Week 07

Week 7: The Riemann Hypothesis by Valzorra

Overall, Week 7 was rather slow as it was Reading Week, which meant that most of the week was free from any workshops or lectures. I took this time to catch up on some of my project proposals, which have already been published, and to document bits of research I did that are quite significant to Project Proposal 4 in particular. I will take this moment to note that the research itself was done last week, however, I am only now getting about to documenting it. Hopefully, it will all make sense and click together once laid out. Additionally, I wanted to take the opportunity to summarise and reflect on what Andy said during our one to one. Now, without further ado, let’s get into the research and updates.

The Riemann Hypothesis

The Euler–Riemann zeta function plays a crucial role in modern analytical number theory and has a variety of applications spanning across fields such as Probability Theory (*wink wink*), Physics, and Statistics. It’s basically a function whose argument can be any complex number other than 1, and whose values are also complex. Euler first studied this function as a real variable and was able to work out its values at even positive integers. In fact, the first even positive value of the function provides a solution to the Basel Problem. Riemann then expanded on Euler’s analysis of the function and established a relationship between its zeros and the distribution of prime numbers. What’s more is that from the Euler-Riemann zeta function stem a variety of other number series such as the Dirichlet Series and L-functions.

The real part and the imaginary part of the Riemann Zeta Function at the critical line.

Now that I have provided a very basic overview of the Euler-Riemann Zeta Function, I can move on to briefly describing the famous Riemann Hypothesis. The Riemann Hypothesis proposes that the Euler-Riemann Zeta Function has all of its zeros at negative even integers, which are all trivial zeros, and complex numbers with real part equal to 1/2, which are the more exciting non-trivial zeros. As the Euler-Riemann Zeta Function is closely connected to the distribution of prime numbers, if this hypothesis is to be proven it would completely revolutionise the way we interpret modern number theory and pure mathematics. What’s important to note here is that if this unsolved problem is proven it could open a series of doors to new ways we can think about mathematics and apply them in the sciences and in invention. Solving this problem would change the way encryption and computer system security functions fundamentally, which may be a reason why some might not want a solution to be found.

The Riemann Hypothesis has a series of parallels to the world and events examined in Project Proposal 4. In that universe, the equivalent of the Riemann Hypothesis, is the problem of humans only being able to use one implant, which is determined genetically. Even though there are a total of seven Alteration Implants developed, no one has managed to crack how one individual can use multiple at the same time. That is the major unsolved mystery of the time and the narrative of the game would revolve around what it would be like if such an important problem were to be solved. Additionally, one reason the protagonist is called Zeta is to echo Riemann Zeta Function and how she essentially managed to solve her universe’s equivalent of that problem. More details on the specific narrative will follow soon, however, even thus far I thought it was a nice nod to this area of mathematics and the potential consequences it may have.

Riemann, 1859

Andy’s Feedback

The Friday of Week 7 was dedicated to one to one sessions with Andy, and I was quite excited to hear what he had to say. As I was most fond of that idea, I presented Project Proposal 4, the game involving dice and managing environments based on what rolls. I gave Andy a very brief overview of Zeta’s world, of her character, and of the main dice-controlling mechanic. I described the special abilities I thought would be appropriate and how one would be able to shift between them. When I was finished with my explanation, Andy seemed pleased with the idea and even mentioned he is not completely sure what to add on to it. He asked me what I was most concerned about at that stage and I mentioned that although I have figured out how the world would work, I have not yet designed an actual level. Andy did not seem incredibly concerned about this and reassured me by saying that it sounds like a game he would like to try. He also recommended a book called The Dice Man by Luke Rhinehart, which revolves around a man who makes most decisions in his life by the roll of a dice. Overall, I was rather pleased with the feedback as Andy was not really able to punch any holes through the idea, which hopefully means that it’s rather solid. I look forward to getting more feedback on it from Adam and my course mates.

Week 7: Project Proposal 4 by Valzorra

Background

The core mechanic, the environment, and the story would all be based on mathematics, making this game a passionate love letter to the field.

