Intelligence and Technology

The Impact of Tools on the Nature and Development of Human Abilities

Robert J. Sternberg, David D. Preiss, Robert J. Sternberg, David D. Preiss

• Publisher: Routledge
• Year: 2005
• ISBN:
  9781136778056
• Edition: 1
• Topic: Education
• Subtopic: Education General

In this volume, Robert J. Sternberg and David D. Preiss bring together different perspectives on understanding the impact of various technologies on human abilities, competencies, and expertise. The inclusive range of historical, comparative, sociocultural, cognitive, educational, industrial/organizational, and human factors approaches will stimula

I

COGNITIVE TECHNOLOGIES IN HISTORICAL AND CULTURAL EVOLUTION

1

Technology and Cognition Amplification

Raymond S. Nickerson

Tufts University

Technology, broadly conceived as the building of artifacts or procedures—tools—to help people accomplish their goals, predates recorded history. As amplifiers of human capabilities, tools may be classified in terms of whether the abilities they amplify are motor, sensory, or cognitive in nature. Those that amplify motor capabilities (muscle power, carrying capacity, striking force, etc.) include lever, shovel, hammer, wheel, and countless modern machines that embody the same principles. Those that amplify sensory capabilities include eyeglasses, microscopes, telescopes, audio amplifiers, and modern instruments that extend detection of both electromagnetic radiation and sound waves far beyond the range that can be sensed by the unaided eye or ear. Tools that amplify cognition include symbol systems for representing entities, quantities, and relationships, as well as devices and procedures for measuring, computing, inferencing, and remembering.

The boundary between tools that aid cognition and those in the other categories is not sharp. Tools that amplify sensory capabilities, for example, greatly extend our ability to observe the world of the very small and the very large (and very far away) and, in doing so, enrich our cognitive understanding of the universe immeasurably. Tools that extend muscle power or that make possible the manipulation and precise control of devices too small to be constructed or controlled by hand also are essential to the modern scientific enterprise and therefore also help amplify cognition in a very real, if indirect, way. Nevertheless, the distinction among tools that extend sensory capability, those that extend muscle activity, and those that amplify cognition is conceptually meaningful, even if sharp dividing lines cannot be drawn.

It is easy to overlook or take for granted cognitive technologies that we use to great advantage in everyday life. Consider, for example, alphabetization. How the order of the letters of the alphabet (of English or any other alphabetic language) became established is not clear, but the fact that a fixed order did become established and that it is universally recognized makes the alphabet an invaluable tool for organizing and finding information in dictionaries, directories, encyclopedias, indexes, almanacs, atlases, and so on. Compare the problem of finding a bird in a bird book if one knows its name with that of finding the bird if one knows only what it looks like. The first task is easy because of the alphabetic organization of the book's index; the second is difficult because there is no comparably simple way of organizing information on the basis of visual features. The ease with which the importance of such a powerful tool is overlooked is illustrated by White's (1962) observation that an elaborate article on “Alphabet” in the Encyclopedia Britannica failed to mention its own organizational system. “That we have neglected thus completely the effort to understand so fundamental an invention should give us humility whenever we try to think about larger aspects of technology” (p. 488).

Much cognitive technology has developed in more or less the same way that the ability to stand, to walk, to run develops in the child. People have done what comes naturally as they have tried to extend their abilities to cope with the problems and to respond to the challenges that life presents. One could make a very long list of technological inventions of antiquity that have served to aid cognition. Here, I want to begin with a focus on some old technological developments that increased people's ability to think quantitatively—to count, measure, and compute—and then to consider how the invention of the modern digital computer and associated developments have extended the range of possibilities for the amplification of cognition.

THE DEVELOPMENT OF MATHEMATICAL SYMBOL SYSTEMS

The origin of symbol systems for representing quantities is not known with certainty, but according to one theory, both writing and number representation developed from the use, more than 11 millennia ago, of token systems to represent the number of items in a collection (Schmandt-Besserat, 1978). The tokens were small objects, coded perhaps by shape, size, and markings and were probably used as bills of lading for merchandise that was being transported from place to place. Initially, the tokens were enclosed in sealed containers, which were broken open by recipients of shipments in order to verify that all that had been shipped had reached the intended destination. Over time, merchants began representing what the sealed containers contained by marks on the containers, and eventually it became apparent that such marks could serve the same purpose as the enclosed tokens, so the tokens were no longer used.

