Darwin Among the Machines (9 page)

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 reproduce 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

Did Babbage grasp the principles of the stored-program digital computer, or has hindsight (and mythology surrounding Lady Lovelace) read too much of the twentieth century into his ideas? Considering the arrangements made for the engine to execute conditionally branched instructions and to change its own course of operation according to a preconceived but not precalculated plan, the evidence in Babbage's favor is substantial. But he never explicitly discussed loading instructions as well as data in the store. In his
Ninth Bridge-water Treatise
, which makes a series of convincing arguments for viewing the universe as a stored-program computer (with God as
programmer and miracles as improbable but not impossible subroutines), Babbage related, “I had determined to invest the invention with a degree of generality which should include a wide range of mathematical power; and I was well aware that the mechanical generalisations I had organised contained within them much more than I had leisure to study, and some things which will probably remain unproductive to a far distant day.”
²⁵

Babbage saw digital computers as instruments by which to catalog otherwise inaccessible details of natural religion—the mind of God as revealed by computing the results of his work. He believed that faster, more powerful computers would banish doubt, restore faith, and allow human beings to calculate fragments of incalculable truth. “A time may arrive when, by the progress of knowledge, internal evidence of the truth of revelation may start into existence with all the force that can be derived from the testimony of the senses,” he exclaimed.
²⁶

Babbage was also a prophet of telecommunications. By analyzing the operations of the British postal system, he determined that the cost of conveying letters was governed more by switching than by distance, and he advocated flat-rate postage based on weight. Instituted by Rowland Hill in 1840 as the penny post, Babbage's reforms led to sorting and routing algorithms followed by all subsequent packet-switched information nets. To eliminate the wasted time and energy of forwarding packets of letters by horse, Babbage proposed a mechanically driven communications network that would operate over steel wires three to five miles in length and terminate in nodes where “a man ought to reside in a small station-house.” A small metal cylinder containing messages and traveling along the wire “would be conveyed speedily to the next station, where it would be removed by the attendant to the commencement of the next wire, and so forwarded.” Babbage knew that it would soon be possible to eliminate the transmission of paper as well as the transmission of the horse. “The stretched wire might itself be available for a species of telegraphic communication yet more rapid,” he suggested in 1835.
²⁷

Babbage was in contact with Joseph Henry and other electrical pioneers but made no attempt to adopt electrical powers in his work. The clock rate of his computer would have been governed by the speed of bronze and iron, with access to its internal memory depending on brute force to shift and spin through an address space with a mass of several tons. But given enough time, enough horsepower, and enough cards, the analytical engine would get the job—any job—done. When Babbage compiled his autobiographical
Passages from the
Life of a Philosopher
in 1864, he conduded that “the whole of the conditions which enable a finite machine to make calculations of unlimited extent are fulfilled. . . . I have converted the infinity of space, which was required by the conditions of the problem, into the infinity of time.”
²⁸
.

While Babbage was realizing Leibniz's ambitions for the mechanization of arithmetic, Leibniz's agenda for the formalization of mental processes was brought closer to fruition through the late-blooming mathematical career of an English schoolmaster named George Boole (1815–1864). The self-educated son of a Lincoln shopkeeper and boot maker, Boole developed a precise system of logic—Boolean algebra—that has supported the foundations of pure mathematics and computer science ever since. Where Leibniz prophesied the general powers of symbolic logic, Boole extracted a working system from first principles. Intended to provide mathematical foundations for the development of logic, Boolean algebra has also provided logical foundations for new areas of mathematics such as set theory, lattice theory, and topology, a success that was not entirely unforeseen. Boole's initial results were presented in a thin volume,
The Mathematical Analysis of Logic
(1847), followed by
An Investigation of the Laws of Thought, on which are founded the mathematical theories of Logic and Probabilities
(1854).

Boole's goal was “to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a Calculus, and . . . to make that method itself the basis of a general method for the application of the mathematical doctrine of Probabilities; and, finally, to collect from the various elements of truth brought to view in the course of these inquiries some probable intimations concerning the nature and constitution of the human mind.”
²⁹
Boole's real achievement, however, was the construction of a system of logic rigorous enough to stand on its own as mathematics, independent of the mysteries of mind.

Ordinary algebra uses symbols in place of quantities, allowing systematic analysis of algebraic functions irrespective of actual magnitudes (or what they happen to represent). In Boolean algebra, symbols represent classes of things and Boolean functions the logical relationships between them, allowing the formulation of what are intuitively perceived as concepts or ideas. In reducing logic to its barest essence, Boole's algebra consisted of the symbols +, –, ×, and =, representing the logical operations “or,” “not,” “and,” and “identity,” operating on variables (
x, y, z
, etc.) restricted to the values 0 and 1. The
Boolean system, seeded with a minimum of axioms and postulates, assumes as initial conditions only the existence of duality—the distinction between nothing and everything; between true and false; between on and off; between the numbers 0 and 1. Boole's laws were configured so as to correspond not only with ordinary logic but also with binary arithmetic, thereby establishing a bridge between logic and arithmetic that communicates both ways. Using Boolean algebra, logic can be constructed from arithmetic and arithmetic can be constructed from logic. The depth of this functional equivalence, on which the effectiveness of digital computers depends, represents the common ancestry of both mathematics and logic in the genesis of the many from the one.

The success of Boolean algebra has left us with the impression of Boole's
Laws of Thought
as an exact, all-or-nothing system of bivalent logic, as intolerant of error and ambiguity as the integrated circuits and binary coding that have made Boolean logic a household word today. It is something of a historical, technical accident that the logical reliability of the integrated circuit has produced this enduring monument to the precisely true–false Boolean algebra that constitutes the first half of Boole's book, while allowing us to largely ignore the probabilistic and statistical (“fuzzy”) logics that made up the final two sections of his work. In the days of vacuum tubes, relays, and hand-soldered plugboards the isomorphism between switching circuits and Boolean algebra was recognized in theory, but in actual practice the function of electrical components over millions of cycles fell short. As Herman Goldstine has pointed out, recalling the ENIAC's seventeen thousand vacuum tubes and one-hundred-kilocycle clock rate, this meant 1.7 billion opportunities per second for a vacuum tube to exhibit logical misbehavior—and occasionally one did.
³⁰
In his last year of life, as one of his final bequests of insight to the successors of the ENIAC, John von Neumann published “Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components,”
³¹
which is closer to the true spirit of Boole's
Laws of Thought
than is the infallible Boolean logic with which solid-state electronics has surrounded us today.

Boole (and von Neumann) showed how individually indeterminate phenomena could nonetheless be counted on, digitally, to produce logically certain results. “We possess theoretically in all cases, and practically, so far as the requisite labour of calculation may be supplied, the means of evolving from statistical records the seeds of general truths which lie buried amid the mass of figures,”
³²
wrote Boole, foreshadowing von Neumann's conclusion that the fundamental
“machine” language of a brain constructed from imperfect neurons must be statistical in nature, at a level deeper than the logical processes that appear fundamental to us.