What do you think?
Rate this book
Power-Up: Unlocking the Hidden Mathematics in Video Games
A fun and lively look at the mathematical ideas concealed in video games
Did you know that every time you pick up the controller to your PlayStation or Xbox, you are entering a game world steeped in mathematics? Power-Up reveals the hidden mathematics in many of today's most popular video games and explains why mathematical learning doesn't just happen in the classroom or from books―you're doing it without even realizing it when you play games on your cell phone.
In this lively and entertaining book, Matthew Lane discusses how gamers are engaging with the traveling salesman problem when they play Assassin's Creed , why it is mathematically impossible for Mario to jump through the Mushroom Kingdom in Super Mario Bros. , and how The Sims teaches us the mathematical costs of maintaining relationships. He looks at mathematical pursuit problems in classic games like Missile Command and Ms. Pac-Man , and how each time you play Tetris , you're grappling with one of the most famous unsolved problems in all of mathematics and computer science. Along the way, Lane discusses why Family Feud and Pictionary make for ho-hum video games, how realism in video games (or the lack of it) influences learning, what video games can teach us about the mathematics of voting, the mathematics of designing video games, and much more.
Power-Up shows how the world of video games is an unexpectedly rich medium for learning about the beautiful mathematical ideas that touch all aspects of our lives―including our virtual ones.
Did you know that every time you pick up the controller to your PlayStation or Xbox, you are entering a game world steeped in mathematics? Power-Up reveals the hidden mathematics in many of today's most popular video games and explains why mathematical learning doesn't just happen in the classroom or from books―you're doing it without even realizing it when you play games on your cell phone.
In this lively and entertaining book, Matthew Lane discusses how gamers are engaging with the traveling salesman problem when they play Assassin's Creed , why it is mathematically impossible for Mario to jump through the Mushroom Kingdom in Super Mario Bros. , and how The Sims teaches us the mathematical costs of maintaining relationships. He looks at mathematical pursuit problems in classic games like Missile Command and Ms. Pac-Man , and how each time you play Tetris , you're grappling with one of the most famous unsolved problems in all of mathematics and computer science. Along the way, Lane discusses why Family Feud and Pictionary make for ho-hum video games, how realism in video games (or the lack of it) influences learning, what video games can teach us about the mathematics of voting, the mathematics of designing video games, and much more.
Power-Up shows how the world of video games is an unexpectedly rich medium for learning about the beautiful mathematical ideas that touch all aspects of our lives―including our virtual ones.
264 pages, Hardcover
Published May 23, 2017
4 people are currently reading
110 people want to read
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 5 of 5 reviews
December 7, 2017
This is great! The author loves his video games and it really helps frame all the math in a fun environment. This book is a collection of his thoughts about and analysis of different aspects of video games in general. There is not so much logical progression throughout the chapters (some towards the end linking Friendship and Chaos, basically synonyms), but it's nicely organized into different buckets of mathematical goodies. The content smoothly glides between interesting concepts about video games and the math that can be extracted from them.
There were some of the familiar topics(at least in the speck of math that has been my experience) :
voting methods- I can never get enough of that. Arrow's Theorem should be taught in all classes/all grades from pre-K to retirement home. It would forcibly make the world a happier place (for me).
Chaos theory - One new idea to me was that a point bouncing around in a square container can have a path that goes through every point in the container once. And only once. It hurts.
Gaming complexity - P vs NP stuff. Games are hard.
Dimensions and Physics - I spent a couple weeks a few years back developing 4D chess with my brother. In the inaugural and only game, I think I won, but really we had no clue, and frankly were lucky to escape back to 3D reality with our faculties relatively intact (Every morning I still count the faces of a handy bedside cube to make sure they don't number more than 6). Apparently, others have made better games.
Some Ideas I'd never really thought of:
Repeating Questions - In games that have a question bank, after how long should you see a repeat? Turns out early on, so let's dump a few million more questions in the bank to make sure the impatient aren't burdened with review exercises. How many questions should there be in the bank so that the completionist can get through them all? Turns out just a few cards could make for a long time to completion (if questions come out randomly), so we might need to send a guy to the bank to retrieve those million questions with a shovel or bulldozer.
Knowing the Score - Some nice analysis of possible scores coming from different scoring systems and, more interesting, trying to recover the game given the score.
Measuring Friendship - I remember seeing the basic model of one lover whose ardour changes positively proportional to the other's affection (the more you love me, the more I love you), while the other's changes positively proportional to the first's disdain (Why don't you love me? I promise to be steadfastly devoted to you until the end of time! Or until you start to show a shadow of affection towards me. Whichever comes first). It was either in a college lecture or firsthand experience in some past relationship that I learned of this model. Well, he introduced some interesting modifications people have made to these models and they were pretty vibrant. I'll be trying out some of the models on my wife and me. Don't worry Jia Yan: the author might have discounted the models with love increasing unbounded as unrealistic, but I haven't ;)
And the coolest section, new/awesome to me.
