90 Years Ago Today: Einstein’s 50th Birthday

This post is made available by the Einstein Papers Project

Einstein’s fiftieth birthday appears to have been more of a cause for celebration by others than for himself. Having lived under intense scrutiny from the (mostly) adoring public and intrusive journalists for 10 years already, Einstein made valiant efforts to avoid attention from the press on this momentous occasion. He was particularly keen to avoid the hullabaloo ratcheting up for his fiftieth in Berlin. The day before his birthday, a New York Times article, Einstein Flees Berlin to Avoid Being Feted reported that: “To evade all ceremonies and celebrations, he suddenly departed from Berlin last night and left no address. Even his most intimate friends will not know his whereabouts.”

Einstein’s decision allowed him and his family relative respite. While Einstein hid in a countryside retreat, “[t]elegraph messengers, postmen and delivery boys had to wait in line hours today in front of the house No. 5 Haberland Strasse, delivering congratulations and gifts to Albert Einstein on the occasion of his fiftieth birthday today,” according to the March 15 issue of the Jewish Daily Bulletin. Above is one card of the many that Einstein received on and around his birthday; it was made by a pupil at the Jüdische Knabenschule, Hermann Küchler.

After all, an intrepid reporter did find Einstein – in a leafy neighborhood of Berlin called Gatow, half an hour from the city center. A report for avid fans, Einstein Found Hiding on his Birthday, in the March 15 edition of The New York Times provides a gamut of details from the color of his sweater to the menu for his birthday dinner and the array of gifts found on a side table. Happy reading, on this, the 140th anniversary of Einstein’s birth!

03-07-19

Einstein’s 50th will be covered in Volume 16 of The Collected Papers of Albert Einstein. Of the many and various resources we refer to for historical research, the two used for this web post were: The New York Times archive: Times Machine and the Jewish Telegraphic Agency Archive. Access to the Times Machine requires a subscription to The New York Times. The card, item number 30-349, is held at the Albert Einstein Archives at HUJI.

Pi: A Window into the World of Mathematics

Mathematicians have always been fascinated by Pi, the famous never-ending never-repeating decimal that rounds to 3.14. But why? What makes Pi such an interesting number? Every mathematician has their own answer to that question. For me, Pi’s allure is that it illustrates perfectly the arc of mathematics. Let me explain what I mean by taking you on a short mathematical adventure.

Picture yourself in a kitchen, rummaging the pantry for two cans of food. Let’s say you’ve found two that have circular bases of different diameters d1 and d2. Associated with each circle is a circumference value, the distance you’d measure if you walked all the way around the circle.

Were you to perfectly measure each circle’s circumference and diameter you would discover an intriguing relationship:

In other words, the ratio of each circle’s circumference to its diameter doesn’t change, even though one circle is bigger than the other. (This circumference-to-diameter number is  (“Pi”), the familiar 3.14-ish number.) This is the first stop along the arc of mathematics: the discovery of a relationship between two quantities.

Where this story gets very interesting is when, after grabbing even more cans and measuring the ratio of their circumferences to their diameters—you seem to have lots of free time on your hands—you keep finding the same ratio. Every. Time. This is the second stop along the arc of mathematics: the discovery of a pattern. Shortly after that, you begin to wonder: does every circle, no matter its size, have the same circumference-to-diameter ratio? You have reached the third stop along the arc of mathematics: conjecture. (Let’s call our circumference-to-diameter conjecture The Circle Conjecture.)

At first you consider proving The Circle Conjecture by measuring the ratio C/d for every circle. But you soon realize that this is impossible. And that’s the moment when you start truly thinking like a mathematician and begin to wonder: Can I prove The Circle Conjecture true using mathematics? You have now reached the most important stop along the arc of mathematics: the search for universal truth.

One of the first thinkers to make progress on The Circle Conjecture was the Greek mathematician Euclid of Alexandria. Euclid published a mammoth 13-book treatise text called Elements circa 300 BC in which he, among other accomplishments, derived all the geometry you learned in high school from just five postulates. One of Euclid’s results was that the ratio of a circle’s area A to the square of its diameter d2 is the same for all circles:

This is close to what we are trying to prove in The Circle Conjecture, but not the same. It would take another giant of mathematics—the Greek mathematician Archimedes of Syracuse—to move us onto what is often the last stop on the arc of mathematics: thinking outside the box.

