Monday, May 30, 2016

The Genetics of Touring

Each student has written three blog posts at this point, so it's now the professors' turn to take over! Yesterday, we started the day with an optional trip to Hollywood Studios to allow students to collect project data. Unfortunately, the park had Extra Magic Hours that morning, so WDW resort guests could enter the park an hour before we could, which made for long lines early in the day. After some time to work on projects back in the hotel in the afternoon, we headed to Animal Kingdom to enjoy another evening in the park. 

The Genetics of Touring
Last week, the students participated in a race to see which team could accomplish a list of 19 tasks in the Magic Kingdom most efficiently.  The tasks ranged from riding an attraction to getting a picture taken with a character.  Differing from the Traveling Tourist Problem at Epcot two years ago, we allowed teams some flexibility in the attractions that they visited.  Here is a list of possible events:

The winning group's tour of the Magic Kingdom.
Space Mountain       
Buzz Lightyear’s Spin            
Seven Dwarfs Mine Train 
Haunted Mansion 
Peter Pan’s Flight           
Under the Sea - Voyage of the Little Mermaid
Splash Mountain              
Big Thunder Mountain Railroad
Pirates of the Caribbean           
Jungle Cruise         
Group Photo with a costumed character  
Group Photo with Walt Disney 

Fantasyland (Pick 3)
It’s a Small World
Winnie the Pooh
The winning group, Zack, Mary Lib, and Johanna.
Mad Tea Party
Hall of Presidents
Enchanted Tales with Belle
Prince Charming’s Royal Carousel
Mickey’s Philharmagic

Tomorrowland (Pick 2)
Astro Orbitors
Stitch’s Great Escape
Monster’s Inc. Laugh Floor
Carousel of Progress
Tomorrowland Speedway

Adventureland (Pick 1)
Magic Carpets of Aladdin
Country Bear Jamboree
Enchanted Tiki Room

The students were assigned into groups of three and were given data on the expected wait, walk, and ride times in the Magic Kingdom that day (supplied by  They had an afternoon to design a tour of the chosen 19 attractions and were allowed time in the park to perform reconnaissance.  The following day we raced, and (drumroll, please) the winning team was Johanna, Mary Lib, and Zack who finished the tour in just under 6 hours.  Their tour is shown above.

Johanna, Mary Lib, and Zack flying with Dumbo.
After the race, the students learned to model the problem using networks and also learned that the problem they were trying to solve is a variation of the Traveling Salesman Problem.  This problem of trying to find an efficient tour of a given list of locations is one that is researched by logistics companies like FedEx and UPS.  A variety of algorithms exist to try to produce optimal, or near-optimal, solutions to these types of problems.  One such method is to use what are known as genetic algorithms.  These algorithms mimic natural selection in that a variety of solutions are produced (called a population) and their tour length (called their fitness) are calculated.  A solution for this problem is just a sequence of attractions in the order that they are visited (called a tour).  Solutions are then subjected to one of two types of operations to produce new, child solutions.  The first type of operation is called a mutator.  These operators take a member of the population and augment it in some way, such as switching the order in which you visit two (or more) attractions.  The second type of operation is called a crossover operator.  These operators take two members of the population and produce a child that resembles both parents.  For instance, a crossover operator might take two members of the population and find the attractions that are sequenced in a common position in both parents and include those attractions in those positions in the child.  The remaining attractions are then randomly placed in the remaining sequence positions in the child.  Every time a child is produced its fitness is calculated and if it is better fit than the least-fit solution in the population, that child replaces the least-fit solution in the population.  These operations reoccur for a fixed number of iterations (usually quite large) and the most-fit solution from the population is chosen as the “optimal” solution. 
The winning group at the finish line and
home of Dole Whip, Aloha Isle.
The second project for the students in the course involved inventing mutators and crossovers for a genetic algorithm to find the optimal solution of an abbreviated Traveling Tourist Problem involving only ten rides.  In fact, the example mutation and crossover operators described above are ones that students came up with.  Here are examples of other inventive operators that the students generated.

Crossover Example
  1. Define Parent 1 as the parent with the single highest wait time.
  2. Find the sequenced attractions that match in P1 and P2.  Include these attractions in these sequenced slots in the child.  Then take P1’s highest non-matching wait time and swap it with other attractions until it is in the location in P2’s sequence of the highest non-matching wait time.
  3. Continue to find a nonmatching ride whose wait time is the highest and switch it with the lowest remaining wait time of the other parent. 
Mutator Example (Frame Shift)
Move an attraction from sequence spot j to sequence spot k and then shift all of the attractions in between sequence spots j and k one slot to the right or left depending on j’s relative position to k.

