Apuntes de la HP

 

C++

 

The C++ Programming Language,Bjarne Stroustrup http://www.research.att.com/~bs/3rd.html

 

Sentencias de Control en C++, http://www1.ceit.es/Asignaturas/Informat2/Apuntes/Sentencias.pdf

 

 

 Opening Black’s Box

Rethinking Feedback’s Myth of Origin

DAV I D A . M I N D E L L

 

The specific triumph of the technical imagination rested on the ability to dissociate

lifting power from the arm and create a crane: to dissociate work from

the action of men and animals and create the water-mill: to dissociate light

from the combustion of wood and oil and create the electric lamp.

—Lewis Mumford

The engineer who embarks on the design of a feedback amplifier must be a

creature of mixed emotions.

Hendrik Bode

Like any modern episteme worthy of the name, the theory of feedback has

a myth of origin. On a sunny August morning in 1927, Harold Black, a

twenty-nine-year-old systems engineer, rode the Lackawanna ferry to work

at the Bell Telephone Laboratories.Many Bell engineers lived in New Jersey,

and on the early morning ferry rides across the Hudson to the Manhattan

laboratories they frequently gathered on the forward deck. This morning

Black stood alone, staring at the Statue of Liberty, and had an epiphany: “I

suddenly realized that if I fed the amplifier output back to the input, in

reverse phase, and kept the device from oscillating (singing, as we called it

then), I would have exactly what I wanted: a means of canceling out the distortion

in the output.”1 As it happened, the New York Times that day con-

Dr. Mindell is Dibner Associate Professor of the History of Engineering and Manufacturing

at the Massachusetts Institute of Technology. He thanks Annette Bitsch, John

Staudenmaier, and anonymous reviewers for helpful feedback to stabilize this paper, and

Sheldon Hochhieser of the AT&T archives and Ronald Kline for their help with documentary

research.

©2000 by the Society for the History of Technology. All rights reserved.

0040-165X/00/4103-0001$8.00

1. Harold S. Black, “Inventing the Negative Feedback Amplifier,” IEEE Spectrum 14

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tained a blank page, and Black sketched his idea, “a simple canonical diagram

of a negative feedback amplifier plus the equations for the amplification

with feedback.” He rushed into work, asked a technician to wire up a

prototype, and gave birth to a foundational circuit of modern electronics.

This story has become enshrined as one of the central “flashes of insight”

in electrical engineering in this century, periodically retold as an inspiration

for engineers.2 A common textbook on control engineering reprints

the story of Black’s vision verbatim in the first chapter.3

At Bell Laboratories from 1927 to 1940, the legend goes, Black, Harry

Nyquist, and Hendrik Bode laid the foundations of feedback control that

engineers then applied to all types of closed-loop systems, from servomechanisms

to thermostats, fire control systems to automatic computers.4

More than other contemporary narratives of control systems such as automatic

pilots or servomechanisms, this story of feedback earned a place in

engineering legend and college textbooks. It produced design methods and

graphical techniques that carry their author’s names (the Bode plot, the

Nyquist diagram) and earned telephone engineering a claim to priority in

feedback history. Feedback theory, moreover, formed the basis of cybernetics,

systems theory, and a host of other post–World War II information sciences,

so Black’s invention is hailed as a foundation of the information age.

Feedback is indeed a fundamental concept in twentieth-century technology,

and the Bell Labs feedback theorists did lay critical foundations for

it. But the origin myth effaces its sources. It skips over the inventors themselves

and the ways in which their backgrounds and prior experience influ-

(December 1977): 54–60. George Stibitz’s memoir describes the early morning ferry

rides; “The Zeroth Generation,” manuscript, 1993, Stibitz Papers, Dartmouth College,

54. For the quotations from Mumford and Bode, see Lewis Mumford, Technics and

Civilization (New York, 1934), 33; Hendrik Bode, “Relations Between Attenuation and

Phase in Feedback Amplifier Design,” Bell System Technical Journal 19 (July 1940):

421–54.

2. For other accounts of Black’s invention, see Hendrik Bode, “Feedback: The

History of an Idea,” Proceedings of the Symposium on Active Networks and Feedback Systems

(Brooklyn, 1960), reprinted in Selected Papers on Mathematical Trends in Control

Theory, ed. Richard Bellman (New York, 1964); M. J. Kelley, “Career of the 1957 Lamme

Medalist Harold S. Black,” Electrical Engineering 77 (1958): 720–22; Prescott C. Mabon,

Mission Communications: The Story of Bell Laboratories (Murray Hill, N.J., 1975), 39–40.

Among historians’ accounts the most thorough is Stuart Bennett, A History of Control

Engineering, 1930–1955 (London, 1993), chap. 3, “The Electronic Negative Feedback

Amplifier.” See also E. F. O’Neill, ed., A History of Science and Engineering in the Bell

System: Transmission Technology (1925–1975) (Murray Hill, N.J., 1985), chap. 4, “Negative

Feedback”; Ronald Kline,“Harold Black and the Negative-Feedback Amplifier,” IEEE

Control Systems (August 1993): 82–85; and a short film, Communications Milestone:

Negative Feedback (Bell Telephone Laboratories, 1977).

3. Richard C. Dorf, Modern Control Systems, 5th ed. (Reading, Mass., 1995).

4. Hendrik W. Bode, Synergy: Technical Integration and Technological Innovation in

the Bell System (Murray Hill, N.J., 1971), 138–40.

enced their work. It reveals little about the concrete problems these men

worked on when they produced their solutions. The story also removes

feedback theory from its engineering culture, that of the telephone network

between the world wars. Black’s version also does not account for the relationship

of his feedback amplifiers to prior traditions of governors and selfregulating

machinery.

Thus a reexamination of the sources is in order, retelling Black’s legend

not as a heroic tale but as the story of an engineer solving the technical

problems of a particular place and time and trying to convince others to

support his solutions. As it turns out, Black did not understand as much

about feedback as he later recalled. To make his idea credible, he needed

Nyquist’s reformulation of the problem of stability and Bode’s analysis outlining

the tight constraints that a feedback amplifier had to meet. He also

needed the Bell System. Negative-feedback amplifiers emerged from efforts

to extend the telephone network across the continent, to increase the network’s

carrying capacity, and to make it work predictably in the face of

changes in season, weather, and landscape—from the context, that is, of

building a large technical system and operating it over a diverse and

extended geography. Black, Nyquist, and Bode worked within a company

that sought to translate ever more of the world into transmissible messages.

This translation required, among other things, ever closer couplings of

human and mechanical elements through the medium of sound, couplings

that left a discernible mark on feedback theory. For telephone engineers,

the network listened, and it spoke.

In 1934, the same year that Black published his amplifier, Lewis Mumford,

in Technics and Civilization, noted technology’s ability to abstract the

world. “Men became powerful to the extent that they neglected the real

world of wheat and wool, food and clothes,” he wrote, “and centered their

attention on the purely quantitative representation of it in tokens and

symbols.”5 In light of Mumford’s observation, a retelling of Black’s story

has greater significance than a simple corrective to the origin myth, for it

concerns the historical emergence of electrical signals as representations of

the world, the technologies developed to manipulate and transmit them,

and the economic and organizational conditions that made those technologies

possible. Black, Nyquist, and Bode contributed to an understanding

of telephony as the transmission of abstract signals, separate from the

electric waves that carried them. The AT&T engineers’ increasing facility

with creating, manipulating, and switching such signals prompted them to

rethink the network not simply as a passive medium but as an active

machine. Then the Bell System became not merely a set of voice channels

but a generalized system, capable of carrying any signal as a new currency:

information.

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5. Mumford, 25.

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Network Geography

The Bell System of 1900 was an engineer’s dream: geographically

expansive, reaching into all types of difficult terrain and climates, and yet

always in control, tied to the central office. Still, in the first decade of the

century American Telephone and Telegraph (AT&T) did not yet have its

later hegemony. The company controlled only about half the telephones in

the country, and long distance was the key to expanding that share.

Originating in New York, the Bell System followed its own frontier on a

western expansion.6 From the turn of the century until the 1930s, AT&T

expressed its technical milestones in geographical terms: the New York/

Chicago line stood for carrier-frequency transmission; the New York/San

Francisco transcontinental line stood for vacuum-tube repeaters; the

Morristown trial simulated the entire country and represented the negative-

feedback amplifier.“People assimilated telephony into their minds as if

into their bodies,” writes telephone historian John Brooks, “as if it were the

result of a new step in human evolution that increased the range of their

voices to the limits of the national map.”7

THE PASSIVE NETWORK

Despite these ambitions, at the turn of the century the telephone network

remained a passive device, as it had been since Bell’s invention.

Carbon microphones added energy from a battery to the weak acoustic signal

from a speaker’s voice, but once the wave entered the line it traveled to

the receiver without further amplification, going the full distance on its

original strength. In fact, impedance in the wire imposed considerable

losses, known as “attenuation.”Around 1900 the telephone network ran up

against the limits of transmission, both in extension, which determined the

furthest distance a signal could travel, and in economy, which determined

the cost of sending a signal over shorter distances.