After these murky beginnings, distinctly different symbol systems were developed by several cultures (Ifrah, 1987; Menninger, 1969). The Hindu-Arabic system that appeared around the 7th or 8th century and is now used almost universally is based on several principles—one-for-one mapping, the use of a standard quantity to serve as a base or radix, one-for-many substitution, use of a single symbol to represent a multiple quantity (e.g., 3 instead of, say, 111), the use of a symbol for representing an empty set (0), and the use of position to carry information. Predecessors of this system also made use of some of these principles—apparently some were invented or discovered more than once independently—but none of them made use of all of them. The current system is more abstract in some ways than most of its predecessors, but it is extremely versatile (faciliating the expresssion of an unlimited range of numbers) and greatly simplifies computation (Ifrah, 1987; Nickerson, 1988). Jourdain (1913/1956) considered the Hindu-Arabic system to be responsible for making many arithmetical problems that were formidable challenges to the ancients seem easy to us.

Archimedes (3rd century B.C.) is widely considered to have been one of the greatest mathematicians who ever lived, but he was seriously limited in what he could do by the Greek system for representing numbers, which was not conducive to computation. Gauss regarded the fact that Archimedes failed to invent a place notation system for numbers as “the greatest calamity in the history of science” (Bell, 1937, p. 256). It was a calamity, in Gauss's view, because he believed that if Archimedes had discovered the place notation principle, which he thought to be within Archimedes's capability to do, many of the subsequent accomplishments in mathematics and science might have occurred centuries before they did.

The history of the development of mathematical notation, especially that of symbolic algebra, also illustrates the importance of a good representational system as an aid to thought. The Greeks had a good system for representing geometric relationships, which tend to be static, but not for representing relationships among variable quantities, which are dynamic. Maor (1994) argues that the inadequacy of the Greeks’ system for representing algebra helps explain why they did not discover calculus, despite the fact that Archimedes managed to apply Eudoxus's “method of exhaustion,” which came close to modern integral calculus, to the finding of the area of the parabola.

LOGARITHMS AND SLIDE RULES

Tools can amplify cognition either by facilitating reasoning directly or by reducing the demand that the solution of a problem makes on one's cognitive resources, thereby freeing those resources up for other uses. The latter types of tools might be considered labor-saving tools in the cognitive domain—thought-saving tools if you will. A 19th-century instruction manual for the carpenter's slide rule (similar in principle to the engineer's slide rule that was, until fairly recently, the engineer's constant companion) describes what the slide rule offers to the user in such terms:

The labour and fatigue of manipulating long series of figures for nautical and astronomical purposes had long been felt to be irksome to those engaged in it . . . One of the earliest attempts, however, by mechanical means, to lessen and facilitate this labour, was made more than two hundred and fifty years ago by Baron Napier, of Merchiston, in Scotland; and this attempt was the precursor of the Sliding Rule. (Anonymous, 1880)

The 16th-century Scottish mathematician, John Napier, of whom the author of this manual spoke, is remembered primarily for his invention of logarithms. Napier had the insight that if numbers are expressed in exponential form, multiplication and division of different powers of the same number can be accomplished by addition and subtraction, respectively, of exponents: thus

(3³ × 3⁴ × 3⁷) (3⁵ × 3²) = 3^{(3+4+7–5–2)} = 3⁷.

Things are easy as long as the numbers involved are integral powers of the same number (the base, also sometimes called the radix or root), but they get complicated quickly when one wants to deal with numbers that do not meet this criterion. Napier spent 20 years working out logarithms that, for the most part, were not integers and published tables of his results. Napier also invented a system of rods that, because they were made of bone or ivory, became known as “Napier's bones,” by which multiplication and division could be done, albeit in a somewhat tedious way.

In 1620, Edmund Gunter, an English mathematician, designed a rule on which the numbers were spaced in such a way that their distances from the end of the rule were proportional not to the numbers themselves but to their logarithms. With the use of such a rule and a pair of compasses, problems of multiplication and division were reduced to those of addition and subtraction. To multiply 3 by 4 with this rule, for example, one would first set the compasses by placing one leg on 1 and the other on 3 and then adding the resulting distance to 4 by setting one leg on 4 and seeing where the other leg would land. Because of the logarithmic spacing of the numbers on the rule, the distance between 1 and 3 represented the logarithm of 3 and when this distance was added to 4 (whose distance from 1 represented the logarithm of 4), the result would be the number (12) whose distance from 1 represented the logarithm of the product of 3 and 4. The same procedure could be used to multiply 30 and 40 or .3 and .4 or any other numbers, and division was accomplished by the inverse procedure.

