time in the control room, marked by the small window peeking over at the top of the decorative stairs going up the building.

Whenever you see an amazing fireworks display, we learned that it's nice to show your appreciation to the unseen pyrotechnicians who safely prep the show for the guests by cheering loudly afterwards.  Next time we're watching Illuminations at Epcot, we'll be sure to applaud the efforts of these dedicated experts after a great show!

Just as we were about to head to lunch, the bottom dropped out of the sky and the rain started to fall -- hard. We delayed by riding the Gran Fiesta ride in Mexico (our group filled an entire boat), but the rain kept coming.  We decided to brave it and so we dashed over to the Land Pavilion for a nice lunch together.

We returned to the hotel for the students to have some work time, and they made the best of that.  After dinner, a small group went over to Downtown Disney for some shopping and snack finding.  The van rides to and from our destinations continue to be sources of great entertainment.  As various songs from students’ playlists play through the speakers, you never know who you will see dancing, singing, or playing air drums!

Fun and Interactive

We had a pretty relaxing Saturday today here at Disney.  We spent the morning working on group projects (or sleeping in some cases).  We have divided into groups to work on poster presentations of the projects we have been working on.  The posters will cover the following: an optimal tour of Magic Kingdom, an optimal tour of Epcot, an analysis of single rider lines for Expedition Everest and Rock n Roller Coaster, and an analysis of the throughput for Kali River Rapids and Tower of Terror.

We had a well deserved change of pace spending time at Camp Hardy. Dr. Marvin Hardy is a Furman grad, classmate of Dr. Harris, and dear family friend of Kate. The Hardy family was incredibly gracious and thoughtful to invite the group over to their  house which happens to sit on a lake. We were greeted with friendly faces and a Mexican feast put together by Mrs. Carla. Kate's dad was in the area for business and able to contribute with his famous homemade guacamole and two delicious desserts and to participate in the fun of course.

After some yummy food and conversation we began to hear the rumbling in the distance of an approaching storm. During the downpour we got a chance to flip through Dr. Hardy's old Furman yearbooks, finding photos of family members and friends including Dr. Harris. Our favorites included the "Harry B-Shucker" intramural football team of Dr. Harris, Dr. Hardy, and friends and the one shown to the right. We recognized a few friendly faces from the 1991 Furman Mathematics Department.

We decided that we could never let a thunderstorm rain on our parade, so once the lightening and thunder ceased, some of the most daring of the group braved the rain to hit the lake for a thrilling turn on the tube slipping and sliding across the lake. I will refrain from mentioning any names, but some were definitely more prone to flying into the lake than others. Whether watching baseball on the couch, conversing on the porch, or being slung back and forth on the tube, all are thankful opportunity this afternoon to regenerate our energy for the final stretch of our time in Orlando.

After a relaxing time at the lake, we returned to the hotel for a little down time before dinner.  We ate at the Nine Dragons Chinese restaurant in Epcot.  The food was delicious.  Popular orders included honey sesame chicken and a ‘fun and interactive’ mix your own noodles dish.  Several of us also tried caramel-ginger ice cream, which was delicious.

After dinner we stayed to watch the Illuminations fireworks show.  We received a Fastpass+ for a special viewing area as part of our Epcot Undiscovered Worlds Tour yesterday.  We got to watch the show from a small overlook in Italy.  We had a great view of the images projected on the rotating globe as it moved through the lake.  The fireworks were amazing.  We were in the front of the crowd, and even the shorter members of the group (i.e. me, Stella) had a great view.  Tomorrow we are going on a behind the scenes Illuminations tour, and we cannot wait to find out how Disney creates such a beautiful display.

Kate and Stella

Report on Epcot's Traveling Tourist Problem

As you may have read recently, our group had some fun on Friday, May 16th participating in the Great Epcot Race, or as we professors called it, the Traveling Tourist Problem.  There were five teams (four student teams and one professor team), and the challenge was to accomplish a list of 18 tasks spread throughout the park and to do so as efficiently as possible.  There was a lot of excitement, competitive spirit, trash talk, and general sneakiness -- and that was just the professor team.

The activity was more than just a game, though.  The race accomplished a lot of things: 

1. It gave the students an opportunity to make decisions and create strategies that relate to a major topic of study this May (the Traveling Salesman Problem), 
2. It gave students the opportunity to collect time/distance data that they will use as part of this project, and 
3. It encouraged cooperation, communication, and the use of good problem solving skills.

As promised, we want to tell you a little about the winning team and their strategy.  The team that finished the tasks in the shortest amount of time was the team of Arianna, Jordan, and Kate.  Here is a photo of them in front of the popular Test Track ride.