Coming from my research on Probability and Chance, as well as Matrices and Markov Chains, I sought out to come up with a game where chance and probability were essential to the main mechanics (for more information on the research itself, please refer to Week 1: A Welcome Return, Week 2: Calculus and Cancer, Week 3: Research on Mathematics, Week 3: The Matrix, Week 4: Markov Chains, Week 5: Mathematics Visualised). With this in mind, I instantly thought of dice, and how dice could potentially be used and controlled within a game environment. Some of the questions I was thinking of were how would different dice impact gameplay, what would be the statistical chances of landing on certain faces, etc. (for more on Fair Dice, please refer to Week 3: Research on Mathematics). Keeping this idea of chance, probability, and dice as central mechanics, and coming back to my goal of creating a fun and empowering experience, with a few cool notches to mathematics (for more on this revelation, please refer to Week 5: Just for Fun), I thought it would be really exciting to assign special abilities to each side of the dice. Additionally, using my research on perspective and concepts like Desargues’ Theorem, I thought it would be quite cool to base the environment on those geometric principles (for more on that, head to Week 4: Dimension). The puzzles and environment in this game could stem from geometric proofs of theorems. This would mean that the core mechanic, the environment, and the story which is loosely based on the Riemann-Zeta Hypothesis, would all be based on mathematics, thus making this game a humble love letter to the field. I have detailed the specifics of the project below.

Project Overview

The action takes place in the late twenty-first century in a world not too dissimilar to our own, where humanity has come up with one of its greatest inventions, the Alteration Implants. There are a multitude of Alteration Implants or Alters for short, all of which give their users special abilities, such as Telekinesis, Teleportation, and more. All of the Alteration Implants developed immensely benefit society and are used in the workforce constantly. For example, the transportation industry has never been more punctual since the introduction of the Teleportation Alters. Each individual is genetically susceptible to only one type of Alter, which means that one person can only use one ability based on their unique genetic code, much like Blood Types. Because of this biological predisposition, individuals can usually only work in professional fields related to their Alter. The entire society is structured upon this principle, and the great scientific mystery of this time is to try and figure out how to enable people to use more than one.

You play as Zeta, a bright and ambitious young woman who has managed to crack this mystery. Zeta is also a highly-skilled and compulsive gambler. She lives in this universe’s equivalent of Las Vegas and plays competitively at the largest tournaments in the city. However, as skilled as she is she could never defeat the top ten players in the city, which is why she was looking for a way to gain an edge. Through her advanced mathematics and engineering skills, she figured out how to infuse standard six-sided die with the Alteration Implants available in this universe. After this breakthrough, she could use the dice in tournaments and gain an advantage over her opponents. Having a Telekinetic Alteration Implant herself, Zeta can also change the way the dice rolls, having freedom to pick and choose which side it would land on. However, unfortunately one of the players eventually catches on to what she is doing, starting a thrilling chase and mystery for Zeta, that will test her wits and determination. More on the specific details of the narrative would follow in future developments and posts relating to this project.

In terms of gameplay, what makes this project exciting is the intricate use of the dice and the opportunity to control chance and incorporate that into problem-solving scenarios. Zeta will have the power to use a total of three die. Whenever the player wants to use their abilities from the dice, they will roll all three and receive a certain value for each. Each value on the die will correspond to an ability. Using her Telekinetic Powers, Zeta would be able to change the way one of the dice rolls. She may change only one dice in the beginning of the game as she would not be particularly skilled at using her Telekinesis. As the player progresses through the game, they would have further control and would be able to change two and maybe all three die. Once the player has decided which dice they would like to change the roll of, all abilities may be used in the order the player chooses. For example, if I rolled a 3, a 1, and a 2, then changed my 3 to a 6, I would end up with a 6, a 1, and a 2. At that stage, I would be able to pick the order in which to use these abilities take place and I would have to make my way through the level based on that selection. Zeta is a gambler, so her risk-taking nature is perfectly incorporated into the gameplay. Additionally, this encourages the player to make the most of a situation with the hand they were dealt, connecting to larger themes of free will and choice.

Concept Pieces

I began some work on concept pieces and mechanics for Zeta’s abilities last week during our Tech Workshop session (for more on that, have a look at Week 6: Exploring Ideas and Mechanics). I have chosen a series of abilities that could potentially make it to the game, predominantly based on what the needs of that society would be. The Alteration Implants would have been researched and developed in order to help mitigate and alleviate some common problems within society, or to make existing practices more efficient. That’s why I have strove to ensure that all abilities have a good reason to exist within this society, which is why people would have invested into their research and development. I already knew I wanted to have some form of Telekinesis in order to help Zeta move the dice. To come up with other appropriate abilities for that purpose, I did a bit of idea generation based on the question If you could have any superpower or special ability what would it be? After I had a list of abilities that answered that question, I then proceeded to filter those answers with the question, Which of these abilities could be commonly used and benefit society? After answering that, I was left with a list of seven abilities, specifically:

  1. Telekinetic - Service Industry, Nursing, Building, Implanting Alters, Military

  2. Electric - Engineering, Computer Science, Chemistry, Robotics, STEM

  3. Teleportation - Transportation, Law Enforcement, Military

  4. Defensive - Firefighters, Law Enforcement, Military, Mining, Dangerous Professions

  5. Light - Agriculture, Ecology, Show Business, Entertainment

  6. Sound - Navigation, Military, Show Business, Entertainment, Ultrasonic Engineering

  7. Stopping Time - Secret Services, Military, Law Enforcement, Security

Idea Generation for all of the abilities functioning within this society.

