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.
Boole also recognized that error and unpredictability, however foreign to the laws of Newtonian physics and formal logic, may be essential to our ability to think. “The slightest attention to the processes of the intellectual world,” concluded Boole, “reveals to us another state of things. The mathematical laws of reasoning are, properly speaking, the laws of right reasoning only, and their actual transgression is a perpetually recurring phenomenon. Error, which has no place in the material system, occupies a large one here.”33
An unbridged chasm separates our understanding of the logic of mental processes from our understanding of how these processes are executed in the brain. “One finds there only a confused mass in which nothing unusual appears but which nevertheless conceals some kind of filaments of a fineness much greater than that of a spider’s web,” wrote Leibniz in 1702. “For the subtlety of the spirits contained in these passages is equal to that of light rays themselves.”34
Among the first to attempt to close the gap between neurology and mind was the English physician Alfred Smee (1818–1877), a prolific investigator whose contributions spanned numerous disciplines, from The Potato Plant, Its uses and properties, together with the cause of the present malady (1846) to a pioneering and widely reprinted sixpence broadsheet, Accidents and Emergencies; A Guide for their Treatment before the arrival of Medical Aid. The son of William Smee, accountant general to the Bank of England, Alfred grew up within the walled compound of the bank, spending long hours in an improvised laboratory on the ground floor of his father’s residence, where he invented a new system for splinting fractures (1839), Smee’s battery (1840), and other innovations that gained him fame if not reward. In 1841, at the age of twenty-two, he was appointed surgeon to the Bank of England, “a post which had been especially created for him by the directors . . . who thought that the bank could turn his scientific genius to good account.”35 Smee, who had a passion for all things electrical, invented the electrotype plate and by applying the technique to the printing of counterfeit-resistant English banknotes proved the directors’ instincts right. Smee’s two great interests were combined in a wide-ranging work of electrophysiology. Elements of Electro-Biology; or, the Voltaic mechanism of Man (1849), abridged and illustrated for a popular audience under the title Instinct and Reason in 1850. Smee introduced the use of electricity in diagnostic medicine and published a pamphlet entitled The Detection of Needles, and other Steel Instruments, impacted in the Human Frame (1844)—an occurrence all too common in the industrial workplace of his day.
Smee worked both in theory and in the laboratory to explain the electrochemical basis of vision, sensation, memory, logic, and the origination and recombination of ideas. He believed that the mental powers of animals, human beings, and mechanisms were different not in kind but in degree. His definition of consciousness has seen scant improvement in 150 years. “When an image is produced by an action upon the external senses, the actions on the organs of sense concur with the actions in the brain; and the image is then a Reality. When an image occurs to the mind without a corresponding simultaneous action of the body, it is called a Thought. The power to distinguish between a thought and a reality is called Consciousness,” he wrote in his Principles of the Human Mind deduced from Physical Laws, published in 1849.36 As Leibniz envisioned the principles of digital computation, so Alfred Smee envisioned the crude beginnings of a theory of neural nets. “On attending the Physiological Lectures of Professor Mayo, I was remarkably struck with the unsatisfactory account of the functions of the brain, and I was surprised that so little appeared to have been done in connecting mental operations with that organ to which they were due,” he wrote in the introduction to his Process of Thought Adapted to Words and Language, together with a description of the Relational and Differential Machines.37
After considering what little was known concerning neural function at the time, Smee concluded that “every idea, or action on the brain, is ultimately resolvable into an action on a certain combination of nervous fibres, which is definite and determinable, and, regarding the sum total of the nervous fibres, is a positive result over a certain portion only, which has a distinct and clearly defined limit.”38 He was on the right track, but only half right, since he neglected the concept of neural inhibition that is central to the computational and representational powers of neural nets. His system was based on loosely defined analogies between the branching, combinatorial nature of the nervous system and the branching, combinatorial structure of language, logic, and ideas.
