Part 3
Yet Lull did leave his mark, and many copies of his wheels have been made and found useful. Where various permutations of numbers or other symbols are required, such a mechanical tool is often the fastest way of pairing them up. Even in the field of writing, a Lullian device was popular a few decades ago in the form of the “Plot Genii.” With this gadget the would-be author merely spun the wheels to match up various characters with interesting situations to arrive at story ideas. Other versions use cards to do the same job, and one called Plotto was used by its inventor William Wallace Cook to plot countless stories. Although these were perhaps not ideas for great literature, eager writers paid as much as $75 for the plot boiler.
Not all serious thinkers relegated Lull to the position of fanatic dreamer and gadgeteer. No less a mind that Gottfried Wilhelm von Leibnitz found much to laud in Lull’s works. The _Ars Magna_ might well lead to a universal “algebra” of all knowledge, thought Leibnitz. “If controversies were to arise,” he then mused, “there would be no more reason for philosophers to dispute than there would for accountants!”
Leibnitz applied Lull’s work to formal logic, constructed tables of syllogisms from which he eliminated the false, and carried the work of the “gifted crank” at bit nearer to true symbolic logic. Leibnitz also extended the circle idea to that of overlapping them in early attempts at logical manipulation that foreshadowed the work that John Venn would do later. Leibnitz also saw in numbers a powerful argument for the existence of God. God, he saw as the numeral 1, and 0 was the nothingness from which He created the world. There are those, including Voltaire whose _Candide_ satirized the notion, who question that it is the best of all possible worlds, but none can question that in the seventeenth century Leibnitz foresaw the coming power of the binary system. He also built arithmetical computers that could add and subtract, multiply and divide.
A few years earlier than Leibnitz, Blaise Pascal was also interested in computing machines. As a teen-ager working in his father’s tax office, Pascal wearied of adding the tedious figures so he built himself a gear-driven computer that would add eight columns of numbers. A tall figure in the scientific world, Pascal had fathered projective geometry at age sixteen and later established hydrodynamics as a science. To assist a gambler friend, he also developed the theory of probability which led to statistical science.
Another mathematical innovation of the century was that of placing logarithms on a stick by the Scot, John Napier. What he had done, of course, was to make an analog, or scale model of the arithmetical numbers. “Napier’s bones” quickly became what we now call slide rules, forerunners of a whole class of analog computers that solve problems by being actual models of size or quantity. Newton joined Leibnitz in contributing another valuable tool that would be used in the computer, that of the calculus.
_The Computer in Literature_
Even as Plato had viewed with suspicion the infringement of mechanical devices on man’s domain of higher thought, other men have continued to eye the growth of “mechanisms” with mounting alarm. The scientist and inventor battled not merely technical difficulties, but the scornful satire and righteous condemnation of some of their fellow men. Jonathan Swift, the Irish satirist who took a swipe at many things that did not set well with his views, lambasted the computing machine as a substitute for the brain. In Chapter V, Book Three, of _Gulliver’s Travels_, the good dean runs up against a scheming scientist in Laputa:
The first Professor I saw was in a very large Room, with Forty Pupils about him. After Salutation, observing me to look earnestly upon a Frame, which took up the greatest part of both the Length and Breadth of the Room; he said, perhaps I might wonder to see him employed in a Project for improving speculative knowledge by practical and mechanical Operations. But the World would soon be sensible of its Usefulness; and he flattered himself, that a more noble exalted Thought never sprang in any other Man’s Head. Every one knew how laborious the usual Method is of attaining to Arts and Sciences; whereas by his Contrivance, the most ignorant Person at a reasonable Charge, and with a little bodily Labour, may write Books in Philosophy, Poetry, Politicks, Law, Mathematicks, and Theology, without the least Assistance from Genius or Study. He then led me to the Frame, about the Sides whereof all his Pupils stood in Ranks. It was a Twenty Foot Square, placed in the Middle of the Room. The Superfices was composed of several Bits of Wood, about the Bigness of a Dye, but some larger than others. They were all linked together by slender Wires. These Bits of Wood were covered on every Square with Papers pasted on them; and on these Papers were written all the Words of their Language in their several Moods, Tenses, and Declensions, but without any Order. The Professor then desired me to observe, for he was going to set his Engine to work. The Pupils at his Command took each the hold of an Iron Handle, whereof there were Forty fixed round the Edges of the Frame; and giving them a sudden Turn, the whole Disposition of the Words was entirely changed. He then commanded Six and Thirty of the Lads to read the several Lines softly as they appeared upon the Frame; and where they found three or four Words together that might make Part of a Sentence, they dictated to the four remaining Boys who were Scribes. This work was repeated three or four Times, and at every Turn the Engine was so contrived, that the Words shifted into new Places, as the square Bits of Wood moved upside down.