Weather exacerbated the problem. The standard method of transmission,

even for long distances, was “open wire,” which meant each circuit literally

had its own wire, separated from others by a few inches of space. This

separation minimized cross talk, where one conversation leaked to an adjacent

wire, and also kept attenuation losses to a minimum. Telephone poles

6. For the general history of the Bell System, see John Brooks, Telephone: The First

One Hundred Years (New York, 1975); Thomas Shaw, “The Conquest of Distance by

Wire Telephony,” Bell System Technical Journal 23 (October 1944); Leonard Reich,

“Industrial Research and the Pursuit of Corporate Security: The Early Years of Bell

Labs,” Business History Review 54 (winter 1980): 511. See also Leonard Reich, The

Making of American Industrial Research: Science and Business at GE and Bell, 1876–1926

(New York, 1985), chaps. 7–8. For another interpretation of the semiotics of telephony,

see Avital Ronell, The Telephone Book: Technology, Schizophrenia, Electric Speech

(Lincoln, Neb., 1991).

7. Brooks, 142.

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with dozens of wires (familiar in turn-of-the-century urban scenes) distinguished

this technology. In addition to cluttering the landscape, the lines

were particularly vulnerable to snow and ice storms. Cables, an alternative to

open wire, collected numerous small wires together into a thick bundle. They

could be buried underground, which made them immune to weather and

cheaper to install. But because the wires were of small diameter and packed

tightly together, cables had higher losses than open wire, twenty to thirty

times more signal attenuation, so they lowered the limits of transmission.

To push these limits, Michael Pupin of Columbia University and

George Campbell of Western Electric, working simultaneously, developed

the loading coil. By adding inductance at intervals along the wire, loading

coils could decrease signal loss by a factor of three or four, and thus increase

the maximum transmission distance proportionally.8 Commercial installation

began in 1904, and loading coils rapidly proliferated through the network,

especially on cabled routes.9 Still, the loading coil remained passive—

it facilitated the propagation of the wave down the line but added no

additional energy.

THE TRANSCONTINENTAL LINE: GEOGRAPHY AND STANDARDIZATION

Not only technical innovations but also organization and policy supported

the network’s expansion. John J. Carty, chief engineer of the Bell

System in 1907, had a clear vision of the social role of the telephone network

as “society’s nervous system.” He and his engineers vigorously pursued

the goals of AT&T President Theodore Vail’s famous motto: “One policy,

one system, and universal service.” Carty strongly supported science

within the company. He had a vision of industrial research that translated

corporate goals into technical problems to be solved in the laboratory

(sometimes as much for protection against competition as for advancement).

10 One of Carty’s longtime associates recalled him as a system-

8. James E. Brittain, “The Introduction of the Loading Coil: George A. Campbell and

Michael I. Pupin,” Technology and Culture 11 (1970): 36–57. See also the discussion of

Brittain’s article by Lloyd Espenschied, Joseph Gray Jackson, and John G. Brainerd,

Technology and Culture 11 (1970): 596–603. Neal Wasserman, From Invention to

Innovation: Long-Distance Telephone Transmission at the Turn of the Century (Baltimore,

1985).

9. M. D. Fagan, ed., A History of Engineering and Science in the Bell System: The Early

Years (1875–1925) (Murray Hill, N.J., 1975), 241–52.

10. Ibid., 32–35, 44. Ironically, in a consolidation of research, Carty closed Western

Electric’s Boston engineering department, which had been investigating Lee De Forest’s

audion for use as an amplifier. Hugh Aitken argues that the closing of the lab may have

cost the company several years toward making a practicable telephone amplifier. A proposed

contract with Reginald Fessenden for radio technology also became a casualty of

Vail’s consolidation. “What slipped through the Telephone Company’s fingers, in short,

was a unique opportunity to come to grips with electronic technology,” Aitken argues,

countering other historians (Hoddeson and Reich) who view the move to a single department

in New York as progress toward industrial research; see Hugh Aitken, The

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builder in the Hughesian sense: “He recognized the interrelationship in the

telephone business of operating methods, design of the plant, and the rate

structure. . . . He had in mind that all of these factors must be considered

in relations to one another.”11 And on all of these factors, Carty believed,

science could be brought to bear.

And science he needed. By 1911, the state of the transmission art had

hit its practical limit: “loaded” lines reached the 2,100 miles between New

York and Denver, but the attenuation and distortion so mangled voice signals

they were barely understandable. Yet in 1909 AT&T’s technical management

initiated a project to extend the Denver line to California, completing

a transcontinental line. This geographical problem had a technical

core. Bridging the distances required an amplifier or “repeater,” an active

device that added energy to the signal, unlike loading coils, which merely

stemmed its decay.12 To solve this problem, in 1911 Carty organized a special

Research Branch of the Western Electric Engineering Department, with

E. H. Colpitts as its head.13

The solution to this problem of long-distance transmission emerged

from a new alliance of corporate interests and the latest academic science.

Carty gave technical responsibility for the transcontinental line to a young

physicist, Frank Baldwin Jewett. Jewett came to Western Electric in 1904

from a stint as an instructor in electrical engineering at MIT.He had earned

Continuous Wave: Technology and American Radio, 1900–1932 (Princeton, 1985), 75–78.

Lillan Hoddeson, in “The Emergence of Basic Research in the Bell Telephone System,

1875–1915,” Technology and Culture 22 (1981): 530, notes that the term “fundamental

research” began to appear in the company’s rhetoric about 1907, a point echoed in Horace

Coon, American Tel and Tel: The Story of a Great Monopoly (New York, 1939), 197. See also

Reich, “Industrial Research” and The Making of American Industrial Research, for the

defensive stance of early industrial research.

11. Bancroft Gherardi, “The Dean of Telephone Engineers,” Bell Laboratories Record

9 (September 1930).

12. Mechanical telephone repeaters, logical extensions of simple and common telegraph

repeaters, had existed for some time. These devices coupled acoustic energy from

a speaker into a microphone, amplified the signal, and retransmitted it. This approach

amounted to connecting two telephone circuits end to end, and numerous such devices

were patented before 1900. More elegant solutions used the same principle but combined

the elements into a single unit. Because of inertia, the mechanical coupling lagged

the electrical signal and the output was not very linear with input, which meant that

mechanical repeaters introduced significant distortion. No more than a few could be

connected in series, and the delicate devices proved especially sensitive to temperature

variations. Developing a repeater had a strategic dimension as well: the rapid rise of new

wireless communications seemed a threat to wired communication, and repeaters would

give the company the opportunity to control radio technology, which required similar

types of amplifiers. Shaw (n. 6 above) reprints Carty’s original proposal for the transcontinental

line.

13. The organization charts of the AT&T/Western Electric Engineering departments

in 1905, 1907, 1909, 1911, 1915, and 1925 are reprinted in Shaw (n. 6 above), 400–406,

and Fagan, 43–55.

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his doctorate in physics at the University of Chicago, where he worked

under Albert A. Michelson and became friendly with Robert Millikan. In

1910, faced with the problem of making repeaters for the transcontinental

line, Jewett imagined that a solution, “in order to follow all of the minute

modulations of the human voice, must be practically inertialess.”14

Mechanical repeaters had existed for some time, but they were impracticable

because the inertia of their elements introduced significant distortion.

Jewett thought the secret to “inertialess,” and hence high-quality, repeaters

lay in the electron physics he had studied at Chicago. At his request,

Millikan sent several recent Ph.D.’s to AT&T to work on the project, and

they formed an important axis of the company’s research for years to come.

In the ensuing decades Jewett would become an important figure in

American science, but within AT&T his name was intimately associated

with long distance transmission.When he retired in 1944, Bell Laboratories

published an “implicitly biographical” tribute: not a description of the

man’s life, but a detailed technical history of the transcontinental line.15

After Jewett, Harold D. Arnold was the first of the Chicago group to

arrive at AT&T, where he joined Colpitts’s new Research Branch. Arnold,

with fellow Millikan disciple H. J. van der Bijl, analyzed electron behavior

within De Forest’s audion tubes, characterized the tubes’ behavior as circuit

elements, and engineered them for mass, interchangeable production. By

1913, Arnold’s “high vacuum thermionic tube,” later known simply as the

vacuum tube, could amplify signals in telephone repeaters.16 This electronic

repeater made possible the transcontinental line, which opened at the Pan

American Exposition in San Francisco in 1915 with great fanfare. From the

east coast, Alexander Graham Bell repeated his famous first conversation

with Thomas Watson, now in California. Vail and President Woodrow

Wilson both chimed in as well. The line consisted of 130,000 poles, more

than 99 percent on open wire (the few cables forded streams and rivers). It

had loading coils every eight miles and eight vacuum-tube repeaters ampli-

14. Jewett to Millikan, quoted in Fagan, 258. Jewett and Millikan had boarded

together at Chicago, and Jewett was the best man at Millikan’s wedding. Robert A.

Millikan, The Autobiography of Robert A. Millikan (New York, 1950), 52–53. Millikan

recounts the story of Jewett’s approach to him, 116–17. Millikan remained a consultant

in long-distance telephony, and his testimony helped settle the protracted suit between

General Electric and AT&T over the vacuum tube, 120–22.

15. Shaw, 533. Bruno Latour uses Jewett’s appropriation of the electron as an example

of “machines” as abstract apparatuses for tying together interested groups; Science in

Action (Cambridge, 1987), 125–26.