After running their genetic algorithms on the subset of rides that they were given, the group consisting of Johana, Mary Lib, Alyssa, and Molly found a tour that could be traversed in 284 minutes.  The sequence of attractions in this tour was
  1. Seven Dwarfs Mine Train
  2. Peter Pan's Flight
  3. Haunted Mansion
  4. Jungle Cruise
  5. Buzz Lightyear
  6. Dumbo
  7. Space Mountain
  8. Splash Mountain
  9. Pirates of the Caribbean
  10. Big Thunder Mountain Railroad
After studying these genetic algorithms, our group met with Len Testa, President of Touring Plans and co-author of The Unofficial Guide to Walt Disney World, which has sold more than 4 million copies worldwide.  Testa’s company, Touring Plans, employs an analytic approach to travel, helping its subscribers not only find good park tours, but also finding affordable options for park tickets, finding the quietest hotel rooms, etc.  His company employs mathematicians, statisticians, and computer scientists to model and produce solutions to many problems related to travel.  Len spoke with our students about the evolutionary algorithms (such as genetic algorithms) that his company employ to produce tours for users in a quick amount of time.  The time that the students put into to developing an intuition about the problem and creating mutation and crossover operators paid off when they saw how Touring Plans employs these types of algorithms to produce solutions to real-world problems.  They came away with an appreciation for the mathematical sophistication that Touring Plans brings to their solution approaches.  For some students this was an experience that caused them to remark that they wished they had brought a resume to the talk to give to Testa.  For the professors, we give many thanks to Len Testa for inspiring a group of students to continue to develop their mathematical creativity and problem-solving skills to make a difference for others. 

Saturday, May 28, 2016

Day 18: Soarin' Through the Day

We're Soarin', Flyin'
Hi everyone, Caroline and Courtney here! Even though we had a late night last night celebrating Animal Kingdom's first night opening, we got up early for rope-drop at Epcot for one reason: the reopening of Soarin'. The popular simulation attraction has been closed for renovations, but reopened this weekend with an updated version of its former California-themed show. The final update will be titled Soarin' Over the World, and will showcase sights from around the world. Shoutout to Dr. Bouzarth for getting us FastPasses and noticing that it would be open today! We were able to ride the attraction once right when the park opened, and again using our FastPasses, and I was very impressed. While it isn't as "thrilling" as some other attractions, the entire simulation is beautifully done.
A selfie with some of the students before Soarin'
The Mouse Himself
In between our two Soarin' expeditions, we took a quick detour to the Character Spot in Epcot. We got to meet Mickey, Goofy, and Minnie, and loved getting to interact with the characters. Goofy seemed to particularly like one member of our group.

Goofy really like Mary Lib!

We made all the guys take a picture with Minnie!
One Day, Two Parks

After our flights at Epcot, we made the trip to Magic Kingdom so that one of our independent project groups could collect more data. When we arrived, my group (Caroline), ate a quick lunch at Casey's on Main Street before heading towards Liberty Square and Frontierland. After missing the showtime for the Hall of Presidents, Dr. Hutson thought it would be a good idea to take some of us to Country Bear Jamboree. I will only say that it was a memorable experience where we also got to see some of the earliest animatronics at Disney World. After helping the Fastpass group collect some data, a few other students and I went back to Main Street for some souvenir shopping.

My group (Courtney) grabbed some food at the Colombia Harbour House then headed to Big Thunder Mountain to gather some data. Since we were only focussed on one ride, not all twelve students were needed to collect data. Therefore, we decided to go to see The Enchanted Tiki Room for the first time this trip. There were some mixed reactions, especially since the song can get stuck in your head throughout the entire day. However, I personally believe that it is a classic that you have to do once every time you go to Disney.

Some Math with our Mouse
Back at the hotel, we began analyzing our data for our independent group projects. My group (Caroline) is looking at the Rock n Rollercoaster and Expedition Everest single rider lines. Disney utilized single rider lines to make their rides more efficient, as they can even out an odd party with an individual. We are trying to analyze their efficiency while also comparing the two lines. By counting party sizes as well as wait times for both of these attractions, we have been able to track the efficiency of the single rider line. We have established a hypothesis for how fast the single rider lines should be moving for each attraction, and plan on testing it tomorrow.

My group (Courtney) spent the past few days gathering data on the Disney characters guests can meet in each park. We continued to organize our data today by the 12 different characters that we observed. We arranged the data further by looking at the time characters spent with guests to analyze the number of autographs that the characters signed from 0 to 2 or more and how this affected the time they spent with each guest. Our second half of our project looks at the number of people a character can visit within 30 minutes. We recorded the party sizes seen by each of the 12 characters to find how many people each character could see a 30 minute time span. We are looking to determine whether the number that a Disney cast member gave us, which was 80 people in 30 minutes, could be correct.
We finally got a good group picture with Mickey!

