Things to Make and Do in the Fourth Dimension: A Mathematician's Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More

by Matt Parker

Overview

A book from the stand-up mathematician that makes math fun again!

Math is boring, says the mathematician and comedian Matt Parker. Part of the problem may be the way the subject is taught, but it's also true that we all, to a greater or lesser extent, find math difficult and counterintuitive. This counterintuitiveness is actually part of the point, argues Parker: the extraordinary thing about math is that it allows us to access logic and ideas beyond what our brains can instinctively do—through its logical tools we are able to reach beyond our innate abilities and grasp more and more abstract concepts.

In the absorbing and exhilarating Things to Make and Do in the Fourth Dimension, Parker sets out to convince his readers to revisit the very math that put them off the subject as fourteen-year-olds. Starting with the foundations of math familiar from school (numbers, geometry, and algebra), he reveals how it is possible to climb all the way up to the topology and to four-dimensional shapes, and from there to infinity—and slightly beyond.

Both playful and sophisticated, Things to Make and Do in the Fourth Dimension is filled with captivating games and puzzles, a buffet of optional hands-on activities that entices us to take pleasure in math that is normally only available to those studying at a university level. Things to Make and Do in the Fourth Dimension invites us to re-learn much of what we missed in school and, this time, to be utterly enthralled by it.

Product Details

ISBN-13:	9780374535636
Publisher:	Farrar, Straus and Giroux
Publication date:	11/24/2015
Edition description:	Reprint
Pages:	480
Sales rank:	57,592
Product dimensions:	5.40(w) x 8.20(h) x 1.30(d)

About the Author

Matt Parker is a stand-up comedian and mathematician. He writes about math for The Guardian, has a math column in The Telegraph, is a regular panelist on Radio 4’s The Infinite Monkey Cage, has appeared in and worked on Five Greatest on the Discovery Channel, and has performed his math stand-up routines in front of audiences of thousands.

Read an Excerpt

Things to Make and Do in the Fourth

A Mathematician's Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More

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By Matt Parker

Farrar, Straus and Giroux

Copyright © 2015 Matt Parker
All rights reserved.
ISBN: 978-0-374-53563-6

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Zero

THE ZEROTH CHAPTER

Have a look around you and find a drinking vessel, like a pint glass or a coffee mug. Despite appearances, almost certainly the distance around the glass will be greater than its height. Something like a pint glass may look like it is definitely taller than it is round, but a standard UK pint glass is actually around 1.8 times greater in circumference than in height. A standard ‘tall’ takeaway cup from omnipresent high-street coffee shop Starbucks is actually 2.3 times further around, but yet they refuse my requests to rename it the ‘squat’.

Using this to your advantage is easy enough: when you are next drinking in a pub, café or whichever drinking establishment serves the sort of beverages you enjoy getting for free, bet someone that their drinking vessel is further around than it is high. If there is a ‘pot’ beer glass (the ones with handles) in the pub, or an obscenely large mug in the café, then you’re sorted: they are typically three times as far around as they are tall, so you can dramatically stack three of them and claim it is still further around than up. Producing a tape measure at this point may cause your victims to question the spontaneity of the whole exercise, so use a nearby straw, or its protective paper sleeve, as a makeshift ruler.

This works for all glasses, except for only the skinniest of champagne flutes. If you’d like to subtly check your drinking glass without arousing suspicion, try to wrap your hand all the way around it. Your fingers and thumb will not meet on the other side. Now, with your thumb and index finger, try to span the height of the glass. You will most likely succeed (or, at worst, come very close). This is a dramatic demonstration of how much shorter glasses are than they are around.

This is exactly the sort of maths I wish more people knew about: the surprising, the unexpected and, most importantly, the type that wins you free drinks. My goal in this book is to show people all the fun bits of mathematics. It’s a shame that most people think maths is just what they were subjected to at secondary school: it is so much more than that.

In the wrong situation, maths can indeed border on the tedious. Walk into a school at random in search of a maths class, and you’ll most likely find a room where the majority of the students are not excited. In the least. You will shortly be asked to leave the premises, and the police may even be called. You’re probably on some kind of list now. The point is, those students in the classroom are following in a long line of generation after generation of uninspired maths students. But there will be a few exceptions. Some of them will be loving maths and will go on to be mathematicians for the rest of their lives. What is it that they’re enjoying which everyone else is missing?

I was one of those students: I could see through the tedious exercises to the heart of maths, the logic behind it all. But I could sympathize with my fellow students, and specifically, the ‘sporty ones’. At school, I dreaded football drills in the same way that other people dreaded maths class. But I could see the purpose of all that messing around dribbling a football between traffic cones: you’re building up a basic repertoire of skills so that you’re better when it comes to an actual game of football. By the same token, I had an insight into why my sporty classmates hated maths: it’s counterproductive to make pupils practise the basic skills needed for maths but then not let them loose into the field of mathematics to have a play around.