16. Shaw, 375, 379–82. Hugh Aitken argues that Arnold simply had a fundamentally

different vision of the audion’s potential than did De Forest. “Arnold . . . saw in it . . .

something its inventor did not see: the possibility of making it into a high-vacuum

device, operating by pure electron emission,”whereas De Forest saw it as a gas-discharge

device. Still, in Aitken’s view, the distance between telephony and wireless delayed the

Bell system’s adoption of the audion for a number of years. Aitken (n. 10 above), 546.

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fying the signal in both directions. Still, calling across country was far from

routine; a three-minute call cost more than twenty dollars, and delivered

only a third of the bandwidth of standard lines, which meant greatly

reduced quality.17 Its scratchy tone notwithstanding, the transcontinental

line brought the entire country within the scope of Vail’s unifying vision.

Amid the fanfare, however, the transcontinental line also marked a lessnoted

but equally critical technical and conceptual shift: the network

became a machine. No longer was the network a passive device; with

repeater amplifiers, the network actively added energy along the route, a

significant change because it effectively decoupled the wave that represented

the conversation from its physical embodiment in the cable. Electricity

was no longer the conversation itself, but “useful only as a means of

transmitting intelligible sounds . . . [with] no appreciable value purely from

the power standpoint.”18 In other words, a working amplifier could renew

the signal at any point, and hence maintain it through complicated manipulations,

making possible long strings of filters, modulators, and transmission

lines. Electricity in the wires became merely a carrier of messages, not

a source of power, and hence opened the door to new ways of thinking

about communications.

Standardization accompanied the conceptual shift. Once voices became

signals, they could be measured and specified. No longer did the system

merely deliver conversations according to some vague notion of clarity.

Now the telephone company delivered products: signals within a specific

frequency range, at a specified volume, and with a specified amount of

noise. This transformation required standard measures: the “mile of standard

cable,” for example, became the “transmission unit,” renamed the

“bell,” and eventually standardized in the “decibel,” smaller by a factor of

ten (and still today the standard measure of attenuation). Noise itself

became a measurable quantity (based on thermodynamics), and the limiting

factor in quality.19 The message was no longer the medium, now it was

a signal that could be understood and manipulated on its own terms, independent

of its physical embodiment.

17. E. H. Colpitts,“Dr.H.D.Arnold,” Bell Laboratories Record 6 (June 1928): 411–13.

Actually,mechanical repeaters initially carried the transcontinental line but were quickly

replaced with electronic ones. Gradually, more repeaters were added and the number of

loading coils reduced; the coils reduced the bandwidth of transmission, and also reduced

the speed of signal propagation, which led to problems with echoes. Shaw, 389–92, provides

a detailed technical description of the transcontinental line. The line was not permanent

but rather was “built up by switches”when needed, as was the New York/Denver

line. Fagan (n. 9 above), 263–64.

18. H. H. Nance and O. B. Jacobs, “Transmission Features of Transcontinental Telephony,”

Journal of the American Institute of Electrical Engineers 45 (1926): 1062.

19. W. H. Martin, “Transmitted Frequency Range for Telephone Message Circuits,”

Bell System Technical Journal 9 (July 1930): 483–86, and “The Transmission Unit and

Telephone Transmission Reference Systems,” Bell System Technical Journal 3 (July 1924):

MINDELLK|KRethinking Feedback’s Myth of Origin

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A Signal Organization

The success of the transcontinental line proved to Carty and AT&T the

value of Jewett’s alliance of physics, electronics, and telephone engineering.

20 Duplicating this success in other arenas, however, would require an

organizational solidity as well. On 1 January 1925, the AT&T and Western

Electric engineering departments combined to form the Bell Telephone

Laboratories Incorporated (BTL). The new entity was responsible to AT&T

for fundamental research and to Western Electric for the products of

research, and the two companies funded it accordingly. Located at 463 West

Street in Manhattan, the lab had thirty-six hundred employees, including

two thousand scientists and engineers. Carty served as chairman of the

board, which also included vice presidents of Western Electric and AT&T.

Frank Jewett became president, and Harold Arnold director of research.

While an important milestone for corporate research, it is easy to overestimate

the importance of the foundation of the laboratory itself. The new

organization resembled the old Western Electric engineering department

with only moderate changes.21 Research conducted at Western Electric carried

on largely unaltered, as did the careers of the engineers. Indeed, it

would be inaccurate to characterize all of BTL’s work as industrial research

addressing fundamental scientific problems. Most of the staff of BTL,

including Harold Black, engaged in the creative, if routine, work of designing

telephone equipment and making it work. Despite the system-oriented

organization, no group within BTL did “system engineering” in the

post–World War II sense. The systems development department, to which

Black belonged, did not formulate an abstract vision of the system overall,

but in fact designed the actual circuits for the network, including equipment

structures, office layouts, and the electric power systems required to

run the equipment.22

Only the research department performed fundamental industrial

research in the classical sense. Headed by Harold Arnold and comprising

five hundred people, its mission was “to find and formulate broadly the

400–408. R. V. L. Hartley, “TU Becomes ‘Decibel,’” Bell Laboratories Record 7 (December

1928): 137–39. J. B. Johnson, “Thermal Agitation of Electricity in Conductors,” and H.

Nyquist, “Thermal Agitation of Electric Charge in Conductors,” Physical Review 32

(1928): 97–113.

20. The transcontinental line so solidified the alliance technically that loading coils

were gradually removed from the network. The transcontinental line was fully unloaded

in 1920, more than tripling the velocity of transmission, which reduced echo effects and

improved the “sense of nearness” of the speakers. Shaw (n. 6 above), 396.

21. Fagan, 54–55, compares BTL with the old AT&T and Western Electric engineering

organizations. Also see the organization charts in Shaw, 406, for its similarity to the

initial BTL organization outlined below.

22. Paul B. Findley, “The Systems Development Department,” Bell Laboratories

Record 2 (April 1926): 69–73.

laws of nature, and to be concerned with apparatus only insofar as it serves

to determine these laws or to illustrate their application in the service of the

Bell System.”Research covered nine main areas: speech, hearing, conversion

of energy between acoustic and electric systems (speakers and microphones),

electric transmission of intelligence, magnetism, electronic physics,

electromagnetic radiation, optics, and chemistry.23 Yet even within the

Bell System, the research department did not have a monopoly on fundamental

exploration, because the development and research (D&R) department

of AT&T, with a similar charter and eleven hundred engineers and

scientists, remained separate from BTL for the labs’ first ten years. The negative-

feedback amplifier emerged from interactions, and even conflicts,

between the concrete, technical culture of systems development and the

more theoretical research world growing within BTL.

The Technical Charge of Bell Labs

After the New York to San Francisco line in 1915, wires couldn’t go

much further (crossing the oceans was considered a problem for radio).

But it was one thing to span the continent and quite another to offer highcapacity,

economical service over that distance. Just keeping up with growing

demand proved a constant problem: the Bell System added eight hundred

thousand new subscribers in 1925 alone. Such expansion entailed

planning and forecasting future requirements based on the rate of growth

and detailed cost analysis to determine when new technologies were

required.24 Engineering studies evaluated a series of tradeoffs between the

diameter of the wire, the number of repeaters, the cost of the terminal

equipment, and the number of available channels. Increasing the capacity

over existing long-distance routes, and thereby cutting costs, began to drive

transmission development at Bell Laboratories.

Bell Labs engineers thus turned their attention to putting more conversations

onto a single line. The most promising method, carrier multiplexing,

modulated several voice signals onto high-frequency carrier signals. If

these modulations occur in distinct frequency bands they can all travel over

the same line, in much the same way that separate radio stations occupy the

single electromagnetic spectrum (indeed, the technique became known as

“wired wireless”).25 At the receiving end, a wave filter separates out the

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23. Paul B. Findley, “The Research Department,” Bell Laboratories Record 2 (June

1926): 164–70.

24. H. P. Charlesworth, “General Engineering Problems of the Bell System,” Bell

System Technical Journal 4 (October 1925), 515–41.

25. John Stone Stone, “The Practical Aspects of the Propagation of High Frequency

Electric Waves Along Wires,” Journal of the Franklin Institute 174 (October 1912),

described high-frequency multiplex telephony as “identical with that of the new continuous

wave train” radio, and included the Alexanderson alternator as an element of a tele-

MINDELLK|KRethinking Feedback’s Myth of Origin

415

voice channel (figs. 1 and 2). The idea had been around for a long time:

both Elisha Gray and Alexander Graham Bell had investigated carrier techniques

in their telephone research.26 But vacuum tubes made carrier

telephony practicable by allowing signals to be cleanly modulated, filtered,

and amplified. The first commercial carrier system, type A, was installed in

1918, putting four two-way channels on open-wire pairs.27 Still, carrier had

its problems: because of the high frequencies, carrier signals faced greater

attenuation than traditional voice-band signals and hence required more

repeaters.

Another means of increasing capacity was transmission through cables,

carrying ten times as many circuits as open wires but at the cost of high

attenuation. In October 1925 a cable opened between New York and

Chicago, but with delicate and precise construction pushing the limits of

the medium. Success came at great cost in machinery and material, requiring

an expensive, low-resistance cable and extensive loading and repeater

equipment.28 Making long cables practicable and economical required

numerous repeaters and vast numbers of technicians distributed along the

route to maintain the delicate devices. A simple comparison clarifies the

difficulties of both carrier and cable transmission: the original (open-wire)

phone design. Also see Lloyd Espenschied, “Application of Radio to Wire Transmission

Engineering,” Bell System Technical Journal 1 (October 1922) 117–41. On “wired wireless,”

see Fagan (n. 9 above), 282.

