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About the Making of Simple Mathematical Machines and the Observation of Jupiter |
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by Albert G. Ingalls |
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"A lot of people will tell you that machines can't think," Bezold said, "and perhaps they are correct. But it seems to me it is largely a matter of what you mean by the word 'thinking.' Some of the purists say that if a machine can do it, you can't call it thinking. Whether it is thinking or not, I have made several machines which do a number of things that human beings do with their brains, and so have many other amateurs. My little machines take in information, remember it, pass judgment, make decisions, reach conclusions and take action. If the gadget I'm working on now pans out, it will play a game with you that is similar to the old match game of 'nim.' As it goes along, this machine will learn from experience to become a better player. It may make a mistake when it begins to play, but it will remember every error and will never pull the same boner again. I'll admit that all of the 'intelligence' exhibited by these devices must be designed into them, and that the little ones I have built are pretty stupid. But in certain ways a mouse can be smarter than a man-and this is so with some of these gadgets." Bezold's nim-playing machine consists of a metal box three feet tall, two feet wide and about a foot thick, housing some 50 relays and accessory apparatus. The front holds three groups of signal lamps with associated push buttons. When the machine is turned on, all lamps light. The player can extinguish lamps by pressing the push buttons. A switch starts the game and tells the machine who gets the first play-itself or the human player. According to the rule, each player in turn may put out as many lights as he wishes in any one of the three groups. The one who puts out the last light wins. As the machine is now constructed, the human player can win if, and only if, he makes the first move and plays a perfect game. Bezold hopes to endow the machine with a touch of human frailty by combining some new relays and associated circuits with those already in the gadget. After this modification the machine will forget all the strategy it knows each time the main switch is turned off. It will then begin competition on an equal footing with inexperienced human players. But the human beginner will have to keep his wits about him and remember perfectly everything he learns, for the machine will catch on quickly and never fall victim twice to the same line of opposing play. As Bezold points out, you do not have to be an electrical wizard to build these machines, nor do you need any mathematics beyond arithmetic. It helps a lot if you enjoy puzzles, and a knowledge of circuit symbols is handy. You can memorize the symbols in a few minutes. Perhaps the most novel idea the beginner will encounter is the use of switches relays, lamps and other circuit elements to express words and logical relationships. The two positions of a simple switch, for example, can mean more than "on" and "off." They can also symbolize yes or no, true or false, or the digits 1 or 0. A relay is not much more than a glorified switch, operated electrically. One part consists of a bar of soft iron surrounded by a coil of insulated wire [see Fig. 1 at left]. When current flows through the coil, the bar becomes a magnet which attracts a similar bar called the armature. The motion of the armature is transmitted through insulators to one or more flat springs that carry contact points. These serve as switches. Current flows through the relay's coil the contact springs are flexed by the armature, and so the switch is operated. When the current stops, everything snaps back to normal. Offhand it may seem that putting a relay in a circuit is the hard way to go about flipping a switch. But in thinking machines most of the switches must flip automatically, usually by current flowing through other switches also operating automatically. Thus one or more input pulses can proceed through complex networks of relays as a spreading chain reaction, modified or conditioned en route according to the requirements of the designer. This, incidentally, is the way the human brain works, with the neurons acting much like relays. In thinking machines the end of the reaction is always the same: an output circuit closes or opens, thus lighting a lamp or putting it out, starting or stopping a motor, or causing some other registering device to work. Essentially the reaction consists in the manipulation of logical relationships. Thus far Bezold has used only five basic circuits in variations and combinations. With these five, he says, an amateur can build automatic devices to solve any puzzle that can be stated precisely in words. In addition to the simple "yes-no" circuit, the designer will need one expressing an "and" relationship. Such a circuit consists of two switches