Brian Kernighan on what we all need to know about computers

KernighanLaptops, tablets, cell phones, and smart watches: computers are inescapable. But even more are invisible, like those in appliances, cars, medical equipment, transportation systems, power grids, and weapons. We never see the myriad computers that quietly collect, share, and sometimes leak vast amounts of personal data about us, and often don’t consider the extent to which governments and companies increasingly monitor what we do. In Understanding the Digital World, Brian W. Kernighan explains, in clear terms, not only how computers and programming work, but also how computers influence our daily lives. Recently, Kernighan answered some questions about his new book.

Who is this book for? What kind of people are most likely to be interested?

BK: It’s a cliché, but it really is aimed at the proverbial “educated layman.” Everyone uses computers and phones for managing their lives and communicating with other people. So the book is for them. I do think that people who have some technical background will enjoy it, but will also find that it will help their less technical friends and family understand.

What’s the basic message of the book?

BK: Computers—laptops, desktops, tablets, phones, gadgets—are all around us. The Internet lets our computers communicate with us and with other computers all over the world. And there are billions of computers in infrastructure that we rely on without even realizing its existence. Computers and communications systems have changed our lives dramatically in the past couple of decades, and will continue to do so. So anyone who hopes to be at least somewhat informed ought to understand the basics of how such things work. One major concern has been the enormous increase in surveillance and a corresponding reduction in our personal privacy. We are under continuous monitoring by government agencies like the NSA in the United States and similar ones in other countries. At the same time, commercial interests track everything we do online and with our phones. Some of this is acceptable, but in my opinion, it’s gone way too far. It’s vital that we understand better what is being done and how to reduce the tracking and spying. The more we understand about how these systems work, the more we can defend ourselves, while still taking advantage of the many benefits they provide. For example, it’s quite possible to explore interesting and useful web sites without being continuously tracked. You don’t have to reveal everything about yourself to social networks. But you have to know something about how to set up some defenses. More generally, I’m trying to help the reader to reach a better than superficial understanding of how computers work, what software is and how it’s created, and how the Internet and the Web operate. Going just a little deeper into these is totally within the grasp of anyone. The more you know, the better off you will be; knowing even a little about these topics will put you ahead of the large majority of people, and will protect you from any number of foolish behaviors.

Can you give us an example of how to defend ourselves against tracking by web sites?

BK: Whenever you visit a web site, a record is made of your visit, often by dozens of systems that are collecting information that can be used for targeted advertising. It’s easy to reduce this kind of tracking by turning off third-party cookies and by installing some ad-blocking software. You can still use the primary site, but you don’t give away much if anything to the trackers, so the spread of information about you is more limited.

If I don’t care if companies know what sites I visit, why should I be worried?

BK: “I’ve got nothing to hide,” spoken by an individual, or “If you have nothing to hide, you have nothing to fear,” offered by a government, are pernicious ideas. They frame the discussion in such a way as to concede the point at the beginning. Of course you have nothing to hide. If that’s true, would you mind showing me your tax returns? How did you vote in the last election? What’s your salary? Could I have your social security number? Could you tell me who you’ve called in the past year? Of course not—most of your life is no one else’s business.

What’s the one thing that you would advise everyone to do right now to improve their online privacy and security?

BK: Just one thing? Learn more about how your computer and your phone work, how the Internet works, and how to use all of them wisely. But I would add some specific recommendations, all of which are easy and worthwhile. First, in your browser, install defensive extensions like like AdBlock and Ghostery, and turn off third-party cookies. This will take you less than ten minutes and will cut your exposure by at least a factor of ten. Second, make sure that your computer is backed up all the time; this protects you against hardware failure and your own mistakes (both of which are not uncommon), and also against ransomware (though that is much less a risk if you are alert and have turned on your defenses). Third, use different passwords for different sites; that way, if one account is compromised, others will not be. And don’t use your Facebook or Google account to log in to other sites; that increases your vulnerability and gives away information about you for minor convenience. Finally, be very wary about clicking on links in email that have even the faintest hint of something wrong. Phishing attacks are one of the most common ways that accounts are compromised and identities stolen.

KernighanBrian W. Kernighan is a professor in the Department of Computer Science at Princeton University. He is the coauthor of ten other books, including the computing classic The C Programming Language (Prentice Hall). He is the author of Understanding the Digital World: What You Need to Know about Computers, the Internet, Privacy, and Security.