Before the day began, they (like all the other groups) did some strategic planning.  They studied the durations of the shows and available times to meet characters, and they looked at attraction wait times from the previous day in an effort to predict the times for the day of the contest.  On game day, the winning group made a few adjustments to their plan and they ended up with an itinerary that accomplished all requirements in the following order:

1. Soarin’
2. Soarin’
3. Test Track
4. Test Track
5. Group Photo with a topiary (Buzz Lightyear outside of Mission Space)
6. Ellen’s Energy Adventure The Seas with Nemo and Friends
7. Turtle Talk with Crush
8. Club Cool
9. Captain EO
10. Journey into Imagination
11. Living with the Land
12. Spaceship Earth
13. Have Cast Member write “Math and the Mouse” in foreign language (Spanish in Mexico)
14. Gran Fiesta
15. Picture with a Character (Donald Duck in Mexico)
16. Watch a movie in the World Showcase (China)
17. Maelstrom
18. End at Rendezvous Point

One very neat thing about the process is that the students used a class set of iPads (provided by Furman’s Buckman iPad grant).  For this activity, they used them to track their paths through the park using a GPS-related app that kept this automatically for them.  A summary of the winning team’s path for the day is shown below (with numbers corresponding to the list above).  The actual GPS output is somewhat unreliable though to visualize walking paths because it thought people were walking when they were experiencing attractions (sometimes going as fast at 64.9 miles per hour on Test Track), so we made modifications to visualize just the walking portions.

You will notice that they did a good job minimizing their walking and crossbacks.  You will also notice that there is a stop at 13.5.  This was a stop at a Fastpass kiosk to pick up a final Fastpass for Maelstrom -- the final attraction on their journey.  Here is a picture (kids these days would call it a selfie) of them at the rendezvous point after they realized that they were the first ones there.

To view all groups' progress another way, consider the grids below that show the attractions on the left and the time of day across the top, broken up into 10 minute intervals between 8:50am and 4:40pm.  The attraction labels may be hard to read, but the order of the attractions on these grids starts at Spaceship Earth and rotates through the park clockwise:

1. Spaceship Earth
2. Ellen's Energy Adventure
3. Test Track 1
4. Test Track 2
5. Gran Fiesta
6. Maelstrom
7. La Cantina de San Angel
8. World Showcase movie
9. "Math and the Mouse" translation
10. Club Cool
11. Captain EO
12. Journey Into Imagination
13. Soarin' 1
14. Soarin' 2
15. Living with the Land
16. The Seas with Nemo
17. Turtle Talk with Crush
18. Topiary
19. Character picture

The grids are posted in order of team finish. You'll notice that the fourth place team (orange) has fewer grid marks than everyone else.  This is due to the fact that they didn't record exact times for some of the non-attraction requirements (taking a picture with a topiary, getting a "Math and the Mouse" translation, etc.).  Rest assured, they provided photographic evidence of them performing these tasks, they just don't have exact times for them.  

1st place: finish at 3:02pm

2nd place: finish at 3:13pm

3rd place: finish at 3:17pm

4th place: finish at 4:34pm

5th place: finish at 4:38pm

Notice that the top three groups all took care of their two trips on Soarin' first thing and their finish times were separated by only 15 minutes.  

Around the World in 14 Hours

World Travelers Stylin'

Hello! Jordan and Annie here to update you on our activities for Wednesday, May 21^st. We spent a full day in Epcot today with lots to report!

Fun with Mickey!

Behind the Seeds

35 Pound Winter Melons

We began the day with a look "Behind the Seeds" of Disney's greenhouses, where they grow a variety of plants and animals for both decoration and food. Our very knowledgeable tour guide, Jake, led us through greenhouses connected to the Living with the Land boat ride as well as through several "backstage" greenhouses that contained a wide range of both domestic and tropical specimens. In addition, we got to see Disney's Biotechnology Lab for Crop Improvement, cosponsored by the United States Department of Agriculture. In the lab, scientists were using a technique called tissue culture to produce thousands of plants without seeds, which is much faster and more efficient for mass production. Disney then uses many of these crops in restaurants throughout the parks and resorts. Yet even in their greenhouses, Disney always adds a little Disney magic... Giant tomato trees, Mickey Mouse-shaped cucumbers, and thirty five pound winter melons were just a few of the unique GMOs created in the lab. In addition, one of the greenhouses even contained a Mimosa Pudica (AKA Touch Me Not), which curled its leaves when touched. Overall, we really enjoyed the tour, which provided interesting information about scientific applications not commonly thought of in relation to Disney World.

