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 6^th or 7^th 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

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.

Epcot

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

What Are the Odds?

We have crossed the halfway point here at Disney World on day 11 of our MayX. Blogging today are Mary Lib and Zack! We started our day later than normal, giving us a chance to make up for the sleep that we missed out on for our Keys to the Kingdom tour yesterday. After class and lunch we spent our afternoon in Animal Kingdom and are currently writing this blog from Panera at dinner.

Morning Class Time

In our class time this morning, we discussed binomial experiments, probability distributions, and applied the idea of conditional probability to the game Liars Dice which we played yesterday. 

A binomial experiment uses a binomial random variable and allows you to calculate the likelihood of an outcome after performing n-trials in which each results in a success or failure and the probability is fixed and independent for each trial.  This technique can give the probability of a coin landing on heads 5 times if you flip it 7 times. The expected value is the weighted average of outcomes which could tell you how many times you would expect heads if you flip a coin a certain number of times.

Related to the binomial random variable is the geometric random variable. It gives the probability of the first success happening on trial k. This can be used in Disney to see when the first person will give up on a line that isn't moving.

In our games of Liars Dice last night, we could see our dice and had to make a guess on how many of any number there were based on what we had in our hands. Conditional probabilities use this kind of information to calculate the probability of A, given B. Knowing our dice, conditional probability would allow us to make a more accurate bet on the total number of dice displaying a certain number.

Animal Kingdom

In the park today we had FastPasses for Finding Nemo the Musical, Expedition Everest, and DINOSAUR! 

Many of our group took the time to ride Expedition Everest, Primeval Whirl, and watch the It's Tough to be a Bug show before our FastPasses. The It's Tough to be a Bug show was a lot more interactive than any of us remembered. We were sprayed with bug spray, poked in the back by bees, and had bugs crawling on the seats under us. This show is actually inside the Tree of Life, so the line to get to it brings you close to the animals carved into the tree.

While a little cheesy at parts, Finding Nemo the Musical was a cool adaptation of the movie. The actors are much more talented than either of us - singing, dancing, and puppeteering - all at the same time. Our favorite scene was with Squirt the turtle who was flying and flipping over the stage. Thanks to Crush and Squirt, Mary Lib will have "Go With the Flow" stuck in her head for the next few days. 

We finished up our park time on Kali River Rapids. The warning that "you will get wet and may get soaked" was quite the understatement. Based on our experience, the warning should have just said, "Plan to get soaked." However, it was a nice refresher in the heat.

Tonight

Tonight our groups are working on our second project of the trip. On Monday groups tested strategies for our traveling tourist problem. This project asks us to design new solutions to the problem by using genetic algorithms. A genetic algorithm creates new tours based on your current best solutions to the problem. Each group has to create their own operators for creating new tours based on altering one parent tour or a crossover tour from two parents. 

Written by: Mary Lib Saine and Zack Miller

Day 10: A Whole New World

Keys to the Kingdom

Hi everyone! McKenna and Alyssa here, checking in for today’s blog post. This morning we had the opportunity to take the Keys to the Kingdom tour, a behind the scenes look at Magic Kingdom. This 4-hour tour really did open up “A Whole New World” to us. The tour focused on the 4 pillars that all Disney cast members uphold: safety, courtesy, show, and efficiency. While we thought that the tour would focus on the backstage operations that contribute to the safety and the efficiency of Walt Disney World, we were amazed by how every element of Walt Disney World is designed to enhance the Disney experience. In other words, it’s all about the show.

The coolest part of the tour was seeing all of the hidden details that contribute to the show. My (McKenna) personal favorite was learning about all of the names printed on the windows of the storefronts on Main Street. It was so awesome learning that each of the names was carefully selected to recognize people who had made significant contributions to the Walt Disney Company. These included family friends of the Disneys who helped with land acquisition for the new theme park and the best friend of both Walt and Roy Disney. The most recently added name was Meg Crofton. She retired as Disney World’s president June 1, 2015 and was honored in October. To keep with atmosphere of Main Street, each honoree is given a title or a time-period-appropriate business that corresponds with their contributions to the company.