Joshua Holden: The secrets behind secret messages

“Cryptography is all about secrets, and throughout most of its history the whole field has been shrouded in secrecy.  The result has been that just knowing about cryptography seems dangerous and even mystical.”

In The Mathematics of Secrets: Cryptography from Caesar Ciphers to Digital EncryptionJoshua Holden provides the mathematical principles behind ancient and modern cryptic codes and ciphers. Using famous ciphers such as the Caesar Cipher, Holden reveals the key mathematical idea behind each, revealing how such ciphers are made, and how they are broken.  Holden recently took the time to answer questions about his book and cryptography.

There are lots of interesting things related to secret messages to talk abouthistory, sociology, politics, military studies, technology. Why should people be interested in the mathematics of cryptography? 
JH: Modern cryptography is a science, and like all modern science it relies on mathematics.  If you want to really understand what modern cryptography can and can’t do you need to know something about that mathematical foundation. Otherwise you’re just taking someone’s word for whether messages are secure, and because of all those sociological and political factors that might not be a wise thing to do. Besides that, I think the particular kinds of mathematics used in cryptography are really pretty. 
What kinds of mathematics are used in modern cryptography? Do you have to have a Ph.D. in mathematics to understand it? 
JH: I once taught a class on cryptography in which I said that the prerequisite was high school algebra.  Probably I should have said that the prerequisite was high school algebra and a willingness to think hard about it.  Most (but not all) of the mathematics is of the sort often called “discrete.”  That means it deals with things you can count, like whole numbers and squares in a grid, and not with things like irrational numbers and curves in a plane.  There’s also a fair amount of statistics, especially in the codebreaking aspects of cryptography.  All of the mathematics in this book is accessible to college undergraduates and most of it is understandable by moderately advanced high school students who are willing to put in some time with it. 
What is one myth about cryptography that you would like to address? 
JH: Cryptography is all about secrets, and throughout most of its history the whole field has been shrouded in secrecy.  The result has been that just knowing about cryptography seems dangerous and even mystical. In the Renaissance it was associated with black magic and a famous book on cryptography was banned by the Catholic Church. At the same time, the Church was using cryptography to keep its own messages secret while revealing as little about its techniques as possible. Through most of history, in fact, cryptography was used largely by militaries and governments who felt that their methods should be hidden from the world at large. That began to be challenged in the 19th century when Auguste Kerckhoffs declared that a good cryptographic system should be secure with only the bare minimum of information kept secret. 
Nowadays we can relate this idea to the open-source software movement. When more people are allowed to hunt for “bugs” (that is, security failures) the quality of the overall system is likely to go up. Even governments are beginning to get on board with some of the systems they use, although most still keep their highest-level systems tightly classified. Some professional cryptographers still claim that the public can’t possibly understand enough modern cryptography to be useful. Instead of keeping their writings secret they deliberately make it hard for anyone outside the field to understand them. It’s true that a deep understanding of the field takes years of study, but I don’t believe that people should be discouraged from trying to understand the basics. 
I invented a secret code once that none of my friends could break. Is it worth any money? 
JH: Like many sorts of inventing, coming up with a cryptographic system looks easy at first.  Unlike most inventions, however, it’s not always obvious if a secret code doesn’t “work.” It’s easy to get into the mindset that there’s only one way to break a system so all you have to do is test that way.  Professional codebreakers know that on the contrary, there are no rules for what’s allowed in breaking codes. Often the methods for codebreaking with are totally unsuspected by the codemakers. My favorite involves putting a chip card, such as a credit card with a microchip, into a microwave oven and turning it on. Looking at the output of the card when bombarded 
by radiation could reveal information about the encrypted information on the card! 
That being said, many cryptographic systems throughout history have indeed been invented by amateurs, and many systems invented by professionals turned out to be insecure, sometimes laughably so. The moral is, don’t rely on your own judgment, anymore than you should in medical or legal matters. Get a second opinion from a professional you trustyour local university is a good place to start.   
A lot of news reports lately are saying that new kinds of computers are about to break all of the cryptography used on the Internet. Other reports say that criminals and terrorists using unbreakable cryptography are about to take over the Internet. Are we in big trouble? 
JH: Probably not. As you might expect, both of these claims have an element of truth to them, and both of them are frequently blown way out of proportion. A lot of experts do expect that a new type of computer that uses quantum mechanics will “soon” become a reality, although there is some disagreement about what “soon” means. In August 2015 the U.S. National Security Agency announced that it was planning to introduce a new list of cryptography methods that would resist quantum computers but it has not announced a timetable for the introduction. Government agencies are concerned about protecting data that might have to remain secure for decades into the future, so the NSA is trying to prepare now for computers that could still be 10 or 20 years into the future. 
In the meantime, should we worry about bad guys with unbreakable cryptography? It’s true that pretty much anyone in the world can now get a hold of software that, when used properly, is secure against any publicly known attacks. The key here is “when used properly. In addition to the things I mentioned above, professional codebreakers know that hardly any system is always used properly. And when a system is used improperly even once, that can give an experienced codebreaker the information they need to read all the messages sent with that system.  Law enforcement and national security personnel can put that together with information gathered in other waysurveillance, confidential informants, analysis of metadata and transmission characteristics, etc.and still have a potent tool against wrongdoers. 
There are a lot of difficult political questions about whether we should try to restrict the availability of strong encryption. On the flip side, there are questions about how much information law enforcement and security agencies should be able to gather. My book doesn’t directly address those questions, but I hope that it gives readers the tools to understand the capabilities of codemakers and codebreakers. Without that you really do the best job of answering those political questions.