Six hours a-day the young Students were employed in this Labour; and the Professor showed me several Volumes in large Folio already collected, of broken Sentences, which he intended to piece together, and out of those rich Materials to give the World a compleat Body of Art and Sciences; which however might be still improved, and much expedited, if the Publick would raise a Fund for making and employing five Hundred such Frames in _Lagado_....
Fortunately for Swift, who would have been horrified by it, he never heard Russell Maloney’s classic story, “Inflexible Logic,” about six monkeys pounding away at typewriters and re-creating the world great literature. _Gulliver’s Travels_ is not listed in their accomplishments.
The French Revolution prompted no less an orator than Edmund Burke to deliver in 1790 an address titled “Reflections on the French Revolution,” in which he extols the virtues of the dying feudal order in Europe. It galled Burke that “The Age of Chivalry is gone. That of sophists, economists, and _calculators_ has succeeded, and the glory of Europe is extinguished forever.”
Seventy years later another eminent Englishman named Darwin published a book called _On the Origin of Species_ that in the eyes of many readers did little to glorify man himself. Samuel Butler, better known for his novel, _The Way of All Flesh_, wrote too of the mechanical being, and was one of the first to point out just what sort of future Darwin was suggesting. In the satirical _Erewhon_, he described the machines of this mysterious land in some of the most prophetic writing that has been done on the subject. It was almost a hundred years ago that Butler wrote the first version, called “Darwin Among the Machines,” but the words ring like those of a 1962 worrier over the electronic brain. Butler’s character warns:
There is no security against the ultimate development of mechanical consciousness in the fact of machines possessing little consciousness now. Reflect upon the extraordinary advance which machines have made during the last few hundred years, and note how slowly the animal and vegetable kingdoms are advancing. The more highly organized machines are creatures not so much of yesterday, as of the last five minutes, so to speak, in comparison with past time.
Do not let me be misunderstood as living in fear of any actually existing machine; there is probably no known machine which is more than a prototype of future mechanical life. The present machines are to the future as the early Saurians to man ... what I fear is the extraordinary rapidity with which they are becoming something very different to what they are at present.
Butler envisioned the day when the present rude cries with which machines call out to one another will have been developed to a speech as intricate as our own. After all, “... take man’s vaunted power of calculation. Have we not engines which can do all manner of sums more quickly and correctly than we can? What prizeman in Hypothetics at any of our Colleges of Unreason can compare with some of these machines in their own line?”
Noting another difference in man and his creation, Butler says,
... Our sum-engines never drop a figure, nor our looms a stitch; the machine is brisk and active, when the man is weary, it is clear-headed and collected, when the man is stupid and dull, it needs no slumber.... May not man himself become a sort of parasite upon the machines? An affectionate machine-tickling aphid?
It can be answered that even though machines should hear never so well and speak never so wisely, they will still always do the one or the other for our advantage, not their own; that man will be the ruling spirit and the machine the servant.... This is all very well. But the servant glides by imperceptible approaches into the master, and we have come to such a pass that, even now, man must suffer terribly on ceasing to benefit the machines. If all machines were to be annihilated ... man should be left as it were naked upon a desert island, we should become extinct in six weeks.
Is it not plain that the machines are gaining ground upon us, when we reflect on the increasing number of those who are bound down to them as slaves, and of those who devote their whole souls to the advancement of the mechanical kingdom?
Butler considers the argument that machines at least cannot copulate, since they have no reproductive system. “If this be taken to mean that they cannot marry, and that we are never likely to see a fertile union between two vapor-engines with the young ones playing about the door of the shed, however greatly we might desire to do so, I will readily grant it. [But] surely if a machine is able to reproduce another machine systematically, we may say that it has a reproductive system.”
Butler repeats his main theme. “... his [man’s] organization never advanced with anything like the rapidity with which that of the machine is advancing. This is the most alarming feature of the case, and I must be pardoned for insisting on it so frequently.”
Then there is a startlingly clear vision of the machines “regarded as a part of man’s own physical nature, being really nothing but extra-corporeal limbs. Man ... as a machinate mammal.” This was feared as leading to eventual weakness of man until we finally found “man himself being nothing but soul and mechanism, an intelligent but passionless principle of mechanical action.” And so the Erewhonians in self-defense destroyed all inventions discovered in the preceding 271 years!