26. E. H. Colpitts and O. B. Blackwell, “Carrier Current Telephony and Telegraphy,”

Journal of the American Institute of Electrical Engineers 40 (1921): 301–15, has a detailed

history of carrier methods in telephony, as well as an elegant explanation of carrier modulation

and transmission.

27. In 1924 the type C system went into service, incorporating lessons from the more

experimental A and B systems. Type C carrier systems were so successful the last one was

not removed from service until 1980. O’Neill (n. 2 above), 3–14.

28. See Charlesworth.

FIG. 1 Spectrum of a voice-band signal modulated onto a carrier.

transcontinental line used fewer than ten repeaters across the continent; a

carrier system over the same distance needed forty, a cable would require

two hundred, and carrier and cables combined would need even more.29

Hence carrier and cable transmission required amplifiers of extremely high

quality.

An ideal amplifier is a pure multiplier, taking an input signal and multiplying

it by some number (called gain) to produce an output. In other

words, a perfect amplifier has a linear relationship between input and output.

On a graph of output versus input, the amplifier’s response is literally

a straight line whose slope is the gain (it might also have a frequency

dependent time delay, called phase shift, which is measured as an angle

between input and output sine waves). For a vacuum tube, however, the

output versus input curve tends to be more S-shaped (fig. 3). This nonlinearity

introduces distortion and causes two problems. First, if the signal is

modulated on a carrier the nonlinearity produces extraneous harmonics

outside of the desired signal band. This becomes a problem with several signals

carrier-modulated onto the same wire. The harmonics from one channel

overlap the bands of others, causing cross talk—one conversation

bleeding through into another (fig. 4). Second, since each amplifier adds a

little distortion, a long line with numerous repeaters can garble the speech

beyond recognition. Thus, for BTL, as the line became longer and longer,

and as more and more signals squeezed onto a single wire, the amplifiers

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29. O’Neill, 63, table.

FIG. 2 Carrier modulation.

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had to become correspondingly higher in quality. This problem became a

high priority for Bell Labs at its founding.

The Search for a Linear Amplifier

The first approach was to make the vacuum tubes themselves more linear.

It was to this problem that Harold Black turned his attention when he

joined the systems development department of Western Electric in 1921. A

Massachusetts native, he had graduated that year from Worcester

Polytechnic Institute in electrical engineering. At Western Electric Black

worked with Mervin Kelley and the vacuum-tube department, but with lit-

FIG. 3 Typical vacuum-tube nonlinearity. The output anode

current is not a linear function of the input grid voltage.

FIG. 4 Nonlinear amplifier causing distortion and cross talk in a carrier system.

30. This account is based on Black, “Inventing the Negative Feedback Amplifier” (n.

1 above), and Harold S. Black to A. C. Dickieson, 16 June 1974, AT&T archives,Warren,

N.J. For a typical effort to design linear vacuum-tube amplifiers, see E. W. Kellogg,

“Design of Non-Distorting Power Amplifiers,” Electrical Engineering 44 (1925): 490.

31. Harold S. Black, U.S. Patent No. 1,686,792, “Translating System.”

32. This assumption holds to within 1/µ, so if the amplifier gain is 100, then 1 percent

of the gain is determined by the vacuum tube and 99 percent by the feedback network.

33. Black, “Inventing the Negative Feedback Amplifier.”

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tle success.Vacuum tubes, despite their utility as circuit elements, remained

subtle, unruly—and nonlinear—devices (hence Kelley’s efforts, years later,

overseeing the development of the transistor).30

Black began to rethink the problem in terms of signals. He conceptualized

the output of the amplifier as containing a pure, wanted component,

the signal, and an impure, unwanted component, the distortion. The problem,

then, was to somehow separate the two and keep only the pure signal.

He came up with a clear, if inelegant, solution: a “feed-forward” amplifier

that generated a copy of its own distortion and subtracted it from the output

signal. Black built a laboratory prototype that achieved the desired

result, and he applied for a patent in 1925.31 Though this setup proved that

a low-distortion amplifier was possible, it was far from practicable. Black’s

overly complex new amplifier required careful attention and continuous

adjustment, which engineers could do in a testing lab but not for a system

deployed in the field.

STABILIZING BLACK’S BOX

For three years Black struggled to simplify his solution. Finally, in 1927,

he had the epiphany on the ferry: if the gain of the amplifier were reduced

by some amount, and that amount fed back into the input, the linearity

could be greatly improved. In fact, distortion was reduced (that is, linearity

improved) by the same factor by which the gain was reduced. Black published

a simple explanation of the idea in a 1934 paper (fig. 5), showing that

the gain of the amplifier depends primarily on the feedback network, , and

not on the gain, µ, of the amplifier itself.32 The feedback network can consist

of only passive elements, such as resistors, capacitors, and inductors,

that are both more linear than vacuum tubes and more stable with respect

to temperature and other changes over time. Consider an example: a feedback

amplifier with a vacuum-tube gain of 100,000 is enclosed in a feedback

loop that reduces its gain to 1,000. The linearity of the amplifier overall

thus increases by a factor of 100, an incredible improvement. The price,

of course, is to throw gain away and settle for a much reduced level of

amplification. On 29 December 1927, Black and BTL engineers succeeded

in making a feedback amplifier whose distortion was reduced by a factor of

100,000 (and whose gain was reduced accordingly).33

34. Ibid., 59–60.

35. Black to Dickieson; Harold S. Black, patent application 298,155, 8 August 1928;

“File History of Black Application Serial No. 298,155,” AT&T archives.

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Still, Black had no easy time convincing others at Bell Labs of the utility

of his idea. He recalled that Jewett supported him, but that the director

of research, Harold Arnold, refused to accept a negative-feedback amplifier

and directed Black to design conventional amplifiers instead.34 Black had

similar difficulties with the U. S. Patent Office. His application for a “Wave

Translation System,” originally filed in 1928, was not granted until 1937.35

To a generation of engineers who had struggled to make the vacuum tube

amplify at all, throwing away the hard-won gain seemed absurd.

More important, no one could understand how an amplifier’s output

could be fed back to its input without a progressive, divergent series of

oscillations. Bell engineers at the time found it difficult to make a high-gain

amplifier without feedback. Subtle, uncontrolled feedback paths would

arise through unintentional effects such as stray capacitance between wires,

or even between elements within the tube itself, and cause the amplifier to

go into “parasitic oscillation” or “singing” (much like the whistling in a

FIG. 5 Harold Black’s negative feedback amplifier. (Harold S. Black, “Stabilized

Feedback Amplifiers,” Bell System Technical Journal 13 [January 1934]: 3.)

poorly tuned public address system). In 1924, for example, two BTL engineers,

H. T. Friis and A. G. Jensen, studied what they called “feed-back or

regeneration” as it occurred through a tube, noting that it “makes the total

amplification vary irregularly in a very undesirable manner and also makes

the set ‘sing’ at certain frequencies.”36 Black’s work went against the grain

for experienced amplifier designers: they sought to eliminate feedback, not

to incorporate it.

Black interpreted the resistance to his ideas as evidence of their radical

nature. Yet he was an engineer with a bachelor’s degree in the systems

department; he did not possess the analytical sophistication, the communications

skills, or the prestige of the research scientists at BTL. His lab

assistant during this period, Alton C. Dickieson, recalled Black as clashing

constantly with his own management and the rest of BTL. Dickieson’s recollections

of Black’s troubles parallel the inventor’s own accounts, so his

memory seems credible.37 Such conflicts were one thing for a lucid genius,

but Black was far from eloquent.“A compulsive, non-stop talker,” Dickieson

recalled, Black “was inventive and intuitive, but not particularly clear at

exposition.” His negative-feedback circuit was only the latest in a series of

attempts over a period of several years, all of which Dickieson wired up and

built, but, as he recalled, “none of the schemes we tried showed any real

promise.” Dickieson also remembered “quite a bit of rivalry” between the

Ph.D.-trained researchers and the systems people. “There seemed to be

some feeling that exploratory development was the exclusive province of the

research people. Mathematicians such as Thornton Fry [head of BTL’s

math department] found Black’s mathematics beneath contempt.”38

Black—restless, creative, and a bit arrogant—was traversing the established

boundaries of the organization, and running headlong into the cultural differences

between the research department and his own lower-status systems

department.

Credible as Dickieson’s recollections seem, no contemporary accounts

exist to support or refute them. The documents do allow, however, a thorough

analysis of Black’s ideas, and how Black himself had to transform

them (and enlist others to transform them) in order to win their acceptance.

A key point involves his claim that the epiphany on the ferry included

a concern for dynamic stability, that if he “kept the device from oscillating

(singing, as we called it then)” it would work. He implies that he understood

“stability” of the amplifier as the central problem. But a look at

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36. H. T. Friis and A. G. Jensen, “High Frequency Amplifiers,” Bell System Technical

Journal 3 (April 1924).

37. See, for example, Black, “Inventing the Negative Feedback Amplifier” (n. 1

above) 59–60, for Black’s conflict with H. D. Arnold and intimations of constant friction

with his superiors.

38. A. C. Dickieson to M. J. Kelley, 6 July 1972, AT&T archives, 43 09 03. Emphasis

added.