The Thrill of the Chase - We get to look at a few interesting situations. As a warm-up, we see some nice bouncing kinematics with straight-faring green shells. He asks great guiding conceptual questions that go beyond the straight-laced equations.
The red shells ("heat seeking") were fascinating. I don't remember ever working with this kind of calculus, but we get to look at how to calculate the shell's path based on the target's path. The Addendum to the chapter, which explains the derivation of the trajectory, was a lot of fun. I don't usually write in my books, but pg 156 earned a "wow" for one step that was too dang insightful. It made me feel small in that cozy way that stars and the size of the universe can do for you.
Then he analyzes a missile defense game (Shoot them missiles, be quick! With what?! With bigger missiles!). We get to see different missile speed ratios and launch locations. The question is: is there a possible point of intersection? What if your commanding officer, not willing to gamble the lives of millions of civilians on your ability to shoot down a zero-dimensional missile of death and doom with your zero-dimensional defensive missile, allows you to use the good ol' splodin kind with a forgiving blast radius? I probably spent as long on this one chapter as the rest of the book. I'd love to see those ideas expanded in the sequel (this is a trilogy right?).
I had a lot of fun with this book. I like exploring the math I perceive in games and life, and this gave me some inspiration and direction.
There were some of the familiar topics(at least in the speck of math that has been my experience) :
voting methods- I can never get enough of that. Arrow's Theorem should be taught in all classes/all grades from pre-K to retirement home. It would forcibly make the world a happier place (for me).
Chaos theory - One new idea to me was that a point bouncing around in a square container can have a path that goes through every point in the container once. And only once. It hurts.
Gaming complexity - P vs NP stuff. Games are hard.
Dimensions and Physics - I spent a couple weeks a few years back developing 4D chess with my brother. In the inaugural and only game, I think I won, but really we had no clue, and frankly were lucky to escape back to 3D reality with our faculties relatively intact (Every morning I still count the faces of a handy bedside cube to make sure they don't number more than 6). Apparently, others have made better games.
Some Ideas I'd never really thought of:
Repeating Questions - In games that have a question bank, after how long should you see a repeat? Turns out early on, so let's dump a few million more questions in the bank to make sure the impatient aren't burdened with review exercises. How many questions should there be in the bank so that the completionist can get through them all? Turns out just a few cards could make for a long time to completion (if questions come out randomly), so we might need to send a guy to the bank to retrieve those million questions with a shovel or bulldozer.
Knowing the Score - Some nice analysis of possible scores coming from different scoring systems and, more interesting, trying to recover the game given the score.
Measuring Friendship - I remember seeing the basic model of one lover whose ardour changes positively proportional to the other's affection (the more you love me, the more I love you), while the other's changes positively proportional to the first's disdain (Why don't you love me? I promise to be steadfastly devoted to you until the end of time! Or until you start to show a shadow of affection towards me. Whichever comes first). It was either in a college lecture or firsthand experience in some past relationship that I learned of this model. Well, he introduced some interesting modifications people have made to these models and they were pretty vibrant. I'll be trying out some of the models on my wife and me. Don't worry Jia Yan: the author might have discounted the models with love increasing unbounded as unrealistic, but I haven't ;)
And the coolest section, new/awesome to me.
The Thrill of the Chase - We get to look at a few interesting situations. As a warm-up, we see some nice bouncing kinematics with straight-faring green shells. He asks great guiding conceptual questions that go beyond the straight-laced equations.
The red shells ("heat seeking") were fascinating. I don't remember ever working with this kind of calculus, but we get to look at how to calculate the shell's path based on the target's path. The Addendum to the chapter, which explains the derivation of the trajectory, was a lot of fun. I don't usually write in my books, but pg 156 earned a "wow" for one step that was too dang insightful. It made me feel small in that cozy way that stars and the size of the universe can do for you.
Then he analyzes a missile defense game (Shoot them missiles, be quick! With what?! With bigger missiles!). We get to see different missile speed ratios and launch locations. The question is: is there a possible point of intersection? What if your commanding officer, not willing to gamble the lives of millions of civilians on your ability to shoot down a zero-dimensional missile of death and doom with your zero-dimensional defensive missile, allows you to use the good ol' splodin kind with a forgiving blast radius? I probably spent as long on this one chapter as the rest of the book. I'd love to see those ideas expanded in the sequel (this is a trilogy right?).
I had a lot of fun with this book. I like exploring the math I perceive in games and life, and this gave me some inspiration and direction.
May 15, 2018
Loved this book! Great look at mathematical themes running through multiple games. However, if you’re a teacher, Chapter 9 is the chapter you need to read. Great ideas and very inspirational!
June 19, 2020
It took me a while to finally finish this, not for lack of interest but because of other commitments. I really enjoyed this authors deep plunge into mathematics within gaming. These examples, and mathematical ideas are a great interpretation of the games we all love to play! It’s got a great link to deep thinking and makes me think outside the systematic education lens.
June 11, 2020
A beautifully produced book with heavy pages and rich colors. The content is so-so. The author thinks video games are the key to all learning.
June 13, 2022
Not a worthwhile read
Displaying 1 - 5 of 5 reviews