Illuminated for the Last Time
For the last time, our group went to Epcot to enjoy a delicious dinner and fireworks. When we arrived at the park, some of us went souvenir shopping and exploring at our favorite pavilions, while others took the opportunity to journey to Mars one last time. We had a great dinner at Nine Dragons. Right after dinner, we caught our last viewing of Illuminations, the Epcot firework and light show. It was just as dazzling as it was the first time, and we left the park with nothing but great pictures and memories!
Written by:

Day 17: Just Look at the Time!

Posing together outside one of our
group's favorite rides, Tower of Terror. 
What do Midway Mania, Markov Chains, Mission Space, and matrices all have in common? They're all integral parts of our magical studies here at Math and the Mouse! Mickey and Minnie Mouse have helped us explore mutations, modeling, mapping, and more - you wouldn't believe how much math can be found from observing the Mary Poppins line, watching MuppetVision 3D, and even riding Mad Tea Party or exploring the Maharajah Jungle Trek! We've enjoyed all of our time and studies in each of the four parks (although, if they have to choose, Molly and McKenna say that their personal favorite park is Magic Kingdom) and it has certainly been a marvelous, mathemagical, and alliterative May X! And today's update on our group's latest adventures is brought to you by Maria and Mary Lib!

Hollywood Studios
This morning we arrived in Hollywood Studios for rope drop! We started our day off at Midway Mania and Tower of Terror, and then continued collecting data at Rock ‘n' Roller Coaster. As mentioned in previous blogs, a couple of the groups are interested in Rock ‘n' Roller Coaster for various research reasons: one group is looking at the efficiency and worth of the FastPass, while the other is concerned with the value of the single rider line. While standing outside the ride itself, we collected entrance and exit data in 15-minute intervals, which will help us determine arrival and departure rates of the ride. While in line, groups recorded data such as the times group members entered the ride, when the FastPass and Standby lines merged, non-single rider line party sizes, when group members boarded the ride, how far apart each consecutive boarding time was, and when each group member exited the ride.

We were so lucky to have had the opportunity to meet
 with a Disney engineer this morning!
After collecting data, we reconvened as a group in front of Rock 'n' Roller Coaster at 11:00 AM to meet with an electrical engineer for Disney that has a family connection to Furman. He talked to us about the mechanical operation and troubleshooting of two park headline attractions, Rock ‘n’ Roller Coaster and Tower of Terror, as well as a few others. Everything he discussed was very interesting, and one of the highlights of his talk was his discussion of the random sequencing of Tower of Terror and Star Tours. Although it’s not obvious, each ride on Tower of Terror and Star Tours is not the same every time. Tower of Terror has a set of possible drop and rise sequences, and one of these is randomly selected for an elevator each time it runs. In a similar manner, the ride sequence for Star Tours is randomized, where each ride includes four of the thirteen possible segments. The random sequencing of both attractions allows for a unique and surprising experience for guests, even if they have ridden the rides repeatedly. Just another example of Disney going above and beyond!

After meeting with our guest speaker, we left the parks and the professors treated us to lunch - the break from PB&Js was greatly appreciated by students! The Chipotle and Panera Bread near our hotel are within a few feet of each other, so we split up and reconvened back at the hotel to eat together.

The Physics Behind Disney World
This afternoon in class, we were able to look more closely at the application of science in Disney World; specifically, we learned more about the physics behind the park.  Dr. Bouzarth gave a very interesting presentation that overviewed some fundamentals of physics and ways that they apply to the operation of Disney - this connected very well to our session with the guest speaker this morning, as we were able to explore in even more depth several ideas that he had discussed.  In the context of discussing such ideas as force, energy, magnetism, and Newton's laws of motion, Dr. Bouzarth helped us to make connections between these concepts and the park operation.  For example, we discussed the Test Track ride in Epcot, which our guest speaker had told us was the fastest ride among the four Disney World parks, in light of the idea of energy transfer.  We also learned that Rock ‘n’ Roller Coaster (the second fastest ride in the park) is able to accelerate from 0 to 57 miles per hour in less than three seconds because it utilizes more than 100 electromagnets which are underneath the tracks.  The quick acceleration is one of the signature features of the ride and one that we have all experienced, and it was interesting to learn more about how it actually works!  We finished the lesson by reviewing limits, derivatives, and integrals (concepts that we had all covered in calculus) and their applications to calculating position, velocity, and acceleration of objects.   

