ENIAC – Literary Art and Illustration

The Age of Science: Computation and Cybernetics, in Astounding Science Fiction – May, 1949 – “Electrical Mathematicians”

From Astounding Science Fiction of May, 1949, the article “Electrical Mathematicians,” by Lorne Maclaughlan, focuses on the the use of computers – specifically, electronic as opposed to mechanical computers – as devices to perform mathematical calculations. It’s one of the four non-fiction articles pertaining to cybernetics and computation published by the magazine that year, the other three having been:

“Modern Calculators” (digital and analog calculation), by E.L. Locke; pp. 87-106 – January

“The Little Blue Cells” (‘Selectron’ data storage tube), by J.J. Coupling; pp. 85-99 – February

“Cybernetics” (review of Norbert Wiener’s book by the same title), by E.L. Locke; pp. 78-87 – September

The identity and background of author Maclaughlan remain an enigma. (At least, in terms of “this” post!) The Internet Speculative Fiction Database lists only two other entries under his name, both in Astounding (“Noise from Outside” in 1947, and “Servomechanisms” in 1948, while web searches yield a parallel paucity of results. This absence biographical information, especially in light of the over seven decades that have transpired since 1949, coupled with the author’s distinctive writing style – combining clarity and economy of expression, and easy familiarity with the language of technology – leads me to wonder if that very name “Lorne Maclaughlin” (note the lack of a middle initial?) might actually have been a pen-name for an engineer or academic. Given the somewhat ambiguous reputation of science-fiction in professional and credentialed circles (albeit a reputation by the 1940s changing for the better) maybe “Maclaughlan” – assuming the name was a pseudonym – might have wanted to maintain a degree of anonymity.

Well, if so (maybe so?!) that anonymity has successfully persisted to this day!

Anyway, the cover art’s cool.

Depicting a scene from the opening of Hal Clement’s serialized novel Needle (the inspiration for the 1987 Kyle MacLachlan film The Hidden?), it’s one of the three (color, naturally) Astounding Science Fiction cover illustrations by Paul Orban, an illustrator primarily known for his fabulously imaginative interior work, whose abundant output was only exceeded by his talent.

As for Maclaughlan’s article itself, it begins with a brief overview of the implications of the increasing centrality of calculating devices in contemporary (1949 contemporary, that is!) society, and the future.

This is followed by a discussion of the very nature of calculation, whether performed by mechanical or electronic devices, which then segues into a comparison of the similarities and differences between binary and decimal systems of counting and computation, and an explanation of the utility of the former in computing devices.

Next, a lengthy discussion of memory. (We’ve all heard of that…) note the statement, “Not only must we “teach” the machine the multiplication table – by the process of wiring in the right connections – but it may also be necessary to provide built-in tables of sine and cosine functions, as well as other commonly used functions. This is a permanent kind of memory – a fast temporary kind of memory is also needed to remember such things as the product referred to above until it is no longer needed. This memory has not been easy to provide in required amounts, but recently invented electronic devices seem to offer some hope that this difficulty can be overcome.” In this, author Maclaughlan is anticipating what we know today as ROM (read-only-memory) and RAM (random-access-memory), respectively.

This is followed by the topic of data input and manipulation, in the context of Hollerith Cards and Charles Babbage’s “Difference Engine”. (For the latter, see “Babbage’s First Difference Engine – How it was intended to work,” and, “The Babbage Engine,” the latter at Computer History Museum.

From this, we come to computation in terms of the technology and operation of then-existing computers. This encompasses ENIAC (Electronic Numerical Integrator and Computer), EDVAC (Electronic Discrete Variable Automatic Computer), and MANIAC (Mathematical Analyzer Numerical Integrator and Automatic Computer Model I), and briefly touches upon the Selectron tube, the latter device the subject of J.J. Coupling’s article in the February 1949 issue of Astounding.

The final part of Mclaughlan’s article is a discussion of the nature, advantages, and use of “analyzers” – Differential Analyzers, and Transient Network Analyzers – in computation: Specifically, in the solution of differential equations pertinent to scientific research, such as, “…the flow of microwave energy in wave-guides, the flow of compressible fluids in pipes, and even the solution of Schrodinger’s Wave Equation,” or military applications, such as aiming anti-aircraft guns or determining the trajectory of nuclear weapons, noting, “These latter-day buzz-bombs will be sufficiently lethal to warrant their carrying along their own computers.”

Prescience, or, inevitability?

And finally, the article concludes with a photograph.

And, so…

ELECTRICAL MATHEMATICIANS

“The differential analyzer is more versatile than the network analyzer discussed above because it can integrate, differentiate – in effect – and multiply, and thus solve rather complicated differential equations. These functions are performed by mechanical or electro-mechanical devices in the differential analyzer. If these things could be accomplished by purely electrical means, we would expect a great increase in speed, and some decrease in size and weight.”

To an extent none of us today can realize, these rapidly growing electrical calculators will become more and more important factors in ordinary life. So far, they are handling only simple, straight-arithmetic problems. They are brains, but so far they think only on low levels. Give them time; they will be planners yet!

In this machine age no one is surprised at the announcement of some new or improved labor-saving device. The scientists and technologists who design our new electronic rattraps, microwave hot-dog dispensers and atomic power plants have succeeded so well that they have created a serious manpower shortage in their own professions. This shortage, which is chiefly in the field of analysis has recently forced them to put an unprecedented amount of effort into the design of machines to save themselves mental labor. The results of their efforts are an amazingly variegated collection of computing machines, or “artificial brains” as they are called in the popular press:

The development of such machines took a tremendous spurt during the war, and today we can scarcely find a laboratory or university in the land which is not devoting some part of its efforts to work of this kind. Progress is so rapid that the machines are obsolete before they are completed, and thus no two identical machines exist.

We cannot say that the computing machine is a new invention – the unknown Chinese originator of the abacus provided man with his first calculating machine in the sixth century B.C. This would seem to make the machine nearly as old as the art of calculating, but man is equipped with fingers and toes which have always provided a handy portable computing device. In fact, as we shall see, the simple fact that we have ten lingers has a definite bearing on the number of tubes and the kind of circuits required in electronic digital computers.