connected in series so that current must flow through first one, then the other to effect closure. The circuit is completed when both switch A and switch B are operated [see diagram at the right of Fig. 1]. Equally useful is the "or" circuit. This has two switches connected in parallel so that operation of either one permits current to flow. Closing switch A or switch B makes the connection [see top diagram Fig. 2]. The fourth basic circuit expresses the logical relationship of "if, then" [second diagram Fig 2]. It requires a two-way or transfer switch in which the switch blade operates between two contacts, connecting with one in the "on" position and with the other in the "off" position. The first of these is called the "make" contact and closes when the switch is operated. The second is called the "break" or "back" contact, and it passes current until the switch operates, when it opens or breaks the circuit. Relays can be equipped with several sets of contact springs of both kinds. By connecting the make and break contacts of one relay to the switch arms of following relays, the designer can build up a branching pyramid of transfer circuits. With only five relays, for example, such a "transfer tree" can switch the input circuit to any one of 32 output circuits. Every relay added to these five will double the number of output choices available. If the machine is to do any sort of advanced thinking, it must have a memory. This is easily contrived by wiring a make contact so that it will connect the coil of its relay to a source of current whenever the relay is operated. When operated by an incoming pulse, the relay will then remain "locked down" by its own internal circuit. To make the relay forget, it is only necessary to insert a break contact in series with the locking circuit. Usually the break contact is actuated by a part of the machine which calls on the memory for information. After the stored information has been delivered, the break contact operates. The relay returns to normal and thus "forgets" in preparation for the next incoming signal [third diagram Fig. 2]. Bezold has put all five of these basic circuits to work in a machine which can solve the old puzzle of the farmer faced with the problem of moving a fox, a goose and a bag of corn across a river in a boat large enough to hold only the farmer and one of the three objects. The fox cannot be left alone with the goose or the goose with the corn, for obvious reasons. The problem is to design a combination of circuits which expresses the logical relationships posed by the farmer's dilemma and which will raise an alarm when the person working the puzzle makes an error. Each of the four principals-farmer, fox, goose, corn-is represented by a pair of switch keys, one on each side of the river [see Fig. 3]. When you press the key on the right next to one of the principals, a signal lamp on that side lights, showing that the member has moved across to the right side of the river, and so on. A relay is tentatively assigned to each of the four, starting on the near side of the river. An analysis of the logical propositions discloses what form the switching circuit shall take. First, it is seen that a safe situation exists whenever the farmer is where the goose is. Things are equally safe when the goose is alone. But trouble threatens whenever the goose is with the fox, with the corn or with both. Obviously the goose needs the most watching. The farmer and goose play opposite roles, the presence of one making for safety, the other for trouble. They act like a pair of switches or relays, one of which is the negative of the other, i.e., one is a make contact and the other a break. The fox and the corn also spell trouble. Relays representing them should, therefore, be of the same type as that for the goose. Suppose, now, that a relay with a make contact is assigned to the farmer. In terms of logic it stands for "not farmer." Its contacts close whenever the farmer crosses the river in the boat, so that the farmer symbol may be contained in the boat. Hence break contacts are assigned to the other three characters. How shall the four relays be interconnected? The situation is always safe when the farmer is present; it is unsafe when he is absent and the goose is present and the fox or the corn is present. Hence the farmer's relay should be connected in series ("and" circuit) with that of the goose. The goose's relay in turn is connected in series with one side of a parallel connection ("or" circuit) between the fox and corn relays. If a lamp and battery are now connected across this circuit, nothing will happen unless the farmer-boat relay is operated, indicating that he has crossed the river. But when he crosses, the contacts of his relay close and the circuit is completed through the break contacts of the unoperated relays symbolizing the goose, fox and corn. The circuit then signals trouble. This takes care of the situation on the near side of the river, but a second circuit must be constructed to