## Ken Steiglitz: It’s the Number of Zeroes that Counts

We present the third installment in a series by The Discrete Charm of the Machine author Ken Steiglitz. You can find the first post here and the second, here.

The scales of space and time in our universe; in everyday life we hang out very near the center of this picture: 1 meter and 1 second.

As we’ll see in The Discrete Charm the computer world is full of very big and very small numbers. For example, if your smartphone’s memory has a capacity of 32 GBytes, it means it can hold 32 billion bytes, or 32000000000 bytes. It’s awfully inconvenient and error-prone to count this many zeros, and it can get much worse, so scientists, who are used to dealing with very large and small numbers, just count the number of zeros. In this case the memory capacity is 3.2×1010 bytes. At the other extreme, pulses in an electronic circuit might occur at the rate of a billion per second, so the time between pulses is a billionth of a second, 0.000000001, a nanosecond, 1 × 10−9 seconds. In the time-honored scientific lingo, a factor of 10 is an “order of magnitude,” and back-of-the-envelope estimates often ignore factors of 2 or 3. What’s a factor of 2 or 3 between friends? What matters is the number of zeroes. In the last example, a nanosecond is 9 orders of magnitude smaller than a second.

Such big and small numbers also come up in discussing the size of transistors, the number of them that fit on a chip, the speed of communication on the internet in bits per second, and so on. The figure shows the range of magnitudes we’re ever likely to encounter when we discuss the sizes of things and the time that things take. At the low extremes I indicate the size of an electron and the time between the crests of gamma-ray waves, just about the highest frequency we ever encounter. The electron is about 6 orders of magnitude smaller than a typical virus (and a single transistor on a chip); the frequency of gamma rays is about 10 orders of magnitude faster than a gigahertz computer chip.

To this computer scientist a machine like an automobile is pretty boring. It runs only one program, or maybe two if you count forward and reverse gear. With few exceptions it has four wheels, one engine, one steering wheel—and all cars go about as fast as any other, if they can move in traffic at all. I could take my father’s 1941 Plymouth out for a spin today and hardly anyone would notice. It cost about \$845 in 1941 (for a four-door sedan), or about \$14,000 in today’s dollars. In other words, in our order-of-magnitude world, it is a product that is practically frozen in time. On the other hand, my obsolete and clumsy laptop beats the first computer I ever used by 5 orders of magnitude in speed and memory, and 4 orders of magnitude in weight and volume. If you want to talk money, I remember paying about 50¢ a byte for extra memory for a small laboratory computer in 1971—8 orders of magnitude more expensive than today, or maybe 9 if you take inflation into account.

The number of zeros is roughly the logarithm (base-10), and plots like the figure are said to have logarithmic scales. You can see them in the chapter on Moore’s law in The Discrete Charm, where I need them to get a manageable picture of just how much progress has been made in computer technology over the last few decades. The shrinkage in size and speedup has been, in fact, exponential with the years—which means constant-size hops in the figure, year by year. Anything less than exponential growth would slow to a crawl. This distinction between exponential and slower-than-exponential growth also plays a crucial role in studying the efficiency of computer algorithms, a favorite pursuit of theoretical computer scientists and a subject I take up towards the end of the book.

Counting zeroes lets us to fit the whole universe on a page.

Ken Steiglitz is professor emeritus of computer science and senior scholar at Princeton University. His books include The Discrete Charm of the MachineCombinatorial OptimizationA Digital Signal Processing Primer, and Snipers, Shills, and Sharks. He lives in Princeton, New Jersey.

## Ken Steiglitz: When Caruso’s Voice Became Immortal

We’re excited to introduce a new series from Ken Steiglitz, computer science professor at Princeton University and author of The Discrete Charm of the Machine, out now.

The first record to sell a million copies was Enrico Caruso’s 1904 recording of “Vesti la giubba.” There was nothing digital, or even electrical about it; it was a strictly mechanical affair. In those days musicians would huddle around a horn which collected their sound waves, and that energy was coupled mechanically to a diaphragm and then to a needle that traced the waveforms on a wax or metal-foil cylinder or disc. For many years even the playback was completely mechanical, with a spring-wound motor and a reverse acoustical system that sent the waveform from what was often a 78 rpm shellac disc to a needle, diaphragm, and horn. Caruso almost single-handedly started a cultural revolution as the first recording star and became a household name—and millionaire (in 1904 dollars)—in the process. All without the benefit of electricity, and certainly purely analog from start to finish. Digital sound recording for the masses was 80 years in the future.