__________

Kelvin Wheel-and-Disk integrator. This device, which gives the integral of a radial distance with respect to an angle, is the most important unit in a differential analyzer of the electromechanical type.

__________

It should be pointed out that there are two distinct types of computing machines in common use today. One type deals with discrete whole numbers, counting them off with the aid of teeth on a wheel, or electrical pulses in vacuum tube circuits. These numbers represent quantities, and they are added and multiplied just as numbers are on paper, but at a much higher speed. These machines called digital computers, range from the simple cash-register adding machine to the complex all-electric ENIAC, with its eighteen thousand radio-type vacuum tubes.

The other type of machine is the analogue type of computer, in which the number to be dealt with is converted into some measurable quantity, such as length along a slide rule, or angle of rotation of a shaft. The operations are performed electrically or mechanically, and the answer appears as a length, an angle, a voltage or some other quantity which must be converted back to a number. The ideal machine of the analogue type will accept mathematical functions, empirical curves and directions for mixing and stirring, and turn out results in the form of curves automatically.

The digital computer is much more accurate than the analogue type for the simple reason that is easy to extend the number of significant digits in such machines to something like thirty or forty. It is impossible to measure a point on a curve to anything approaching one part in 1040. However, the analogue computers are in many ways faster and more versatile, because they can perform certain difficult mathematical operations directly, while digital machines require that these operations be reduced to addition and multiplication.

One of the first things we must do to understand modern digital computing machines is to disconnect our minds from the decimal number system, and get a more basic concept of number representation. The decimal system of numbers is a natural choice, based on the fact man has that ten fingers. We would perhaps be more fortunate had evolution given us twelve, for then our number system would be the more convenient duo-decimal system. Let us examine this system as a starting point, by studying the table of numbers below.

1	2	3	4	5	6	7	8	9	*	t	10
11	12	13	14	15	16	17	18	19	1*	t	20
21	22	23	24	25	26	27	28	29	2*	t	30

The six-fingered man would count to six on one hand, and then continue, seven, eight, nine, star, dagger, ten on the other. His ten would be our twelve, of course, but it would be a resting point for him while he got his shoes off to continue to his twenty – our twenty-four – on his twelve toes.

If we continue the table for twelve lines of twelve numbers each we will get to his one hundred, which corresponds to our one hundred forty-four. This number is his ten squared – our twelve squared – as it would be, and is preceded by his daggerty-dagger, ††. This duodecimal system has the advantage that ten can be divided by 2, 3, 4 and 6, giving in each case whole numbers – 10/4 = 3, 10/6 = 2, et cetera – while our ten is only divisible by 2 and 5. The ancient Babylonians were fond of this system, and also used sixty as a number base. These systems remain today as the bases of our measurement of time in seconds, minutes and hours.

Now let us examine the binary system, based on two. In this system all numbers are made up of combinations of just two digits, one and zero. The simplicity of this system makes it possible to use simple devices such as electromagnetic relays to represent numbers. The simple relay has two possible positions, open and closed, and we can represent zero by means of the open position, and one by the closed position, and then build up any number as shown in the table below.

Decimal System	Binary System
1	1
2	10
3	11
4	100
5	101
6	110
7	111
8	1000
9	1001
10	1010

Computation is easy with this system, once we get the hang of it. Thus our two cubed becomes, 1011 = 10 x 10 x 10 = 1000, and our two times three becomes 10 x 11 = 110, which is our six, as it should be.

With our minds cleared for action on any number base let us consider the capabilities which are necessary in a digital computer. Digital computation requires that all operations be reduced to those of addition, subtraction, multiplication and division whether a machine is used or not. These operations involve certain reflex actions, such as the response “six” when presented with the numbers “two” and “three” and the idea “multiply.” The trained human mind possesses such reflex actions, and the machine must also possess them, as a first requirement. Simple computing devices such as the commercial accounting machine possess a few reflexes. It is necessary to build many rapid reflexes into mathematical computing machines.

The next “mental” capability the machine must possess is that of memory. When we must multiply two numbers together before adding them to a third, memory is needed to preserve the product until the second operation can be performed. Commercial calculating machines have limited memory – after multiplication, for example, the number appears on the output wheels, and the third number can easily be added. The memory requirements in a good mathematical machine are much, much more stringent, and provide some of the toughest problems in design. Not only must we “teach” the machine the multiplication table – by the process of wiring in the right connections – but it may also be necessary to provide built-in tables of sine and cosine functions, as well as other commonly used functions. This is a permanent kind of memory – a fast temporary kind of memory is also needed to remember such things as the product referred to above until it is no longer needed. This memory has not been easy to provide in required amounts, but recently invented electronic devices seem to offer some hope that this difficulty can be overcome.

There are still two capabilities left. These are choice and sequence. The computing machine should be able to choose between two numbers, or two operations it can perform, in accordance with certain rules. Sequence involves, as the name implies, the proper choice of order of numbers or operations according to some rule which applies in the particular problem being solved.

These last two capabilities are not found to any great extent in any but the most modern mathematical computing machines. On the other hand there are a multitude of other mental capabilities found in humans which are undesirable in mathematical machines. Emotion, aesthetics, creative ability and so forth are not desirable, for these help to make humans unfit for much routine computing work. What we want is perfect slave, fast, untiring and industrious, who will never embarrass or disconcert us with unexpected response. (Of course the engineers in charge of some of the complicated modern mathematical machines are quick to accuse them of temper tantrums and other undesirable emotions.)

Perhaps the fanciest digital computing machine today is the IBM Automatic Sequence Controlled calculator at Harvard. The letters IBM International Business Machines Corporation, which has developed a series of machines intended for use in accounting work. These machines use a punched card – a device with quite a history, as histories go in the computing field. It would seem that weaving machines which could be used to more or less automatically weave patterned cloth excited the imagination of a good many inventors in in the early eighteenth century. In such weaving it was necessary to sequence automatically the “shredding,” or controlling of the warp threads so that weft threads could be passed through them to weave a pattern. Punched tape and punched cards had already been by 1727. The punched cards we use today get the name Jacquard cards from the name of the inventor of an improved weaving machine around the year 1800.