Joshua Holden is professor of mathematics at the Rose-Hulman Institute of Technology in Terre Haute, IN. His most recent book is The Mathematics of Secrets: Cryptography from Caesar Ciphers to Digital Encryption.

Ben Peters: Announcing “555 Questions to Make Digital Keywords Harder”

This post appears concurrently at Culture Digitally.

I have relatives who joke that our family motto ought to be “if there’s a harder way, we’ll find it.” Like all jokes, this one rings true–at times painfully true. Everyone, of course, seeks convenience and yet we discover so often the opposite—new hardness, challenges, problems—that prove both uncomfortable and useful. Perhaps (if you’ll forgive the perverse suggestion!), critical digital teaching and scholarship should be harder as well.

How should we make digital technology criticism harder? How should critical engagement with tech discourse best carry on? What intellectual challenges does it currently face? What challenges must it face?

If you haven’t already seen it, Sara Watson released her new and significant report on the state of tech criticism last week. I am excited to announce the release of another kind of resource that just might help us keep after such questions—especially in our classrooms.

Please enjoy and share this freely downloadable, 35-page teaching resource now available on the Princeton University Press website:

“555 Questions to Make Digital Keywords Harder: A Teaching Resource for Digital Keywords: A Vocabulary of Information Society and Culture

555 questions image 2Use this document as you will. Many may use it to support preexisting courses; a bold few may organize critical responses to it. The questions that prompted its creation are straightforward: Is it possible to gather enough material to generate and sustain a semester of discussion in undergraduate and graduate courses based on or around the volume Digital Keywords: A Vocabulary of Information Society and Culture? Can this document, paired with that volume, sustain a stand-alone course? Whatever the answers, the document’s purpose is to complicate—not to simplify—keyword analysis for all. Keywords are supposed to be hard.

Each essay in the volume receives four sections of notes. (1) Background music suggests music that could be played in the classroom as students shuffle in and out of class; the music is meant to prompt students’ talking and thinking about the topic at hand. (2) What can we learn from the contributor listing? fosters the vital habit of learning to understand not only the reading content but also the author and his or her background. (3) Exercise suggests an activity to prompt discussion at the start of a lecture or seminar—and to be shared at the end of a class in order to encourage sustained thinking about a given keyword essay in the next class. Students may also be asked to bring prepared lists with them at the start of a class. Finally, (4) discussion prompts are meant to raise one thread of harder questions, not easy answers, for classroom debate. Most of these 555 questions are meant to model conversation pathways that elevate the theoretical stakes of thinking with and in language.

This document is in some ways an antidote to the editorial instinct to consolidate, polish, and finalize the topics raised in this volume. As the editor of this fine volume, I stand convinced that these twenty-five essays constitute state-of-the-art and definitive scholarly approaches to significant keywords. In fact it is because I am convinced of the volume’s virtues that I seek here to test them—and I know no better way to do that than to ask questions that unravel, challenge, and extend the threads of thought woven together in the essays themselves. I am sure I join my fellow contributors in inviting readers, students, and scholars to do the same with these essays.