39. Friis and Jensen, 204.

40. Dickieson to Kelley.

41. “When many amplifiers are worked in tandem . . . it becomes difficult to keep the

overall circuit efficiency constant, variations in battery potentials and currents, small

when considered individually, adding up to produce serious transmission changes in the

overall circuit”; Harold S. Black, “Stabilized Feedback Amplifiers,” Bell System Technical

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Black’s conception of stability at the time reveals it to be different from the

standard meaning of freedom from oscillation. In fact, Black’s conceptions

of both negative feedback and stability differed markedly from those of

much of the engineering community at the time, although they would have

been familiar to engineers working on the telephone network.

TWO CULTURES OF FEEDBACK AND STABILITY

Today the “negative” in negative-feedback amplifiers means that the

feedback signal subtracts from the input signal rather than adding to it

(that is, the sign of the feedback signal is reversed). James Watt’s flyball governor

on a steam engine offers an analogy: when the engine speeds up, the

spinning balls slow it down; when the balls spin slower, they speed up the

engine. Hence the feedback is negative.

In Black’s time, however, the definition of this specific-sounding term,

“negative feedback,” had yet to be settled. The idea of positive feedback had

become current in the 1920s with the introduction of the regenerative

amplifier. Positive feedback, or regeneration, in a radio amplifier increased

the sensitivity of a receiving tube by sending a wave back through an amplifier

many times. Black insisted that his negative feedback referred to the

opposite of regeneration: gain was reduced, not increased. Yet, to return to

the analogy of the steam engine governor, Black’s use of “negative” means the

energy required to spin the balls reduces the energy output of the engine, not

that the balls trigger an action that slows it—hardly a significant effect for a

steam engine. In their 1924 paper Friis and Jensen had made the same distinction

Black had between positive feedback and negative feedback, that is,

distinguishing one from the other not by the sign of the feedback itself but

rather by its effect on the amplifier’s gain.39 In contrast, Nyquist and Bode,

when they built on Black’s work, referred to negative feedback as that with

the sign reversed. Black had trouble convincing others of the utility of his

invention in part because confusion existed over basic matters of definition.

Misunderstanding also arose over the critical idea of stability. Dickieson

recalled why those concerned with singing in amplifiers did not take Black

seriously: “Harold did not even approach the question of stability—he simply

assumed that it did not sing.”40 Actually, Black was deeply concerned

with stability: his first published paper on the amplifier appeared in 1934

with the title, “Stabilized Feedback Amplifiers.” But to Black “stability”

referred not to freedom from oscillation but to the long-term behavior of

components in the telephone network.41 Life in the network exposed a tele-

phone repeater to a harsh world, and Black sought to insulate the signal

from brutal reality.He wanted to use feedback to stabilize the characteristics

of the amplifier over time. Temperature changes, aging of components,

changes in the power supply, and any number of other factors could affect

the performance of an amplifier. Rain and temperature fluctuations, for

instance, changed the resistance of the wire and caused significant variations

in attenuation, sometimes by a factor of a hundred or more over the course

of a single day, and to comparable degree across the change of seasons.42

These fluctuations could greatly alter the physics of transmission, a potentially

disastrous effect for systems operating close to their physical limits.

Yet to the scientifically trained engineers at BTL, stability, in the sense

of freedom from oscillation, was the main difficulty of the feedback amplifier.

Homer Dudley, discussing Black’s paper in the journal Electrical

Engineering, listed freedom from singing as one of the two most important

problems for the amplifier.43 Yet this type of stability was not Black’s concern.

His original patent application, filed in 1928, makes no mention of

even the possibility of singing or oscillation.44 When resubmitting the

application in 1932, he added this clarification: “Another difficulty in

amplifier operation is instability, not used here as meaning the singing tendency,

but rather signifying constancy of operation as an amplifier with

changes in battery voltages, temperature, apparatus changes including

changes in tubes, aging, and kindred causes . . . Applicant has discovered

that the stability of operation of an amplifier can be greatly improved by

the use of negative feedback.”45 Black even acknowledges the other meaning

of stability, but assigns it unequivocal second billing: “Applicant uses

negative feedback for a purpose quite different from that of the prior art

which was to prevent self-oscillation or ‘singing.’To make this clearer, applicant’s

invention is not concerned, except in a very secondary way . . . with the

singing tendency of a circuit. Its primary response has no relation to the

phenomena of self-oscillation” (emphasis added).46 In the patent, Black

“simply assumed” that the amplifier did not oscillate.

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Journal 13 (January 1934). This paper was presented at the winter convention of the

American Institute of Electrical Engineers,New York, January 1934, and also published in

Electrical Engineering 53 (January 1934): 114–20. See also the discussions of the paper in

Electrical Engineering by F. A. Cowan (April 1934): 590; G. Ireland and H. W. Dudley

(March 1934): 461–62; and H. Nyquist (September 1934): 1311–12.

42. H. A. Affel, C. S. Demarest, and C.W. Green, “Carrier Systems on Long Distance

Telephone Lines,” Bell System Technical Journal 7 (July 1928): 384. Green was Harold

Black’s boss.

43. Dudley, discussion of Black, “Stabilized Feedback Amplifiers.”

44. Harold S. Black, patent application 298,155; “File History of Black Application

Serial No. 298, 155” AT&T archives.

45. Harold S. Black, U.S. Patent No. 2,102,671, “Wave Translation System,” 2.

46. Ibid.

47. In 1921, for example, Colpitts and Blackwell wrote that singing in a carrier system

could arise when the gain was greater than one and when there existed “sufficient

unbalance” between the circuits. Colpitts and Blackwell (n. 26 above), 313.

48. In 1926 Harvey Fletcher analyzed the howling telephone as a dynamic electrical

system to understand the relationship between impedance, frequency, and the tendency

to break into the oscillation; “The Theory of the Operation of the Howling Telephone

with Experimental Confirmation,”Bell System Technical Journal 5 (January 1926): 27–49.

Fletcher’s paper does not employ the terms “stability” or “feedback” in its analysis,

although it does analyze electro-acoustic circuits that greatly resemble canonical feedback

systems. Shaw (n. 6 above), 382–83. On the problems of handset howling, see Fagan

(n. 9 above), 146–50.

49. Bennett (n. 2 above), 77. See also Ronald M. Foster, “A Reactance Theorem,” Bell

System Technical Journal 3 (April 1924): 266.

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Black’s conception of stability, strange as it may seem, derived from his

position in the systems development department as opposed to the

research department. Where a researcher might focus on the theoretical

behavior of the system, Black was concerned with its concrete, daily characteristics.

To system engineers such as Black, “stable” amplifiers were those

that retained consistent performance in the face of the varying conditions

experienced by equipment in the telephone network. Consistency, regularity,

and stability of the circuit elements were critical to transmission systems.

Black employed this operational conception of stability in the analysis

of his amplifier. He used the term stability as an engineer who saw the

system as a concrete, operational entity, not as one who thought in abstract

diagrams.

Nevertheless, system engineers, despite their emphasis on transmission

stability, should also have been familiar with dynamic stability. Repeater

amplifiers had always had problems with singing; they would sing if the signal

from one direction of transmission leaked into the other (a full repeater

requires two amplifiers, one for each direction of transmission). In

response to these problems, telephone engineers filtered out the singing frequencies

and limited the amount of gain in each repeater. Carrier systems

also tended to sing, either locally or through the transmission line.47 The

now familiar telephone handset, introduced in the late 1920s, depended on

understanding and preventing the singing or “howling” that resulted from

the mouthpiece picking up sound from the earpiece.48 Moreover, the stability

of motion had been a popular topic in physics in the late nineteenth

century, and at least some telephone engineers in the 1920s were aware of

it, although they were unsure of its relevance to vacuum-tube circuits.49

Multiple, overlapping conceptions of negative feedback and stability

thus surrounded the introduction of Black’s amplifier. The Bell Laboratories

research culture was not monolithic, but rather comprised at least

two engineering subcultures: Ph.D.-level mathematicians and scientists

interested in fundamental questions, and system engineers such as Black,

concerned with building the network and keeping it running. Their differing

backgrounds, and differing notions of ideas such as “stability,” help

explain why the research department did not take Black seriously. As

Nyquist and Bode’s contributions make clear, it would take both approaches

to make the feedback amplifier a practical reality.

When Black invented the negative-feedback amplifier, he invented a

different machine from both the one it eventually became and the one he

remembered. Especially in light of his claim that he recognized feedback as

a unifying principle across different types of systems, these clashing visions

raise the question of whether Black drew on the long tradition of regulators

and governors that preceded him.

SINGING AND HUNTING

Feedback techniques had of course been commonly used for a long

time in governors, regulators, thermostats, automatic pilots, and numerous

other devices. In his memoirs, Black said that he understood his feedback

amplifier as part of that technological trajectory. The significance of the

origin myth rests on Black’s supposed recognition that negative feedback is

isomorphic across diverse types of systems. Indeed, Black’s patent, as

issued, states that the negative-feedback principle applies to more than

electronic amplifiers: “the invention is applicable to any kind of wave transmission

such as electrical, mechanical, or acoustical . . . the terms used have

been generic systems.” But the patent never specifies what those other

applications might be, and a steam-engine governor, an automatic pilot, or

a servomechanism fit only loosely into the category “wave translation system”

(the title of Black’s patent). Black likely had in mind more directly

analogous systems, such as the numerous electro-acoustic translations

required in telephony. Neither the patent, nor any of Black’s early writings,

nor the writings of any of the BTL feedback theorists for at least ten years,

mention regulators, governors, automatic pilots, or any of the myriad

devices we now understand as employing negative feedback.

