Butler was a satirist by trade, a prophet who knew that prophets who take themselves too seriously end up preaching to an audience of one. “There is a period in the evening, or more generally towards the still small hours of the morning, in which we so far unbend as to take a single glass of hot whiskey and water,” he admitted to the readers of the Canterbury Press in 1865. “We will neither defend the practice nor excuse it. We state it as a fact which must be borne in mind by the readers of this article; for we know not how, whether it be the inspiration of the drink, or the relief from the harassing work with which the day has been occupied, or from whatever other cause, yet we are certainly liable about this time to such a prophetic influence as we seldom else experience.”68
Although multimedia communication has so far neglected our sense of taste, Butler got the rest of it right. Anticipating modern purveyors of global networking, he presented his vision in terms of the content to which people would subscribe and locally understand. He knew that the development of telecommunications, facilitating the exchange of intelligence among human beings, brings with it the exchange of intelligence among machines. The drift of his thinking and the unspoken secret that he hinted at may be detected in a later comment, in Unconscious Memory, that “the component cells of our bodies unite to form our single individuality, of which it is not likely they have a conception, and with which they have probably only the same partial and imperfect sympathy as we, the body corporate, have with them.”69
3
THE GENERAL WIND
Far as all such engines must ever be placed at an immeasurable interval below the simplest of Nature’s works, yet, from the vastness of those cycles which even human contrivance in some cases unfolds to our view, we may perhaps be enabled to form a faint estimate of the magnitude of that lowest step in the chain of reasoning, which leads us up to Nature’s God.
—CHARLES BABBAGE1
At the close of a long and otherwise flattering letter, twenty-four-year-old Gottfried Wilhelm von Leibniz complained to eighty-two-year-old Thomas Hobbes in 1670, “I also wish that you might say something more clearly about the nature of the mind.”2 Ever since Hobbes and Leibniz, the nature of mind has been inextricably linked to the nature of machines. Mind has either been defined as a property of the machine, mysterious as the inner workings may be, or, alternatively, as a property beyond the machine, no less mysterious through being so diffused. Just as a cathedral organ, no matter how elaborate, cannot produce music without wind, philosophers have sought to identify the invisible ingredient that leads from the predictability of logic to the unpredictability of mind. Can the unlimited power of a mind be evoked by the limited substance of a machine?
Leibniz’s lifelong reflections on the nature of mind culminated in his Monadology of 1714, a universe of elementary mental particles that he called monads, or “little minds.” These entelechies (the local actualization of a universal mind) reflect in their own inner state the state of the universe as a whole. According to Leibniz, relation gave rise to substance, not, as Newton had it, the other way around. Our universe had been selected from an infinity of possible universes, explained Leibniz, so that a minimum of laws would lead to a maximum diversity of results. God was the supreme intelligence at both extremes of the scale. As Olaf Stapledon would later put it, “God, who created all things in the beginning, is himself created by all things in the end.”3
Leibniz enrolled in the University of Leipzig as a law student at age fifteen. His affinity for the law was a mixed blessing, which exercised and supported his interests in formal logic but throughout his life distracted him from scientific work. He became a mathematician by way of reputation, yet remained a courtier by way of life. “Leibniz’s tragedy was that he met the lawyers before the scientists,” concluded E. T. Bell.4 Nonetheless, Leibniz made fundamental contributions to mathematics on several fronts. The development of a calculus of continuous functions he shared, controversially, with Isaac Newton, while in combinatorial analysis—the study of relations among discrete sets—Leibniz had the field to himself.