“555 Questions” is also something of a methodological extension of Williams’s keywords project—that is, these 555 questions are meant not to provoke particular responses so much as, in admittedly sometimes slapdash and zigzag ways, to model the type of language-based discussion that all sensitive users of language may engage in on their own terms. In other words, most of the questions raised in these pages require little more than taking language and its consequences seriously—at least initially. I am sure I have not done so in these pages with any more fertility or force than others; nevertheless, I offer these pages as a working witness to the generative capabilities of language analysis to get along swimmingly with both the real-world empiricism of the social sciences and the textual commitments of the humanities. I have not questioned my own introduction to the volume, which I leave to others, although I’ll leave off with this quote from it:

“No one can escape keywords so deeply woven into the fabric of daily talk. Whatever our motivations we—as editor and contributors—have selected these keywords because we believe the world cannot proceed without them. We invite you to engage and to disagree. It is this ethic of critical inquiry we find most fruitful in Williams. Keyword analysis is bound to reward all those who take up Williams’s unmistakable invitation to all readers: Which words do unavoidably significant work in your life and the world, and why?”


Digital Keyword: “Hacker”

This post appears concurrently at Culture Digitally.

digital keywords peters jacketGabriella Coleman critiques the stereotype of a hacker as a white male libertarian. In its place, and through a rich history of its varied sources and expressions, she uncovers an underlying hacker commitment to what she calls “craft autonomy,” or the freedom to do technical work that motivates contemporary classes of computing experts. In this, Coleman’s essay engages in productive conversation with Christina Dunbar-Hester’s equally superb essay on geeks, Adam Fish’s mirror, and John Durham Peters’ cloud in the computer classes.

Hackers, among other actors in the technical classes, are not as we may have thought.

Gabriella Coleman: Hacker

This comment may have been adapted from the introduction to Benjamin Peters’ Digital Keywords: A Vocabulary of Information Society and Culture. 25% discount code in 2016: P06197

From “Brexit” to “dumpster fire”: Benjamin Peters on why digital keywords matter

petersIn the digital age, words are increasingly important, with some taking on entirely different meanings in the digital world. Benjamin Peters’ new book, Digital Keywords: A Vocabulary of Information Society & Culture  presents modern humans as linguistic creatures whose cultural, economic, political, and social relations are inseparable from these “keywords”. Recently, Peters took the time to answer some questions about the book:

Why digital keywords? Why now?

BP: “Brexit” and “Trumpmemtum.”

What are these but marked keywords that—together with, say, the trendy new phrase “dumpster fire”—trigger anxieties very much alive today? What work do such words do?

40 years ago, in 1976, the Welsh literary critic Raymond Williams published his classic Keywords: A Vocabulary of Culture and Society, establishing a critical and ongoing project for taking seriously the work of over 100 words in postindustrial Britain. This book, taking Williams as its (all too) timely inspiration, seeks to refresh the keywords project for English-language information societies and cultures worldwide.

This book seeks to change the conversation about the digital revolution of language at hand. The real world may not be made out of language but our access to it surely is. Modern humans are linguistic creatures: our cultural, economic, political, social, and other relations cannot be separated from the work our words do. And as everyone who has ever put pencil to paper knows, our words do not always oblige. This is especially true in the age of search. Digital keywords are both indispensable and tricky. They are ferociously important and often bite back.

Digital Keywords also seeks to offer a teachably different approach to “digital keywords” than currently championed, as a simple Google search will reveal, by the meddling reach of search engine optimizers (SEO). No older than the OJ Simpson trial and valued at no less than $65 billion (about the economy of Nebraska), the SEO industry is arguably the dominant approach to taking keywords seriously online at the moment: and yet reason strains at the massive capital flows that, say, the term “insurance” alone commands. SEO, with its shady markets of pay-per-click advertising and results manipulation, cannot be the best approach to working with digital keywords.

How else might we begin (again)?

I’m hooked. So which keywords does the book take up? And what makes those words key?

BP: Let me answer that in reverse. As editor I figured I had a choice: I could either start by choosing the words I thought were key for the information age and then find people to write about them, or I could invite the best contributors to the project and then let them choose their keywords. As it happens, this volume does both. On the one hand, the appendix lists well over 200 candidate keywords—from access to zoom—and we’ll be soliciting other keywords to that growing list on the scholarly blog Culture Digitally this July.