represent events on the other side. There the situation will be the negative of that on the near side; for example, the presence of the farmer on one side means that he is absent on the other. Hence, to give a complete picture of both sides we need a second circuit, the reverse of the first. In the second circuit a break contact is assigned to the farmer, while make contacts go to the goose, fox and corn. As long as the farmer is with them, his break contacts are open and there is no alarm signal. Suppose now that the farmer leaves the goose and the fox across the river and returns to the near side for the corn. As soon as he does, the break contacts close and the lamp lights. An investigation of the twin circuits will disclose that their operation in unison conforms to every logical requirement of the puzzle and that they accurately respond to every combination of events within the logical limits of the situation. This portion of Bezold's machine could be constructed with four simple toggle switches and corresponding sets of make-break contacts. But such a machine would not be very convenient as a parlor game, because the player would have to throw the farmer's switch and one of the other three at precisely the same instant or the alarm would flash. Hence Bezold made a fancy affair in which each relay also functions as a memory element. This enabled him to simplify the logic circuit somewhat, although, as he confesses, the gadget's extravagant use of contacts would make a switching engineer very unhappy. "The extra contacts were on the keys and relays," he said, "so I just wired them in for the fun of it." Noel Elliott of Kellogg, Idaho, who is preparing for a career in electronics at Washington State College, is another amateur who likes to build thinking machines. In 1950 his ticktacktoe machine won for him a Westinghouse Annual Science Talent Search Award. "The design of this machine," Elliott writes, "closely resembles that of all electrical calculating devices, although on a much simpler scale than most. It can remember, calculate and transfer information from one circuit to another. The calculation and transfer, however, occur as soon as the information is received rather than in a timed sequence such as takes place in a big calculator like ENIAC. This is possible because of the simple nature of the information. The operator informs the machine of his move by throwing a switch, and the machine, after carrying out its calculation, makes its reply move by lighting a pilot lamp in the appropriate space on the playing field. "The machine has two basic functions: to prevent its human opponent from occupying three spaces in a row, and to prevent him from establishing a fork-the threat of making three-in-a-row along either of two lines. The work of design began with the classification of all possible moves. "Since there are nine spaces on a ticktacktoe playing field, there are nine possible first moves. The moves are of three types: center, corner and side. Statistics show that the best move against a center opening is a corner, and against any outside opening, the center. The circuits that carry out this strategy consist of 'or' switches in all outside positions and a direct connection between the center switch and a lamp in one of the corners. "After the opening move and the reply, the human player has a choice of seven remaining spaces. This means that for his first two moves he has a total of 63 possible combinations. The machine's replies to these are handled by an 'and' circuit, with current from the battery flowing through the first-move switch and the second-move switch to the lamp. Circuits that respond to subsequent moves are designed in the same way, although in some of them provision must be made against setting up duplicate paths and thus causing more than one lamp to light. Conflicts of this type are avoided by equipping the circuit with memory relays interconnected so that operation of one switch automatically opens the circuit of another which would otherwise interfere." Neither Bezold nor Elliott has constructed a digital computing machine so far. These require too much apparatus for the average amateur's pocketbook if their capacity for numbers goes beyond a couple of digits. But Bezold has set up small circuits for the basic operations of arithmetic. A set of relays equipped with transfer and lockdown contacts, for example, can easily be interconnected to count pulses. Two relays are needed for each digit. A pulse (in the form of a momentary ground connection) enters the transfer contact of the first relay and energizes the coil of the second relay. The second relay locks down and simultaneously applies energy to a lead connecting with the coil of the first relay. But since the transfer contact of the first relay also is connected to this lead, thus grounding it during the pulse, no current can enter the coil of the first relay. When the ground connection is removed at the end of the pulse, the first relay operates, locks down and