Archimedes went back to Euclid’s five postulates, all but one of which dealt with lines, and extended some of Euclid’s postulates to handle curves. With these new postulates Archimedes was able to prove in his treatise Measurement of a Circle (circa 250 BC) that the area, circumference, and radius r of a circle are related by the equation:

(You may recognize this as the area of a triangle with base C and height r. Indeed, Archimedes’ proof of the formula effectively “unrolls” a circle to produce a triangle and then calculates its area.) Combining Archimedes’ formula with Euclid’s result, and using the fact that r = d/2, yields:

Et Voilà! The Circle Conjecture is proved! (To read more about the mathematical details involved in proving The Circle Conjecture, I recommend this excellent article.)

This little Pi adventure illustrated the core arc of mathematics: discovery of a relationship between to quantities; discovery of a more general pattern; statement of a conjecture; search for a proof of that conjecture; and thinking outside the box to help generate a proof. Let me end our mathematical adventure by encouraging you to embark on your own. Find things you experience in your life that are quantifiable and seem to be related (e.g., how much sleep you get and how awake you feel) and follow the stops along the arc of mathematics. You may soon afterward discover another universal truth: anyone can do mathematics! All it takes is curiosity, persistence, and creative thinking. Happy Pi Day!

 

Oscar E. Fernandez is associate professor of mathematics at Wellesley College. He is the author of Calculus Simplified, Everyday Calculus, and The Calculus of Happiness (all Princeton).

Ken Steiglitz: Happy π Day!

As every grammar school student knows, π is the ratio of the circumference to the diameter of a circle. Its value is approximately 3.14…, and today is March 14th, so Happy π Day! The digits go on forever, and without a pattern. The number has many connections with computers, some obvious, some not so obvious, and I’ll mention a few.

The most obvious connection, I suppose, is that computers have allowed enthusiasts to find the value of π to great accuracy. But how accurately do we really need to know its value? Well, if we knew the diameter of the Earth precisely, knowing π to 14 or 15 decimal places would enable us to compute the length of the equator to within the width of a virus. This accuracy was achieved by the Persian mathematician Jamshīd al-Kāshī in the early 15th century. Of course humans let loose with digital computers can be counted on to go crazy; the current record is more than 22 trillion digits. (For a delightful and off-center account of the history of π, see A History of Pi, third edition, by Petr Beckmann, St. Martin’s Press, New York, 1971. The anti-Roman rant in chapter 5 alone is worth the price of admission.)

A photo of a European wildcat, Felis silvestris silvestris. The original photo is on the left. On the right is a version where the compression ratio gradually increases from right to left, thereby decreasing the image quality. The original photograph is by Michael Ga¨bler; it was modified by AzaToth to illustrate the effects of compression by JPEG. [Public domain, from Wikimedia Commons]

Don’t condemn the apparent absurdity of setting world records like this; the results can be useful. Running the programs on new hardware or software and comparing results is a good test for bugs. But more interesting is the question of just how the digits of π are distributed. Are they essentially random? Do any patterns appear? Is there a message from God hidden in this number that, after all, God created? Alas, so far no pattern has been found, and the digits appear to be “random” as far as statistical tests show. On the other hand, mathematicians have not been able to prove this one way or another.

Putting aside these more or less academic thoughts, the value of π is embedded deep in the code on your smartphone or computer and plays an important part in storing the images that people are constantly (it seems to me) scrolling through. Those images take up lots of space in memory, and they are often compressed by an algorithm like JPEG to economize on that storage. And that algorithm uses what are called “circular functions,” which, being based on the circle, depend for their very life on… π. The figure shows how the quality of an original image (left) degrades as it is compressed more and more, as shown on the right.

I’ll close with an example of an analog computer which we can use to find the value of π. The computer consists of a piece of paper that is ruled with parallel lines 3 inches (say) apart, and a needle 3 inches long. Toss the needle so that it has an equal chance of landing anywhere on the paper, and an equal chance of being at any angle. Then it turns out that the chance of the needle intersecting a line on the piece of paper is 2/π, so that by repeatedly tossing the needle and counting the number of times it does hit a line we can estimate the value of π. Of course to find the value of π to any decent accuracy we need to toss the needle an awfully large number of times. The problem of finding the probability of a needle tossed this way was posed and solved by Georges-Louis Leclerc, Comte de Buffon in 1777, and the setup is now called Buffon’s Needle. This is just one example of an analog computer, in contrast to our beloved digital computers, and you can find much more about them in The Discrete Charm of the Machine.