Nonetheless, such devices were themselves in wide use within the telephone

network. Telephone repeaters needed regular adjustment as the

characteristics of the transmission lines changed in response to environmental

changes. In the late 1920s AT&T installed automatic regulators in

about every fourth repeater station; these devices adjusted amplifier gain in

response to a feedback loop that sensed the wire’s characteristics. In 1929,

for example, the New York/Chicago line included six regulating stations

among its twenty repeaters.50 In this light, Black’s stability of transmission

was a kind of automation: his stable feedback amplifiers relieved network

maintenance personnel of the task of adjusting the delicate amplifiers.51

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50. E. D. Johnson, “Transmission Regulating System for Toll Cables,” Bell Laboratories

Record 7 (January 1929): 183–87.

51. Ireland (n. 41 above).

52. Hugh M. Stoller, “Synchronization and Speed Control of Synchronized Sound

Pictures,” Bell System Technical Journal 8 (January 1929): 184–95. Also see H. M. Stoller

and E. R. Morton, “Synchronization of Television,” Bell System Technical Journal 6

(October 1927): 604–15, and H. M. Stoller “Speed Control for the Sound-Picture

System,” Bell Laboratories Record 7 (November 1928): 101–5. W. Trinks, Governors and

the Governing of Prime Movers (New York, 1919).

53. H. M. Stoller, “Speed Control for the Sound-Picture System,” Bell Laboratories

Record 7 (November 1928): 101–5. Stoller also published on voltage regulators; H. M.

Stoller and J. R. Power, “A Precision Regulator for Alternating Voltage,”Transactions of the

American Institute of Electrical Engineers 48 (1929): 808–11.

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Regulators and governors could also be found within BTL’s engineering

culture. Sound movies, for example, required tight control lest variations in

film speed change the pitch of the sound and become annoying to the

viewer. Similarly, early television systems in development at BTL in the

1920s employed large mechanical disks to scan the picture (instead of the

later electron beams). Keeping these disks exactly aligned required precise

regulators. In a series of papers published between 1927 and 1929, Hugh

Stoller of the apparatus department explicitly compared his speed controls

to steam engine governors and even discussed the phenomenon of “hunting,”

equivalent to singing in an amplifier.52 He included a drawing of a flyball

governor in the Bell Laboratories Record, and used “stability” in the

sense of freedom from oscillation. Stoller even used the term “feed back”

for the electrical speed regulation in his own circuits.53 Had Black looked,

he would have found discussion of traditional mechanical regulators in his

own organization and its publications

In fact, the analogy between a mechanical regulator and an electronic

one would not have been a great leap for Black, as Stoller made the connection

clearly but without much fanfare. But Black did not take that step.

He did not see his negative-feedback amplifier as analogous to regulators

and governors and he did not see hunting in those devices as comparable

to singing in an amplifier.

This critical look at Black’s conception of his amplifier provides some

perspective on the origin myth. Black’s flash of insight, however much it

enlightened him on the structure of negative feedback, did not give him an

artifact he could sell, nor did it give him the modern conception of a negative-

feedback amplifier or a broadly applicable notion of feedback. But it

would be wrong to suggest that Black would have found a more receptive

audience for his invention had he realized that the amplifier’s stability was

a key problem, that negative feedback worked similarly to regulation, that

singing resembled hunting. These judgments we can only make with hindsight.

The important historical point must be made positively: to Black the

amplifier was a means of throwing away gain to achieve linearity in a vacuum

tube, a way of stabilizing the repeaters in the telephone system subject

to variation and hazard. On these points he was always clear, consistent,

and determined.

In his 1934 paper “Stabilized Feedback Amplifiers,” Black presented his

amplifier to the world. He attributed the delay from his 1927 insight to the

1934 paper to corporate secrecy, but that can account for at most five of the

seven years. Black’s paper, in fact, was not the first word from the telephone

company on the negative-feedback amplifier; that word, a paper that Black

cited and discussed, had appeared two years earlier. It was the work of an

ally, to whom Black had turned for help, but who remade Black’s box.Harry

Nyquist rethought negative feedback by redefining stability.

DIAGRAMMING STABILITY

Harry Nyquist, a Swedish immigrant with a Ph.D. in physics from Yale

University, brought negative feedback from Black’s curiosity into the network.

Nyquist belonged not to BTL but to the development and research

department of AT&T; he stabilized Black’s box by bringing it into the frequency

domain.54

In May 1928 Nyquist asked Black to join in developing a new carrier

system and to include the negative-feedback amplifier in a demonstration

of new transmission techniques. This project, known as the Morristown

Trial, installed seventy-eight repeaters of Black’s design spaced every

twenty-five miles of cable. The cable folded back on itself, so all the amplifiers

were located in the same laboratory in Morristown, New Jersey.55

Before his work on the Morristown trial, Nyquist had worked on problems

of both transmission stability and regulation.56 With the Morristown trial,

Nyquist brought this experience to amplifiers.

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54. Hendrik W. Bode, “Harry Nyquist” (obit.), IEEE Spectrum 14 (April 1977).

55. For a detailed account of the Morristown Trial, see A. B. Clark and B.W. Kenall,

“Carrier in Cable,” Bell System Technical Journal 12 (July 1933): 251–62; see also O’Neill

(n. 2 above), chap. 5, “Carrier on Cable.”Making the system work as planned proved no

simple matter, but such was the purpose of an engineering trial. Repeater amplifiers did

not pose the only problems: cable design (the number, size, and shielding of each of the

many wire pairs) proved especially critical as well. Shielding, grounding, and interference

between signals plagued the system. Because of the depression, AT&T changed its

emphasis from new systems to improving capacity with the existing plant. Engineers at

BTL had several years to refine the results of Morristown and to work on ways of compressing

more transmission onto existing wires. The Morristown Trial formed the basis

for the K-type carrier system, introduced in the late 1930s, which carried twelve voice

channels on cables at frequencies from 12 to 50 kHz for distances up to 4,000 miles. Kcarrier

furnished 70 percent of the increased capacity in the country (which doubled

from 1940 to 1947) and remained in service until at least 1980. K-carrier also included a

pilot wire-transmission regulation scheme, with an automatic self-balancing regulator

and a self-synchronizing motor. C.W. Green and E. I. Green, “A Carrier Telephone System

for Toll Cables,” Bell System Technical Journal 17 (January 1938).

56. H.Nyquist,U.S. Patent No. 1,887,599, “Constant Current Regulation”; U.S. Patent

No. 1,683,725, “Phase Regulating System.” Applications filed in 1928 and 1926, respectively.

B. P. Hamilton, H. Nyquist, M. B. Long, W. A. Phelps, “Voice-Frequency Carrier

Telegraph System for Cables,” Transactions of the American Institute of Electrical Engineers

44 (February 1925): 327–39. This paper (which erroneously gives Nyquist’s first initial as

N.) also includes a discussion of the precision governor required for generating carrier

frequencies for this telegraph system, suggesting that Nyquist had exposure to regulation

before his 1932 paper on feedback, “Regeneration Theory,” Bell System Technical Journal

11 (January 1932): 126–47.

57. Nyquist, discussion of Black, “Stabilized Feedback Amplifiers” (n. 41 above).

58. Nyquist, “Regeneration Theory”; Bennett (n. 2 above), 82–84.

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His 1932 paper, “Regeneration Theory,” provided a rigorous set of

measurable conditions by which to determine the stability of a feedback

amplifier. He redefined feedback as a frequency-dependent phenomenon,

and stability in terms of transient disturbances composed of different frequencies

(essentially shocks to the system). “For the purpose of studying

the singing condition,” he wrote, “it is permissible to regard the feed-back

phenomenon as a series of waves.”57 For Nyquist, if all disturbances die out

after a finite period of time, the circuit is stable. If any disturbance goes on

indefinitely, the circuit is unstable (fig. 6).58 In light of this definition, it

became clear to Nyquist that two conditions are necessary and sufficient to

make an amplifier unstable and cause singing: first, if the wave coming

around the feedback loop equals or exceeds in magnitude the input to the

amplifier, that is, if the gain is equal to or greater than one; second, if the

FIG. 6 “For the purpose of studying the singing condition, it is permissible to

study the feedback condition as a series of waves. . . .” (H. Nyquist, discussion

of a paper by H. S. Black, “Stabilized Feedback Amplifiers,” Electrical Engineering

53 [September 1934], 1311.)

feedback wave is inverted compared to the input wave (that is, its phase

shift is 180°). If these conditions are both met for any frequency, then the

amplifier is unstable and will oscillate.Nyquist turned these conditions into

a simple, empirical method for determining stability: open the loop, measure

the amplifier’s parameters (gain and phase shift) for varying frequencies,

record them on a polar plot, and use the plot to graphically determine

stability (fig. 7).59 This plot became known as a “Nyquist diagram,” and the

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59.Nyquist’s method was this: First, break the loop so the amplifier will not feed back

on itself. Then measure its “open loop characteristics,” plotting two easily measured quantities,

gain and phase, against each other as they vary with the frequency of the input signal.