_Early Mechanical Devices_
During the nineteenth century, weaving was one of the most competitive industries in Europe, and new inventions were often closely guarded secrets. Just such an idea was that of Frenchman Joseph M. Jacquard, an idea that automated the loom and would later become the basis for the first modern computers. A big problem in weaving was how to control a multiplicity of flying needles to create the desired pattern in the material. There were ways of doing this, of course, but all of them were unwieldy and costly. Then Jacquard hit on a clever scheme. If he took a card and punched holes in it where he wanted the needles to be actuated, it was simple to make the needles do his bidding. To change the pattern took only another card, and cards were cheap. Patented in 1801, there were soon thousands of Jacquard looms in operation, doing beautiful and accurate designs at a reasonable price.
To show off the scope of his wonderful punched cards, Jacquard had one of his looms weave a portrait of him in silk. The job took 20,000 cards, but it was a beautiful and effective testimonial. And fatefully a copy of the silk portrait would later find its way into the hands of a man who would do much more with the oddly punched cards.
At about this same time, a Hungarian named Wolfgang von Kempelen decided that machines could play games as well as work in factories. So von Kempelen built himself a chess-playing machine called the Maelzel Chess Automaton with which he toured Europe. The inventor and his machine played a great game, but they didn’t play fair. Hidden in the innards of the Maelzel Automaton was a second human player, but this disillusioning truth was not known for some time. Thus von Kempelen doubtless spurred other inventors to the task, and in a short while machines would actually begin to play the royal game. For instance, a Spaniard named L. Torres y Quevedo built a chess-playing machine in 1914. This device played a fair “end game” using several pieces, and its inventor predicted future work in this direction using more advanced machines.
Charles Babbage was an English scientist with a burning desire for accuracy. When some mathematical tables prepared for the Astronomical Society proved to be full of errors, he angrily determined to build a machine that would do the job with no mistakes. Of course calculating machines had been built before; but the machine Babbage had in mind was different. In fact, he called it a “difference engine” because it was based on the difference tables of the squares of numbers. The first of the “giant computers,” it was to have hundreds of gears and shafts, ratchets and counters. Any arithmetic problem could be set into it, and when the proper cranks were turned, out would come an answer—the right answer because the machine could not make a mistake. After doing some preliminary work on his difference engine, Babbage interested the government in his project since even though he was fairly well-to-do he realized it would cost more money than he could afford to sink into the project. Babbage was a respected scientist, Lucasian Professor of Mathematics at Cambridge, and because of his reputation and the promise of the machine, the Chancellor of the Exchequer promised to underwrite the project.
For four years Babbage and his mechanics toiled. Instead of completing his original idea, the scientist had succeeded only in designing a far more complicated machine, one which would when finished weigh about two tons. Because the parts he needed were advanced beyond the state of the art of metalworking, Babbage was forced to design and build them himself. In the process he decided that industry was being run all wrong, and took time out to write a book. It was an excellent book, a sort of forerunner to the modern science of operations research, and Babbage’s machine shop was doing wonders for the metalworking art.
Undaunted by the lack of progress toward a concrete result, Babbage was thinking bigger and bigger. He was going to scrap the difference engine, or rather put it in a museum, and build a far better computer—an “analytical engine.” If Jacquard’s punched cards could control the needles on a loom, they could also operate the gears and other parts of a calculating machine. This new engine would be one that could not only add, subtract, multiply, and divide; it would be designed to control itself. And as the answers started to come out, they would be fed back to do more complex problems with no further work on the operator’s part. “Having the machine eat its own tail!” Babbage called this sophisticated bit of programming. This mechanical cannibalism was the root of the “feedback” principle widely used in machines today. Echoing Watt’s steam governor, it prophesied the coming control of machines by the machines themselves. Besides this innovation, the machine would have a “store,” or memory, of one thousand fifty-digit numbers that it could draw on, and it would actually exercise judgment in selection of the proper numbers. And as if that weren’t enough, it would print out the correct answers automatically on specially engraved copper plates!