Animal Kingdom After Dark!
After riding Everest seven times tonight, we became pros
at having fun with the coaster's camera!
After class this afternoon, we left the hotel at 4:30 PM and headed to Animal Kingdom - this was very exciting, as it had been almost a week since we were in this specific park.  Also, today was an unusually special day in the park - for the first time ever, Animal Kingdom was open until 11:00 PM (a big difference from its traditional 6:30 closing time)!  Tonight was also the unofficial premiere (or “soft opening”) of the Jungle Book show in Animal Kingdom, so there was an extra amount of excitement within the park this evening which only added to the fun of the atmosphere. Once we had arrived at the park, our entire class rode the Dinosaur ride, a thrill ride that takes groups of 12 on a dark and bumpy journey through a path filled with a variety of moving dinosaur figures.  All of the students in our class were able to fit on the same car, which turned out to be quite the adventure!  The ride, which can be fairly unnerving at the best of times, became extra scary today when our class got stuck on it, and we were in complete darkness for what seemed like quite a while (though probably was only about two minutes).  After this unexpected adventure, the group had free time to visit other attractions in the park and to continue collecting data at Expedition Everest for the single rider line project group. We also had evening FastPasses for the Kilamanjaro Safari; while we had done this safari once before in the daytime, it was an even more fun activity around dusk, and we were able to see a wide variety of animals.  

Tonight definitely had the shortest wait times for rides we have ever experienced in any of the parks, and as a result we were able to ride Kali River Rapids five times and Expedition Everest seven times over the course of the day!  Undoubtedly, one of the highlights of the evening was getting to ride Expedition Everest at night.  Although approximately half of the ride takes place indoors and the other half takes place outdoors, the darkness outside made the ride transitions feel even more seamless than usual - plus, it was extra fun to know that we were some of the first park visitors to get to ride the coaster at night! After closing out the evening by riding Everest as a class for five consecutive times, we headed out right at closing at 11:00 PM.

Looking Ahead
Tomorrow, we will be heading to Epcot at 9:00 AM for rope drop and will spend the afternoon continuing some FastPass data collection in Magic Kingdom.  On Sunday, we will be back in Animal Kingdom for part of the day - and we also have FastPasses to see the Jungle Book!  While we’re certainly sad that the trip is coming to a close, we are doing our best to enjoy every minute left and we know that there is definitely still much more excitement ahead!         

Written by: Maria Bartlett & Mary Lib Saine

Thursday, May 26, 2016

Day 16: Happy Happy Birthday

Hey guys, its Alyssa and Zack blogging our way through day 16 of our 21 day adventure. Today we had some choices for our morning activities (Animal Kingdom or sleeping), a birthday party, and spent the night in Hollywood Studios.

Morning Choices

This morning our group had the choice to be early birds and go to Animal Kingdom for rope drop or to act like Sleepy at the hotel.

We both chose to arrive at rope drop, we saw the pre-show for opening the park where a flock of brightly colorful parrots flew over us. We were able to ride Expedition Everest three times, Primeval Whirl, and Dinosaur in about an hour and a half. Time well spent if you ask us! Three of the four students that chose to go to the park this morning are working on the single rider project, collecting data to compare the single rider lines of Expedition Everest in Animal Kingdom and Rock 'n' Roller Coaster in Hollywood Studios. We found that Everest's single rider line is easily observable while you are in it and we gathered a large number of data points to use in our project.

Birthday Cake Time!

After our morning adventure it was time to celebrate Dr. Bouzarth’s son’s birthday! William turned a whopping four years old today, and we had a Cars themed birthday bash full of cake, gifts, and festive party hats.

After the party we met to sort through all the data we had been collecting for the past few days. Each group met to evaluate the data they had, look for potential anomalies or patterns, and establish marching orders for tonight in Hollywood Studios. 

Our group is still playing with different hypotheses we might test once we finish data collection. One thing we've found interesting is that Rock 'n' Roller Coaster and Expedition Everest both have two people per row, but the single rider lines move at different speeds. There are many obvious reasons, such as larger train capacity at Everest, but it is evident that Rock 'n' Roller Coaster's single rider line takes more time to go through.

Hollywood Studios

After we made it to Hollywood Studios, project groups split up to collect data in the park or ride a few rides before dinner at Backlot Express. Dr. Harris and Dr. Hutson tried out the newly opened third track on Toy Story Mania and gave positive reviews of it. The FastPass project group worked on Rock 'n' Roller Coaster, collecting data on the relative speeds of the FastPass and standby lines and the number of riders entering each line. Working on the character meet project, the third group of students gathered data from the Disney Junior characters.

We met for dinner at Backlot Express where I (Alyssa) got the opportunity to fight the dark side by eating a Darth Vader waffle. After dinner we split up again to collect data and ride some more attractions. Our group worked on counting party sizes at Rock 'n' Roller Coaster. I (Alyssa) also ran into one of my Furman friends Elise, who went to all four parks in one day! 

