Like many electrical engineers, I grew up in a world shaped by Richard Hamming. My graduate thesis was based on coding theory; my early career on digital filters and numerical methods. I loved these subjects, took them for granted, and had no idea how they came to be.

I got my first hint upon encountering “You and Your Research,” Hamming’s electrifying sermon on why some scientists do great work, why most don’t, why he did, and why you should too. Most thrilling was Hamming’s vivid image of greatness, and its unapologetic pursuit. Not only was it allowable to aim for greatness, it was cowardly not to. It was the most inspirational thing I’d ever read.

The Art of Doing Science and Engineering is the full, beautiful expression of what “You and Your Research” sketched in outline. In this delightfully earnest parody of a textbook, chapters on “Digital Filters” and “Error-Correcting Codes” do not, in fact, teach those things at all, but rather exist to teach the style of thinking by which these great ideas were conceived.

This is a book about thinking. One cannot talk about thinking in the abstract, at least not usefully. But one can talk about thinking about digital filters, and by studying how great scientists thought about digital filters, one learns, however gradually, to think like a great scientist.

Among the most remarkable attributes of Hamming’s style of thinking is its sweeping range of scale. At the micro level, we see the close, deliberate examination of everyone and everything, from the choice of complex exponentials as basis functions to the number of jokes in an after-dinner speech. Nothing is taken for granted or left unquestioned, but is picked up and turned over curiously, intently, searching for fundamentals.

And then, even in the same sentence, a zoom out to the wide shot, the subject contextualized against the broad scientific landscape, a link in the long chain of history. Just as nothing is taken for granted, nothing is taken in isolation.

For one accustomed to the myopia of day-to-day work in a field, so jammed against the swaggering parade of passing trends that one can hardly see beyond them or beneath them, such shifts in viewpoint are exhilarating — a reminder that information may be abundant but wisdom is rare.

After all, where today can the serious student of scientific creativity observe the master at work, short of apprenticeship? Histories are written for spectators; textbooks teach tools, not craft. We can gather small hints from the loose reflections of Hadamard, the lofty theories of Koestler, the tactical heuristics of Pólya and Altshuller.

But Hamming stands alone. Certainly for the thoroughness with which he presents his style of thinking, and more so for explicitly identifying style as a thing that exists and can be learned in the first place. But most of all, for his expectation — his insistence — that the reader is destined to join him in extending the arc of history, to become a great person who does great work. In this tour of scientific greatness, the reader is not a passenger, but a driver in training.

This book is filled with great people doing great work, and to successfully appreciate Hamming’s expectations, it is valuable to consider exactly what he meant by “great people,” and by “great work.”

* * *

In Hamming’s world, great people do and the rest do not. Hamming’s heroes assume almost mythical stature, swashbuckling across the scientific frontier, generating history in their wake. And yet, it is well-known that science is a fundamentally social enterprise, advanced by the intermingling ideas and cumulative contributions of an untold mass of names which, if not lost to the ages, are at least absent from Wikipedia.

Hamming’s own career reflects this contradiction. He was employed essentially as a kind of internal mathematical consultant; he spent his days helping other people with their problems, often problems of a practical and mundane nature. Rather than begrudging this work, he saw it as the “interaction with harsh reality” necessary to keep his head out of the clouds, and at best, the continuous production of “micro-Nobel Prizes.” And most critically, all of his “great” work, his many celebrated inventions, grew directly out of these problems he was solving for other people.

Throughout, Hamming insisted on an open door, lunched with anyone he could learn from or argue with, stormed in and out of colleagues’ offices, and otherwise made indisputable the social dimensions of advancing a field.

All this is true. Also true is Hamming’s personal experience that one cannot work alongside John Tukey, share an office with Claude Shannon, eat lunch with Bardeen and Brattain, get bossed by Bethe and Bode, study the lives of Newton and Einstein, even hang out with Feynman a bit, without being struck by the utter obviousness that these are extraordinary people, whose work has had an extraordinarily discontinuous effect.

Hamming couldn’t deny this, but he couldn’t merely accept it either. He needed to know where this extraordinariness came from. The joke around Princeton was that John von Neumann “was not human, but a demigod who had made a detailed study of humans and could imitate them perfectly.” Bad news for any aspiring von Neumanns of more terrestrial stock.

Hamming’s conviction — indeed, obsession — was the opposite: that this greatness was less a matter of genius (or divinity), and more a kind of virtuosity. He saw these undeniably great figures as human beings that had learned how to do something, and by studying them, he could learn it too.