If the resulting curve encloses the point that represents a unity gain and 180° shift, the

system is unstable. If the point lies outside the curve, the system is stable. Nyquist,

“Regeneration Theory.” In 1934, BTL engineers compared Nyquist’s criterion to Routh’s

test from his 1877 Adams Prize paper on stability in dynamic mechanical systems. They

FIG. 7 Original-style Nyquist diagram, showing gain (magnitude) versus phase

shift (angle) plotted for several different frequencies on a polar plot. Since the

curve does not enclose the point (1,0), the system is stable. If curve did enclose

that point, the system would be unstable. (After H. Bode, “Feedback: The History

of an Idea,” reprinted in Selected Papers on Mathematical Trends in Control

Theory, ed. Richard Bellman [New York, 1964], 114.)

test remains the “Nyquist stability criterion” or the “Nyquist criterion.”60

This technique reduced a significant amount of calculation to a simple procedure,

a literary technology, and a tool for engineers to think with. It is still

used today.

FEEDBACK AS A NETWORK PROBLEM

It remained for one more BTL engineer, Hendrik W. Bode, to complete

telephony’s prewar phase of feedback theory. Bode came to BTL in 1926,

fresh from a master’s degree at Ohio State, where had also done his undergraduate

degree; he received a Ph.D. in physics from Columbia in 1935.

Bode’s expertise was not in feedback, nor even in amplifiers or vacuum

tubes, but in the useful but esoteric network theory. The theory of electrical

networks dealt not with the telephone network itself but with abstractions

of the numerous small networks of resistance, capacitance, and inductance

that determined its behavior.61

As the Bell System adopted carrier transmission and began to manipulate

signals in the frequency domain, electrical networks became increasingly

critical. Filter networks, for example, separated specific frequencies

out of the spectrum, and equalizer networks compensated for the distortion

in a transmission line. In 1934, Bode developed and published a general

theory that accounted for all types of networks. Bode called this work

“a sort of algebra” that allowed designers to manipulate network designs

graphically, without solving their tangled equations.62

Bode’s work on networks merged with feedback amplifiers because of

yet another new transmission medium, coaxial cable, which had only one

conductor surrounded by a conductive shield. These cables allowed several

hundred conversations to be multiplexed together and could also carry the

new broadband television signals. As with the jump from open wire to

cable, the jump to coaxial cables placed heavier demands on repeaters,

equalizers, and system performance overall.63

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found the two stability analyses compatible, and thus linked the new feedback theory to

the older work on dynamic stability. Despite this link, however, their work makes no mention

of applying feedback amplifier theory to other dynamic systems. E. Peterson, J. G.

Kreer, and L. A. Ware, “Regeneration Theory and Experiment,” Bell System Technical

Journal 13 (October 1934): 680–700.

60. Bennett, 83.

61. S.Millman, ed., A History of Engineering Science in the Bell System: Communications

Sciences (1925–1980) (Murray Hill, N.J., 1984), 16–17. Also see O’Neill (n. 2 above),

204–8. For a good summary of the work on network theory in the twenties and thirties,

see Karl L. Wildes and Nilo A. Lindgren, A Century of Electrical Engineering and Computer

Science at MIT, 1882–1982 (Cambridge, 1985), chap. 9, “Network Analysis and

Synthesis: Ernst A. Guillemin.”

62. H. W. Bode, “General Theory of Electric Wave Filters,” Journal of Mathematics

and Physics 13 (November 1934): 275–362.

63. L. Espenschied and M. E. Strieby, “Systems for Wide-Band Transmission over

In 1934, Bode set about designing an equalizing network for a repeater

amplifier for coaxial cable.64 The trouble was, Bode had to design the equalizer

network after the amplifier had already been designed, and such post

hoc modification made the amplifier unstable. “I sweated over this problem

for a long time without success,” Bode recalled. Finally, “in desperation,” he

redesigned the entire amplifier using techniques from network theory.

Where Nyquist had provided a way to determine if an existing amplifier

was stable, Bode now aimed to design a stable amplifier to meet specified

parameters for performance.

Bode’s 1940 paper “Relations Between Attenuation and Phase in Feedback

Amplifier Design,” remains his best-known and most succinct contribution

to feedback theory. The opening pages have a decidedly pessimistic

tone, as Bode notes that the stability of a feedback amplifier “is always just

around the corner.”He begins: “The engineer who embarks upon the design

of a feedback amplifier must be a creature of mixed emotions. On the one

hand, he can rejoice in the improvements in the characteristics of the structure

which feedback promises to secure him. On the other hand, he knows

that unless he can finally adjust the phase and attenuation characteristics

around the feedback loop so the amplifier will not spontaneously burst into

uncontrollable singing, none of these advantages can be actually realized.”65

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Coaxial Lines,” Bell System Technical Journal 13 (October 1934): 654–79. M. E. Strieby, “A

Million-Cycle Telephone System,” Bell System Technical Journal 16 (January 1937): 1–9.

See also O’Neill, chap. 6, “Coaxial Cable,” especially 131–39. The system Bode worked on

became known as the L1; it was tested on a line from New York to Philadelphia in

1936–38 and put into service just before the war.

64. Here Bode came to a critical realization. The overall amplifier behaves like the

reciprocal of its feedback elements—when the feedback path divides, for example, the

amplifier overall multiplies, when the feedback element passes certain frequencies, the

amplifier overall blocks those frequencies, and vice versa. A passive equalizer had to

mimic the reciprocal of the transmission line to cancel out its effects. In network theory,

however, creating the inverse of a physical network could be a complicated affair, and

might not even be physically possible. Bode realized, however, that since the feedback

amplifier inverted the behavior of the feedback network, the problem of equalizer design

reduced to the simpler problem of designing a feedback network to simulate the transmission

line exactly, rather than to invert it. H. W. Bode, “Variable Equalizers,” Bell

System Technical Journal 17 (April 1938): 229–44. Black wrote in 1934: “For many types

of frequency characteristics it is difficult, and for some impossible, to construct a passive

network having the exact inverse characteristic [as the transmission line].With this type

of [feedback] amplifier, however, it is only necessary to place in the feedback circuit

apparatus possessing the same characteristic as that to be corrected.” Black, “Stabilized

Feedback Amplifiers” (n. 41 above), 294.

65. Bode, “Relations Between Attenuation and Phase in Feedback Amplifier Design”

(n. 1 above). For other discussions of this paper, see Bennett (n. 2 above), 84–86;Millman,

29–30; O’Neill, 68–70. In later years, Bode displayed some aversion to Black’s version of

events. He wrote to A. C. Dickieson in 1974, after reviewing Black’s account, that “this is

not exactly how one ordinarily writes formal technical history [interestingly, Bode had

some notion of ‘formal technical history’]. . . . Have you thought of a less personalized

treatment in which pieces of Black’s account are woven in with expository text of your

own? . . . It might be possible to eliminate, for example, the references to Steinmetz and

Hartley, which seem to me to be irrelevancies. In a less personalized account, it might be

possible to present basic technological issues in a more satisfactory way. For example, as

the paper now stands it seems to imply that Black deserves credit for the pioneer investigation

of nonlinear effects in long systems. I doubt whether this is really accurate. . . . I was

also a little disturbed by Harold’s claim that he outfaced the U. S. Patent office on every

one of 126 claims. I didn’t know that the Patent Office gave ground that easily. In any case,

credit should probably go to the long-suffering patent attorney who wrote all those letters.”

Bode to Dickieson, 17 September 1974, AT&T archives.

66. Elsewhere he likened the feedback amplifier designer to “a man who is trying to

sleep under a blanket too short for him. Every time he pulls it up around his chin his feet

get cold.” H. W. Bode, “Design Method for Feedback Amplifiers—Case 19878,” 1 May

1936, AT&T archives.

67. Bode, “Relations Between Attenuation and Phase in Feedback Amplifier Design.”

68. Ibid., 426–35.

69. Bode, “Feedback: The History of an Idea,” in Bellman (n. 2 above), 117.

70. H.W. Bode,Network Analysis and Feedback Amplifier Design (New York, 1945), iii.

MINDELLK|KRethinking Feedback’s Myth of Origin

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Bode likens a feedback amplifier to a perpetual motion machine that

would work “except for one little factor” that never quite goes away, despite

all the tweaking.66 Bode elucidates the parameters (gain and phase shift)

“which impose limits to what can and cannot be done in a feedback design

. . . and [forbid] the building of a perpetual motion machine.” The price of

using feedback, he continues, “turns out to be surprisingly high.” It “places

a burden on the designer,” and without new tools “he is helpless.” Bode

seems to be addressing Black himself and his uncritical exuberance for the

benefits of feedback, regardless of stability problems. “Unfortunately, the

situation appears to be an inevitable one. The mathematical laws are inexorable.”

67 Like Nyquist, Bode developed simple, graphical techniques to

determine stability by plotting observed and analytic quantities. Like

Nyquist diagrams, these graphs survive today as “Bode plots.”