Since Hollywood Studios closed at 8:30, we had time to stop at Twistee Treat and eat some delicious ice cream. We returned to the hotel with enough time to enjoy the pool before resting up for the fun that awaits us tomorrow. We are headed right back to Hollywood Studios at rope drop for data collection and a guest speaker!

Sitting in the (medium sized) giant chair.

Written By: Alyssa Ciurlik and Zack Miller

Day 15: Spy Kids

Hi everyone! It’s Lindsay and McKenna with your day 15 blog post. It’s hard to believe that we only have a week left! 

Morning of Math
We started off this morning with another class in Dr. Hutson and Dr. Harris’s hotel room. The morning’s subject was hypothesis testing. This is something all of us do every day, although we may not be aware of it or be making any explicit calculations. Dr. Harris introduced the concept by playing a game with cards. Zack picked 10 cards from a deck, one at a time, to see how many red cards he would draw. We were all surprised when the first four cards he drew were red, and by the 6th or 7th red card we were all very suspicious. After Zack had drawn his tenth red card in a row, Dr. Harris revealed to us that all of the cards in the deck except for one were red.

Our suspicion of Dr. Harris’s deck is an example of using hypothesis testing. We started off with the assumption that half the cards in the deck were red and half were black. If this assumption were true, the likelihood of Zack drawing all red cards would have been extremely low (a 1 in 1024 chance). Statistical testing follows a similar method. We first start off with a “null hypothesis.” In the example from this morning, the null hypothesis was that the deck contained half red cards and half black cards. If the analysis makes it very unlikely that the null hypothesis is true, we reject the null hypothesis.

Lunch with Lara Larberg
After class, we headed to Pammie’s Sammies for lunch and a meeting with Furman alumna, Lara Larberg. Lara works for Universal Studios, and while the May X is called “Math and the Mouse,” we thought it would be really cool to sneak over to the “other side” to see how she uses math in her job at Universal. Lara is the Assistant Project Manager for Universal, so basically she manages over twenty interactive effects. Her most recent project is Volcano Bay, which will be opening in 2017 in Orlando. Lara graduated summa cum laude from Furman in 2006 with degrees in music and sociology. She also had a non-degreed focus and passion for theatre. It was actually her involvement with the Pauper Players that she credits for propelling her into her career.  Lara couldn’t stress enough how important her Furman education was for getting her to where she is today. She noted that although it may not seem like she is using her two degrees specifically, she is using all of the skills and connections she acquired at Furman. Furthermore, she was also quick to point out that even though she started working more with the creative side of things, she now works very closely with industrial engineers. Her work combines art and math to produce an awesome interactive experience.

Projects at the Park
After our meeting, we headed to Magic Kingdom to do a bit of spying, otherwise known as more data collection. As yesterday’s blog post mentioned, we all spent some time making observations about several characters. Today, we were able to split off into our groups to focus on our particular topics.

My (Lindsay), Mary Lib, Molly, and Maria’s group is comparing FastPass+ lines to the regular standby lines. We want to determine whether getting a FastPass actually saves you a significant amount of time. To do this, we are collecting data from the three Mountains in Magic Kingdom—Big Thunder Mountain, Splash Mountain, and Space Mountain. Since we won’t be going back to Magic Kingdom again until Tuesday (our last day!) today was our only chance to collect data. Luckily, the other groups were very supportive and helped us collected data. We collected many types of data, but my personal favorite was counting the number of people entering and exiting the line. I’m sure we all looked very suspicious sitting by ride entrances and exits counting people walking by and scribbling in notepads.

Like Johanna yesterday, I (McKenna) am in “the character group.” While the data we were gathering was the same as yesterday (number of families in line, number who entered and exited, time spent by the character with each family, and number of autographs per family), the characters were not. Today, we had the opportunity to observe Peter Pan and Aurora.

Magical Memories
After we finished meeting those characters, we took a detour to see Winnie the Pooh and Tigger, for my own personal benefit. When I was just over a year old, I went to Disney World for the first time. I had already developed an affinity for Tigger, so when I saw the long line in front of me, I just couldn’t handle it. I had to see Tigger IMMEDIATELY. I ran away from my parents, skipped all of the other people in line, and attached myself to Tigger’s leg. Since then, Tigger has remained one of my favorite characters, and I have gotten a picture with him every time. This time, I was able to tell Tigger the story of my toddler mischief, and he decided that it was his turn to attach himself to me and not let go! Mary Lib also recreated some childhood memories today. Not only did she ride Barnstormer again, but she also wore the same exact shirt that she wore while riding Barnstormer—twelve years later!