On the other hand, the 25 words featured in this book are “key” simply because the scholars that populate this book demonstrate that they are. That may sound tautological, but I actually uphold it as the high standard in keyword scholarship: a word is key because it does meaningful social work in our lives. It is the task of each essay to prove such work. The reader too is invited to take up Williams’ search for themselves and to test these essays accordingly: do they convince that these terms, once understood, are somehow tectonic to the modern information society and culture—and why or why not? Which words would you add—and why?

Fair enough. Can you give us a sample of what the authors claim about their keywords?

BP: Sure thing. The freely available extended introduction critically frames the project as a first step toward a grammar for understanding terministic technologies; it also summarizes each essay and draws critical connections between them, so I won’t do any of that here. Since the book itself is organized alphabetically by keyword, I’ll list the essays alphabetically by author last name. Rosemary Avance critically reclaims community online and off, Saugata Bhaduri risks the collective action baked into gaming, Sandra Braman tackles Williams’ keyword flow in information systems, Gabriella Coleman decrypts hackers and their crafts, Jeffrey Drouin takes on document surrogates in copy cultures, Christina Dunbar-Hester critically appraises the gender in computing geeks, Adam Fish reflects on what mirror is doing in data mirroring, Hope Forsyth grounds the online forum in ancient Rome, Bernard Geoghegan telegraphs back the origins of modern information, Tarleton Gillespie demystifies the omnipresent algorithm, Katherine D. Harris unpacks the digital archive, Nicholas A. John rethinks sharing cultures online, Christopher Kelty unearths root causes and consequences of participation, Rasmus Kleis Nielsen separates democracy from digital technologies, John Durham Peters seeds an outpouring of the cloud in cloud computing, Steven Schrag reworks memory and its mental and mechanical discontents, Stephanie Ricker Schulte repossesses personalization, Limor Shifman reanimates the meme online, Julia Sonnevend theorizes events beyond media, Jonathan Sterne and I, separately, deconstruct the analog and digital binary, Thomas Streeter pluralizes the internet, Ted Striphas rereads culture alongside technology after Williams, Fred Turner goes Puritan on the Silicon Valley prototype, and Guobin Yang launches the book with the de-radicalizing of activism online.

Who is the audience for this book? Who are you writing for?

BP: Students, scholars, and general interest readers interested in the weighty role of language in the age of search in particular and the current information age in general. Ideally, each essay will prove plain and short enough (average length 3000 words) to sustain the attention of the distracted undergraduate, substantial enough to enrich the graduate students, and pointed enough to provoke constructive criticism from the most experienced scholar. Of course this ideal will not hold uniformly across this or any other volume, but perhaps this group of contributors delivers on the whole, I must say, and that is enough for this editor.

I’m also excited to note that later this year Princeton University Press also plans to release for free download my teaching notes for this book. These notes aim to offer in an easily editable format enough material to teach the book as the main course text for a semester-long undergraduate or graduate course in media and communication studies. We hope this will benefit courses worldwide. Meanwhile, the scholarly blog Culture Digitally maintains, with Princeton University Press’ generous support, the early drafts of fair share of the published essays here.

Benjamin Peters is assistant professor of communication at the University of Tulsa in Tulsa, Oklahoma. He is also affiliated faculty at the Information Society Project at Yale Law School.




Language in the age of “search”

digital keywords peters jacketHow does language function in today’s information revolution? Keywords, and these days, “digital keywords” organize research, teaching, even thought itself. In Digital Keywords: A Vocabulary of Information Society & Culture, Benjamin Peters compiles essays on keywords by major digital media scholars, as well as an extensive list of these keywords themselves. Here’s a look at five words that have completely changed in today’s search-driven culture.

1. “Activism” has become one of the most popular terms found on the internet and it’s nearly decimated the use of “revolution”.

On the one hand, aspirations for political struggle continue to take both radical and nonradical forms . . . On the other hand, the history of activism and protest since the 1990s remains marked more by moderation than by radicalism in both Western democracies and other countries.

2. “Archive” is a word that has had its concept completely re-imagined as each person can individually decide what is important to them and should be saved permanently through digital means.

An archive is less about the printed word and can be about all facets of materiality, form, and its subsequent encoding–even the reader herself.

3. “Cloud” today does not only invoke images of nature, but streams of data held and protected somewhere.

Perhaps it is exactly their apparent blankness, mutability, and vanishing mode of being that makes them such a ripe canvas for human creativity and criticism.

4. “Meme” is an exception in that its meaning hasn’t changed so much as its relevance has. It is a word that was largely ignored when it was first conceived and now is in common use on the internet.