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 (Princeton). He lives in Princeton, New Jersey.

Marcia Bjornerud: Grandmothers of Geoscience

A sheepish admission:  I intermittently check the reviews of my books posted by readers on the website of an online retail behemoth.  I smile at benevolent judgments, cringe at misspellings and misreadings, wonder whether some of the more generic entries were written by bots, and occasionally obsess about comments that get under my skin.  A few weeks ago, in a generally positive review of my PUP book Timefulness: How Thinking Like a Geologist Can Help Save the World, a reader commented that the tone of the text was “grandmotherly”.    

In an instant, several thoughts collided in my head.  The first was indignation – I’m not a grandmother!  Nanoseconds later, I reminded myself that as a fifty-something mother of three sons I certainly could be (and in fact hope to be in a few years).  Next, I chastised myself for falling into the very trap of vanity-rooted time denial that my book exhorts us all to avoid.  And then, my mind moved to the question of what exactly “grandmotherly” means in our culture, and whether a reader would apply the word “grandfatherly” to a work written by a male scientist in his 50s.  On that count, I felt less sure about the right answer.

So many words for women in our culture are tinged with accusation or insult: “mistress” is freighted in a way that “master” is not; “dame” has been demoted to slang (and has horsy connotations) but “sir” hasn’t; “matronly” is not exactly a compliment.  And I chafe, as a “Fellow” of a couple of professional organizations that there is no obvious female equivalent:  Am I a “Gal of the Geological Society of America”?

But as I turned the word “grandmotherly” over in my mind, viewing it from all sides, I saw mostly respect: acknowledgment of experience, persistence, hard-won wisdom, and the right to a voice that should be heard and heeded. 

The fact is that there are far too few grandmothers in any of the sciences and certainly the geosciences in particular.  There was Mary Anning (1799-1847) of Lyme Regis, discoverer of Jurassic sea monsters and arguably the first professional paleontologist;  geophysicist Inge Lehmann (1888-1993), who showed that the Earth’s inner core is solid, a discovery essential to understanding the planet’s magnetic field;  Marie Tharp (1920-2006) who created the first maps of the deep seafloor – more than half of Earth’s surface; Tanya Atwater (born 1942) who worked out the tectonic evolution of western North America over the past 60 million years. 

But I personally had no senior female mentors in my undergraduate and graduate school years.  And according to the American Geological Institute, even today women represent only 15% of the full professors in the geosciences in US universities[1].  I wasn’t fully aware of it as a student, but I see now that the absence of academic grandmothers was an impediment to my own development as a scientist.  There were no exemplars for how to be taken seriously in an overwhelmingly male, highly competitive work environment; no instructions for how to synchronize biological and tenure clocks; no reassurances that success was even possible.  In graduate school, the small cohort of women in my program supported each other but on our own could not allay the chronic anxieties we all shared.  How different our experiences as young scientists would have been with just one grandmotherly figure to turn to.

So, if I am now being bestowed the mantle of grandmother, honoris causa, I humbly accept.  Perhaps one day, our most esteemed scientists, both male and female, will be recognized with that most coveted of all awards: “Grandmother of the National Academy of Sciences”.

Marcia Bjornerud is professor of geology and environmental studies at Lawrence University. She is the author of Reading the Rocks: The Autobiography of the Earth and a contributing writer for Elements, the New Yorker’s science and technology blog. She lives in Appleton, Wisconsin.

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.

SteiglitzKen 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: Garage Rock and the Unknowable

Here is the second post in a series by The Discrete Charm of the Machine author Ken Steiglitz. You can access the first post here

I sat down to draft The Discrete Charm of the Machine with the goal of explaining, without math, how we arrived at today’s digital world. It is a quasi-chronological story; I take what I need, when I need it, from the space of ideas. I start at the simplest point, describing why noise is a constant threat to information and how using discrete values (usually zeros and ones) affords protection and a permanence not possible with information in analog (continuous) form. From there I sketch the important ideas of digital signal processing (for sound and pictures), coding theory (for nearly error-free communication), complexity theory (for computation), and so on—a fine arc, I think, from the boomy and very analog console radios of my childhood to my elegant little internet radio.