This basic idea was good enough to attract the attention of Charles Babbage, an English actuary, who is regarded as the lather of the modern computing machine. His “difference engine” was designed, in his words, “to perform the whole operation” – of the computing and printing of tables of functions – “with no mental attention when numbers have once been fed in the machine.” When this “engine” was nearly complete the government withdrew its support of the Project, and Babbage began the construction of an analytical machine on his own. This machine, a wholly mechanical device, was to use punched Jacquard cards for automatic sequencing. In 1906 his son successfully completed a machine with which he calculated pi to twenty-nine significant figures.

Hollerith, in this country, made a great advance in the use of punched cards when he invented a card sorter to aid in classifying the results of the 1880 census. Most people today are familiar with the kind of things that a sorter can do. Thus if we have a sorter and a stack of cards with personal and alphabetical information punched thereon we can request the machine to pick out all left-handed individuals with cross-eyes and Z for a second initial, and bzzzzt, bzzzzt, bzzzzt – there they are.

The IBM Company, by catering to the needs of organizations which handle – and have – a good deal of money, was able to put the manufacture of computing machines on a paying basis. It need not be pointed out that it is much more difficult to produce profitably machines which will only be used for such tasks as the calculation of pi to umpteen places. However the punched card machines built for accountants have found their way into scientific computing laboratories, and the IBM Company has a research laboratory which is actively developing new machines for scientific use as well as for accounting.

A punched card machine operating on the Hollerith principle interprets numerical and operational data according to the positions of holes punched on cards, and then perform various mathematical operations. The cards, which are familiar to most people – postal notes, government checks, et cetera – have twelve vertical positions in each of eighty columns. The vertical positions are labeled y, x, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Thus an 80 digit or two 40 digit numbers can be set up on one card, and the y space, for example, may be used to indicate sign.

The cards are read for purposes of sorting et cetera by a simple mechanism involving a metal cylinder and sets of electrically conducting brushes. As the card moves between the rotating cylinder and the eighty brushes, one for each column, an electrical contact is made whenever a punched hole passes under a brush. The position of the cylinder at the time that the brush makes contact indicates the number, or letter, represented. Any number system could be used, but the decimal system is selected because of its familiarity. The various IBM machines now on the market include Card Punchers, Card Interpretaters [sic], Card Sorters, Collators and others, all operating on the same basic principles. The most useful machine to scientific workers is the Automatic Multiplying Punch. This machine will multiply factors punched in cards, and will automatically punch the product in a card, or even add and punch out products.

The computer lab at Harvard, mentioned above, uses a combination of these machines and a device for sequencing their operations – whence the name IBM Automatic Sequence Controlled. This calculator is one of the half-dozen large machines in this country which can be used to tear into a tough problem and quickly reduce it to a neat column of figures – or a stack of cards, in this case. Since it is a digital type of computer capable of great accuracy, but because it is partly mechanical in operation it is slow compared to the newer all electronic machines. The automatic sequencing apparatus is not easy to set up, and thus type of machine is best suited to the solution of repetitive types of problems, such as the calculation of tables. The punched card is a convenient form in which to store tables of simple functions, e.g. Sin x, Log x, which are often needed in computation of tables of more complicated functions.

Of course, if you want to prepare a table umpteen places Bessell Functions, or evaluate some determinants, or make some matrix algebra manipulations you will have to wait s time for your turn on this or any similar machine. You will have to have a pretty good story too, for these machines are at work today, and sometimes night as well with important problems. It must be realized too, that a problem be rather important and complex before it is even worthwhile to the labor of setting it up for solution in such a complicated machine.

Punched cards are often used to store scientific data other than tables with the advantages of machine sorting et cetera possible with IBM machines. Thus at the Caltech wind tunnel data from instruments is punched directly on cards. Astronomers locate star images by pre-computed co-ordinates on punched cards, and then measure the star positions accurately and record the new information on new cards. The Census Bureau makes a great deal of use of punched cards at present, but plans are being made to go over to the faster electronic computers for this work.

__________

Basic flip-flop vacuum-tube circuit used in the ENIAC and in other digital computers. Tube number 2 – shaded – is conducting, and tube number 1 is “cut-off”, in the diagram above. A positive pulse on tube 1 will cause it to conduct and the resultant drop in its plate voltage will cause tube 2 to cease conducting. This condition is stable until another pulse arrives, on the grid of tube 2.

__________

Shortly before the war, G.R. Stibitz and others at the Bell Telephone Laboratories developed a relay type of computer which could handle not only real numbers but complex numbers as well. The binary number system is convenient in a relay computer as we have pointed out. There is some difficulty entailed in the process of getting from a number expressed in the ordinary decimal system to the binary system and back again. For this reason Stibitz likes what he calls a bi-quinary system, which uses base 2 to tell if a number is between 0 and 4, or 5 and 9, and base 5 to tell which digit it is of the five. Early in the war the Army and Navy each ordered one of these relay computers, and machine computation was off to a flying start.

Dr. H.H. Aiken, who had built the IBM computer at Harvard has recently gone over to the relay type of computer, and his “Mark II” will soon be in operation on the complicated guided missile ballistics problems being studied at the Dahlgren Proving Ground. IBM has also been playing around with relay computers, and has delivered two sequence controlled machines of this type for ballistic research workers. Aiken does his sequencing with standard teletype tape, while some of the IBM jobs use plugboards.

An interesting example of a similar parallel development is the Zuse computer, named after its designer Conrad Zuse, who developed his machine in Germany during and since the war. Like the Bell Laboratories machine it uses a keyboard to feed numbers into its relays. The sequence is prepared in advance by an operator who punches instructions into a strip of film.

The art of machine computation took a tremendous jump ahead when in the fall of 1946 the ENIAC, the first electronic digital machine, was placed in operation. This machine was built for Army Ordnance at the Moore School of Engineering by J.W. Mauchly, J.P. Eckert and others. The ENIAC – Electro Numerical Integrator and Calculator – with its eighteen thousand tubes is over a thousand times faster than the relay machines, which in turn were twelve times faster than the original punched card machine at Harvard. This tremendous increase in speed is the result of shifting over from the use of one gram relay armatures to the use of 10^-31 gram electrons as moving parts. Of course a number of new problems appeared when this one limitation was removed. They are being cleared up one by one, chiefly by electronic means.

