THE CODEBREAKERS

by DAVID KAHN

  He began his program by sending a series of messages to teach the terms “plus” and “equals.” His first message might be beep beep beep beep bloop beep beep tweet beep beep beep beep beep beep. Next he might send beep beep bloop beep tweet beep beep beep. After sending enough of these for the outerspacelings to catch on to the idea that bloop is “plus” and tweet is “equals,” he might transmit a message with a new signal, like beep beep beep blip beep tweet beep beep. Soon the spacelings would realize that blip means “minus.” Similarly, Freudenthal would build up an entire mathematical vocabulary.

  He would then introduce the notion of time by sending, say, a seven-second dash, then a Lincos word meaning “second,” then seven pulses. By repeating this pattern with dashes of different lengths, the listeners would eventually notice that the duration of the dash is proportional to the number following, and would thus ascertain the length of Earth’s time-unit.

  A page of the cosmic language “Lincos” in the notation of mathematical logic which its inventor uses as its script, showing a discussion between Human a and Human b

  Human behavior would be demonstrated through a kind of Lincos radioplay. A new signal would be followed by an incomplete Lincos statement, such as “six plus four equals …” A second new signal would be followed by the Lincos word for “ten.” These two new signals would continue querying one another on mathematical problems—the only topic available for discussion to beginning speakers of Lincos. During these colloquies they would use—and therefore teach—the Lincos terms “says,” “good,” “bad,” “who,” “allows,” and so forth. The outer-space listeners would also divine, Freudenthal expected, that the signals are actually the Lincos names for sapient beings. Eventually, Freudenthal would have two beings perceive the same event at different times—and therefore in different places. This new notion, location, would lead into definitions of distance, motion, and mass, and hence into the whole field of mechanics. Universal constants, such as the speed of light or the hydrogen atom’s radio wavelength, would (with the known Earth time-unit) establish Earth’s units of length. This important step would permit description of the earth, the solar system, human beings, and so forth. From here, Freudenthal planned to strike out into geography, anatomy, and physiology, and, on a more profound level, into human behavior.

  The plan is well founded and elaborately prepared, with hundreds of proposed messages fully worked out in Freudenthal’s book, Lincos: Design of a Language for Cosmic Intercourse. But some interesting criticisms have been made. One mathematician wondered how Freudenthal can be so certain that the outer-spacelings would think as he does? Perhaps their mathematics is different. Perhaps they would try to seek a pattern in the meaningless variation of the numbers of beeps used as illustration in teaching the elementary concept of “plus” instead of concentrating on the invariant “plus” signal. To these Freudenthal has replied: “I suppose that the receivers are mentally humanlike. Otherwise I would not know how to communicate with them.” He went on to explain that he referred primarily to mutual possession of the mathematics known to humans, the only kind that humans can imagine. As for the variations, “The words ‘plus’ and ‘equal’ are so different from the regularly fluctuating signals that you cannot be mistaken. I am absolutely sure that any Chinese peasant who has never understood the English words ‘plus’ and ‘equal’ will understand what you have said.”

  Lancelot Hogben, a Fellow of the Royal Society, editor of the best-selling The Loom of Language, and himself inventor of an interstellar language, agreed with Freudenthal up to the establishment of temporal signals. But he thought—and, many believe, rightly—that the step after that would be to set up a common factual framework based on mutual experience, which would have to be celestial phenomena. “The last topic about which we could hope to achieve understanding would be the actions of persons in general and the concept of the ego in particular,” he wrote. Hogben also saw no advantage in converting the messages into the Lincos logistical form. The only necessity for cosmic speech is that “terms and constructions conform to the requirements of rigorous semantic rectitude,” he said. But he seems to have missed the point that the very purpose of Lincos is to secure that rectitude.

  Hogben’s own proposal, called “Astraglossa,” shared many of the basic principles of Lincos, but it does not give the impression of solid logical structure, and hence of communicative power, that Lincos does. He devised it at the invitation of the British Interplanetary Society early in the 1950s, before thoughts of other worlds had ripened. He envisioned it in the form of a communication by light flashes with Mars, but explained that it could be generalized to any planet, using radio waves.

  Hogben began, like Freudenthal, by teaching elementary signals for “plus” and “equals.” He suggested teaching time in conjunction with astronomy. By selecting a reference point on Mars and a celestial event visible there, Earth would send n dashes at n time-intervals before the event would be seen at the Martian point, then n- 1 dashes at n- 1 time-intervals, and so on. For example, 9 dashes might be sent 9 minutes before Martian eyes would see Earth occult its moon, then 8 dashes 8 minutes before, and so on. The danger that they would think this simply a lesson in astronomy could be averted by sending the numbers as triangular factors: 1 @ 2 instead of 3, 1 @ 2 @ 3 instead of 6, 1 @ 2 @ 3 @ 4 instead of 10. Hogben suggested moving from simple flashes for integers to numeration, which is more efficient, proposing base 2 or base 12, preferably the latter because it is more compact. The Martians—who, if they are picking up the communication, can detect electromagnetic energy—may have also discovered the absorption lines in spectrograms of the portion of the electromagnetic spectrum that is visible to humans. “This opens the possibility of associating the concept of number and duration with the concept of matter in its several elementary forms,” Hogben hypothesized.