Idea Generation for all of the abilities functioning within this society.

After narrowing down what all of the abilities within this society would be, I made a few storyboard-like sketches to showcase these mechanics individually within the game. The illustrations below do not really show how they would work in combination with each other, but the main idea is that these would be used to navigate through the environment. Additionally, levels would be designed in such a way that a multitude of combinations of abilities could solve the problem, resulting in a series of different approaches to the same situation. I have also explored a few different versions of some of these abilities, as I have yet to fully make my mind up about how they would function within the game. In any case, this would be something to explore within my prototypes over the coming week.

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Thoughts and Reflection

So far, this is definitely my favourite idea as it seems the most fun, it connects the best to my research, and overall has the potential to achieve all of the goals I want it to. I have yet to decide whether this experience would take place in three-dimensional or two-dimensional space as both have their pros and cons. If I make this a two-dimensional game, it would incorporate a lot of the things I am interested in, such as perspective and what type of information gets lost within perspective. My only reservation about making it two-dimensional is that I am not fully certain how to make it an exciting puzzle-solving experience that does not entirely rely on traditional platforming techniques. Whereas if I were to make the project three-dimensional, I would be making the idea slightly more generic and it may lose some of its mathematical flare, however, it is practically guaranteed to work efficiently. Overall, I am quite confident I will be taking this idea forward, at this stage it is only a matter of time to try and figure out how to present it. Hopefully some feedback from the presentations next week will help me get that clarified.

Week 7: Project Proposal 3 by Valzorra

Background

During our lecture on Markov Chains, James mentioned that they are primarily used in the fields of Marketing, Software Engineering, and Computer Science and have not necessarily been explored to their full potential in video games. That’s why I would be interested in creating a game which heavily features Markov Chains and individualised AI in its algorithms. That way the player would have a unique experience with the game, as its AI will continuously change based on their actions. For example, enemies may record and observe how the player behaves in order to predict their movements and become better managing them, which would involve Machine Learning, an area that I find rather exciting. Similarly, if the player happens to consistently overpower challenges set out within the game, enemies may become more vigilant and careful around them. The project would be all about adaptability of the AI and crafting a personalised experience based on what the user does, not dissimilar thematically to Project Proposal 2. Although there could be potential ethical considerations that might prevent this from happening, implementing some of James’s work on emotive AI into such a project might result in an interesting and unpredictable experience.

Project Overview  

I have always been fascinated by Edgar Allan Poe’s The Raven, which I briefly analysed in Week 3: Research on Poetry, and I believe some of the poem’s themes would connect perfectly with the idea of an individualised, possibly emotive AI. It deals with universal themes like consciousness, handling emotion, overcoming challenges, grief, loss, whether or not the mind and senses can be trusted and many more. Those themes in combination with my desire to create individualised AI, made me come up with the idea of a horror experience loosely based on Poe’s work where the main antagonists are seemingly unpredictable NPCs, whose personalities and behaviour would be dictated by Markov Chains. Additionally, what would make this experience even more impactful would be to design it for Virtual Reality as the medium would increase player immersion, thus making the characters seem more real.

This exponentially chaotic experience is essentially personalised horror based on sophisticated AI and themes from Poe’s work.

The events of this experience would start in a modern-day hotel room, with no specific explanation of what is going on, however, the environmental would suggest that we have just checked in (open suitcases, clothes on the bed, and so on). As the player explores the empty hotel room, they will discover the room door to be open, leading to a long hallway. Down the corridor there would be an old and shaken man, pointing towards an open elevator at the end of the hallway. As that is the only clear direction to go in, the player would naturally enter the elevator. At this stage, the elevator doors would close and could lead the player across a journey through the different floors. Each floor would reveal a different part of the hotel which the player can explore, such as the reception area, a bar lounge, an entertainment centre, and more. What’s more is that each time the player enters a new floor, it will appear as though the overall style and time era the hotel is in has changed. This will add to the overall idea of increasing chaos, horror, and disorientation. This connects to the themes of consciousness and questioning one’s own sanity found in Poe’s work.