[Illustration:
_Space Technology Laboratories_
“As soon as an Analytical Engine exists, it will necessarily guide the future course of science. Whenever any result is sought by its aid, the question will then arise—by what course of calculation can these results be arrived at by the machine in the shortest time?” Charles Babbage—_The Life of a Philosopher_, 1861. ]
It was a wonderful dream; a dream that might have become an actuality in Babbage’s own time if machine technology had been as advanced as his ideas. But for Babbage it remained only a dream, a dream that never did work successfully. The government spent £17,000, a huge sum for that day and time, and bowed out. Babbage fumed and then put his own money into the machine. His mechanics left him and became leaders in the machine-tool field, having trained in Babbage’s workshops. In despair, he gave up on the analytical engine and designed another difference engine. An early model of this one would work to five accurate places, but Babbage had his eyes on a much better goal—twenty-place accuracy. A lesser man would have aimed more realistically and perhaps delivered workable computers to the mathematicians and businessmen of the day. There is a legend that his son did finish one of the simpler machines and that it was used in actuarial accounting for many years. But Babbage himself died in 1871 unaware of how much he had done for the computer technology that would begin to flower a few short decades later.
Singlehandedly he had given the computer art the idea of programming and of sequential control, a memory in addition to the arithmetic unit he called a “mill,” and even an automatic readout such as is now standard on modern computers. Truly, the modern computer was “Babbage’s dream come true.”
_Symbolic Logic_
Concurrently with the great strides being made with mechanical computers that could handle mathematics, much work was also being done with the formalizing of the logic. As hinted vaguely in the syllogisms of the early philosophers, thinking did seem amenable to being diagrammed, much like grammar. Augustus De Morgan devised numerical logic systems, and George Boole set up the logic system that has come to be known as Boolean algebra in which reasoning becomes positive or negative terms that can be manipulated algebraically to give valid answers.
John Venn put the idea of logic into pictures, and simple pictures at that. His symbology looks for all the world like the three interlocking rings of a well-known ale. These rings stand for the subject, midterm, and predicate of the older Aristotelian syllogism. By shading the various circles according to the major and minor premises, the user of Venn circles can see the logical result by inspection. Implicit in the scheme is the possibility of a mechanical or electrical analogy to this visual method, and it was not long until mathematicians began at least on the mechanical kind. Among these early logic mechanizers, surprisingly, was Lewis Carroll who of course was mathematician Charles L. Dodgson before he became a writer.
Carroll, who was a far busier man than most of us ever guess, marketed a “Game of Logic,” with a board and colored cardboard counters that handled problems like the following:
All teetotalers like sugar. No nightingale drinks wine.
By arranging the counters on Carroll’s game board so that: All M are X, and No Y is not-M, we learn that No Y is not-X! This tells the initiate logician that no nightingale dislikes sugar; a handy piece of information for bird-fancier and sugar-broker alike.
[Illustration:
Lewis Carroll’s “Symbolic Logic.” ]
Charles, the third Earl Stanhope, was only slightly less controversial than his prime minister, William Pitt. Scientifically he was far out too, writing books on electrical theory, inventing steamboats, microscopes, and printing presses among an odd variety of projects; he also became interested in mechanical logic and designed the “Stanhope Demonstrator,” a contrivance like a checkerboard with sliding panels. By properly manipulating the demonstrator he could solve such problems as:
Eight of ten children are bright. Four of these children are boys.
What are the minimum and maximum number of bright boys? A simple sliding of scales on the Stanhope Demonstrator shows that two must be boys and as many as four may be. This clever device could also work out probability problems such as how many heads and tails will come up in so many tosses of a coin.
In 1869 William S. Jevons, an English economist and expert logician, built a logic machine. His was not the first, of course, but it had a unique distinction in that it solved problems faster than the human brain could! Using Boolean algebra principles, he built a “logical abacus” and then even a “logical piano.” By simply pressing the keys of this machine, the user could make the answer appear on its face. It is of interest that Jevons thought his machine of no practical use, since complex logical questions seldom arose in everyday life! Life, it seems, was simpler in 1869 than it is today, and we should be grateful that Jevons pursued his work through sheer scientific interest.
More sophisticated than the Jevons piano, the logic machine invented in America by Allan Marquand could handle four terms and do problems like the following:
There are four schoolgirls, Anna, Bertha, Cora, and Dora. When Anna or Bertha, or both, remain home, Cora is at home. When Bertha is out, Anna is out. Whenever Cora is at home, Anna is too. What can we tell about Dora?
The machine is smart enough to tell us that when Dora is at home the other three girls are all at home or out. The same thing is true when Dora is out.
_The Census Taker_
Moving from the sophistication of such logic devices, we find a tremendous advance in mechanical computers spurred by such a mundane chore as the census. The 1880 United States census required seven years for compiling; and that with only 50 million heads to reckon. It was plain to see that shortly a ten-year census would be impossible of completion unless something were done to cut the birth rate or speed the counting. Dr. Herman Hollerith was the man who did something about it, and as a result the 1890 census, with 62 million people counted, took only one-third the time of the previous tally.