While researchers continue arguing about the usefulness of this construct, netizens have delivered their verdict. By the end of the first decade of the twenty-first century, the term Meme had become an integral part of online vernacular.

5. “Sharing” is a huge part of media and social relations on computers today, between friends or between millions of people who have never met each other except over the Internet. This concept has challenged concepts about copyright and how criminal activity can be conducted online.

However, while the term data sharing would not appear controversial in any way . . . File sharing . . . is not sharing, but rather theft.

Learn more about Digital Keywords this summer as we share a series of posts from Culture Digitally.

An interview with Nicholas Higham on The Princeton Companion to Applied Mathematics

Higham jacket

We are excited to be running a series of posts on applied mathematics by Nicholas Higham over the next few weeks. Higham is editor of The Princeton Companion to Applied Mathematics, new this month. Recently he took the time to answer some questions about the book, and where the field is headed. Read his popular first post on color in mathematics here.

What is Applied Mathematics?

NH: There isn’t any generally agreed definition, but I rather like Lord Rayleigh’s comment that applied mathematics is about using mathematics to solve real-world problems “neither seeking nor avoiding mathematical difficulties”. This means that in applied mathematics we don’t go out of our way to consider special cases that will never arise in practice, but equally we do not sidestep genuine difficulties.

What is the purpose of The Companion?

NH: The Companion is intended to give an overview of the main areas of applied mathematics, to give examples of particular problems and connections with other areas, and to explain what applied mathematicians do—which includes writing, teaching, and promoting mathematics as well as studying the subject. The coverage of the book is not meant to be exhaustive, but it is certainly very broad and I hope that everyone from undergraduate students and mathematically interested lay readers to professionals in mathematics and related subjects will find it useful.

What is an example of something aspect of applied mathematics that you’ve learned while editing the book?

NH: Applied mathematics is a big subject and so there are many articles on topics outside my particular areas of expertise. A good example concerns applications of computational fluid dynamics in sport. An article by Nicola Parolini and Alfio Quarteroni describes the mathematical modeling of yachts for the America’s cup. The designer wishes to minimize water resistance on the hull and maximize the thrust produced by the sails. Numerical computations allow designs to be simulated without building and testing them. The article also describes mathematical modeling of the hi-tech swimsuits that are now banned from competition. The model enables the benefit of the suits on race times to be estimated.

The Companion is about 1000 pages. How would advise people to read the book.

NH: The book has a logical structure, with eight parts ranging from introductory material in Part I, the main areas of applied mathematics in Part IV (the longest part), through to broader essays in the final part. It is a good idea to start by reading some of the articles in Part I, especially if you are less familiar with the subject. But a perfectly sensible alternative approach is to select articles of interest from the table of contents, read them, and follow cross-references. Or, you can just choose a random article and start reading—or simply follow interesting index entries! We worked very hard on the cross-references and index so an unstructured approach to reading should lead you around the book and allow you to discover a lot of relevant material.

What was the hardest thing about editing The Companion?

NH: The hardest aspect of the project was ensuring that it was completed in a reasonable time-frame. With 165 authors it’s hard to keep track of everything and to to ensure that drafts, revisions, and corrected proofs are delivered on time.

How much of the book did you write?

NH: I wrote about 100 of the 1000 pages. This was great fun, but it was some of the hardest writing I’ve done. The reason is partly that I was sometimes writing about topics that I don’t normally write about. But it was also because Companion articles are quite different from the papers I’m used to writing: they should have a minimal number of equations and formal statements of theorems, lots of diagrams and illustrations, and no citations (just Further Reading at the end of the article).

How did you choose the cover?

NH: We considered many different ideas. But after a lot of thought we settled on the motor boat picture, which captures the important topics of fluid mechanics, waves, and ocean, all of which are covered in the book in a number of articles.

What is the most unexpected article?

NH: Perhaps the article Mediated Mathematics: Representations of Mathematics in Popular Culture and Why These Matter by sociologist of education Heather Mendick. She discusses the way mathematics is represented in numerous TV shows and films.

What would you be doing if you hadn’t become a mathematician?

NH: I’d be playing a Hammond B3 organ in a jazz or blues band. I’m a keen musician and played keyboards semi-professionally for many years, starting in my teens.

How did you go about organizing the book?