Collecting Data

Data Collection Fun

Though the tour opened our eyes to the biology and chemistry associated with the greenhouses in Epcot, we were excited to get back to math and work on our project of creating a network map of the park. To do this, we needed a series of nodes, so each attraction in Epcot was marked as such. However, measuring the distance from every attraction to every other attraction in the entire park would be unbelievably time-consuming, so we took Len Testa’s advice of establishing (centralized) “way points” that one has to walk past in order to get to multiple attractions. In doing so, we minimized the number of edges in our network that we had to measure, since we could instead measure distances from attractions to only the four waypoints and other nearby attractions. Since measuring distances requires walking back and forth between attractions with a stopwatch, minimizing the edges (while still maintaining an effective model) is ideal. Thus, our morning at Epcot was spent timing the walk from way point to attraction, attraction to attraction, and way point to way point; of course, we were obligated to take breaks to ride some of our favorite rides (because walking past Test Track and Soarin’ all day without being drawn in for a ride, we learned, is near impossible). We each ended up with travel times for all of our predetermined edges, so our next step is to calculate an average time for each edge from our collective data to incorporate into our model.

Biergarten

After our long day of data collecting, we had a few hours of free time in the park before our group dinner reservation at Biergarten, a Germany-themed buffet in Epcot. Not only was the food delicious, but the restaurant is decorated so that the patrons feel as though they’re dining in a German, nighttime, outdoor setting, which of course would not be complete without live music. We loved being able to catch up on each other’s afternoon activities over a good meal in a fun setting.

Biergarten

 IllumiNations: Reflections of Earth

Following our delicious German meal, we remained together as a group to watch the IllumiNations: Reflections of Earth firework show, which occurs each night at 9 p.m. over the Epcot World Showcase Lagoon. A breath-taking display of fireworks, lasers, giant torches, and a giant globe that displayed beautiful images of locations all around the world dazzled viewers. We are looking forward to an exclusive, behind-the-scenes tour of the show toward the end of our trip, but, for now, we simply enjoyed the magic!

IllumiNations: Reflections of Earth

The Keys to a Mathemagical Adventure

Selfie by our tour guide with another cast member

Hayden and Rahul are back to give you the most recent updates from our mathemagical adventures. 

The Mouse

 

This morning we got to go “backstage” in Magic Kingdom on the Keys to the Kingdom tour given to us by our hilarious tour guide Megan. This signature Disney tour goes behind the magic of Disney World, explaining some of the little known history and secrets of the happiest place on earth. And lucky you, we’re going to share some of these “secrets” with you. One of the coolest parts of the tour was getting to explore part of the Utilidor; that’s right, the Magic Kingdom really does have secret underground tunnels! The Utilidor is the real ground level to the Magic Kingdom that is used by staff and cast members to help maintain the four keys to the Kingdom- safety, courtesy, show, and efficiency. Cast members and characters can use the Utilidor to travel across the park without being seen out of costume or in the wrong “land.” Maintenance use the corridors to quickly transport any require tools or equipment, and Reedy Creek Emergency Services (Disney has to provide their own emergency services due to its size and spread across two counties) can use the tunnels to quickly access guests in need without dealing with crowds above. Part of the Utilidor is also used to vacuum trash collected above into a tunnel that sucks the over 80,000 pounds of trash produced each day to backstage trash compactors.

Students take picture on tour

We also learned interesting new facts about some of the more visible “upstairs” Disney secrets. As you walk down Main Street, you may have noticed some of the writing on the stores’ upstairs windows; this is what Disney World considers its “credits.” When you first walk in and look above the Confectionery, you see Roy Disney’s name. Roy, Walt’s brother and partner, helped start Disney World, taking care of most of the business’s finances. Walt in on the other end of Main Street, above the Ice Cream Parlor since he had a nightly bowl of ice cream. We also learned about the cues they use to transition between the different lands, such as changes in the sidewalk color and texture, different music, changes in decorations, and some less obvious and more symbolic details. For example in Liberty Square, the light-colored stone path throughout this section of the park, symbolizes towns before plumbing where waste was thrown into the street. Each branch of the stone path leads to a bathroom, all of which are technically outside of Liberty Square and in the next land. This is just one of the many details that helps to make the “show” by bringing guests back to pre-twentieth century United States. Overall the tour was an incredible experience, that exposed the hard work and detailed ingenuity needed to create such a magical destination.