  To establish negation, Hogben would set up a new flash and insert an erroneous term in the series in juxtaposition to a foregoing correct message. By repeating the lesson, the Martians would infer that the new flash indicates negation. He would explain interrogation by substituting, for the affirmative declaratory annunciatory flash that normally precedes a message, a new dual flash meaning “what” is the “xth” term in a number series. Next, Hogben would set up assent and denial. Eventually a question-and-answer technique, combined with ability to detect signals from different transmitting stations, would make possible the differentiation of “we” and “they.” Hogben would then be in a position to ascend to new levels of communication.

  The earliest system proposed for cosmic talk partakes of some features of both the mathematical and the pictorial approaches, but its feet stand firmly in the former. It was devised in 1896, after a near approach of Mars to the Earth, by Sir Francis Galton, the founder of eugenics and an early proponent of the use of fingerprints to identify criminals. It being before the days of radio, Galton imagined that the Martians were communicating with Earth by flashing an immense assemblage of large heliographs, all worked simultaneously, to reflect sunlight back toward Earth. The Martians used three signals—a dot of 1¼ seconds, a dash of 2½ seconds, and a line of 5 seconds. With these three they built up a system of numeration to the base 8, either because, Galton speculated, they were using only three different signals (8 = 23), or because they are highly developed ants who count to eight on six limbs and two antennae. After instruction in addition, subtraction, and the other arithmetical processes, the Martians transmitted figures giving, for each of the five major planets, its mean distance from the sun, radius, and time of rotation, with Earth’s measurements given as 100.

  Next, the Martians industriously sent over signals defining π, and with the help of this drew a polygon of 24 sides. They named each side, and, by transmitting one name after another, used the polygon to draw pictures. The first was of half of Saturn—the other half not being needed because the planet is symmetrical. This took 105 “stitches.” Next came a picture of the North American continent,
which required 88 stitches, 16 of them fractional because of the indentation of its shores, while South America, which followed, required only 52. Night after night the scintillations came down, progressing to domestic and sociological drawings. Galton implied that communication ceased only when the two planets drew too far apart along their orbits.

  Galton sugared his discussion with some humor, and he deserves credit as the pioneer in a new field of communication. Both his program and Hogben’s, however, suffer a serious loss of generality in assuming communication with a planet so close that external phenomena are visible—eclipses or occultations in Hogben’s Astraglossa, terrestrial geography in what might be called Galton’s Martiansprache. This gives them an easy way out of what is the hardest step for the mathematically based languages—the leap from the conceptual to the physical, from ideas to things. In Lincos, which is much more rigorously logical than either of the others, this transfer is the weakest point.

  Concreteness is, on the other hand, the strength of the pictorial approach. The astute space expert and writer Arthur C. Clarke first mentioned this idea, which television apparently suggested to him. Like the logico-mathematical approach, the pictorial has roots in precosmic human activity.

  Writing itself, of course, began as a series of pictures. In China, a script that consists of formalized pictures is read and understood to mean identical things by Chinese whose speech is mutually unintelligible. The principle is that of a skull and crossbones on a medicine bottle, which means danger or poison to an American, a Frenchman, a German. Many other symbols serve to communicate between persons whose languages differ: road signs, chemical formulas, notes of music, Arabic numerals.

  The first attempts to signal man’s presence on Earth to the creatures of another planet—Mars—employed diagrams. The German mathematician Karl Friedrich Gauss, whose name lives in English today in the verb “degauss,” meaning to neutralize the magnetic field of a ship, suggested planting broad lanes of forest in Siberia in the form of a gigantic right-angled triangle, filling the inside with wheat to make it stand out more clearly. This geometric shape would clearly be an artificial creation. Man could drive the point home by erecting squares on each side of the triangle to illustrate the Pythagorean theorem. Not long thereafter, the Viennese astronomer Josef Johann von Littrow proposed digging canals in the Sahara to form geometric figures with twenty-mile sides. At night kerosene would be poured upon the water and set ablaze. Charles Cros in France conceived the idea of a huge mirror to reflect sunlight, like a giant heliograph, toward Mars.

  These devices could not convey much more than that intelligence exists on Earth. Moreover, they depend upon a visual contact, which is not possible in interstellar communication. To express any real information, man would have to radio a plurality of pictures or detailed diagrams to the other world. Two ways of doing so have been proposed. Both expect that the recipients would arrange the message, which arrives in a long one-dimensional string of pulses, in a two-dimensional array. One method depends upon spatial relationships to clue the recipients to this rearrangement, the other upon temporal relationships.