Yet the path through the book is not quite so breezy and trouble-free. In the final three chapters we encounter three mysteries, each progressively more fundamental and thorny. I hope your curiosity and sense of wonder will be piqued; there are ample references to further reading. Here are the problems in a nutshell:

  1. Is it no harder to find a solution to a problem than to merely check a solution? (Does P = NP?) This question comes up in studying the relative difficulty of solving problems with a computing machine. It is a mathematical question, and is still unresolved after almost 40 years of attack by computer scientists.
    As I discuss in the book, there are plenty of reasons to believe that P is not equal to NP and most computer scientists come down on that side. But … no one knows for sure.
  2. Are the digital computers we use today as powerful—in a practical sense—as any we can build in this universe (the extended Church-Turing thesis)? This is a physics question, and for that reason is fundamentally different from the P=NP question. Its answer depends on how the universe works.
    The thesis is intimately tied to the problem of building machines that are essentially more powerful than today’s digital computers—the human brain is one popular candidate. The question runs deep: some believe there is magic to found beyond the world of zeros and ones.
  3. Can a machine be conscious? Philosopher David Chalmers calls this the hard problem, and considers it “the biggest mystery.” It is not a question of mathematics, nor of physics, but of philosophy and cognitive science.

I want to emphasize that this is not merely the modern equivalent of asking how many angels could dance on the point of a pin. The answer has most serious consequences for us humans: it determines how we should treat our android creations, the inevitable products of our present rush to artificial intelligence. If machines are capable of suffering we have a moral responsibility to treat them compassionately.

My first reaction to the third question is that it is unanswerable. How can we know about the subjective mental life of anyone (or any thing) but ourselves? Philosopher Owen Flanagan called those who take this position mysterians, after the proto-punk band ? and the Mysterians. Michael Shermer joins this camp in his Scientific American column of July 1, 2018. I discuss the difficulty in the final chapter and remain agnostic—although I am hard-pressed even to imagine what form an answer would take.

I suggest, however, a pragmatic way around the big third question: Rather than risk harm, give the machines the benefit of the doubt. It is after all what we do for our fellow humans.

SteiglitzKen 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.

SteiglitzKen 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.

Browse our 2019 Mathematics Catalog

Our new Mathematics catalog includes an exploration of mathematical style through 99 different proofs of the same theorem; an outrageous graphic novel that investigates key concepts in mathematics; and a remarkable journey through hundreds of years to tell the story of how our understanding of calculus has evolved, how this has shaped the way it is taught in the classroom, and why calculus pedagogy needs to change.

If you’re attending the Joint Mathematics Meetings in Baltimore this week, you can stop by Booth 500 to check out our mathematics titles!

 

Integers and permutations—two of the most basic mathematical objects—are born of different fields and analyzed with different techniques. Yet when the Mathematical Sciences Investigation team of crack forensic mathematicians, led by Professor Gauss, begins its autopsies of the victims of two seemingly unrelated homicides, Arnie Integer and Daisy Permutation, they discover the most extraordinary similarities between the structures of each body. Prime Suspects is a graphic novel that takes you on a voyage of forensic discovery, exploring some of the most fundamental ideas in mathematics. Beautifully drawn and wittily and exquisitely detailed, it is a once-in-a-lifetime opportunity to experience mathematics like never before.

Ording 99 Variations on a Proof book cover

99 Variations on a Proof offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.

 

Bressoud Calculus Reordered book cover

Exploring the motivations behind calculus’s discovery, Calculus Reordered highlights how this essential tool of mathematics came to be. David Bressoud explains why calculus is credited to Isaac Newton and Gottfried Leibniz in the seventeenth century, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus presents a sounder way for students to learn this fascinating area of mathematics.

Ken Steiglitz on The Discrete Charm of the Machine

SteiglitzA 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.

Browse our 2019 Computer Science Catalog

Our new Computer Science catalog includes an introduction to computational complexity theory and its connections and interactions with mathematics; a book about the genesis of the digital idea and why it transformed civilization; and an intuitive approach to the mathematical foundation of computer science.