thereby transfers the input connection to the next pair of relays, where the second incoming pulse causes the cycle of operation to be repeated. The train of relay pairs may be extended indefinitely to count as many pulses as desired. One or more break contacts can be inserted along the line, of course, to unlock previously operated pairs. Two relays may also be interconnected in such a way that each responds to alternate pulses, the incoming pulses causing one relay to lock down and the other to release in seesaw fashion. Such a pair in effect divides incoming pulses by two. Like the counting relays, these can be cascaded, each succeeding pair dividing the output of its predecessor. Such "flip-flop" circuits find extensive application in computing machines that work with binary numbers-in which all quantities are expressed by combinations of 1 and 0. In the binary system 1 plus 1 equals 0 with 1 to carry. The first relay of the flip-flop pair symbolizes the binary digit. If it is holding a digit when the pulse arrives, the circuit flip-flops, thus restoring the first relay to 0. The second relay then sends a pulse to the next succeeding pair, the first relay of which operates and thus stores the digit 1. The two sets of relays then stand at 10-which in binary notation means 2. The machine has, in short, performed an addition. Its capacity to add is limited only by the number of relays built into it. UNLIKE MARS the planet Jupiter has never been seen. What we see of Jupiter is not the planet itself but an unbroken canopy of banded clouds hiding some wholly unknown entity beneath. The spectrograph tells us that these clouds consist of ammonia and probably methane, and the thermocouple reports that their temperature is more than 200 degrees below zero Fahrenheit. A six-inch telescope magnifies this cloud-enveloped body to the apparent size of our moon as seen with the naked eye. A 12-inch telescope used visually reveals an appearance similar to that in the photograph on the preceding page. In it the two most prominent dark bands, a number of fainter dark bands and certain markings near the bottom and around the polar regions are red- brown clouds. The bright bands in between are white or yellowish-green clouds. The cause of the colors is unknown. The nature of the eye-shaped object called the Great Red Spot, which has been observed closely since 1878, also is still unknown. The dark spot above it is the shadow of Jupiter's satellite Ganymede, which is visible in space to the right of the planet. Ganymede, about 40 per cent as large as the Earth in diameter, is now being mapped by amateur astronomers. None of the visible features of Jupiter is fixed. The cloud bands vary from year to year-in number, in width and in latitude. Most of them last only a few weeks or months. Each rotates at a different rate. The broad bright equatorial band rotates most rapidly: its period is 9 hours and 50 minutes. The periods of the others are five or six minutes shorter; each rotates at a different rate without system or relation -to latitude. Their edges are sharply bounded. Each drifts slowly past its neighbor. Within the bands there are many minor markings, and these continually change. Watching the changes provides such variety that the observation of Jupiter is a lively business, especially since the planet rotates so rapidly. However, the observation would soon lose interest were it not for the intriguing riddle beneath, to which the puzzling visible performances seem in some mysterious way related. From the known mass and volume of Jupiter it is easy to calculate that the density of the planet averages but one and one third times that of water, and from this and the gradual shifting of the clouds it has been conjectured that the planet is partly fluid. Almost the only systematic observers of Jupiter's ever-changing clouds have been serious amateurs, working mainly in organizations. Such work was begun several decades ago in Great Britain and has been taken up in the last few years in the U. S. and Canada. The observers have accumulated detailed records of the dark belts, the intervening bright zones and the many markings within each. These have been published as occasional reports in the memoirs of the British Astronomical Association. In the U. S., observers' reports and drawings of changes are collected by the Jupiter Recorder for publication in The Strolling Astronomer, the periodical of the Association of Lunar and Planetary Observers, which any amateur may join ( 1203 N. Alameda St., Las Cruces, N. M.). One A.L.P.O. member who has done outstanding work in observing Jupiter and in using observational data accumulated by others is Elmer J. Reese of Uniontown, Pa. Reese selected two of Jupiter's bands in which changes recorded since 1940 had persisted uncommonly long, and minutely observed them himself between 1940 and 1951 with his homemade six-inch reflector. A brief analysis of his findings has been published in The Strolling Astronomer, and a longer article on them