Fireworks Finale
By ten o’clock we were all finishing up with data collection and were able to catch Magic Kingdom’s end of the night fireworks show, “Wishes.” The fireworks at Disney are spectacular, probably some of the best in the world. Though we had all seen the fireworks show multiple times from the Big Thunder Mountain Railroad roller coaster, for many in the group (including the two of us) this was our first time watching the show from Main Street. The night ended with a special treat: a projection show on Cinderella’s Castle. Clips from Disney films, including classics like the Lion King and newer films like Frozen, were projected onto the castle, accompanied by music and fireworks. It was the perfect ending to another great day of math and magic.

Written by: Lindsay Eddy and McKenna Luzynski

Wednesday, May 25, 2016

Day 14: Don't Try This at Home

Aloha, everyone! Molly and Jamie here giving you the scoop on on our Day 14 of Math and the Mouse! We had an early morning in Epcot, did some data collection for our third project, ventured around Disney Springs, and ended the day with Disney's Spirit of Aloha Dinner Show at the Polynesian Resort.

We arrived at the park as soon as it opened for breakfast and a meeting with Len Testa, the co-author of The Unofficial Guide to Walt Disney World and president of, a website that creates personalized routes through different parks, including Disney and Universal. During his presentation he talked with us about many different resources that he and his team have come up with in order to create optimal touring plans. Since this is essentially a larger scale traveling salesman problem, like we learned about earlier in our trip, he uses evolutionary or genetic algorithms to provide optimal solutions. This part was very interesting to us because just yesterday we all presented our projects for which we had to use genetic algorithms of our own design to generate efficient routes that included ten rides in the Magic Kingdom. Touring Plans uses steps that are similar to those that we took in our own projects, however with more constraints and on a far greater scale. In addition, they are exploring other applications of various optimization methods, including the Disney Dining Plan and ticket purchases. Furthermore, he has recently extended his focus to the world of medicine by using his experience to guide doctors' prescriptions of medication to diabetes patients in an effort to minimize cost and maximize benefit to the patients.
Our group with Len Testa (second row, third from the right)
Data Collection
McKenna collected data on Alice and got a picture too!
Following our meeting with Len Testa, we split up into pairs for some data collection regarding character meet and greet lines. Each pair was assigned a character to collect data on for two 15 minute time periods. In those time periods we took note of how many families were in the line before we started our time, how many entered and exited, how long each family spent with the character, and how many autographs were given per group. At the end of our collection, we were all relieved that none of us were picked up by Disney Security since we were lingering around the character meeting spots collecting data. For our next project, this data will be used to analyze the efficiency of character meeting lines all over Disney.

Disney Springs!
After collecting data and lunch in World Showcase, we took our first trip to Disney Springs, formerly known as Downtown Disney. This area is similar to an outdoor mall filled with Disney merchandise along with well-known stores and some restaurants. Our favorite place in Disney Springs was the World of Disney, which is the largest merchandise store on Disney's property. If you are looking for something Disney, there is no better place to shop! Following an hour and a half of shopping, we all met back at Sprinkles Cupcakes for a sweet treat. We all enjoyed trying different ice creams, cupcakes, and shakes! As we were finishing our treats, it began to rain, so we decided to head back to the hotel for some free time before we had to leave for the Luau. 

Everyone with their Sprinkles Treats!
You won't like him when he's angry.
Spirit of Aloha Show!
For dinner we went to the Polynesian Resort for a Hawaiian Luau. There was a lively atmosphere with delicious food, live music, and traditional dances from around the Polynesian Islands; Molly was even called up to dance on stage. Our favorite part of the performance was the fire dance. Watching him throw his flaming stick up in the air and balancing them on his fight had us captivated on the edge of our seats. The whole experience was so fun and definitely worth seeing! 
The Fire Dance

Polynesian Dancers

Written By:

Tuesday, May 24, 2016

Time Flies When You're Having Fun... With Math!

Hello! It’s Johanna and Alex here. We can’t believe that we only have nine days left in our Math and the Mouse adventure and can't wait to share another day's worth.

Mind your P's and "Queues"

Johanna's group presenting their winning strategy
We were given a late start to the day, and while some of us used it to catch up on sleep, others used it to put the last touches on our second project. We started our day out by giving presentations of our genetic algorithm projects. My group (Johanna) had the shortest optimal path, making it around ten of Magic Kingdom’s biggest attractions in just 284 minutes. All the groups had fun coming up with different algorithms to try to figure out the best path. It was interesting to see that all three groups had some close similarities and big differences in their approaches. After our presentations, we learned about queuing theory, which is the mathematics behind lines at places as fantastic as Disney and as ordinary as grocery stores. Because there are so many opportunities to wait in line at Disney, it is directly applicable to what we have witnessed in the parks. Queuing theory basically uses throughput, total number of people in the line at the start of the period, and the probability of a person entering or exiting the line in that period to calculate the wait time. 