If you’re attending the Information Theory and Applications workshop in San Diego this week, you can stop by the PUP table to check out our computer science titles!

 

Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. Avi Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field that has shaped and will further shape science, technology, and society. 

 

Steiglitz Discrete Charm of the Machine book cover

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, and challenges us to think about where its future trajectory may lead.

Lewis Zax Essential Discrete Mathematics for Computer Science

Discrete mathematics is the basis of much of computer science, from algorithms and automata theory to combinatorics and graph theory. This textbook covers the discrete mathematics that every computer science student needs to learn. Guiding students quickly through thirty-one short chapters that discuss one major topic each, Essential Discrete Mathematics for Computer Science can be tailored to fit the syllabi for a variety of courses. Fully illustrated in color, it aims to teach mathematical reasoning as well as concepts and skills by stressing the art of proof.

Calling Girls Who Love Math: Register for Girls’ Angle’s SUMIT 2019!

Get ready for a new mathematical adventure! SUMIT 2019 is coming April 6 and 7 with an all-new plot and math problems galore.

If you’re a 6th-11th grade girl who loves math, you’ll love SUMIT! There will be challenges for all levels and key leadership roles to fulfill. You’ll emerge with an even greater love of math, new friends, and lasting memories.

Princeton University Press has been a major sponsor of SUMIT since its inception in 2012, and is always proud to promote this magical escape-the-room-esque event where girls join forces to overcome challenges and become the heroines of an elaborate mathematical saga. The event offers one of the most memorable opportunities to do math while forming lasting friendships with like-minded peers. Together, girls build mathematical momentum and frequently surprise themselves with what they’re able to solve. All previous SUMITs have garnered overall ratings of 10 out of 10 by participants.

Created by Girls’ Angle, a nonprofit math club for girls, together with a team of college students, graduate students, and mathematicians, SUMIT 2019 takes place in Cambridge, MA.

Registration opens at 2 pm ET on Sunday, February 10 on a first-come-first-served basis and there are limited slots, so register quickly!

For more information, please visit http://girlsangle.org/page/SUMIT/SUMIT.html.

Erika Lorraine Milam on Creatures of Cain: The Hunt for Human Nature in Cold War America

After World War II, the question of how to define a universal human nature took on new urgency. Creatures of Cain charts the rise and precipitous fall in Cold War America of a theory that attributed man’s evolutionary success to his unique capacity for murder. Drawing on a wealth of archival materials and in-depth interviews, Erika Lorraine Milam reveals how the scientists who advanced this “killer ape” theory capitalized on an expanding postwar market in intellectual paperbacks and widespread faith in the power of science to solve humanity’s problems, even to answer the most fundamental questions of human identity.

What surprised you when you were researching the book?

I never intended to write about violence. The book started as a kernel of a story about the development and reception of an educational program called Man: A Course of Study, or MACOS. When Americans learned that the Soviet Union had launched the world’s first man-made satellite into orbit, they feared the technological prowess of Soviet engineers and scientists would quickly outstrip their own, unless they poured significant energy into science education. The result was a series of educational programs developed by experts and made available for use in elementary school classrooms around the country: the PSSC, BSCS, and others. MACOS was the first to tackle questions central to the social sciences. Led by cognitive psychologist Jerome Bruner, it focused students’ attention on three questions: “What is human about human beings? How did they get that way? How can we become more so?” I wanted to know more. The program, I discovered, used a wide array of materials—among them: films, booklets, and board games—to get students to contemplate these larger questions about the diverse communities in which they lived. But quickly I realized, too, that when MACOS was adopted by local school systems it was met with protests from community members who objected to the violent content of the materials. It was difficult for me to square the project’s intentions with the accusations hurled at it only a few years later. My research snowballed. Debates over violence during the Cold War—its causes and consequences—served as proxies for scientists thinking about questions of sex, race, and their own contested authority to answer these fundamental issues. This book is the result.

You interviewed a lot of people for the book, what was that like?