That is what the maths kids knew. This is why people can make a career out of being a mathematician. If someone works in maths research, they’re not simply doing harder and harder sums, or longer divisions, as people imagine. That would be like a professional footballer merely getting faster at dribbling up the field. A professional mathematician is using the skills they’ve learned and the techniques they’ve honed to explore the field of mathematics and discover new things. They might be hunting for shapes in higher dimensions, trying to find new types of numbers, or exploring a world beyond infinity. They are not just practising arithmetic.

Herein lies the secret of mathematics: it’s one big game. Professional mathematicians are playing. This is the goal of this book: to open up this world and give you the freedom to play with maths. You too can feel like a premier-league mathematician, and if you were already one of those kids who embraced maths, there are still plenty of new things to discover. Everything here starts with things you can really make and do. You can build a 4D object, you can dissect counter-intuitive shapes and you can tie unbelievable knots. A book is also an amazing piece of technology with a state-of-the-art pause function. If you do want to stop and play around with a bit of maths for a while, you can. The book will sit here, the words static on the page, waiting for you to return.

All the most exciting bits of cutting-edge technology are mathematical at heart, from the number-crunching behind modern medicine to the equations that help carry text messages between mobile phones. But even technology which relies on bespoke mathematical techniques still ultimately rests on mathematics that was originally developed because a mathematician thought it would be fun to try to solve a puzzle.

This is the essence of mathematics. It is the pursuit of pattern and logic for their own sake; it is sating our playful curiosity. New mathematical discoveries may have countless practical applications – and we may owe our lives to them – but that’s rarely why they were discovered in the first place. As the Nobel Prize-winning physicist Richard Feynman allegedly said of his own subject: ‘Physics is a lot like sex; sure it has a practical use, but that’s not why we do it.’

I also hope to bring the maths you did learn at school into focus. Without it, all the other interesting bits of maths would not be within reach. Every student has vague memories of learning about the mathematical constant pi (roughly equal to 3.14), and some may recall that it is the ratio of the diameter to the circumference of a circle. It is because of pi that we know the distance around a glass is over three times greater than the distance across it. And it is the distance across which most people use when judging how big a glass is, forgetting to multiply by pi. This is more than memorizing a ratio, this is taking it for a test-run in the real world. Sadly, very little school maths focuses on how to win free drinks in a pub.

The reason that school maths cannot be completely dismissed is that the more exciting bits of mathematics rest on the less exciting bits. This is partly why some people think maths is so hard: they’ve missed a few vital steps along the way, and without them the higher ideas seem impossibly out of reach. But if they had tackled the subject one step at a time, in the correct order, it would have been fine.

No one bit of mathematics is that hard to master, but sometimes it’s important that you do things in the optimal order. Sure, getting to the top of a very high ladder may take a lot of effort from start to finish, but each individual rung is no more work to reach than the last one was. It’s the same with mathematics. Step by step, it’s great fun. If you understand prime numbers, then exploring prime knots is much easier. If you get to grips with 3D shapes first, then 4D shapes are not that intimidating. You can imagine all the chapters in this book as a structure, where each one rests upon several of the previous chapters.

You can even choose your path through the chapters, as long as, before tackling a later chapter, you’ve read all the ones that support it. As the book goes on, the chapters cover more advanced mathematics, the sorts of things you generally won’t hear about in a classroom. This can be daunting at first glance. But as long as you pass through them in the right order, by the time you reach the far-flung corners of mathematics, you’ll be fully equipped to enjoy all the delights and surprises there are on offer.

Above all else, remember that the motivation for climbing this structure should be merely to enjoy the view as you go. For too long, maths has been synonymous with education; it should be about fun and exploration. One puzzle at a time, one maths game after another, and soon we’ll be at the top, enjoying all the maths most people never know even exists. We’ll be able to play with things beyond normal human intuition. Mathematics allows access to the world of imaginary numbers, to shapes that exist only in 196,883 dimensions, and objects beyond infinity. From the fourth dimension to transcendental numbers, we’ll see it all.

Copyright © 2014 by Matt Parker

(Continues...)