has been written by Walter H. Haas, A.L.P.O. director and editor, for The Griffith Observer, publication of the Griffith Observatory in Los Angeles. Reese's chosen bands are the ones in the photograph between the shadow of Ganymede and the Great Red Spot. In the standard nomenclature these are respectively the South Temperate Zone and the South Temperate Belt (south because astronomical telescopes invert). Like all other zones and belts on Jupiter, these encircle the planet. The drawing (left) shows the bands unrolled. The dusky lower section in each band is the South Temperate Belt. The brighter upper part is the South Temperate Zone. The elongated white markings BC, DE, and FA show eruptive disturbances from beneath. They have persisted for several years longer than any disturbance recorded on Jupiter except the Red Spot and a nearby eruption which lasted for several decades. Reese watched these white sections diminish in length as the dusky sections CD, EF and AB gradually encroached on them during the period indicated. He also saw them drift to the left at differing distances from the Red Spot. This spot lies in a third band called the South Tropical Zone. As the lower drawing shows, the Red Spot is in a depression called the Red Spot Hollow. At times the spot itself disappears. Reese next plotted drift curves, shown at right, for six longitudinal sections-three dusky, three bright. The slope of these curves indicates duration and shows the rate at which the feature is moving. To make measurements he needed a way to time the markings as the planet rotated. While this can be done with a filar micrometer or by measuring photographs, the amateur uses a primitive method which may be equally precise. As a feature approaches the central meridian of rapidly rotating Jupiter, he decides to the nearest minute when it is centered on the disk and records the time. It is no more difficult to estimate accurately when a marking is centered on a planetary disk than to center a picture accurately in a frame with the eye alone. When the same marking is observed for a number of days, any error is reduced proportionately; in a month the error is reduced from minutes to seconds. On the drift curves drawn by Reese the shaded strips represent the three longitudinal dusky sections of the South Temperate Belt and the white strips the bright sections. (The strips should not be confused with the actual bands.) It is easy to see that in 1940 the white sections were wider, longitudinally, than the dusky sections. By 1950 the dusky sections had encroached so far on the bright that the bright eruption had almost ceased to exist. In 1948 the motion of the six sections which had been uniform, suddenly decelerated, as shown by the knee in the curve. At that date their rotation period lengthened by four seconds to 9 hours, 55 minutes, 10 seconds. Some unknown influence had also applied a brake to the entire band from the beginning in 1940: in that 11-year period it fell back nine laps (note nine spaces) in the race with adjacent bands. It is not nearly as easy to keep track of a protean marking on Jupiter at the telescope eyepiece as it is to examine crisp drawings in an armchair. Another source of perplexity is the annual conjunction of Jupiter with the Sun, which makes it invisible for several months. When it comes into view again, the marking under observation may have changed so much that it must be identified by projecting its drift line on the chart. Nor is the seeing always good. Haas points out that a telescope of the very best optical quality and 10 or 12 inches in diameter gives the best results in the search for long-enduring markings on Jupiter. He asks, however, whether the scarcity on Jupiter of long-lasting features, such as the eruptions observed by Reese, is real or only apparent: "The ability of the telescopist to fail to see what he is not looking for is at times most remarkable!" Haas calls Reese's work "an outstanding piece of Jupiter research done by an outstanding amateur astronomer." What have his 11 years of observations proved? Are the eager amateurs who sit up all night and hastily record 100 transits of markings on Jupiter accomplishing anything or merely accumulating useless statistical data on some clouds of gas? The basic data of science have often looked useless until the key to a riddle has turned up. Then the statistical data suddenly become valuable. As this account was being completed a news circular arrived from the British Astronomical Association. It says: "Observations by members of the Jupiter Section indicate the dark material from the South Equatorial Belt overflowed into the South Tropical Zone just preceding the Red Spot round which it passed to form a dark narrow belt on the following side." This means that the gaseous cohorts from a dark belt, which is dimly visible in the photograph on page 107, have crossed the border into the zone containing the Red Spot, and a conflict may result.
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