The ENIAC, despite the light weight of its moving parts, is no vest-pocket machine, as the number of vacuum tubes would indicate. The filaments of these tubes alone require eighty kilowatts of power, and a special blower system is needed to take away the heat. The whole machine occupies a space about 100 feet by 10 feet by 3 feet. Tube failures were a source of a good deal of trouble, because for while at least one of the eighteen thousand tubes burned out each time the power was turned on. This trouble was reduced by leaving the filaments of the tubes on, night and day, to eliminate the shocks involved in heating and cooling, so that now the ENIAC burn-outs at only about one per day, which take on the average of only fifteen minutes to repair. Experience with this machine has aided the design of a series of successors, such as the EDVAC, the UNIVAC, and the MANIAC – inevitable name.

The most important type of unit in the ENIAC is a device which uses two triode tubes, called a flip-flop circuit. These tubes will do electrically what the relay does mechanically. Normally one of the two tubes is conducting current, and the other is “cut off.” A very short – 0.000001 seconds long – pulse of voltage can cause this tube to cut off or cease to conduct, and the other to begin to conduct. Since only these two stable states are possible, we have the beginning of a binary computer. We must add a small neon bulb to indicate when the second tube is conducting, and then add as many such units in series as there are binary digits in the number we wish to handle. These circuits are used as a fast memory device. The ENIAC has a fast memory of only twenty ten-digit numbers, a serious limitation which can only be overcome by adding to the already large lumber of tubes, or by going to other types of fast memory.

Adding is accomplished by connecting flip-flop circuits in tandem so that they can count series of electrical pulses. This counting works in the same way that the mileage indicator works in a car, except that the scale of two is used. Thus, suppose that initially all our flip-flop circuits are in one condition – call it flip. The first pulse causes the first circuit to go from flip to flop. The next one will return it to flip, and this causes the first circuit to emit a pulse which sends the second circuit to flop. This continues on throughout the chain of circuits, all connected in tandem, as long as pulses are fed into the first circuit. When two series of pulses have been fed in we can get our number by noting which circuits are on flip – binary zero – and which on flop – binary one. The result may be converted back to pulses for use elsewhere. The speed per digit in the adding operation is a comfortably short ten microseconds.

The description of the adding scheme above has omitted one added complication in circuit design which gives a considerable simplification in reading of numbers. The binary system is used to count only to ten in the ENIAC and the number is then converted to a decimal number. This is a bit of a nuisance, circuit-wise, but handy – the decimal system is familiar.

The ENIAC also has electronic circuits for multiplying, dividing, square-rooting and so forth. The multiplier uses a built-in electrical multiplication table to aid it in its high-speed, ten digit operation. One very important unit in the ENIAC is the master programmer, which changes the machine from one computing sequence to another, as a complex computation progresses, in accordance with a pre-set plan. The master programmer even makes possible connections which enable the machine to choose the proper computing sequence when faced with the necessity for a choice. Thus it would almost seem that the machine does possess a kind of built-in judgment, and that there is some reason for the term “electrical brain.”

It was mentioned that the fast memory of the ENIAC was limited. The slow memory, using punch cards, and IBM machines causes a great reduction in speed when it must be used. Also, although computation is all-electronic, data is fed in and results are taken out by electromechanical means – punch cards again. The limitations incurred may best be realized if we compare the time for a punch, about half a second, with the unit time of a flip-flop circuit, ten microseconds. The ratio is fifty thousand times.

Even more serious is the problem common to all digital machines, namely the difficulty of setting up a problem. These machines are not easy to use, and the sequence of operations for an easy problem may be very involved. If the problem is difficult, then, of course, the sequence gets more difficult, but the use of machine methods is mandatory. So, when faced with a real stinger of a problem, the scientist gets down to work, perhaps for months, just to figure out how to set up the machine. Considerable time is needed for the physical setting up of sequence connections too, but after that – brrrrrrrrrrrrrp, and a solution which would take years by former methods begins to roll out in a matter of minutes.

Professor D.R. Hartree of England, who recently worked with the ENIAC, describes the solution of problem in which this machine had to handle two hundred thousand digits. Now try writing digits as fast as possible. At a rate which will lead to errors and writer’s cramp you may put down ten thousand digits in an hour. Even at this speed it will take twenty hours just to write down two hundred thousand digits – and no computation has been performed. The machine handled the numbers and performed the computation in this example in four minutes flat. It is not surprising that Professor Hartree is impressed by such speeds – he once spent fifteen years on the computation of the electron orbits of atoms. This is the kind of job that a machine calculator can be coerced into doing in a few hours, or days at most.

Their utility to science is obvious!

The ENIAC is only the first of its kind. The EDVAC – Electronic Discrete Variable Computer – is an improved machine, also built Army Ordnance at the r of Pennsylvania. One of the chief improvements is a larger capacity memory device, made possible use of acoustical delay lines for storage of numbers. Numbers get stored as trains of compression pulses is bouncing back and forth in a two-inch column of mercury. Each delay line of this type does the work of five hundred fifty electronic tubes in the ENIAC, so that a substantial saving results.

The MANIAC – Mechanical and Numerical Integrator and Computer – is another Army Ordnance computer. It is being built at the Institute of Advanced Study at Princeton under the direction of Dr. J. von Neumann and Dr. H.H. Goldstine. This machine is to use a new type of fast memory tube which is being perfected by Dr. Jan Rajchman of RCA. This tube, called the Selectron, is a kind of cathode ray tube which is designed to store four thousand ninety-six off-on or binary signals – equivalent to about twelve hundred decimal digits. The binary digits are to be stored as charge on points on a cathode screen which are behind the interstices of two orthogonal sets of sixty-four wires each. An ingenious method of connecting certain of these wires together will enable electric signals to be fed in to pull the electron beam to any position for purposes of reading” or “writing” with just thirty-two leads brought out. Even so a pre-production model of the tube looks a bit formidable, but it is phenomenally small for the memory it possesses.