At the end of class, we all discussed our initial data collection from the parks yesterday. From this we brainstormed ideas for final projects. In the end, we split into three groups, each group focusing on a project idea of their choice. In some way or another, all of us are using queuing theory as part of our projects. Both of us are in the same group, and we are studying the wait lines for various Disney characters throughout the parks. We found interest in this project after noticing the high demand for some characters and how families (including ourselves) were turned away after a certain point. Other groups are studying single rider lines or how efficient the FastPass line is compared to the standby line. These projects are still in the works, so tune in later for more details!

Hollywood Studios

We took time from collecting data to take one goofy picture
In the afternoon, the group headed to Hollywood Studios for more data collection and a little free time. At the beginning, many of us split up in the single rider line at Rock 'n' Roller Coaster to collect data. Some data we wrote down in line were the actual wait time in the single rider line (from start to finish) and the party numbers going on to the ride. While many of us got great data (some of us went through multiple times), the group didn't let our FastPasses go to waste! Today we used FastPasses for Rock 'n' Roller Coaster, Tower of Terror, and Star Tours, all of the group's favorites. 

I (Johanna) along with three others in our group had a very eclectic afternoon. After riding Rock 'n' Roller Coaster, we collected queuing data on Sophia the First and Jake the Neverland Pirate in the Disney Junior section of Hollywood Studios. We spent a relaxing afternoon wandering around the park, going through all the gift shops to find souvenirs for our families. We also rode Toy Story Mania and saw The Voyage of the Little Mermaid, where I discovered that Ursula is just as terrifying now as she was when I was little. 

Some of the best ice cream sandwiches around!
Show ready with the Mickey hat atop my head

I (Alex) and a few others had an afternoon full of Disney Princesses! After collecting data and riding some of the thrill rides, we saw Beauty and the Beast Live, Frozen Sing-a-Long, and The Voyage of the Little Mermaid. It's not surprising that we were all singing classic Disney songs for the rest of the night. To top it off a few of us even treated ourselves to ice cream sandwiches which were bigger than our hands! We've made a goal to try and finish an entire one by the end of this trip (probably a lot easier said then done). I also used some of the afternoon to practice for my Fantasmic audition for Mickey Mouse, which has now become my career goal ever since seeing the show!

Look who spotted Chewbacca!

The Star Wars fanatics in the group used time after collecting data to explore the new Star Wars area and even get a photo with Chewbacca. We stayed in the park until closing and ended the day with watching the Star Wars themed fireworks show. Even after watching it again, the fireworks never cease to amaze us!

Big News for Dr. Bouzarth!

Congratulations to Dr. Bouzarth who received tenure today! In honor of her huge accomplishment, the group gave her a personalized movie clapperboard from Hollywood Studios so that she could remember the day. We all signed it at the park and presented it to her at the end of the evening. We are all so lucky to have amazing professors leading this experience and giving us memories of a lifetime.

Written By:

Alex Doxey
Johanna Swab

Monday, May 23, 2016

Markov Chains, Matrices, Mutations, Magic, and More!

Hi everyone, Maria and Courtney here! Today was another exciting day of both math and park exploration, and it included further study of probability concepts, project work, and time in Epcot and Hollywood Studios.  Here’s a quick look at all that we learned and did today:    

Markov Chains & Matrices
An example tree diagram that we studied
this morning in class.  The branch values
display the probabilities of each
event in the chain and the values to the
right show conditional probabilities.
Our class this morning provided a more in-depth look at probability, and today’s material focused most on a topic called Markov Chains. Essentially, a Markov Chain is a series of phases in which the outcome of each phase is one of a set number of possibilities, and the probability of a certain outcome occurring given the event of a prior state can be determined exclusively from the data from these two phases.  A Markov Chain qualifies as a stochastic process, meaning that at each phase of the chain there is more than one possible outcome, and the chosen outcome is variable.  

For example, this can be more easily visualized by studying a tree diagram; with this type of display, the tree begins with a single state (or event) and has a set number of offshoots of different possible states (see picture).  The probability that one event occurs given the previous state is calculated by multiplying the probability values along the two branches (this is known as conditional probability).  Additionally, we were able to utilize matrices in order to learn how to work with Markov Chains that have more states than can be easily displayed on a tree diagram, and we learned that matrix multiplication can be used to find the conditional probabilities of a Markov Chain.  Questions that Markov Chains may ask are ones like: “Given the fact that a person rides Rock ‘n' Roller Coaster once, what is the probability that that person gets back in line for the ride? What is the probability that they choose to ride another particular attraction in the park?”  These are the types of ideas Markov chains can describe and matrices can help us to solve!    