Leibniz continued reasoning about reasoning where Hobbes left off. He attempted to formalize a consistent system of logic, language, and mathematics by means of an alphabet of unambiguous symbols manipulated according to definite rules. A fascination with formal systems and an insight into mechanical computation were combined in the person of Leibniz from the start. Encouraged by his initial steps toward symbolic logic—and by a working model of a calculating machine—Leibniz declared in 1675 to Henry Oldenburg, secretary of the Royal Society and Leibniz’s go-between with Isaac Newton, that “the time will come, and come soon, in which we shall have a knowledge of God and mind that is not less certain than that of figures and numbers, and in which the invention of machines will be no more difficult than the construction of problems in geometry.”5
Leibniz thus helped set in motion the two great movements that led to the age of digital computers in which we live. His calculating machine, demonstrated to the Royal Society of London on 22 January 1673, opened a new era in the mechanization of arithmetic. With his logical calculus, or calculus ratiocinator, he took the first steps toward the arithmetization of logic, and in his grand but fragmentary vision of a “universal symbolistic in which all truths of reason would be reduced to a kind of calculus,” he predicted the arithmetization of thought itself.6
Leibniz credited the invention of his calculator to the inspiration of “an example of the most fortunate genius,”7 the adding machine constructed in 1642 by nineteen-year-old Blaise Pascal. Leibniz’s invention, like Pascal’s, was commercially unsuccessful (“It was not made for those who sell oil or sardines,” Leibniz explained)8 and is now represented by a single specimen that was lost in an attic until 1879. But the Leibniz “stepped reckoner,” executing a multiple-digit addition cycle with each revolution of a stepped cylindrical gear, was reinvented several times, advancing the mechanization of accounting and finance as inexorably as the mechanization of industry was driven by steam. “Many applications will be found for this machine,” wrote Leibniz in 1685, “for it is unworthy of excellent men to lose hours like slaves in the labor of calculation, which could be safely relegated to anyone else if the machine were used.”9
Leibniz’s calculator, based on decimal arithmetic, was widely imitated, whereas his work in binary arithmetic languished for centuries before being embodied in mechanical form. He himself credited the invention of binary notation to the Chinese, seeing in the binary hexagrams of the I Ching the remnants of mathematical insights long obscured. “The 64 figures represent a Binary Arithmetic . . . which I have rediscovered some thousands of years later. . . . In Binary Arithmetic there are only two signs, 0 and 1, with which we can write all numbers. . . . I have since found that it further expresses the logic of dichotomies which is of the greatest use.”10 Leibniz saw binary arithmetic as both a practical aid to calculation and a logical calculus leading from the simple to the complex. Multiplication and division could be simplified by switching to numbers encoded in binary form. His notes show the development of simple algorithms, or step-by-step mechanical procedures, for translating between decimal and binary notation and for performing the basic functions of arithmetic as mechanically iterated operations on strings of 0s and 1s.
In 1679, Leibniz imagined a digital computer in which binary numbers were represented by spherical pellets, circulating within a kind of pinball machine governed by a rudimentary form of punched-card control. “This [binary] calculus could be implemented by a machine (without wheels),” he wrote, “in the following manner, easily to be sure and without effort. A container shall be provided with holes in such a way that they can be opened and closed. They are to be open at those places that correspond to a 1 and remain closed at those that correspond to a 0. Through the opened gates small cubes or marbles are to fall into tracks, through the others nothing. It [the gate array] is to be shifted from column to column as required.”11 In the shift registers at the
heart of the electronic microprocessor voltage gradients and pulses of electrons have taken the place of gravity and marbles, but otherwise things are running exactly as envisioned by Leibniz in 1679.