Among some of the other schemes for digital memory being worked on are delay networks using loops of wire in wire recorders. This scheme may not be as fast as the acoustical delay line used in the EDVAC, but it has the advantage that the pulses do not have to be periodically removed for reshaping. One practical difficulty here is the necessity of waiting for the right point on the wire to come around before reading begins. Of course all memory of a number can easily be erased when need for it is finished, and the wire loop is ready to be re-used.

It seems that the Selectron is one of the best bets to speed up the operation of all-electronic computers. With its aid it should be possible to multiply two twelve-digit numbers in one hundred millionths of a second.

Such speeds may seem fantastic, but problems have been formulated and shelved because even the fastest present-day computing machines could not complete the solution in thousands of years.

The Bureau of Standards, aided by Mauchly and Eckert of ENIAC fame and others, is now constructing some new machines of a general purpose type. This new digital computer is called the UNIVAC – Universal Automatic Computer – and is to be of a general purpose type suited for Bureau of Census work as well as, Army and Navy ballistics and fire control research. The UNIVAC is to be very compact, using only about eight hundred tubes, and occupying only about as much space as five file cabinets.

It is rather interesting that one of the limitations of this and other digital machines is the slow rate at which numbers are printed at the output. This limitation may be overcome in future machines by the use of a device called the “Numero-scope,” recently announced by the Harvard Computation Lab. This device is nothing but a cathode-ray oscilloscope, which can trace the outline of any number, if the right signal is fed into its deflecting plates. This is no mean trick – it takes six vacuum tubes to make the numeral 2, for example, but it has been done, and numbers may now be flashed on the screen of a cathode-ray tube and photographed with exposures as short as one five-hundredth of a second.

The analogue computer, as we have stated works with analogous quantities rather than with whole numbers. Thus we may represent quantities by lengths, angles, voltages, velocities, forces and so on. Thus an electrical or an hydraulic circuit problem may be solved on a mechanical device, while an electrical problem may be solved on a mechanical device. One simple example of an analogue computer is the slide rule. Here quantities of any sort are converted into lengths and since a logarithmic scale is used it is possible to multiply by adding lengths. If a linear scale is used we can add by adding lengths. Division and subtraction are possible by simply subtracting lengths in each case.

__________

The basic mechanism in the punched-card machine is the brush and roller combination shown. As the card passes over a steel roller, metallic brushes make an electrical connection – between A and B in the diagram – and a signal can be produced to reject the card, or set a counter wheel, et cetera.

__________

If we use angles, or angular displacements, to represent quantities successive displacements readily add to give a total. We can also use a differential like the one in the rear end of a car to add the angular displacements in two different shafts. The answer in this case, or a constant factor – gear ratio – times the answer appears on a third shaft. Direct voltages add conveniently, and alternating voltages add like vector or directed quantities, and so are convenient in the solution of problems involving directed lengths or forces.

Before going any further into discussion of the specific details or these devices it might be well to examine the relative advantages and disadvantages of the analogue type of computer. In the digital computer the accuracy can usually be increased at the expense of speed, so that if we want to go from 10 digit to 20 digit accuracy we must suffer a decrease to half the original speed.

With the analogue type of computer it is only possible to increase accuracy if the lengths – or angles, or voltages, or whatnot – are measured with greater percentage accuracy. This may call for watchmaker techniques unless we can afford lengths or other analogous quantities. The difficulties encountered in any case are such that the accuracy is always much less than in any digital machine.

There are several advantages possessed by the analogue computer which tend to offset the decreased accuracy. One of these is its greater speed, which results partly from the fact that most problems are more easily set up for solution by analogue methods. Sometimes the analogue computer is used for a quick look at a problem, to narrow down the field which must be investigated with greater accuracy by the more involved digital computer. Another advantage possessed by the analogue computer is its ability – if the ability is built in – to perform certain mathematical operations in direct fashion. Thus, for example, a pivoted rod can be used to give the sine of an angle. This ability also accounts in part for the greater speed by the analogue method. Still another advantage is ease with which empirical data in the form of curves may be fed into an analogue machine.

The first successful large-scale analogue computer was the Differential Analyzer designed by Dr. Vannevar Bush and others at M.I.T. The same type of machine has also been built by General Electric for its own use and for use in various Universities. The latest and most highly improved of these machines was recently installed at the new engineering school at U.C.L.A.

____________________

“1948-08-06: UCLA’s Differential Analyzer Begins Rise to Stardom“, at TomOwens YouTube channel.

Note that this YouTube clip shows the incorporation of the differential analyzer in the movies When Worlds Collide, from 2:00 to 4:13 (full length version here), and, Earth Versus the Flying Saucers, from 4:36 to end (in full-length version at Archive.org, from 59:28 to 107).

____________________

The differential analyzer is used chiefly for the solution of differential equations. In view of this fact it is rather strange that the machine cannot differentiate. However it can integrate, and since this is the inverse of differentiation its mastery over the calculus is quite complete. (The inverse of an arithmetical process is commonly used by clerks in stores who count back our change, and thus use addition in place of subtraction). The integrators in a differential analyzer are of the Kelvin wheel-and-disk type in which an integrator wheel rides on a rotating disk, and is turned when the disk turns. The amount of angular rotation of the integrator wheel depends on its distance, R, from the center of the disk, and the angle the disk turns through, θ. This, by definition, is the integral of R with respect to θ.

The integrator is the most important device in the differential analyzer, and as such has received a great deal of attention. In 1944 G.E. engineers came up with a device in which troubles caused by slipping of the integrator wheel on the disk were virtually eliminated. This device was essentially a servo follow-up system in which light beams were passed through a polaroid disk attached to a very light integrator wheel. These light beams then went through other polaroid disks, then to phototubes, to an amplifier and a motor. The motor then caused the second and third polaroid disks to follow the disk on the integrator wheel with the customary boost in power level, or torque level.

Among other important components in the differential analyzer are the input tables. At these tables, in the older machines, operators followed plotted curves of functions which were to be fed into the machine with pointers, and thus converted distances on the curve sheets to angular rotations. In the newer machines light beam photocell servo-mechanisms accomplish the same thing without the aid of skilled operators. Known functions, of course, are generated by other and simpler means.