Nyquist’s stability conditions produced an answer: the amplifier is stable

or it is not. Bode’s technique assessed how much stability it had, with

quantitative measures. Bode also imposed limits on the possible performance

of the feedback amplifier by proving that “we cannot obtain unconditionally

stable amplifiers with as much feedback as we please” because too

much feedback could make the amplifier unstable.68 His name is permanently

associated with feedback, but he always linked it to its network roots:

“it is still the technique of an equalizer designer,” he wrote in retrospect. “I

can imagine that the situation may well seem baffling to someone without

such a background.”69 The title of Bode’s 1945 book Network Theory and

Feedback Amplifier Design reflects his primary experience in networks, with

secondary application to amplifiers. During World War II, Bode and BTL

widely distributed the unpublished manuscript to other laboratories working

on control systems.70 Bode acknowledged a certain amount of “unnec-

71. Ibid., iv.

72. H. Nyquist, “Certain Factors Affecting Telegraph Speed,” Bell System Technical

Journal 3 (April 1924): 324–46. For telegraph sampling, the main paper was H. Nyquist,

“Certain Topics in Telegraph Transmission Theory,” Transactions of the American Institute

of Electrical Engineers 47 (February 1928): 617–44. See also the discussion of this paper by

Nyquist’s son-in-law, John C. Lozier, “The Oldenberger Award Response: An Appreciation

of Harry Nyquist,” Journal of Dynamic Systems,Measurement and Control 98 (June 1976):

127–28. Nyquist’s measure, that a wave must be sampled at twice its bandwidth to be

transmitted without distortion, is frequently referred to as “the Nyquist rate.” A modern

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essary refinement” of the design methods in the book, but explains that

they were required for telephone repeater amplifiers, with their unusually

high standards for performance.71 Even today, through Bode’s plots, feedback

techniques retain the traces of the network theory of the 1920s.

Speaking Machinery and the Transmission of Information

The work done by Black, Bode, and Nyquist brought negative feedback

and the vacuum tube within the realm of signals, frequencies, and networks.

The high-quality linear repeater amplifiers these men developed

furthered the separation of the message inherent in the telephone signal

from the energy required to transmit it down the line. Black’s feedback

amplifier aimed to regulate transmission and insulate the performance of

the technical network from its physical and meteorological environment.

Nyquist and Bode addressed the immediate problems of frequency

response and dynamic stability. Because self-regulation could rapidly turn

to oscillation, avoiding instability became a primary concern of feedbackamplifier

design. Developing the feedback amplifier connected at every

point to problems of the telephone network, including long-distance transmission,

carrier modulation, and the role of fundamental research in the

system overall.

Negative-feedback amplifiers evolved together with a conception of the

network as a social device, and of machines as active speech producers—a

vision actively supported by the new research organization. Technically, this

vision incorporated both telegraphy and telephony, text and speech (and

later images), into theories of processing signals, manipulating them in the

frequency domain, and precisely matching them to transmission channels.

Indeed, at the same time that Nyquist was theorizing negative feedback he

was working out the relations between bandwidth and channel capacity, the

interchangeability of telephone and telegraph signals, and the effect of noise

on transmission rates. Nyquist also attacked the problem of chopping up a

signal into discrete bits or “signal elements,” transmitting them individually,

and then using them to reconstruct the original signal. Today, Nyquist’s

“sampling theorem” still determines the rates at which our analog world is

sampled and converted into digital form.72 Similarly, BTL researcher Ralph

Hartley’s work proposed quantitative measures for the transmission of signals

independent of their nature or content. Nyquist and Hartley laid the

groundwork for the theory of information that Claude Shannon would

articulate in 1948.73 And Homer Dudley, in an article titled “The Carrier

Nature of Speech,” explicitly compared human language to network traffic.

At the Century of Progress Exposition in Chicago in 1933, the AT&T exhibit

featured Dudley’s speech synthesizer and promoted the company’s new

Teletypewriter services.74 Other BTL researchers during these years developed

automatic switches, talking movies, stereophonic sound, artificial

organs for listening and speaking, and “invisible orchestras” for transmitting

high-fidelity audio over the network.75 Each furthered, in its own way,

the abstraction of signals and the extension of human activity by the telephone’s

spreading network.

Developments in communications theory did not simply reflect technical

systems and facilitate their convergence. They also supported AT&T’s

corporate goals. Frank Jewett, speaking to the National Academy of Sciences

in 1935, rejected the distinctions between types of signals: “We are

prone to think and, what is worse, to act in terms of telegraphy, telephony,

radio broadcasting, telephotography, or television, as though they were

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CD player, for example, samples music at 44 kHz in order to reproduce it in the audible

band of about 20 kHz. For Nyquist’s work on noise, see “Thermal Agitation of Electric

Charge in Conductors,” 110–13.

73. R. V. L. Hartley, “Transmission of Information,” Bell System Technical Journal 7

(July 1928): 535–63. See brief discussions of Nyquist and Hartley by E. Colin Cherry, “A

History of the Theory of Information,” Proceedings of the Institution of Electrical Engineers

98 (September 1951): 386, and by J. R. Pierce, “The Early Days of Information Theory,”

IEEE Transactions on Information Theory, no. 1 (January 1973): 3. In his foundational paper

on information theory, Shannon cited Nyquist’s two papers on telegraph transmission,

“Certain Factors Affecting Telegraph Speed” and “Certain Topics in Telegraph Transmission

Theory,” and Hartley’s “Transmission of Information” in the first paragraph.

Claude Shannon, “A Mathematical Theory of Communication,” parts 1 and 2, Bell System

Technical Journal 27 (July/October, 1948), 379–423, 623–56, reprinted in Claude Elwood

Shannon: Collected Papers, ed. N. J. A. Sloane and Aaron D.Wyner (New York, 1993), 5–83.

74. Homer Dudley, “The Carrier Nature of Speech,” Bell System Technical Journal 19

(October 1940): 495–515. “The Bell System Exhibit at the Century of Progress Exposition”

Bell Laboratories Record 11 (July 1933).

75. Kenneth Lipartito, “When Women Were Switches: Technology, Work, and

Gender in the Telephone Industry, 1890–1920,” American Historical Review 99 (October

1994): 1074–111. Sheldon Hochheiser, “What Makes the Picture Talk: AT&T and the

Development of Sound Motion Picture Technology,” IEEE Transactions on Education 35,

no. 4 (November 1992): 278–85. Harvey Fletcher, “The Nature of Speech and Its

Interpretation,” Bell System Technical Journal 1 (July 1922): 129; “Physical Measurements

of Audition and Their Bearing on the Theory of Hearing,” Bell System Technical Journal

2 (October 1923): 145; “Useful Numerical Constants of Speech and Hearing,” Bell

System Technical Journal 4 (July 1925): 375–86. Robert E. McGinn, “Stokowski and the

Bell Telephone Laboratories: Collaboration in the Development of High-Fidelity Sound

Reproduction,” Technology and Culture 24 (1983): 43.

things apart.” Jewett argued instead that these technologies merely represented

different embodiments of a common idea of communication.

“[T]hey are merely variant parts of a common applied science. One and all,

they depend for the functioning and utility on the transmission to a distance

of some form of electrical energy whose proper manipulation makes

possible substantially instantaneous transfer of intelligence.”76 Government

regulation persisted in making distinctions between media (radio, telephony,

and so on), each controlled by their own vested interests.When policy

followed science and treated all signals as equivalent, Jewett argued, then

AT&T, with its natural monopoly, would emerge as the unified communications

company: a builder of transmission, a carrier of long-distance signals,

and a switcher of information.

Jewett’s vision echoed Theodore Vail’s “one policy, one system” motto,

updated by the advances in technology, theory, and the organization of

research at AT&T in the 1920s and 1930s. Feedback theory at Bell Labs contributed

to the rapidly converging ideas about signals and communications

that Jewett articulated. It was in this environment that Harold Black had his

vision of feedback on the Lackawanna ferry in 1927.

Still, despite Jewett’s call to unify communications, Black, Nyquist, and

Bode kept their ideas within the existing network. They did not see their

contributions to feedback theory as significant to the world of governors,

regulators, servomechanisms, or automatic controls. Contrary to Black’s

recollection, the realization that feedback described common phenomena

in a variety of settings did not crystallize until World War II, when new

institutions brought engineers from diverse backgrounds together to construct

military control systems. Only then were the techniques developed at

BTL to deal with feedback, frequencies, and noise applied to mechanical

and hydraulic systems, and to the human operators themselves. Only then

did feedback become prominent as a general principle in engineering, and

only afterward, with the work of Norbert Wiener, Claude Shannon, and

numerous others, did Black’s, Bode’s, and Nyquist’s ideas move beyond

amplifiers and into a broad range of disciplines. Feedback is indeed fundamental

to our technological world, but Harold Black’s epiphany, more than

a foundational moment, was one of a series of technical insights that

allowed engineers to separate human communications from their electrical

substrates, to send them through geographically extensive networks, and to

represent the world in a common language of signals.

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76. Frank B. Jewett, “Electrical Communication, Past, Present, and Future,” speech to

the National Academy of Sciences, April 1935, reprinted in Bell Telephone Quarterly 14

(July 1935): 167–99.

 

 

 

In the Dec. 77 issue of IEEE Spectrum [1] Harold S. Black wrote:

http://digilander.libero.it/paeng/feedforward_concepts.htm

 

Inventing the ‘black box’: mathematics as a neglected enabling technology

in the history of communications engineering

Chris Bissell

The Open University, UK

Milton Keynes MK7 6AA

http://www.ieee.org/organizations/history_center/cht_papers/bissell.pdf

 

 

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