And he did, or so his narrative goes: against a background of colleagues more talented, more knowledgable, more supported, better equipped along every axis, Hamming was the one to invent the inventions, found the fields, win the awards, and generally transcend his times.

And if he could, then so could anyone. Hamming was always as much a teacher as a scientist, and having spent a lifetime forming and confirming a theory of great people, he felt he could prepare the next generation for even greater greatness. That’s the premise and promise of this book.

Hamming-greatness is thus more a practice than a trait. This book is full of great people performing mighty deeds, but they are not here to be admired. They are to be aspired to, learned from, and surpassed.

* * *

Hamming leaves the definition of “great work” open, encouraging the reader to “pick your goals of excellence” and “strive for greatness as you see it.” Despite this apparent generosity, the sort of work that Hamming considered “great” had a distinct shape, and tracing that shape reveals the deepest message of the book.

Consider the examples of great work that Hamming returns to. Shannon’s information theory, continually. Einstein’s relativity. Tukey’s work on spectrum analysis and the fast Fourier transform, Grace Hopper’s work on high-level programming, Kaiser’s work on digital filters. His own error-correcting codes, of course.

There are many commonalities we can admire in these endeavors: the dazzling leap of imagination, the broad scope of applicability, the founding of a new paradigm. But let’s focus here on their form of distribution. These are all things that are taught. To “use” them means to learn them, understand them, internalize them, perform them with one’s own hands. They are free to any open mind.

In Hamming’s world, great achievements are gifts of knowledge to humanity.

Looking at this work in retrospect, it can be hard to imagine it having taken any other form. It’s possible to see these past gifts as inevitable, without realizing how much the present-day winds have shifted. Many of the bright young students who, in Hamming’s day, would have pursued a doctorate and a research career, today find themselves pursued by venture capital. Steve Jobs has replaced Einstein as cultural icon, and the brass ring is no longer the otherworldly Nobel Prize, but the billion-dollar acquisition. Universities are dominated by “technology transfer” activities, and engineering professors — even some in the sciences — are looked at askance if they aren’t running a couple startups on the side.

One can imagine the encouraged path, the inevitable-seeming path, for a present-day inventor of error-correcting codes: error-correcting.com, encoding as a service, all ingenuity hidden behind an API. Bait to be swallowed by some hulking multinational. Hamming wrote books.

It’s crucial to emphasize that the “great work” Hamming extols had no entrepreneurial component whatsoever. Gifts to humanity — to be learned by minds, not downloaded to phones. 

As we read Hamming’s reminiscences of lunching with Shockley, Brattain, and Bardeen — lauded today as “inventors of the transistor” — let us keep in mind how they viewed themselves: “discoverers” of “transistor action.” A phenomenon, not a product; to be described, not owned and rented out. Their Nobel Prize reads “discovery of the transistor effect.” Hamming’s account lingers on the prize and is silent on the patents.

Hamming’s outlook was formed at Bell Telephone Laboratories, that legendary anomaly of American invention. Partly responsible for the Labs’ astounding output was its concentration of brilliant people and access to funds — but of course, brilliance concentrates in any age, as does capital. The true magic lay in motivation. As a regulated monopoly, cautious of a Federal Trade Commission which had not yet been declawed, Bell Labs imposed upon itself an unusual responsibility — its workers saw themselves as bound to operate in the public interest. And what fruits that restriction yielded.

This book is adapted from a course that Hamming taught at the U.S. Naval Postgraduate School, to cohorts of “carefully selected navy, marine, army, air force, and coast guard students with very few civilians.” In a recording of the introductory lecture, we hear Hamming tell his students:

The Navy is paying a large sum of money to have you here, and it wants its money back by your later perfomance.

The United States Navy does not want its money back with an IPO. Regardless of one’s orientation toward military engineering, there is no question that these students are expected and expecting to serve the public interest.

Hamming-greatness is tied, inseparably, with the conception of science and engineering as public service. This school of thought is not extinct today, but it is rare, and doing such work is not impossible, but fights a nearly overwhelming current.

Yet, to Hamming, bad conditions are no excuse for bad work. You will find in these pages ample motivation to use your one life to do great work, work that transcends its times, regardless of the conditions you find yourself in.

As you proceed, I invite you to study not just Hamming’s techniques for achieving greatness, but the specific kind of greatness he achieved. I invite you to be inspired not just by Hamming’s success, but by his gifts to humanity, among the highest of which is surely this book itself.

Bret Victor
Cambridge, Massachusetts
December 2018