Taking the same top-down approach to semantic analysis that would be followed by the artificial intelligence industry in another hundred years, Smee developed a method for parsing natural language by means of a geometric series of symbols (“cyphers”) that would render the meaning of any given sentence exact. “This mode of notation may, at first sight, appear more complicated than ordinary language,” he wrote, “but if carefully studied, it will be found to afford us an artificial mode of reasoning, which, although immensely inferior to that which is in actual operation by the elaborate machine furnished us by nature, yet as far as it goes, may be conducted by fixed and immutable laws.”39 By analysis of “this most exact form of language,” Smee made the leap between mind and mechanism, concluding that “it is apparent that thought is amenable to fixed principles. By taking advantage of a knowledge of these principles it occurred to me that mechanical contrivances might be formed which should obey similar laws, and give those results which some may have considered only obtainable by the operation of the mind itself.”40
Unlike later proponents of neural and semantic nets, Smee made no grand promises of thinking machines, but merely suggested the development of small-scale logical automata for research. “When the vast extent of a machine sufficiently large to include all words and sequences is considered, we at once observe the absolute impossibility of forming one for practical purposes, inasmuch as it would cover an area exceeding probably all London,” he cautioned. “Nevertheless, those lesser machines containing but a few elements, exemplify the principles of their operation, and demonstrate those laws of induction, deduction and relation, the right use of which cannot fail to render our thoughts more accurate, and our language more precise.”41
Smee understood the inescapable bureaucracy and rigidly enforced assumptions of formal systems. He suggested, with an unspoken nod to the thirteenth-century Ars Magna of Ramon Lull, that one of his differential machines “might be beneficially brought into use by those who use fixed and unchangeable creeds; for if they be arranged correctly then any deviation from them would be immediately registered. It must be apparent that such a machine would not estimate the quality of the creed, but only show whether any new creed, or portion of creed, coincided or not with the former creed. For whether the creed inferred a belief in the true God, in Mohammed, in ibises, crocodiles, or saints, in the power of the Virgin, or winking pictures of her, or the qualities of relics, or the virtues of images, or in the parties’ own inspiration, the effect would be the same.”42
“By using the relational and differential machines together,” concluded Smee, “from any definite number of premises the correct answer may be obtained, by a process imitating as far as possible, the natural process of thought.”43 But Smee advised his public to “rely upon the abilities which it has pleased Providence to give to them, and not seek assistance from extraneous sources,” and made only passing reference to the potentials of electrical logic machines, keeping the prospect of so upstaging nature to himself. “In animal bodies we really have electro-telegraphic communication in the nervous system,” he had written in Instinct and Reason, juxtaposing micrographic plates of brain tissue with electrotyped illustrations of how he imagined the electrical network to be c
onfigured in the brain. He built his own simple electric telegraph, a system “of a somewhat similar character, as it communicates intelligence from one spot to another,”44 and connected it to a thermometer in his greenhouse so as to transmit an alarm signal when extreme temperatures threatened his collections of exotic plants. In 1849 he suggested “in a remote and imperfect manner” how to construct an artificial ear that would translate sound into electrical signals and expressed “no doubt but that a perfect acoustic telegraph could be made, which shall be acted upon by sounds, and have the power of transmitting them to any distance.”45
Speculating how vision might be processed by eye and brain, Smee introduced concepts we now know as pixelization, bit mapping, and image compression. He suggested both digital facsimile and analog television at a time when photography was still in its formative years. “From my experiments I believe that it is sufficiently demonstrated that the light falling upon the [optic] nerve determines a voltaic current which passes through the nerves to the brain,” he wrote. “From this fact we might make an artificial eye, if we did but take the labour to aggregate a number of tubes communicating with photo-voltaic circuits. . . . Having one nervous element, it is but a repetition to make an eye; and . . . there is no reason why a view of St. Paul’s in London should not be carried to Edinburgh through tubes like the nerves which carry the impression to the brain.”46
But Smee’s loyalty was to the vegetable kingdom, not the kingdom of machines. “There is nothing to prevent man from forming an elaborate engine, which should work by change of matter [i.e., electricity] . . . but . . . he must, with the Psalmist, exclaim, ‘Such knowledge is too wonderful and excellent for me.’”47 Smee devoted the rest of his life to horticulture and ecology, publishing a monumental volume, My Garden; its Plan and Culture together with a general description of its geology, botany, and natural history (1872), illustrated with thirteen hundred plates. “Its author has endeavoured, so to speak, to catch Nature, animate and inanimate, in a trap of some seven acres and a half, and to chronicle all its everyday features with a sort of Boswellian fidelity,” wrote the Saturday Review.48 Babbage died alone, obsessed by the unfulfilled promise of his machines; Smee died at peace, surrounded by a garden full of grandchildren and plants. “Had Smee lived a few years later,” wrote D’arcy Power, “he would have made himself a great reputation as an electrical engineer.”49
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