Leibniz’s ambitions in symbolic logic were similarly prescient, but also incomplete. He believed that “a kind of alphabet of human thoughts can be worked out and that everything can be discovered and judged by a comparison of the letters of this alphabet and an analysis of the words made from them.”12 But he never got around to completing more than a bare outline of his plan. “I think that a few selected men could finish the matter in five years,” he claimed, with an optimism echoed by developers of computer operating systems from time to time. “It would take them only two, however, to work out, by an infallible calculus, the doctrines most useful for life, that is, those of morality and metaphysics. . . . Once the characteristic numbers for most concepts have been set up, however, the human race will have a new kind of instrument which will increase the power of the mind much more than optical lenses strengthen the eyes. . . . Reason will be right beyond all doubt only when it is everywhere as clear and certain as only arithmetic has been until now.”13
Leibniz proposed a universal coding of natural language based on underlying logical relationships and forms. Primary concepts would be represented by prime numbers. From this initial mapping between numbers and ideas a grand, omnipotent combinatorial system could be constructed by arithmetic alone. Leibniz saw that the correspondence between logic and mechanism worked both ways. To his “Studies in a Geometry of Situation,” sent to Christiaan Huygens in 1679, Leibniz appended the observation that “one could carry out the description of a machine, no matter how complicated, in characters which would be merely the letters of the alphabet, and so provide the mind with a method of knowing the machine and all its parts.”14
This ambition was fulfilled, some 150 years later, by the English mathematician, engineer, and patron saint of the programmable computer, Charles Babbage (1791–1871). “By a new system of very simple signs I ultimately succeeded in rendering the most complicated machine capable of explanation almost without the aid of words,” wrote Babbage, describing the notation developed in working out the design of his series of difference and analytical engines over the years. “I have called this system of signs the Mechanical Notation. . . . It has given us a new demonstrative science, namely, that of proving that any given machine can or cannot exist.”15
Babbage’s analytical engine aimed to multiply or divide two fifty-digit numbers, to one hundred decimal places, in under a minute’s time. Its mechanism was detailed in hundreds of drawings, but only a fragment of it was ever built. The engine could be programmed to evaluate polynomial expressions of unlimited degree, passing intermediate results back and forth between the engine’s “store” of internal memory (one thousand registers of fifty decimal digits each) and its arithmetic “mill.”
A design of such unprecedented complexity, reported Babbage’s associate Harry Wilmot Buxton, “seemed well calculated to overwhelm the most robust intellect. It was therefore only by means of his happy invention of the ‘Mechanical Notation,’ that he was enabled to alleviate this arduous labour, and partially relieve his brain from a pressure which menaced his bodily health.”16 Although framed in a dialect of gears, levers, and camshafts, Babbage anticipated the formal languages and timing diagrams that brought mechanical logic into the age of relays, vacuum tubes, transistors, microprocessors, and beyond. Computers have been paying their respects to Babbage ever since.
The analytical engine linked the seventeenth-century visions of Hobbes and Leibniz to the twentieth century that digital computation has so transformed. “Mr. Babbage entertained no doubt,” wrote Buxton, “of the possibility of extending the powers of the Analytical Engine, far beyond the domain of abstract analysis, and Thomas Hobbes of Malmsbury, as early as 1650, seems to have remarked the analogy existing between the operations of mental computation, and those other operations of the mind.”17 As Hobbes had inspired Leibniz—who admitted that even those works with which he disagreed “usually contain something good and ingenious”18—Leibniz in turn inspired Babbage with computational ideas. As an undergraduate at Cambridge, Babbage founded the Analytical Society, seeking to revitalize English mathematics by following the continental lead. To a university enamored of Newton and a nation at war with France, this was a controversial stance. The argument over whether to favor Newton’s or Leibniz’s notation for the calculus reflected an underlying divergence in mathematical philosophy: Newton’s seeking to encompass the kingdom of nature within the mathematical bounds of natural law versus Leibniz’s seeking to construct the unbounded kingdom of God from mathematical truth. Babbage believed that the powers of a calculating engine would illuminate both approaches to natural philosophy with the clarity that numbers alone can provide. His motives for the invention of his engines went deeper than the errors that plagued the manually calculated mathematical tables of his time.