My (Alyssa) favorite part of the tour was learning about the Roy and Walt’s partnership. Before today I did not know that Walt Disney had an older brother. It turns out not only did he have a brother in Roy, he had a best friend. Roy was an integral part in the making Walt’s visions for Disney World a reality. Since Walt passed away from complications from lung cancer before the park was opened, Roy was the one who took charge and made sure that not only did the park open on time, but that the project was also below budget. Our tour guide then went on to describe the opening day of Disney World during which Roy started to give the dedication, but was overcome with emotion at the loss of his brother. As a result he left the stage, and returned with Mickey, who he saw as the embodiment of Walt. 

As we moved through the park, and the utilidors underneath the park, it was evident that the history of the family and the company is closely linked with the showmanship and presentation of Walt Disney World today. Throughout the park, for instance, you can see examples of both earlier audio animatronics like the bears in the Country Bear Jamboree and current audio animatronics like those found on the Pirates of the Caribbean ride.

After riding Pirates of the Caribbean, we headed down to the utilidors. Unfortunately, we can’t really talk much about what we saw and what we were told because there is nothing more important than preserving the magic. However, we found that by the end of the tour, Disney World seemed even more magical to us because we discovered just a portion of the work that goes into putting on the spectacular show that is Magic Kingdom.

Probability and Liar’s Dice

However, since this May X is not entitled Mouse and the Mouse, at some point the fun had to stop at Magic Kingdom so that we could have a different kind of fun learning some math. Today’s class was a bit different. And so begins my (Alyssa) tale of sorrow and great loss. To introduce the new topic of probability, the class was divided into two groups and taught the game of Liar’s Dice, made famous by Pirates of the Caribbean.

This game is basically a more risky, dice version of the card game B.S. Each player guesses the total number of dice of a particular number held by the collective group of players. Each subsequent bet must increase in either dice value or number of dice. For example, if the person before you guesses there are at least 4 dice showing the number 5, you could bet that there are at least 5 dice showing the number 5 or 4 dice showing the number 6. When a player gives a bet that seems too high the next person can call “liar.” At this point, all players show their dice. If you are correct that the player’s guess was too high, he or she loses a die. If you guess incorrectly you suffer the loss. Once you lose all five of your starting dice, you are out.

Once the game started, one by one my worthy opponents fell. With four people left, I was in the lead with four dice. However, the tides quickly turned when the other players started teaming up against me. I would like to note, I played a polite and completely innocent game by rarely challenging the claim of the player before me. Despite their mischievous methods, I was able to use my "expansive" high school knowledge of probability, and my keen power to tell when people are bluffing to outlast both Molly and Dr. Hutson. However, since it was 3 versus 1 they whittled me down to two dice, and I could not recover my losses. While my blogging partner may seem docile in her account of Disney let me assure you that she is devious when it comes to betting and weighing her odds. She also has a knack for disarming opponents with talk of pizza!  So at the end of this game Maria, and unfortunately McKenna, won the highly coveted treats.

Just to defend myself (McKenna) a little bit, Alyssa played a phenomenal game. I do have a fair amount of experience with dice games, and we might have teamed up on her just a little bit! In the end, our friendship survived my victory, and my parents are even more concerned that I’ll run off to Las Vegas instead of finishing my education. For more on that, visit my bio page (http://mathandthemouse.blogspot.com/p/mckenna-luzynski.html).

After our strenuous class, we were given the rest of the evening to meet with our groups to work on our new projects. This time, we will be using genetic algorithms to create the optimal route to visit a certain list of attractions in Magic Kingdom. With the rest of our free time, we will be washing clothes and catching up on our sleep so that we can tackle tomorrow’s challenges—whether they come in the form of genetic algorithms or Liar’s Dice!

Written by:

Alyssa Ciurlik and McKenna Luzynski