To many stockbrokers, business people, and newspaper editors the computer terminal at their desk is a stranger, spoken to in a few overworked phrases of pidgin computerese. They feed their raw data into it and get back statistics that mean something to them. Only the programmer knows that happened in between.

He yawns a potential chasm.

Michael Berry, an applications programmer and a sort of translator between people and computers for a Canadian-based company, puts it simply: "Managers become more dependent on people like me."

"We could be headed toward a more split society," Mr. Berry speculates. The split is between those illiterate in the language of computers and those, mostly of the generation now coming of age, who have had "the right kind of exposure early."

Eight years ago the Royal Canadian Mounted Police noted an unusual number of electronic "footprints" into some sensitive government files. They traced them to a precocious 16-year-old student on a computer terminal at a private school in Montreal.

"I had managed to log a large number of accesses," he says dryly, speaking correct computerese.

Lesley Goldsmith had, in effect, while tied to a common computer network by telephone, broken the codes -- electronic, mathematical barricades programmed into the agency's computer system.

It was innocent trespassing. He was simply tiptoeing through the invisible barbed wire to examine the security codes. He was putting his school's grading records on computer and needed to make them tamperproof. In Ottawa they understood, eventually.

But the consultant responsible for encoding this agency's data proposed a private test: Each would get four hours, young Goldsmith and the consultant, and each give the other basic, initial access to his own data base -- a key to the front door. But the locked doors they had programmed into their systems should stop any further access. They would see how far each of them could get.

The student won. In just five minutes Goldsmith had "fooled the system" and gained free run of restricted information, while his counterpart was stymied, unable to sneak through to the computerized grade files.

At I. P. Sharp Inc., the Toronto-based computer company that hired Goldsmith, they call these kids, often in their teens, "elves." To them, computers are "glass boxes"; they can see through them. They are fluent in the language.

Soon after his encounter with the Mounties, Goldsmith went on to create an electronic mailbox system that Sharp, a company with offices in many countries, now uses for most of its internal communications and sells to clients.

In a similar case last spring, Federal Bureau of Investigation agents discovered that prowlers in come Canadian corporate records were three eighth-graders at the Dalton School in New York City.

They had tapped into the computer network the corporations use, Datapac, by telephone and, again, broke the security code to bluff their way into forbidden territory.

These incidents are not isolated. They signal the coming of age of a generation whose world is beginning to be permeated and woven together by powerful computers.

"This generation," remarks Michael Berry, a 23-year-old veteran at I. P. Sharp who teaches a class on the computer language APL, "doesn't have what most adults have: a fear and awe of computers."

An expansive thinker on the subject, Dr. Donald McIntyre, is a geologist of wide-ranging interests at Pomona College in Claremont, Calif. He has begun to teach basic computer courses, not just to students, but to his fellow faculty members: "I'm anxious to avoid a generation gap." Young people take new technology in stride as part of daily life, like the telephone, he explains. And the older people are left out.

But the "elves" have an edge in the computerized world beyond just an easy familiarity with the terminal screen.

"It's not that they know a whole lot more than anyone else," says Steve Davis of the North Carolina School of Science and Mathematics in Durham. "It's a certain talent and a way of thinking." This way of thinking, he notes, is the ability to break a problem down into its component elements -- an ability honed through play.

And to the elves, a computer often began as an invisible playground. Highly sophisticated computer games, often based on physics problems, first absorbed the interest of many, drawing them for hours at a time to a keyboard in the back of a physics classroom or in a math teacher's office, all the time building a mental construct of the computer's labyrinthine, mathematical world -- learning to think like a computer.

Lesley Goldsmith had spent much of his free time at school exploring the computer, giving himself problems such as teaching the machine the math formulas in one of his textbooks. His projects grew more complicated, and soon he was beyond the range of his teachers. When his school approached I. P. Sharp about computerizing its grading data, it was the company that suggested the student take on the task.