NH: I recruited five Associate Editors with expertise in different areas and we met and planned out the eight parts of the book and the articles, along with a list of authors to invite. We looked for authors who are leading international experts in their field and are at the same time excellent expositors. Signing up the 165 authors was quite a long process. We were able to find authors for almost every article, so just a very small number had to be dropped. In some cases the authors suggested changes of content or emphasis that we were happy to agree with.

What range of readers is The Companion aimed at?

NH: The target audience for The Companion is very broad. It includes mathematicians at undergraduate level or above, students, researchers, and professionals in other subjects who use mathematics, and mathematically interested lay readers. Some articles will also be accessible to students studying mathematics at pre-university level.

Why not just seek information online? Why is there a need for a book?

NH: When Princeton University Press asked me to edit The Companion they told me that reference books still have great value. Many people have trouble navigating the vast amount of information available online and so the need for carefully curated thematic reference works, written by high calibre authors, is as great as ever. So PUP’s experience is that print is definitely not dead, and indeed my own experience is that I have many books in PDF form on my computer, but if I want to read them seriously I use a hard copy.

How have you ensured that the book will not go out of date quickly?

NH: This was a major consideration. This was a five and a half year project and we wanted to make sure that the book will still be relevant 10, 20, or 50 years from now. To do that we were careful to choose articles on topics that have proven long-term value and are not likely to be of short-term interest. This is not to say that we don’t cover some relatively new, hot topics. For example, there are articles on compressed sensing (recovering sparse, high-dimensional data from a small number of indirect measurements) and on cloaking (hiding an object from an observer who is using electromagnetic, or other, forms of imaging, as in Harry Potter or Romulan space ships in Star Trek), both of which are areas that have grown tremendously in the last decade.

What sort of overview of applied mathematics does the book give?

NH: Applied mathematics is a huge subject, so we cannot cover everything in 1000 pages. We have tried to include the main areas of research as well as key underlying concepts, key equations, function and laws, as well as lots of example of applied mathematics problems. The examples range from the flight of a golf ball, to robotics, to ranking web pages. We also cover the use of applied mathematics in other disciplines such as engineering, biology, computer science, and physics. Indeed the book also has a significant mathematical physics component.

Where is the field going?

NH: Prior to the 20th century, applied mathematics was driven by problems in astronomy and mechanics. In the 20th century physics became the main driver, with other areas such as biology, chemistry, economics, engineering, and medicine also providing many challenging mathematical problems from the 1950s onwards. With the massive and still growing amounts of data available to us in today’s digital society information, in its many guises, will be an increasingly important influence on applied mathematics in the 21st century.

To what extent does The Companion discuss the history of applied mathematics?

NH: We have an excellent 25-page article in Part I titled The History of Applied Mathematics by historians of mathematics June Barrow-Green and Reinhard Siegmund-Schultze. Many articles contain historical information and anecdotes. So while The Companion looks to the future it also gives an appreciation of the history of the subject.

How do you see the connections between applied mathematics and other disciplines developing?

NH: Applied mathematics is becoming ever more interdisciplinary. Many articles in The Companion illustrate this. For example,

  • various facets of imaging feature in several articles, including those on compressed sensing, medical imaging, radar, and airport baggage screening,
  • the article on max-plus algebras shows how what may seem like an esoteric area of pure mathematics has applications to all kinds of scheduling processes,
  • the article on the spread of infectious diseases shows the value of mathematical models in epidemiology,
  • several articles show how mathematics can be used to help understand the earth’s weather and climate, focusing on topics such as weather prediction, tsunamis, and sea ice.

What are you thoughts on the role of computing in applied mathematics?

NH: Computation has been a growing aspect of applied mathematics ever since the first stored program computer was invented here in Manchester. More and more it is the case that numerical computations and simulations are used in tandem with, or even in place of, the classical analysis that relies just on pen and paper. What I find particularly interesting is that while the needs of mathematics and of science in general have, naturally, influenced the development of computers and programming languages, there have been influences in the other direction. For example, the notation for the ceiling and floor functions that map a real number to the next larger or smaller integer, respectively, was first introduced in the programming language APL.

Of course numerical computations are expressed in terms of algorithms, and algorithms are ubiquitous in applied mathematics, and strongly represented in the book.

Do you have any views on ensuring the correctness of work in applied mathematics?

NH: As the problems we solve become every more complicated, and the computations we perform run for longer and longer, questions about the correctness of our results become more important. Applied mathematicians have always been good at estimating answers, perhaps by an asymptotic analysis, so we usually know roughly what the answer should look like and we may be able to spot gross errors. Several particular aspects of treating correctness are covered in The Companion.