Thanks for asking me this! Creatures of Cain would have been a very different book without the generosity of the scientists and writers who took the time to speak with me about their research. In reconstructing past events, historians necessarily rely on archival research. This works brilliantly when people have already deposited their correspondence and papers in an archive, but those collections are more rare than you would think, are often highly curated, and are usually available only after someone has died. (Not everyone is keen to have future historians read through old letters.) When working on recent history, talking with scientists while they are still alive allows historians like myself access to voices and perspectives that would otherwise be difficult to include. Much about a scientist’s life is never recorded in a paper trail: from the books and experiences people found inspiring when they were teenagers to the friends and colleagues who sustained them during and after graduate school. Talking with people about their histories is thus invaluable, especially in trying to recreate informal networks of collaboration that I would have otherwise missed. Plus, I find it thrilling to meet people in person. The lilting cadence of a voice, the disorderliness of an office, or the art on a wall: each of these things leaves a singular impression impossible to glean from the written word alone.

How did you choose the images for the book?

For centuries images have played a crucial role in communicating scientific ideas, including concepts of human nature. After the Second World War, with the exciting coverage of paleoanthropological fossil discoveries in Africa and nature documentaries about modern human cultures from all over the world, still and moving images stirred audiences’ interests in anthropological topics. When selecting images for the book, I chose to emphasize drawings and illustrations that depicted the theories under discussion or scientists hard at work. Their striking visual styles reflect both the artistic conventions of the time and the highly visual nature of scientific conversations. More so than photographs, which can easily be read as flat representations of the past, I hope these images center readers’ attentions on the creativity required to bring theories of human nature to life.

How did you become a historian of science?

I came to the history of science fortuitously. In my undergraduate and early graduate work, I studied biology. Only in my second year of graduate school in the Ecology and Evolutionary Biology program at the University of Michigan did I come to realize that there was a whole community of people, like me, who were interested in the humanistic study of science, technology, and medicine. I started reading books on the history of evolutionary theory, on gender history, and on the history of American science. I was gripped. Now I study how intellectual and social concerns are tightly bound together within scientific inquiries. I find especially fascinating research on the biological basis of sex and aggression in human behavior—each of which touches on the broader question of what it means to be human in a naturalistic world.

What are the lessons for us today that we learn from Creatures of Cain?

When I talk about my project, people ask me whether the growing violence of the struggle for Civil Rights domestically or the escalating Vietnam War made it easier for scientists and citizens to embrace the idea that humans were naturally murderous. The “killer ape” theory, as it came to be known, posited that the crucial divide between humans and all other animals lay in our capacity to kill other members of our own species. Did the violence of the era, perhaps, explain why it was easy to imagine the history of humanity as characterized by violence and only punctuated by moments of peace? I answer by saying that only a decade earlier, in the wake of the death and horrific atrocities of the Second World War, scientists chose instead to emphasize the importance of emphasizing the fundamental unity of humankind. Only through a common struggle against the environment, they argued, had our human ancestors survived life on the arid savannah—we humans may have clawed our way to the present, but we did it together. Biological theories of human nature have been used both to dehumanize and to promote progressive anti-racist conceptions of humanity as a whole. As these accounts demonstrate in juxtaposition, there is no consistent correlation between the desire to biologize human nature and either periods of violence or schools of ideological persuasion.

Equally important, fundamental questions about the nature of humanity—in the colloquial scientific books I make the center of my analysis—have helped recruit and inspire generations of students to pursue careers in the natural and social sciences. Even though such discussions rarely appear in the pages of professional scientific journals, they are central to how scientific and popular ideas about human nature change. Drawing a sharp distinction between specialist and non-specialist publications would thus distort the history of ideas about human nature in these decades. After all, scientists read (and reviewed) colloquial scientific publications, too, especially when exploring new ideas outside their immediate expertise.

When observations that chimpanzees also killed chimpanzees became broadly known in the latter half of the 1970s, it spelled the end of the killer ape theory. Although the idea that aggression provided the secret ingredient to the unique natural history of humanity has faded, this theory helped lay the groundwork for how scientists conceptualize human nature today.

Bonus question (if you dare): Please summarize the book in a tweet.

Oh wow! Okay, here’s a sentence from the introduction that actually fits: “In its broadest scope, Creatures of Cain demonstrates that understanding the historical fate of any scientific vision of human nature requires attending to the political and social concerns that endowed that vision with persuasive power.”

Erika Lorraine Milam is professor of history at Princeton University. She is also the author of Looking for a Few Good Males: Female Choice in Evolutionary Biology.