Gunter's rule, especially with the inclusion of logarithms of trigonometric functions, simplified calculations of the sort required in navigation considerably. Nevertheless the use of compasses in calculating was tiresome and errors could be made easily. Someone noticed that the compasses could be dispensed with and computation would be easier and less error prone if one simply laid two Gunter's scales side by side. To multiply one number, x, by another, y, for example, one simply placed the number 1 on one scale beside x on the other and then read from the latter scale the number opposite y on the former.

About 10 years after Gunter invented his rule, someone got the idea of adjoining two such rules so one could be slid along the other in a controlled fashion and the logarithmic slide rule was born. There is some debate as to who first had this insight. Edmund Wingate and William Oughtred are generally considered the primary candidates. The anonymous writer of the 1880 instruction manual mentioned previously credits the idea of the sliding rule to William Forster, a pupil of Oughtred's. Apparently the idea was more easily conceived than executed; a functional sliding rule was not built until some time, perhaps decades, following its invention. Again, the author of the instruction manual writes:

It may be supposed that at first the sliding rule was not much used, if only from the difficulties found in its construction. This may be judged of somewhat from the following extract from the interesting diary of Mr. Pepys, secretary to the Admirality in the time of Charles II. Under the date of the 10th of August, 1664, Pepys says: ‘Abroad to find out one to engrave my tables upon my new sliding rule with silver plates, it being so small that Browne, that made it, cannot get one to do it. So I got Crocker, the famous writing master, to do it, and I set an hour beside him to see him design it all; and strange it is to see him, with his natural eyes to cut so small at his first designing it and read it all over, without missing, when, for my life, I could not, with my best skill, read one word or letter of it.’ (Anonymous, 1880, p. 11)

The same writer points out that the difficulty of obtaining good rules was not much less nearly a century later. Only an exceptionally skilled craftsman could produce scales with the degree of precision needed to ensure accurate calculations with a rule. One notable craftsman who was up to the task was James Watt, who is remembered primarily for turning Thomas Newcomen's steam engine into a viable commercial product; but the necessity of making the rules by hand and the limited number of people who could do so meant that the devices were not readily available to people of modest means.

Numerous improvements in the designs of slide rules were made during the 17th and 18th centuries and many different scales were invented to make the instruments useful for a variety of purposes, including gauging, ullaging, and the computing of taxes and tariffs. Among the names commonly associated with such developments are those of Robert Bissaker, Henry Coggeshall, Thomas Everard, William Nicholson, John Robertson, and Robert Shirtcliffe.

About 1811, Joshua Routledge, an English engineer, designed a rule that, in addition to Gunter's logarithmic scale, contained scales with several gauge points, or constants that facilitated certain calculations of special interest to engineers. This rule became known as the engineer's slide rule. The carpenter's slide rule, which was designed a few decades later by Sir William Armstrong, a British hydraulic engineer, was very similar to Routledge's rule but differed in certain respects that made it more convenient for doing the types of calculations needed in carpentry (Roberts, 1982). Instruction manuals for the engineer's rule (Routledge, 1867) and the carpenter's rule (Anonymous, 1880) were published by John Rabone and Sons, the first company established to manufacture rules. Reprints of both were published by the Ken Roberts Publishing Company in 1982 and 1983.

Calculating with a slide rule requires judging how the scale marks on a slider are aligned with those on one of the scales of the stationary part of the rule. Especially with the earlier rules, the precision with which this could be done was quite limited. At some point in the 18th century, someone—perhaps John Robertson (Hopp, 1999)—got the idea of increasing the accuracy of reading by adding a sliding index, runner, or cursor, a transparent device with a cross hair, that could be positioned over the area of the rule where the alignment had to be read. The runner was especially helpful in comparing readings on noncontiguous scales and was even more helpful when made of magnifying glass. (Although, strangely, the runner did not become a standard part of t...