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Excerpted from Things to Make and Do in the Fourth by Matt Parker. Copyright © 2015 Matt Parker. Excerpted by permission of Farrar, Straus and Giroux.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents

0 The Zeroth Chapter 0

1 Can You Digit? 7

2 Making Shapes 27

3 Be There and Be Square 47

4 Shape Shifting 64

5 Shapes: Now in 3D 87

6 Pack It Up, Pack It In 109

7 Prime Time 130

8 Knot a Problem 155

9 Just for Graphs 175

10 The Fourth Dimension 201

11 The Algorithm Method 224

12 How to Build a Computer 251

13 Number Mash-ups 275

14 Ridiculous Shapes 306

15 Higher Dimensions 325

16 Good Data Die Hard 346

17 Ridiculous Numbers 369

18 To Infinity and Beyond 399

n +1 The Subsequent Chapter 420

The Answers at the Back of the Book 424

Text and Image Credits 448

Acknowledgements 450

Editorial Reviews

“Things to Make and Do in the Fourth Dimension shows off math at its most playful and multifarious, ranging from classics like knot theory and ruler-and-compass constructions to more whimsical topics like the topology of beer logos and error-correcting scarves.” —Jordan Ellenberg, author of How to Not Be Wrong

“Matt Parker is some sort of unholy fusion of a prankster, wizard and brilliant nerd--maths is rarely this clever, funny and ever so slightly naughty.” —Adam Rutherford, author of Creation

“This is the best book on recreational mathematics since Martin Gardner's My Best Mathematical and Logic Puzzles.” —Library Journal

From the Publisher

★ 10/01/2014
If you don't believe that mathematics can be fun you should read this book. Parker, a mathematician and stand up comic, takes the reader on an entertaining voyage through many recreational topics. These include some more or less familiar aspects of number theory but also polygonal numbers, packing problems, graph theory, and computer logic and algorithms. The fascinating excursions into geometry and topology including discussions of noncircular wheels, knot theory, and the geometry of four-dimensional objects are especially noteworthy. Throughout the text, subjects are enhanced by clever problems that immediately grab one's attention. The writing style is friendly, humorous, and relaxed as the author reveals the problems' solutions. Parker makes it sound easy, even when it is not, and some of the material can be pretty heavy going. However, most important, he reveals the social aspects of the field, describing his interactions with other mathematicians as they bounce problems around, challenging one another's imaginations. VERDICT This is the best book on recreational mathematics since Martin Gardner's My Best Mathematical and Logic Puzzles.—Harold D. Shane, Mathematics Emeritus, Baruch Coll. Lib., CUNY

Library Journal

01/01/2015
Gr 8 Up—For readers who haven't balked at Stephen Hawkings's A Brief History of Time (Bantam, 1988) or Robert P. Crease and Alfred Scharff Goldhaber's The Quantum Moment (Norton, 2014), this sustained ramble through the thickets of mathematics offers similarly lucid but challenging insights into our universe's deeper patterns and principles. Building not on a chronological but a conceptual framework outlined in the opening chapter, "Zeroth Chapter," the author explores the historical evolution of mathematical tools, conjectures, and concepts from numbers and geometrical shapes to primes, knots, algorithms, multiple dimensions, computers from the Antikythera Mechanism on, probability, "ridiculous" (i.e., negative, transcendental, surreal, and the like) numbers, and infinities of diverse flavor. He adds lots of small diagrams and photos to illustrate his topics, but appends no index or, aside from follow-up comments on scattered posers, back matter. A stand-up comedian as well as a trained mathematician, Parker lightens the intellectual load considerably with zingers ("That's the problem with binary jokes: they either work or they don't") and everyday examples from bar bets to dating algorithms. Still, even confirmed math geeks will find this pleasurable but not casual reading.—John Peters, Children's Literature Consultant, New York City

School Library Journal

2014-10-01
Guardian and Telegraph writer and comedian Parker aims "to show people all the fun bits of mathematics."For starters, take out paper and pencil, compass, straight edge, maybe a balloon or a bag of oranges, because the author will challenge you to tackle puzzles, whether it's cutting a pizza in equal slices so some pieces never touch the center or passing a quarter through a nickel-size hole. Parker begins with the easier elements like number systems, primes and the polygons of Euclidean geometry. But his approach has the acceleration of a Ferrari, so readers are quickly racing into higher dimensional space. Parker explains how a square becomes a cube in 3-D and a hypercube (a tesseract) in four dimensions or a doughnut (a torus) becomes an object called a Klein bottle. This branch of math is topology, but in arriving there, Parker makes forays into subfields like tiling (think bathroom floors), packing (how to ship oranges efficiently) and knot theory. Some readers will lose their way—the visualizations alone are tough. Also, by this point, it's clear that the author does not aspire to create a math-for-dummies handbook. Instead, he provides one man's take on the history of math, emphasizing the puzzles that led to profound discoveries or to tantalizing conjectures that remain neither proved nor disproved. But this one man is also a dedicated denizen of the digital universe, and some of the best parts of the book are Parker's explanations of how computers work. This includes the feat in which he and math colleagues set up a field of thousands of dominoes to demonstrate how a computer adds two binary numbers. Parker goes on to explain how smartphones digitally code a photo and why a text sent across the globe arrives error-free despite all the relays along the way. Parker should be commended. He may not convert all readers to loving math, but he does provide a glimmer of understanding of how it works.

Kirkus Reviews