Enrico Caruso drew this self portrait on April 11, 1902 to commemorate his first recordings for RCA Victor. The process was completely analog and mechanical. As you can see, Caruso sang into a horn; there were no microphones. [Public domain, from Wikimedia Commons]

The 1904 Caruso recording I mentioned is perhaps the most famous single side ever made and is readily available online. It was a sensation and music lovers who could afford it were happy to invest in the 78 rpm (or simply “78”) disc, not to mention the elaborate contraption that played it. In the early twentieth century a 78 cost about a dollar or so, but 1904 dollars were worth about 30 of today’s dollars, a steep price for 2 minutes and 28 seconds of sound full of hisses, pops, and crackles, and practically no bass or treble. In fact the disc surface noise in the versions you’re likely to hear today has been cleaned up and the sound quality greatly improved—by digital processing of course. But being able to hear Caruso in your living room was the sensation of the new century.The poor sound quality of early recordings was not the worst of it. That could be fixed, and eventually it was. The long-playing stereo record (now usually called just “vinyl”) made the 1960s and 70s the golden age of high fidelity, and the audiophile was born. I especially remember, for example, the remarkable sound of the Mercury Living Presence and Deutsche Grammophon labels. The market for high-quality home equipment boomed, and it was easy to spend thousands of dollars on the latest high-tech gear. But all was not well. The pressure of the stylus, usually diamond, on the vinyl disc wore both. There is about a half mile of groove on an LP record, and the stylus that tracks it has a very sharp, very hard tip; records wear out. Not as quickly as the shellac discs of the 20s and 30s, but they wear out.

The noise problem for analog recordings is exacerbated when many tracks are combined, a standard practice in studio work in the recording industry. Sound in analog form is just inherently fragile; its quality deteriorates every time it is copied or played back on a turntable or past a tape head.

Everything changed in 1982 with the introduction of the compact disc (CD), which was digital. Each CD holds about 400 million samples of a 74-minute stereo sound waveform, each sample represented by a 2-byte number (a byte is 8 bits). In this world those 800 million bytes, or 6.4 billion bits (zeros or ones) can be stored and copied forever, absolutely perfectly. Those 6.4 billion bits are quite safe for as long as our civilization endures.

There are 19th century tenors whose voices we will never hear. But Caruso, Corelli, Domingo, Pavarotti… their digital voices are truly immortal.

Ken Steiglitz is professor emeritus of computer science and senior scholar at Princeton University. His books include The Discrete Charm of the MachineCombinatorial OptimizationA Digital Signal Processing Primer, and Snipers, Shills, and Sharks. He lives in Princeton, New Jersey.

## Ken Steiglitz on The Discrete Charm of the Machine

A few short decades ago, we were informed by the smooth signals of analog television and radio; we communicated using our analog telephones; and we even computed with analog computers. Today our world is digital, built with zeros and ones. Why did this revolution occur? The Discrete Charm of the Machine explains, in an engaging and accessible manner, the varied physical and logical reasons behind this radical transformation. Ken Steiglitz examines why our information technology, the lifeblood of our civilization, became digital, and challenges us to think about where its future trajectory may lead.

What is the aim of the book?

The subtitle: To explain why the world became digital. Barely two generations ago our information machines—radio, TV, computers, telephones, phonographs, cameras—were analog. Information was represented by smoothly varying waves. Today all these devices are digital. Information is represented by bits, zeros and ones. We trace the reasons for this radical change, some based on fundamental physical principles, others on ideas from communication theory and computer science. At the end we arrive at the present age of the internet, dominated by digital communication, and finally greet the arrival of androids—the logical end of our current pursuit of artificial intelligence.

What role did war play in this transformation?

Sadly, World War II was a major impetus to many of the developments leading to the digital world, mainly because of the need for better methods for decrypting intercepted secret messages and more powerful computation for building the atomic bomb. The following Cold War just increased the pressure. Business applications of computers and then, of course, the personal computer opened the floodgates for the machines that are today never far from our fingertips.

How did you come to study this subject?

I lived it. As an electrical engineering undergraduate I used both analog and digital computers. My first summer job was programming one of the few digital computers in Manhattan at the time, the IBM 704. In graduate school I wrote my dissertation on the relationship between analog and digital signal processing and my research for the next twenty years or so concentrated on digital signal processing: using computers to process sound and images in digital form.

What physical theory played—and continues to play—a key role in the revolution?

Quantum mechanics, without a doubt. The theory explains the essential nature of noise, which is the natural enemy of analog information; it makes possible the shrinkage and speedup of our electronics (Moore’s law); and it introduces the possibility of an entirely new kind of computer, the quantum computer, which can transcend the power of today’s conventional machines. Quantum mechanics shows that many aspects of the world are essentially discrete in nature, and the change from the classical physics of the nineteenth century to the quantum mechanics of the twentieth is mirrored in the development of our digital information machines.