It is precisely within those strange environments that the player will encounter the two main entities in this experience, the lovers Lenore and Arcadia. Lenore and Arcadia are seemingly all powerful beings who have a ghost-like presence in every single room. They would be the agents of chaos within this world, turning the tides from sanity to insanity and madness. They are everywhere, the span across space, across time, and the player will know that they are more powerful than them. Lenore and Arcadia would both adapt to the environment based on what the player does. For example, if they run through the whole experience without stopping to look around, they may become more aggressive and grab the player’s attention. Whereas if the player is rather calm and takes the time to look around at all details within the space, Lenore and Arcadia may be more subtle, leaving smaller hints about their presence. This would all be based on the variety of player personality types for example the Four Bartle Types, namely Killers, Achievers, Explorers, and Socialisers and the Unified Model (for more information, please refer to this wonderful Gamasutra Article).

The Keirsey and Bartle Model for Player Personalities

The Keirsey and Bartle Model for Player Personalities

Chris Bateman's DGD1 Model, which may feature in parameters that would dictate AI reactions

Chris Bateman's DGD1 Model, which may feature in parameters that would dictate AI reactions

I have constructed a very loose narrative that will be primarily conveyed through the environmental design and occurring events. In short, Arcadia is a talented singer, dancer, and performer, who unfortunately was never given the opportunity to perform in front of an audience as various managers and organisers would continuously deny her access. That is why Lenore, who is Arcadia’s demon-like lover, has created this hotel that perpetually traps its visitors. That way every night there would be an ever-expanding audience for Arcadia, keeping her happy and fulfilled. In a way, it’s a rather romantic gesture. Simulating the cyclic nature of The Raven and the idea of no way to escape circumstances, at the end of this experience, it will be uncovered that the player has actually been the old and shaken man from the beginning, guiding an unaware guest. At this stage, the player will have a series of options to reflect upon. They will have to decide whether these supernatural and time-bending events actually occurred, whether they have been trapped in this hotel with no escape, whether they have been playing as a mentally ill man who’s consciousness and senses betray them, whether this has all been a dream, or whether this has been a constructed scenario in the imagination of the old man. Either way, this personalised horrific experience would make players question notions of sanity, of how much we can rely on the senses, of consciousness, all built upon sophisticated AI.

Concept Pieces

Without going into too much detail, I have taken the liberty of developing visuals and a storyboard for a few of the key scenes in order to better convey the feeling and setting of this experience. Below I have attached a few sketches of Lenore, the main villain within this experience. She is an elegant beautiful woman, who has incredible confidence in her own ability. She is entirely devoted to Arcadia and would go to extreme lengths to keep her happy.

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Below I have attached an environmental sketch of one of the areas within the hotel. I thought an impressive lounge/bar area would be rather exciting to look at and explore. It is based on a few night clubs and bar spaces that I found quite atmospheric and that could potentially feel both welcoming and frightening depending on the events that take place inside. I also quite enjoy the architectural choices, especially placing the bar itself in the middle of the room, with seating areas around the walls, which I have applied onto the storyboards. Additionally, this would be the main area Arcadia performs in, so it should be quite interesting to have a look around the space and try to interact with the guests that would be in a very similar position to the player. This would also provide dozens of opportunities to feed information to the AI and make them take adapt to player choices.

Below are the first few pages of storyboard based on a scene that would take place within this performance area. I have not finished the scene just yet as I am not still undecided on whether this project will be going forward or not. The text around the images should explain what is happening in the scene and the actions/movements taking place. Hopefully, this will convey a small part of what Lenore is like and how she may behave when interacting with the player.

Thoughts and Reflection

I am quite fond of this experience because it has the potential to be a thrilling VR adventure, built upon sophisticated AI and some of the world’s greatest literary work. Additionally, I quite like the idea of slow descend into chaos, up until the world of this hotel seems to be falling apart. All of this to conclude with the player questioning what has happened and whether they are actually trapped within the hotel or their own mind. However, although the foundations of the project are based entirely on mathematics and code, I do believe it veers away from the overall theme of Maths, Chance, and Probability. Therefore, I am not convinced I will be taking this project forward, but I would still like to hear what others have to say about it before I make my mind up. Until then, onward with ideation and prototyping.