Because the differential analyzer handles quantities in the form of angular displacements the process of adding is accomplished by the use of differential gearing. To solve a differential equation the machine must first be set up so that the right shafts are connected together by the right gear ratios. When all is ready the data in the form of curves is fed into the machine at the input tables, the known functions are fed in from function generators, and the output pens are moved from left to right, all in synchronism. Adding wheels, integrators, input table lead-screws and so forth all begin to move and perform the operations required by the equation being solved. The totals of the quantities on each side of the equation are held equal by a servo-mechanism and the shaft which will give the function which is the desired answer moves the output pen up and down as it is pulled across a sheet of graph paper. Thus the answer appears as a curve, or a set of curves.

The accuracy of these results depends not only upon the accuracy with which these final curves can be read, but also upon the accuracy of the original data, and the accuracy of the various servos involved in the solution. Typically, about one-tenth of one percent, or three digit accuracy can be expected. If some of the components have been forced to accelerate too rapidly because of a poor choice of gear ratio, or if a lead screw has been forced to the end of its travel, the solution may be completely wrong – the analyst still has his headaches. These troubles are ordinarily avoided by making preliminary runs to determine the proper ranges of operation of all components.

Among the other types of analogue computers commonly used engineering work are the various kinds of network analyzers. A large electrical power network may be exceedingly complex, due to the more or less random geographical distribution of loads and generating plants. The effect of short circuits, arc-overs due to lightning, and load distribution must be studied with the aid of models, so that the design of circuit breakers, lightning arresters and so forth can proceed intelligently. Tests cannot be made on the actual power network, as they can on communication networks, because of the possibility that damage to large and expensive equipment might result.

The earliest type of power network model was the D-C Network Analyzer. The representation of three-phase alternating current systems by direct-current models of this kind has definite limitations, and the next step was the development of A-C Network Analyzers. These models, although they represent a three-phase system by a single system are much more versatile than the D-C Analyzers.

We may ask if such models should really be classed as computers. Fundamentally, these analyzers are merely models of systems which are too complicated for direct analysis, and too large for direct measurement of variables under all possible conditions. Much the same kind of model-making is carried on in the study of aircraft antennas using model planes and microwaves in place of short waves. However, if we examine some of the uses to which Network Analyzers have been put, it seems safe to class them as computers. Because of the use of electrical quantities in these devices and because of the flexibility of interconnections possible, they have been used for the solution of such problems as the flow of microwave energy in wave-guides, the flow of compressible fluids in pipes, and even the solution of Schrodinger’s Wave Equation.

Another type of network analyzer is the Transient Network Analyzer, which can show more clearly what happens in a power network when short circuits and overloads occur. This device may also be used to study analogous problems such as the amplitude of transient vibrations in mechanical systems when sudden shocks or overloads occur. The inverse of this kind of thing is the mechanical model used to study what goes on in a vacuum tube. In these models stretched sheets of dental rubber are used to represent electrostatic fields, and ball bearings serve as electrons.

The differential analyzer is more versatile than the network analyzer discussed above because it can integrate, differentiate – in effect – and multiply, and thus solve rather complicated differential equations. These functions are performed by mechanical or electro-mechanical devices in the differential analyzer. If these things could be accomplished by purely electrical means, we would expect a great increase in speed, and some decrease in size and weight. Such machines have been built by Westinghouse and Caltech, and seem to promise a fair increase in speed over the old differential analyzer. It seems inevitable that the use of many vacuum tubes will lead to somewhat lower accuracy and less dependability. Another difficulty with present types of electronic differential analyzers is that integration can only be performed with respect to time as the independent variable, so that the solution of certain problems is not easily possible.

Many other kinds of analogue computers have been perfected in the last few years – the field is definitely “hot.” Completed designs include such gadgets as the Bell Telephone M-4 Director, which used radar signals to figure out in a twinkling where an antiaircraft gun should be aimed so that the shell and a plane might meet. Undoubtedly work is in progress on computers which will make possible solution the “problem of delivery” of the modern atomic warhead. These latter-day buzz-bombs will be sufficiently lethal to warrant their carrying along their own computers.

Many scientists are disconcerted by the fact that by far the greater part of the computer research being carried on today is under the auspices of the Armed Forces. To be sure, we in the United States seem to be far ahead of anyone else in the world in computers. This may augur well for National Security if some desperate bludgeoning struggle is soon to occur. From the longer range point of view it seems that it is particularly desirable that the scientist whose pure research may lead him to yet undiscovered fundamental truths be also equipped with this new and powerful tool.

__________

Three types of computers. Top: General Electric’s A.C. Network analyzer. Middle: The differential analyzer – of the analogue computer group – at General Electric. Bottom: The Bell Laboratories relay-operated digital computer.

A Bunch of References

Network Analyzer (AC power), at Wikipedia

Differential Analyzer, at Wikipedia

The UCLA Differential Analyzer: General Electric in 1947, Video at Computer History Museum

“The Differential Analyzer. A New Machine for Solving Differential Equations”, by Vannevar Bush, at WorryDream

Differential Analyzer History, at LiquiSearch.com

A Brief History of Electrical Technology Part 3: The Computer, at Piero Scaruffi’s website

War In Space, 1939 – II: “Space War Tactics” by Malcolm Jameson, in Astounding Science Fiction, November, 1939

Here’s the second of three posts about war in space – circa 1939 – covering Malcom Jameson’s article “Space War Tactics” in the November issue of Astounding.

________________________________________

Three months after the appearance of Willy Ley’s article “Space War” in the August, 1939 issue of Astounding Science Fiction, Malcolm Jameson penned (well, in all probability, he typed – remember typewriters?) an article of similar length and concept, but focused on a different aspect of spacecraft-to-spacecraft combat: The actual tactics of battle. Thus, Jameson – perhaps reflective of his background as a naval officer – accorded attention to the maneuvers utilized by opposing spacecraft, only later in his article discussing weapons, and unlike Ley, being an advocate of “rocket torpedoes”.

Jameson’s article is supplemented by two diagrams which illustrate the trajectories of opposing spacecraft engaged in combat. (You can see his signature at the lower right in each.) In both diagrams – here limited to two dimensions, and viewed from “below” – the track of “our” spacecraft is on the left, and the enemy ship to the right.
In the first diagram, our craft is on a straight trajectory, with the enemy ship taking an abrupt “right” turn at position “7”, the weapons employed by our spacecraft presumably being rocket-torpedoes.