  Shortly after the Green Bank conference on extraterrestrial life in 1961, Frank Drake sent to the participants, and later to other scientists as well, a message based on the spatial form. It consisted of 551 binary digits—zeros and ones, which might have been transmitted as pulses and blanks or as two kinds of pulses. The solution of the problem resembled the cryptanalysis of a columnar transposition cipher. The fact that 551 is the product of two primes, 19 and 29, suggested arranging the digits in a rectangle of those dimensions. With 29 digits across the top, no pattern emerged, but when the digits were laid out in lines of 19 characters, several groupings of the units—which might be envisioned as dots or marks lying amid the white space of the zeros—appeared. Drake’s message was highly concentrated, depicting a two-legged creature rather like a man, evidently the sender of the message; schematic drawings of the carbon and oxygen atoms, implying that the creature’s chemistry was, like man’s, based on them; the sun and five planets of the creature’s solar system, with modified binary numbers for 1 to 5 opposite them and a series of longer binary numbers that probably represent the populations of the planets (No. 4, with 7 billion, apparently being the home planet and two others, with 3,000 and 11, apparently being colonized or explored by astronauts); and, finally, the creature’s height, given as 31, probably 31 times the wavelength on which the message was sent. Of course, a great deal of this information is read into the message on the basis of human experience, and it is doubtful whether so compact a message would be transmitted at first. But Drake remarked:

  The content of the message was designed to contain the data we would first like to know about another civilization, at least in the opinion of many scientists who have thought about this problem.

  In preparing the message, an attempt was made to place it at a level of difficulty such that a group of high quality terrestrial scientists of many disciplines could interpret the message in a time less than a day. Any easier message would mean that we are not sending as much information as possible over the transmission facilities, and any harder might result in a failure to communicate. In trying this puzzle on scientists, it has been true so far that scientists have understood the parts of the message connected with their own discipline, but have usually not understood the rest. This is consistent with the philosophy behind the message.

  The use of two dimensions has made possible the transmission of a great deal of information with few bits. This is because it is possible to arrange the symbols of the message in positions relative to one another such that even the arrangement carries information, when we employ logic and our existing knowledge of what may possibly occur in another planetary system. Thus the 551 bits are equivalent to approximately 25 English words, but the information content of the message appears much greater than that. This is because much of the message tells us, by the placement of a single symbol, which of several complicated possibilities is the one that has occurred in the other planetary system, without using bits to spell out precisely the possibility that has occurred.

  Even though Drake’s message was too compressed, the principle certainly works. It could even be extended to produce a three-dimensional model. The use of a number of pulses that is the product of three primes might hint at this, just as a number resulting from two primes suggested the two-dimensional array. So far, it seems not to have been tested.

  Interstellar communication by picture: the position of the clashes among the dots inside the picture frame builds up the image of a human form

  The temporally based method of transmitting images has been urged by Philip Morrison. To mark off each line of the picture, he would send two synchronizing pulses. These would be distinctive and each pair would be separated in time by the same interval as every other pair. They would frame the picture. Between the beginning and ending pulses of each line, Morrison would transmit the information-carrying signals. The outer-spacelings would have to align these one under the other to form the picture, hopefully being guided to do so by the frame of the synchronizing pulses, and perhaps helped by the near-similarity and slight divergencies of successive lines.

  Morrison would send as his first picture a circle—a kind of test pattern. The message would consist of a number of units, all equal in time, all marked off at the beginning and end by identical pulses. The first segment would consist of these two synchronizing pulses with a single distinctive message pulse sent midway between them. The second segment would have two message pulses, one sent slightly before and the other slightly after the middle of the segment. The third segment would likewise have two message-pulses, both likewise symmetrically spaced in time about the midpoint but farther from it. Successive lines would continue to widen the interval between the two pulses until a maximum was reached, then would begin to narrow it again, until the final segment would again comprise a single message pulse in the middle of the time inter
val. When these are lined up one under the other—voilà! A circle.

  “Of course,” said Morrison, imagining the use of this method by the outer-spacelings in sending messages to Earth, “they may not scan linearly. Maybe they scan in logarithmic spiral. It makes no difference to the method. As long as they supply us with a simple geometric pattern and some algebraic clue to it, we cannot take very long to make out the nature of their scanning raster.” The method, is, of course, adaptable to sending more complex images, like Drake’s, though it is perhaps not as suitable for three-dimensional structures.

  The temporal scanning principle is, of course, that used in television. Actual television as known here on Earth would not be used for interstellar communication, even if it were taught to the outer-spacelings, because it requires too much power for long distances and is not efficient in transmitting information. But two of its characteristics—moving pictures and tones of gray (instead of just black or white, as in Drake’s diagram)—might eventually help convey additional information. For motion, the simple principle of movie cartoons would serve. A series of images, each differing slightly from its predecessor, would be sent. When viewed in rapid succession they would appear to move—at least to humanlike eyes. For tint gradations, Drake would convert the brightness of each spot in an image into a number proportional to the brightness. White spots might be coded as 10, medium-gray as 5, very dark gray as 2, black as 1. These numbers would be transmitted instead of the binary digits of his basic scheme. In a test of just such a system for commercial purposes (because it uses less bandwidth than television), Bell Telephone Laboratory engineer R. L. Carbrey found that pictures of a pretty girl with only three levels of brightness were perfectly recognizable. By using a special transmission code, he used seven pulses per spot to obtain 128 levels of brightness (27 = 128). But this might be rather sophisticated early in the interstellar game.