Now earning his master of applied science degree in electrical engineering at the University of Toronto, Goldsmith describes a type of student who, often in introductory courses, gets caught up by a fascination for computers. "Someone will plant a seed in [his thinking] and it will really grow." Their consuming enthusiasm -- self-motivated and self-directed -- carries them well beyond the demands any teacher could ever make on them, sometimes at the expense of other courses.

Meanwhile at I. P. Sharp, elves drop by after school and on Saturdays to write programs for client companies. "We've looking at hiring them younger and younger," Rosanne Wild says; she is marketing services manager at Sharp headquarters in Toronto. "They live and breathe this stuff."

Mr. Berry was reared in a household where APL was spoken. His father, Paul Berry, coined the term "glass box" (the "glass box" is the exact opposite of the black box, the symbol of machines we use in our daily lives but can't see into or understand) and has been a major figure in developing the APL language -- finding new mathematical "verbs," "nouns," and rules of grammar. The inventor of the language, Kenneth Iverson, began working on it in 1957 while teaching at Harvard. The language is now spoken by computers at IBM, Xerox, Massey-Ferguson , and Dome Petroleum, among others. To those who feel, like Ken Iverson, that the venerable FORTRAN, BASIC, and COBOL languages make clumsy mathematical tools with their tedious procedures, APL is a watershed.

As Donald McIntyre puts it, "It frees you from having to deal with the innards of the machine" -- that is, to a greater extent than most languages. It's simple. It's ordinary English and standard mathematical notation, "simplified and generalized."

Most languages were designed to suit computers. APL was first written as an improvement on mathematical language -- with or without computers. Years later it was adapted to machines.

When Michael Berry was in eighth grade he began to teach himself the language on a terminal at home. He programmed some basic mathematical laws into it and made it a calculator. In high school he programmed it to be an electronic text editor and wrote his papers on it. By the time he entered college at Oberlin, he taught a course in APL to his fellow students, beginning in his freshman year. He started working summers at I. P. Sharp at 17.

In a sense, he's a mathematical linguist. And like other linguists, he learned his language by growing up with it. Dr. Iverson believes his language should be taught the way, say, Spanish is commonly taught: in a classroom where only Spanish is spoken. On a computer this means figuring things out, rather than learning textbook programming routines.

Prof. Seymour Papert at Massachusetts Institute of Technology carries the idea further. Dr. Papert believes that a child's innate sense of mathematics can be tapped into in the same way as his sense of language. He speaks of teaching children math by immersing them in a "math land" parallel to learning French by living in France.

Dr. Papert's math land is, of course, the computer. It's language is LOGO, one he created that, at its simplest, small children can use to manipulate geometric shapes. Three-and four-year-olds, he says, learn to make computer-directed, moving graphics as easily as learning to talk.

Papert, a confessed "educational utopian and romantic" who once worked under Jean Piaget in Switzerland, may be ahead of his time in cutting toddlers' teeth on computers. But then the times may be catching up.

Prospective students considering Pomona College have recently wanted to know if their personal computers can tie into the college's system, Donald McIntyre remarks. If not, he figures, they won't enroll, and the college will lose some of its best potential students. And Pomona is a liberal arts college without a computer science department.

Those, like McIntyre himself, who work in other fields now need to be familiar with computers. "I'd like to see the whole title of computer programmer become obsolete," Mr. Berry says. He feels everyone should be comfortable with computers to some extent, and be able to do basic programming work. Black boxes would become more transparent.

How transparent is a real question. Black boxes serve their purpose. "In general," Lesley Goldsmith says, "the notion of a canned utility program is very valuable." Most simply, it's something we don't have to think about.

It comes down to levels of explanation, Dr. McIntyre explains. When we type a letter, for example, do we demand to know how the typewriter-key linkage is designed? Some do; some don't. "All of us must decide at what level we want an explanation." No one wants to know evertyhing; everything isn't important. McIntyre's preference for the APL language lies in that, with its simple, flexible, symbol-for-concept programs, we the users can decide for ourselves to what level we want an explanation.

"It's an art to know where to draw the line," McIntyre continues. "When is it packaged -- an obstacle to thought -- and when does it encourage thought?"

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