In the second diagram, the pair of spacecraft are on a converging trajectory, the weapons being mines as well as rocket-torpedoes.

Paralleling my post about Willy Ley’s article about space war, here are some general “take-aways” from Jameson’s article:

1) Military conflicts, regardless of the era or the nature of weapons employed, can be expected to follow the same general principles. Thus, though “space” is ostensibly different from traditional battle settings, traditional concepts and assumptions about warfare can be expected to hold there, as well.

However (!) two primary differences stand out: “Space” differs from taken-for-granted terrestrial settings (any planetary setting, really) in terms of its (apparently limitless) extent, and, the speed of the craft involved. The implications and challenges of the latter, in terms of maneuver, as well as locating, tracking, aiming, and firing at enemy craft, cannot be underestimated.

2) Given the speed of combat between spacecraft, gunnery computations will demand the use of a “differentia calculator”. (Like Willy Ley’s August article, Jameson’s analysis is based on the assumption that spacecraft armament will comprise some form of weaponry firing either simple mass weapons or explosive projectiles, rather than an energy weapon of unknown design and function.) Though he doesn’t elaborate, Jameson seems to have been conceptualizing such a device as ENIAC (Electronic Numerical Integrator and Computer), the existence of which was announced to the public ten months after his death.

3) The spacecraft’s armament is simple, whether by the standards of the late 1930s or the 2020s: The craft shoots projectiles comprised of “a simple sphere of meteoric iron”. Due to the velocities involved, explosives are entirely unnecessary: The momentum of such a projectile is entirely adequate to damage or destroy an enemy spacecraft.

4) A substantial portion of Jameson’s text – specifically pertaining to Figure 1 – pertains to the manner in which “our” spacecraft will locate, identify, and track the enemy vessel, and, plot a firing trajectory for its weapons. Here, Jameson description of the craft’s “plotting room,” the “most vital spot in the ship,” seems (unsurprisingly, given his naval background) akin to a description of a battleship or aircraft carrier’s combat information center, “the counterpart of the brain”.

Then, his essay gets really interesting, for – in the context of describing the tracks of two spacecraft engaged in combat, as diagrammed in Figure 2 – he postulates the nature of space-borne rangefinders and target-bearing transmitters, suggesting for the former determining distance – “sounding” by radio waves – and the latter something akin to a thermoscope, or simply put, a device showing changes in temperature, against a given background.

In other words, he seems to have been respectively anticipating both radar, and, what is now known as IRST: Infrared Search and Track.

5) Interestingly, unlike Willy Ley, Jameson’s also an advocate of the use a form of what he dubs “rocket torpedoes” rather than shells, due to the latter’s “advantage of auto-acceleration” and the “ability to build up speed to any desired value after having been launched,” versus the delay inherent to the sequence of events involved in the the actual firing and movement of a shell from a gun. Of course, even assuming the enemy vessel is attacked with “rocket torpedoes”, such devices – in the context and era of Jameson’s article – would have no internal guidance or tracking system of their own, their “flight” path being entirely dependent on course adjustments of the firing platform – “our” spacecraft – itself.

6) Where mentioned, I’ve included conversions of given velocities (“miles per second”) to velocities per hour, in both English and Metric systems, the former in statue miles. These are denoted by brackets. (e.g., [90,000 mph / 144,840 kph]).

As in the post covering Ley’s article, the most notable passages of the text are italicized and in dark red, like these last thirteen words in this sentence. The post concludes with links to a variety of excellent videos covering spacecraft-versus-spacecraft battles, and “space war”, in greater detail, in light of (quite obviously!) contemporary knowledge.

__________

You can read the Wikipedia article about Malcolm Jameson here, while the Internet Speculative Fiction Database compilation of his writing can be found here.

Jameson’s memorial tribute (I guess penned by John W. Campbell, Jr.?) from the July 1945 issue of Astounding, follows:

MALCOLM JAMESON

December 21, 1891 – April 16, 1945

Malcolm Jameson, a man possessed of more shear courage than most of us will ever understand, died April 16, 1945, after an eight-year writing career, initiated when cancer of the throat forced him to give up the more active life he wanted. Any author can tell you that you can’t write good stuff when you’re feeling sick. Jamie never quite understood that – perhaps because he began when he did. X-ray and radium treatment controlled the cancer for a time, but only at a price of permanent severely bad health.

He sold his first story to Astounding in 1938. [“Eviction by Isotherm“, August, 1938.] That was followed by such memorable and sparklingly light stories as “Admiral’s Inspection,” the whole Commander Bullard series, and his many other stories in UNKNOWN WORLDS.

The man who could accomplish that under the conditions imposed on him was not of ordinary mold.

The Commander Bullard series grew out of Jameson’s own experiences as a Lieutenant in the United States Navy from 1916 till his retirement in 1927. He had much to do with the development of modern naval ordnance; his work is fighting in this war, though he himself was not permitted to do so.

He is survived by his wife, his daughter, Corporal Vida Jameson, of the WAC, his son, Major Malcolm Jameson, in the Infantry and now overseas, and his brother, House Jameson, better known as “Mr. Aldrich” of the “Aldrich Family” program.

The Editor.

____________________

You’ll notice that Hubert Rogers’ iconic depiction of a space fleet control center (for E.E. Smith’s “Gray Lensman”) as the cover of the November, 1939 issue of Astounding, appears below. Further down in the post are two interior illustrations – from the November, 1941, and February, 1948 issues of Astounding – in which Rogers created views of the same scene for Smith’s “Second Stage Lensman” and “Children of the Lens”, respectively. (The image of the control center in the 1948 issue was scanned from an original copy, and photoshopifically “niced up” to bring out the details, for this post.)

____________________

And so, on to Malcolm Jameson’s “Space War Tactics” from the month of November, in the year 1939…

SPACE WAR TACTICS

Expanding on Willy Ley’s recent article, Jameson brings out some important details – not the least of which is that a space battle fleet gets one shot at the enemy in months of maneuvering!