Genetic Algorithms
As the genetic project presentations are continuing to approach, each group spent several hours making progress on their respective projects this morning after class. To complete this project, we are using the same data that we were given for the traveling tourist problem and are asked to meet the same basic objective; however, this time we only need a path that completes 10 rides in the shortest time instead of 19 attractions. The time it takes to complete the path is called the "tour fitness", and the goal is to find a tour with as minimal a time as possible to complete all the attractions. The project requires that we first choose a set number of parent tours that represent different paths that could be potentially used to complete the 10 rides. We then use different operators to mutate a parent or cross over two parents to come up with a new child tour. Ideally, the child will have a better fitness than at least one of the parents in the population, and it will be able to replace the parent in the new population. After performing 30 mutations or crossovers (called iterations), we will have achieved a population of paths of the best fitness we have calculated, and the goal is to have a population of more fit tours than the ones with which we began.

Data Collection in the Parks   
There is always time for data collection in the parks, even on
Rock 'n' Roller Coaster!
As many of us began to express interest in using our own data for our future projects, the professors thought that today would be a good time to have us begin collecting data in the parks. For our final project, students will have the option to either work on a project involving queuing theory or a project of their own choosing. Based on the ideas that we brainstormed this morning, the professors decided that we would spend part of the day in Hollywood Studios instead of only in Epcot as we had previously planned.

Some of us have expressed interest in a project involving the fastpass line. How many people with fastpasses do Disney employees let onto the rides in comparison to the number of people in the standby line? Is it variable to the ride, the employee, or the time of day? To begin collecting data for this project, as we neared the front of a line, we attempted to count the number of people from each line that the employees let into the next segment of the line.  

Another set of students wants to look into how accurate Disney’s posted wait times are. Therefore, for each attraction we rode we recorded the ride, the time of day, the type of line, the posted wait time, the time we entered the line, and the time we got on the ride.

A third group of people is interested in the single rider line and measuring how beneficial the single rider line is for each of the rides that offer it. Test Track in Epcot, Rock ‘n’ Roller Coaster in Hollywood Studios, and Expedition Everest in Animal Kingdom all utilize a single rider line.

The simulator at Sum of All Thrills that visitors ride in order
to experience the coasters they have designed.
After project time at the hotel, our group loaded the van and headed to Epcot for the afternoon. As stated, the time in the park provided a valuable opportunity to begin the data collection for our upcoming projects.  Because official groups haven’t yet been decided on for each project, we all worked collectively on gathering data throughout the day to help with all of the potential future projects.  For example, I (Maria) worked on gathering data about single rider lines; specifically, at Test Track (and later at Rock ‘n’ Roller Coaster), I observed the group size of people that were let onto the rides consecutively (which is usually called out by the worker heading the line) and how often single riders are asked to board the ride.  I also worked on collecting data for the project that seeks to compare posted wait times with actual wait times; with a group of several other people, I visited multiple attractions in order to time my wait in each queue and compare them to the posted times.

During our time at Epcot, we were also able to visit an attraction called Sum of All Thrills for the first time, which involves pairs of people designing their own rollercoasters on a computer and entering a simulator to ride the coaster they have designed.  This provided a perfect example of the prevalence of math and science in the park, and as the ride voiceover reminded us before we worked on our designs: “Control the math, control the ride!”  When my group (Courtney) was designing our rollercoaster, we were able to choose what types of thrills we wanted the track to do, the height of the track, as well as the speed. A small crash robot on our design screen would test the ride to make sure it was safe. After our first try, the robot reminded us that our speed had to be compatible with the height of the track. We manipulated our design for another minute and discovered that the higher we made the track, the faster the coaster needed to travel. It is exciting to see how Disney makes an effort to not only give children a fun experience on a ride, but also make it an educational experience.

Before leaving Epcot, we got to eat dinner in the World Showcase - the variety of cuisine among all the countries in the park always makes for a delicious event!

Hollywood Studios

After our Epcot dinner, we reconvened as a group and headed toward Hollywood Studios. This is the first occasion that we have visited two parks in the same day, and the change provided a good way to continue to diversify our data collection.  Our group spread throughout the park and were able to visit and collect information from a number of attractions.  I (Maria) visited Rock ‘n’ Roller Coaster twice over the course of the evening; the first time, I went with a large group and we spread throughout the line in order to broaden the amount of consecutive data we could collect.  As explained above, we focused on recording the group sizes called onto the ride; by spreading ourselves throughout the ride, we could collect information about group sizes for a long line of people.  Many people from the group were also able to visit Tower of Terror, Star Tours, a Frozen Sing-Along - and Dr. Hutson even reached a new high score at Toy Story Midway Mania!  Of course, no evening at Disney World is complete without a fireworks show, and our group enjoyed getting to see the impressive Star Wars-themed fireworks display before leaving the park.

Tomorrow, each group will present its genetic algorithm project results in the morning, and after class we’ll head back to Hollywood Studios to continue our data collection!

Written By:

Maria & Courtney