The Math
 

The tour was far from the end of our day. We had lunch at the park and then returned to our hotel. After a quick 20 minute break, we were back at work. We had previously been split up into groups and assigned to read mathematical papers and present on the mathematical models they described. These papers related to various problems faced at amusement parks like Disney: optimizing hotel reservations, golf tours and crowd flow.  These were peer reviewed papers published in respected journals, not aimed at undergraduate students. Mirroring last week, we, Hayden and Rahul, had contrasting yet similar experiences here. I, Hayden, am a rising sophomore Chemistry major, so before this I’ve had almost no experience reading mathematics journals. However, each of our groups included students with a wide range of experience with this type of work. Students like Rahul were able to explain some of the math notation and terminology that was new to me, so ultimately, I was able to fully understand the paper I had read. I, Rahul, am a rising senior Mathematics major, and have done Mathematical research both of my previous summers at Furman and have as a result have read a number of mathematical papers. However, reading a mathematics paper on an unfamiliar topic is always challenging, no matter your background, it took time and effort before I had any idea how the model worked. At the presentations today, it was clear that all three groups had put in a good deal of work and displayed a full understanding of the situations being modeled as well as the mathematics behind it: objective function being optimized, the variables and the constraints.

Planning locations of Waypoints

Now that we had shown that we had a solid grasp of how mathematical modeling worked, we finally began what we hope will be our primary project for the remainder of the course. We are going to create our own model for optimizing tours of Disney World. Like with any other project, the key is to start small. The first step is to gather data about a small segment of the park. We will use our data gathered from the Epcot Challenge last Friday as a starting point. We plan to gather more information tomorrow while visiting the park and will combine this with data scraped from the internet. Rather than trying to calculate travel time between every single attraction at the park, we created a set of “waypoints” on the map of Epcot which will form the nodes of our graph. We will only need to know the travel times to the central node. Other travel times can be computed with this data using, for example, Dijkstra's Algorithm. Another advantage of using such a system with waypoints is that it is easily expandable, thus making for a robust model.

The Fun
 

About half the group chose to stay at the hotel this evening, but the rest of us decided to venture back into Disney, this time to Hollywood Studios. This was mostly just for fun, although we did try to test out a few theories we had developed about wait times, with some success. We finished up the night watching the fantastic Fantasmic! show, featuring everything from fireworks and lights to costumed actors and animations projected onto sheets of water. As we left the park, we noticed cast members closing the gates to Tower of Terror and Rock ‘n’ Roller Coaster. Just this morning, Megan had described Disney’s closing process of checking one attraction at a time and moving toward the main exit from there, and she assured us there was no way to hide out over night with this thorough shutdown plan. Dr. Harris, however, seemed to have taken this as a challenge and was working on an algorithm or two to solve this particular problem as we walked out.

Third Day - The Epcot Escapade

Hi, Hannah and Kelly here to tell you about the excitement of May 16th in Epcot!  Today has been a flurry of planning, scheming, and ruthless competition as we made our way through Epcot.

The Goal:

To get your team through 18 attractions and activities in the most efficient way possible.  These included popular attractions such as Soarin' and Test Track (both which had to be ridden twice), interesting shows like Ellen's Energy Adventure and Captain EO, and other activities such as posing with characters and sampling sodas at Club Cool.  While traveling around the park, teams had to record the time at which they entered the attraction's line, the time the attraction started, and the time the attraction ended.  Additionally, each team had to have photographic evidence of themselves participating in each attraction.

The Rules:

Since teams were highly competitive and ice cream was on the line, rules were made to ensure fair competition.  Teams were only allowed to use a park map and the Disney app to plan and execute their touring plans throughout the day.  This allowed teams to check ride times and FastPasses, but limited their ability to use established planning websites.  Sabotage was strictly forbidden, although bluffing and psych-out techniques were used and pretty much encouraged by all.  We were also encouraged "to eat lunch, drink plenty of water, wear sunscreen, and take breaks as needed," though it was mutually agreed that breaks were for the weak and that it was totally okay to eat lunch on attractions.  That being said, no member of our group was hauled off by Disney security today, so it was a winning situation for all.

Network Models and Touring Plans:

Ultimately, this competition provided a fun way to gather data on ride times, wait times, and distances between attractions.  In addition, it allowed each team to have a hands-on attempt at optimizing a touring plan for those attractions.  Each team had to consider many obstacles such as crowds, FastPass availability, and unexpected breakdowns.  In order to gather data about each team's route, each team member used an iPad app to keep track of their GPS location throughout the day.  This app will later provide the means to determine the time needed to walk (or run) from attraction to attraction.

The Aftermath:

After our whirlwind tours through Epcot, the group had dinner together to unwind and chat about their experience.  While the day was competitive and jam-packed, everyone had tons of fun planning, riding, and experiencing Epcot during the day.

Now you are probably wondering, who won? This question and many more will be answered in another post, which will give the itinerary and details of the winning group's tour plan and more detailed information about our Epcot network. Tomorrow we are excited to visit the last of Disney's four parks: Animal Kingdom. Keep posted for more exciting adventures!