Uncertainty quantification is about understanding how uncertainties in the data of a problem affect the solution. It’s particularly important because often we don’t know the problem data exactly—for example, in analyzing groundwater flow we don’t know the exact structure of what lies under the ground and so have to make statistical assumptions, and we want to know how these impact the computed flows.

A different aspect of correctness concerns the reproducibility of our computations and treats issues such as whether another scientist can reproduce our results and whether a computation on a high-performance computer will produce exactly the same answer when the computation is repeated.

All of these issues are covered in multiple articles in the book.

Nicholas J. Higham is the Richardson Professor of Applied Mathematics at The University of Manchester. Mark R. Dennis is professor of theoretical physics at the University of Bristol. Paul Glendinning is professor of applied mathematics at The University of Manchester. Paul A. Martin is professor of applied mathematics at the Colorado School of Mines. Fadil Santosa is professor of mathematics at the University of Minnesota. Jared Tanner is professor of the mathematics of information at the University of Oxford.

Alan Turing’s handwritten notebook brings $1 million at auction

turing jacket

Alan Turing: The Enigma

Old journals can be fascinating no matter who they belong to, but imagine looking over the old notebook of the mathematician credited with breaking German codes during WWII.

The Associated Press and other venues reported that a handwritten notebook by British code-breaker Alan Turing, subject of the 2014 Oscar-winning film “The Imitation Game,” a movie based on our book, Alan Turing: The Enigma, brought more than $1 million at auction from an anonymous buyer on Monday. Originally given to Turing’s mathematician-friend Robin Gandy, the notebooks are thought to be the only ones of their kind, and contain Turing’s early attempts to chart a universal language, a precursor to computer code. (In an interesting personal wrinkle, Gandy had used the blank pages for notes on his dreams, noting that, “It seems a suitable disguise to write in between these notes of Alan’s on notation, but possibly a little sinister; a dead father figure, some of whose thoughts I most completely inherited.”)

Andrew Hodges, author of Alan Turing: The Enigma, commented that “the notebook sheds more light on how Turing ‘remained committed to free-thinking work in pure mathematics.'” To learn more about the life of Turing, check out the book here.

Celebrating the genius of Alan Turing

Considered by many to be the father of computer science, Alan Turing is remembered today for his many contributions to the study of computers, artificial intelligence, and code breaking. On December 24, Queen Elizabeth II officially pardoned the late British mathematician and the action recalled attention to his groundbreaking work as well as his personal life. In 1952, Turing was charged with homosexuality, which was considered a criminal act in England at the time. Two years later, he took his own life. Today, mathematicians and computer scientists celebrate Turing’s broad contributions to his field.

For more on the life and work of Turing, check out these resources:


 Princeton University Press recently re-released Andrew Hodges’s biography of Alan Turing: Alan Turing: The Enigma — The Centenary Edition.

It is only a slight exaggeration to say that the British mathematician Alan Turing (1912-1954) saved the Allies from the Nazis, invented the computer and artificial intelligence, and anticipated gay liberation by decades–all before his suicide at age forty-one. This classic biography of the founder of computer science, reissued on the centenary of his birth with a substantial new preface by the author, is the definitive account of an extraordinary mind and life. A gripping story of mathematics, computers, cryptography, and homosexual persecution, Andrew Hodges’s acclaimed book captures both the inner and outer drama of Turing’s life.

Read Chapter One of the book here.


Turing earned his Ph.D. in mathematics from Princeton in 1938. Watch the video below to hear Andrew Appel (chair of the department of computer science at Princeton) discuss Turing’s legacy.

Andrew Appel on Alan Turing’s legacy
(Princeton School of Engineering and Applied Science)


Appel, a Princeton graduate, is the editor of another recent release by Princeton University Press, Alan Turing’s Systems of Logic: The Princeton Thesis.

Though less well known than his other work, Turing’s 1938 Princeton PhD thesis, “Systems of Logic Based on Ordinals,” which includes his notion of an oracle machine, has had a lasting influence on computer science and mathematics. This book presents a facsimile of the original typescript of the thesis along with essays by Andrew Appel and Solomon Feferman that explain its still-unfolding significance.

Preview the book by reading Chapter One.


Appel_AlanTuring's_F12Hodges_Alan Turing_F12