by Steve Ditlea

From time immemorial there have been those who see everything as black-or-white, either/or propositions. This "binary" or singularly two-sided view of life has caused them moments of discomfort at the hands of those who find more nuance in the world. In the fourth century, for example, Roman emperors and popes alike were known to behead believers in the Manichaean heresy, which divided the world into the duality of good and evil.
    At other times the Either/Or crowd has turned the tables, successfully categorizing everything in terms of opposites: West or East, North or South, Rich or Poor, Old or Young, Liberal or Conservative, and the ever popular Male or Female. Such dualities have provoked confrontations throughout history, including our own occasionally frustrating era.
    Now some psychologists, like Solomon Asch, feel there may in fact be a human need to define complex concepts in terms of binary choices. Only then, they say, can the gray areas be understood. The "cognitively simple" person distinguishes only a few categories. The "cognitively complex" distinguishes many. But can the incredible complexity of our universe be adequately described through binary choices? And how does this relate to these words being composed on a home computer?

Binary Logic
A familiar application of the simplicity and complexity of binary choices is the familiar Morse code, used in transmitting messages over telegraph lines. Developed in the 1830s, Samuel Morse's combinations of dots and dashes-short and long bursts of electricity-can represent any letter in the alphabet and by extension any human thought that can be put in writing. (Silence is a third alternative in Morse; in fact, pauses are essential for differentiating letters between bursts of code.) Each dot/dash, either/or choice delivers one elementary "bit" of information.
    Without actually using numbers, Morse code embodies "digital" information. A message has been translated into a symbolic language of pulses following certain rules of composition. By contrast, an "analog" transmission of the same information might be a steady electronic signal modified to take on the characteristics of a speaker's voice. Because digital bits can be transmitted more simply and efficiently, they are the lingua franca of today's computers.

The Human Computer

Only since World War II has the word "computer" (from Latin computare, "to reckon," "sum up") been applied to machines. The Oxford English Dictionary still describes a computer as "a person employed to make calculations in an observatory, in surveying, etc." Above, a computer at work circa 1940.

    "Bytes," on the other hand, are the actual groupings of code used to identify individual letters, numbers or other characters. In the 1920s the development of the teletype raised a fundamental question: how many electrical either/or alternatives would it take to transmit signals for every key on a modified typewriter keyboard, including upper- and lower-case characters, numbers, punctuation marks and special character codes? A standards board decided that seven either/or's could communicate the necessary information; the various combinations, a total of 2x2x2x2x2x2x2=128, offered enough possibilities for necessary key codes. An eighth either/or was added as a way of checking for transmission errors over the line. These groupings of eight bits became known as bytes, and the code for representing keyboard characters became the American Standard Code for Information Interchange.

Digital Input

When I push the keys on my computer keyboard, each key in turn triggers a series of electrical pulses in ASCII code so the appropriate letters can appear on the display screen or be printed out later. These same pulses will be used to typeset this book directly from my storage disks. If I push an "a" (lower case), the computer will receive a characteristic code of either/or pulses that can be noted as 0s and 1s in the sequence 1100001. If I push an "A" (upper case), the computer reads this as 1000001.
    These either/or, 0/1 component bits of information are transmitted within the computer as pulses of either lower- or higher-voltage electricity. (The voltage levels are lower than those in a portable radio and can't shock you.) The actual choice of pulses is determined by a series of microscopic switches that can be set for either 0 or 1 voltages. Such two-way switches are at the heart of all that takes place in a personal computer.
    Binary switches are responsible for the machine's information processing, internal memory, graphics and other abilities. Everything a home computer can do, from juggling words to simulating space flight, from toting up financial figures to communicating with other computers, is the result of setting thousands of binary switches, all based on either/or, 0/1 alternatives. There would be no home computers, no electronic computers at all, were it not for the discovery of the binary numbering system. True to the scheme of most important scientific developments, its origins span thousands of years and its central theory was confirmed by a fortunate accident. In 1679 a centuries-old Chinese manuscript fell into the hands of German philosopher Gottfried Wilhelm Leibniz, who was then perfecting his notion of the binary system. For all his imagination, Leibniz still lacked confirmation of his theory when proof came to him in the form of an eleventh-century commentary on the I Ching-a far older system of portraying the complexity of the universe with a series of either/or combinations. The manuscript illustrated an orderly sequence of the sixty-four I Ching hexagrams, which Leibniz perceived as graphic proof that his own system of 0s and 1s was valid.
    The I Ching, or Book of Changes, is one of the oldest books in existence. Its present form dates back to China's King Wen, who ruled over three thousand years ago, and is based on sixty-four different six-line figures, or hexagrams, each made up of combinations of broken and unbroken lines. The lines correspond to Taoist dualities: Yin and Yang, dark and light, receptive and creative, female and male. The hexagrams can be obtained by the traditional casting of stalks from the yarrow plant, a rather involved procedure, or by the simpler method of tossing coins. The coins are thrown six times. Each combination of heads and tails corresponds to a broken or unbroken line. Once the six lines have been obtained, the resulting figure is interpreted in an appropriate section of the book, relating it to the movements of nature, proper conduct in society and the individual's fate in the world.
    The variety of the I Ching's concerns is indicated in some of the names linked to specific hexagrams: Inexperience, Conflict, Prospering, Deterioration, Innocence, Danger, Family, Adversity, Cosmic Order, Meditation, Limitations. Each hexagram, suggesting an image drawn from nature and the affairs of humans, elicits personal insight into the moment at hand. From six either/or alternatives, the I Ching's sixty-four possibilities sagely sum up the cycles of existence. Thus the I Ching goes beyond elementary dualisms: from six binary choices, it weaves a subtle view of life.