What mathematical theory plays a key role in understanding the limitations of computers?

Complexity theory and the idea of an intractable problem, as developed by computer scientists. This theme is explored in Part III, first in terms of analog computers, then using Alan Turing’s abstraction of digital computation, which we now call the Turing machine. This leads to the formulation of the most important open question of computer science, does P equal NP? If P equals NP it would mean that any problem where solutions can just be checked fast can be solved fast. This seems like asking a lot and, in fact, most computer scientists believe that P does not equal NP. Problems as hard as any in NP are called NP-complete. The point is that NP-complete problems, like the famous traveling problem, seem to be intrinsically difficult, and cracking any one of them cracks them all.  Their essential difficulty manifests itself, mysteriously, in many different ways in the analog and digital worlds, suggesting, perhaps, that there is an underlying physical law at work.

What important open question about physics (not mathematics) speaks to the relative power of digital and analog computers?

The extended Church-Turing thesis states that any reasonable computer can be simulated efficiently by a Turing machine. Informally, it means that no computer, even if analog, is more powerful (in an appropriately defined way) than the bare-boned, step-by-step, one-tape Turing machine. The question is open, but many computer scientists believe it to be true. This line of reasoning leads to an important conclusion: if the extended Church-Turing thesis is true, and if P is not equal to NP (which is widely believed), then the digital computer is all we need—Nature is not hiding any computational magic in the analog world.

What does all this have to do with artificial intelligence (AI)?

The brain uses information in both analog and digital form, and some have even suggested that it uses quantum computing. So, the argument goes, perhaps the brain has some special powers that cannot be captured by ordinary computers.

What does philosopher David Chalmers call the hard problem?

We finally reach—in the last chapter—the question of whether the androids we are building will ultimately be conscious. Chalmers calls this the hard problem, and some, including myself, think it unanswerable. An affirmative answer would have real and important consequences, despite the seemingly esoteric nature of the question. If machines can be conscious, and presumably also capable of suffering, then we have a moral responsibility to protect them, and—to put it in human terms—bring them up right. I propose that we must give the coming androids the benefit of the doubt; we owe them the same loving care that we as parents bestow on our biological offspring.

Where do we go from here?

A funny thing happens on the way from chapter 1 to 12. I begin with the modest plan of describing, in the simplest way I can, the ideas behind the analog-to-digital revolution.  We visit along the way some surprising tourist spots: the Antikythera mechanism, a 2000-year old analog computer built by the ancient Greeks; Jacquard’s embroidery machine with its breakthrough stored program; Ada Lovelace’s program for Babbage’s hypothetical computer, predating Alan Turing by a century; and B. F. Skinner’s pigeons trained in the manner of AI to be living smart bombs. We arrive at a collection of deep conjectures about the way the universe works and some challenging moral questions.

Ken Steiglitz is professor emeritus of computer science and senior scholar at Princeton University. His books include Combinatorial OptimizationA Digital Signal Processing Primer, and Snipers, Shills, and Sharks (Princeton). He lives in Princeton, New Jersey.

## Brian Kernighan on what we all need to know about computers

Laptops, 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?

Brian 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.

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

In 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.

# Click here to learn how to win copies of all 6 books

Giveaway ends February 7, 2014.

One of the questions we field most often is, “Why can’t I buy an electronic version of this bird book?” So we are delighted to announce that starting this month, several of our most popular birding and natural history titles are now available as ebooks through the iBooks store.

The books are affordable and look simply amazing in digital form — zoom in on Katrina Van Grouw’s intricate drawings of skeletons in The Unfeathered Bird, explore The Crossley ID Guide‘s layered plates in greater detail, or simply revel in the majestic photos and artwork in The World’s Rarest Birds.

To view sample pages and explore these titles further, please use these links:

 Birds of Peru This is easily one of our all-time best-selling field guides and this ebook features all of the same great information and illustrations as the print edition, but makes it more portable and easier to search. The Crossley ID Guide: Eastern Birds This has always been a book screaming for a digital edition. To say the plates in this book look incredible on a tablet would be a massive understatement– they are absolutely jaw-dropping beautiful. The Warbler Guide The complete text, photos, and sonograms at your fingertips in time for spring migration. Keep the print copy at home for reference and take this digital book into the field. The Unfeathered Bird Zooming in on the drawings reveals new details about structure, function, and evolution. Hawks at a Distance Even more useful now that you can zoom in and examine the profile and silhouette of the birds. The World’s Rarest Birds Not only do the photos and illustrations look incredible, but built-in search functions mean it is easier to find the information you want.