Babbage stated that it was “either in 1812 or 1813” that he began “thinking that all these Tables . . . might be calculated by machinery,” thereby avoiding mental drudgery as well as the inevitable errors that, especially in tables used for navigation, presented a hazard to life and limb.19 Although fond of pointing out the “Erratum of the Erratum of the Errata of Taylor’s Logarithms” in the Nautical Almanac for 1836, Babbage saw the creation of accurate tables as only one of many applications for his machine. Buxton related the genesis of Babbage’s idea: “It was whilst endeavouring to reconcile the difficulties involved in the several ideas of Leibnitz and Newton, that Mr. Babbage was led to . . . consider the possibility of making actual motion, under certain conditions, the index of the quantities generated, in arithmetical operations. Thus motion, by means of figure wheels might be . . . conveyed or transferred through racks or other contrivances to successive columns of other wheels, and dealt with arithmetically, under any conditions, which the mechanist thought proper to impose.20
A working model of a portion of Babbage’s difference engine was soon constructed and successfully used, but completion of a larger engine was bogged down by design changes, engineering difficulties, and negotiations over government support.
Babbage began the design of the analytical engine in 1834 and was still constructing pieces of it in his own workshops when he was eighty years of age. The engine was designed to be able to manipulate its own internal storage registers while reading and writing to and from an unbounded storage medium—strings of punched pasteboard cards, adapted by Babbage from those used by the card-controlled Jacquard loom. A prototype Jacquard mechanism had been introduced in 1801; some eleven thousand Jacquard looms were in use by 1812. In specifying punched-card peripheral equipment, Babbage set a precedent that stood for 150 years. The technology was proven, available, and suited to performing complex functions on extensive data sets. (One demonstration weaving project, a silk portrait of Jacquard, required a sequence of twenty-four thousand cards.) Babbage designated two species of cards for his machine: operation cards, containing programs to be executed; and variable cards, which indexed the location of data in the machine’s internal store that was to be processed by the mill. Microprograms were kept at hand in the mill, encoded on toothed cylinders and positioned similarly to the readonly memory (ROM) plugged into the motherboards of most computers today. The analytical engine possessed theoretically unlimited powers of calculation, the recognition of which by Babbage anticipated Alan Turing’s demonstration, a hundred years later, that even a very simple analytical engine, given an unlimited supply of cards, can compute any computable function—though it may take a very, very long time.
“The Analytical Engine is therefore a machine of the most general nature,” explained Babbage, who understood the value of reusable coding, although programs (referred to as “laws of operation”) were not so named. “The Analytical Engine will possess a library of its own. Every set of cards once made will at any future time reprodu
ce the calculations for which it was first arranged.”21 Babbage pursued the design, engineering, and programming of the analytical engine to a stage at which the machine could probably have been built. With extensive debugging, it might have even worked. In 1991, to commemorate the bicentenary of Babbage’s birth, a team led by Doron Swade at the Science Museum in London assembled some four thousand components reconstructed according to Babbage’s 1847 drawings of Difference Engine No. 2. The three-ton device “flawlessly performed its first major calculation,” and “affirmed that Babbage’s failures were ones of practical accomplishment, not of design.”22
Babbage associated with the famous and powerful of his day (“I . . . regularly attended his famous evening parties,” recalled Charles Darwin)23 and held Isaac Newton’s Lucasian chair at Cambridge University from 1828 to 1839. His most celebrated collaboration was with the mathematically gifted Lady Augusta Ada Lovelace, daughter of the poet Lord Byron and protégée not only of Babbage but, to a lesser extent, of logician Augustus de Morgan, who was at the same time encouraging work on the Laws of Thought by George Boole. Lovelace’s extensive notes, appended to her translation of Luigi Menabrea’s description of the analytical engine (compiled after Babbage’s visit to Italy in 1841 as a guest of the future prime minister) convey the potential she saw in Babbage’s machine. “In enabling mechanism to combine together general symbols, in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental processes of the most abstract branch of mathematical science,” wrote Lovelace. “A new, a vast, and a powerful language is developed for the future use of analysis, in which to wield its truths. . . . We are not aware of its being on record that anything partaking of the nature of what is so well designated the Analytical Engine has been hitherto proposed, or even thought of; as a practical possibility, any more than the idea of a thinking or of a reasoning machine.”24
Darwin Among the Machines Page 6