The First Data Base

It can be argued that the I Ching was the first primitive computer. With astonishing mathematical precision the early Chinese cataloged all natural and social phenomena, then, with binary transformations, interrelated every possible physical interaction. The I Ching was a universal organization of symbolism, a cosmic filing system that directly interacted in binary fashion, anytime, anyplace. As a computer it was not always user-friendly, but it was extremely portable.


The decimal number system in which we're used to counting, with digits from 0 to 9, might seem the most natural for humans born with ten fingers (the word "digit" itself comes from Latin for "finger"). This 10-based number system, however, can be considered a historical accident since humans in fact have only eight fingers (and two thumbs). So why not a base-8 or even a base-2 system?
    A binary system using just 0s and 1s has many advantages, not the least of which is its simple representation by mechanical or electronic means; hence its use in computers. Counting in binary can be easily mastered. A binary 1 is the same as a decimal 1, a decimal 2 is noted as 10 in binary, a 3 is 11 in base-2, and a 4 is 100.
    From right to left, every column of digits in binary is a higher power of 2. To convert a binary number into its decimal equivalent, simply add the values of the binary columns. For example, 10110 can be broken down into:

Decimal    16 8 4 2 1
Binary      1 0 1 1 0

 or 1x16+0x8+1x4+1x2+0x1=22

   All binary arithmetic can be simplified to a series of additions. Adding binary numbers consists of summing columns and carrying over each remainder to the next higher column. Subtraction is accomplished by converting the number to be subtracted into its "inverse" (all its 0s into 1s and vice versa) and then adding. Multiplication involves shifting the number to be multiplied one place to the left for each 1 in the multiplier and then adding these partial results. Division is
With simple binary choices, Kanda the Great, a gorilla in the Dallas Zoo, has done better than a panel of local sportswriters in picking the winners of pro football games.

a variation on subtraction, with the number of times one number can be subtracted from another providing the quotient.
    Beyond arithmetic, binary also lends itself to an elegant system of symbolic logic. According to Boolean algebra, all logical statements can be analyzed for their validity with just three functions: "and," "or" and "not." Each of these logical operators transforms binary alternatives according to specified rules. For example, if two incoming bits are the same, the "and" function will combine them into a single identical bit. A "not" operation will transform a bit into its opposite. By combining series of these functions in electronic circuits known as logic gates, a computer can evaluate, compare and contrast not just numbers, but any thoughts the human mind can conceive.

    The ability of the I Ching's hexagrams to relate accurately to a particular moment was explained by psychologist Carl Jung as the principle of "synchronicity"-that what seems coincidental actually follows from the interdependence of all things. A hexagram, according to Jung, is "the Chinese picture of the moment."
    Synchronicity is essential to the operation of a personal computer. Constant as the cosmic order that connects all natural phenomena, at the heart of each computer system is a tiny quartz crystal, which, upon electrical stimulation, vibrates at a steady rate. The rhythms of the universe that keep the Earth turning and distant pulsars pulsing also activate a home computer's quartz crystal at a rock-steady rate of millions of vibrations per second. These vibrations provide the beat for a computer's operations. Each beat in turn calls up another of the series of thousands of 0/1 electrical pulses necessary for a particular computer application. If the quartz clock were to fall out of step, the result would be anarchy within the computer. Yet the quartz keeps vibrating, steady as the cycles of nature.

 The Tao Today

Following his belief that "things are like number," Leibniz had hoped to come up with a mathematics of logic in which all complex ideas could be expressed by a series of elementary symbols that could then be calculated for their basic truth or error. This goal eluded him for the rest of his life.
    It wasn't until the nineteenth century that George Boole in England produced his algebra of logic, which could systematize any logical proposition into a series of binary, either/or choices. Operations based on Boole's algebra of logic in combination with numerical operations made possible by Leibniz' binary system provided the theoretical groundwork for computers.
    All those binary switches in your personal computer dance to the numbers and logic of Leibniz and Boole. Software tells hardware what to do, setting the appropriate switches to execute the thousands of individual 0 and 1 operations needed for a useful computer application. Hardware and software are yet another duality in the Tao of personal computers.
    From the simplicity of 0s and 1s, a computer can create sufficient complexity to aid or intrigue the human mind. From these elementary binary choices come the variety and range of human/computer interaction. The pages that follow attest to just how varied the powers of two can be.

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