By Malcolm Jameson
Illustrated by Malcolm Jameson
Astounding Science Fiction
November, 1939

Ship to Ship Engagement

A working knowledge of the game of chess is a useful adjunct in understanding the art of war. War is not a series of haphazard encounters hut a definite understanding governed by principles that never change, however much the weapons and uniforms and the colors of the flags may. Like chess it is a continuing struggle between two opponents, each trying to estimate the strength of the other and to divine his purposes and most probable objective, and what his next move will be. It is a marauding and movement of forces, a series of threats and feints, of advances and withdrawals, punctuated by sharp conflict as one or the other forces the issue.

As the rules of chess govern the movement of each piece, so does the field of operations in war, whether it is rocky terrain or swampy, the open sea or the cloud-streaked skies, or the vast reaches of space itself. Tactics, and in a measure the weapons, are rigidly determined by the controlling environment.

We can, therefore predict with some assurance the general nature of space warfare, for we already know something of the properties of the void and what characteristics ships that traverse it arc likely to have. With such ships and in such a theater of operations, we have only to apply the principles of warfare developed by men through centuries of strife to arrive at an approximation of the tactics they will use. We can be fairly certain of the kind of weapons and instruments they will have, for the very advent of spaceships is presumptive of continued advance in science along much the same lines we have already come.

There are two great factors in space warfare that will set it off sharply from anything else in human experience, and those two factors will modify fighting-ship types, strategy and tactics profoundly. They are: (a) the extent of space, and (b) the tremendous speed of the vessels.

At the risk of boring those who have already read and thought a good deal about travel in space and who feel that they long ago formed a satisfactory idea of what the limitless reaches of the void are like, I want to dwell a moment on the subject of the vastness of space. It deserves all the emphasis we can give it.

Psychologists assert that it is beyond the capacity of the human mind to conceive of quantities, extents or durations beyond rather close limits. We may nod understandingly at hearing mention of a billion-dollar appropriation, but we grasp the idea solely because we are thinking of those billion dollars as a unit sum of money.

If we tried to visualize them as coins we would fail utterly. The mind cannot picture ten hundred thousands of thousands of silver disks. “Many” is the best it can do – there are too many dollars there for one mindful. And so it is with distance.

It has been my good fortune to have traveled extensively; I have crossed oceans as navigator, stepping off the miles made good each day or watching them slide by under the counter. Thus I have a hazy notion of the size of the Earth – it is oppressively huge. What, then, of the two or three million-mile straightaway covered in a single day’s run of a rocket-ship – represented by a quarter-inch pencil mark on the astragator’s chart of the ecliptic? The Earth he left but yesterday had already dwindled to a small bright disk and before the week is over it will be seen only as a brilliant blue star. In that incredibly vast celestial sphere in which lie is floating – stretching as it does without limit before, behind and to every side, above and below – where and how can we hope to find his enemy?

For even if he passed another ship close aboard, he would not so much as glimpse it. Speeds in space are as stupendous as the spaces they traverse. Needing seven miles per second to escape the Earth and another twenty to make any reasonable progress between the planets, even the slowest vessels will have speeds of twenty-five miles per second [90,000 mph / 144,840 kph]. Warships. presumably. according to type, will have correspondingly higher speeds – perhaps as high as fifty miles per second [180,000 mph / 289,682 kph … or, 0.000268 c] for the faster scouts.

Speeds of that order are as baffling to the imagination as the depths of the void. When we recall that the fastest thing most of us are familiar with is the rifle bullet, whizzing along at a lazy half-mile per second [1,800 mph / 2,897 kph], we see that we do have a yardstick. The ships mentioned above proceed at from fifty to one hundred times that fast – invisible, except under very special circumstances. It is barely possible, we know, for a quick eye to pick up twelve-inch shells in flight if he knows just where, when and how to look, but a momentary glimpse is all he gets.\

When we talk of gunfire or any other means of offense, we have to bear these dizzy speeds firmly in mind. The conclusion is irresistible that scouting, tracking, range finding and relative bearings will all be observed otherwise than visually. Even on the assumption of attack from the quarter, the most obvious approach – and for the same reason that aviators “get on the tail” – the overtaking vessel must necessarily have such an excess of speed that the visual contact can last but a few seconds.

Each of the combatants must compute the other’s course from blind bearings and ranges and lay their guns or point their torpedo tubes by means of a differentia calculator.

However, in this blind tracking there is one peculiarity of these ships that while it is in one sense a source of danger to them, is of distinct assistance. In the fleeting minutes of their contact, neither can appreciably alter course or speed! This is a point that writers of fiction frequently ignore for the sake of vivid action, but nevertheless it is an unavoidable characteristic of the [e]ther-borne [?!] ship.

The human body can withstand only so much acceleration and the momentum these vessels carry has been built up, hour after hour, by piling increment of speed on top of what had been attained before. In space there is no resistance. Once the rockets are cut, the ship will soar on forever at whatever velocity she had at the moment of cutting. Her master may flip her end over end and reverse his acceleration, but his slowing will be as tedious and cautious as his working up to speed. Jets flung out at right angles merely add another slight component to the velocity, checking nothing.

Rocket experts have stated that an acceleration of one hundred feet per second per second can be withstood by a human being – perhaps one hundred and fifty in an emergency. The master of a vessel proceeding at forty miles per second [144,000 mph / 231,745 kph] applying such an acceleration at right angles would succeed in deflecting his flight about one hundred miles by the end of the first minute, during which he will have run twenty-four hundred – a negligible turn, if under fire. Applied as a direct brake, that hundred miles of decreased velocity would slow him by one twenty-fourth – obviously not worth the doing if the emergency is imminent.

With these conditions in mind, let us imagine a light cruiser of the future bowling along at forty miles per second on the trail of an enemy. The enemy is also a cruiser, one that has slipped through our screen and is approaching the earth for a fast raid on our cities. He is already decelerating for his prospective descent and is thought to be about one hundred and fifty thousand miles ahead, proceeding at about thirty-five miles per second [126,000 mph / 202,777 kph]. Our cruiser is closing on him from a little on his port quarter, and trying to pick him up with its direction finders.

So far we have not “seen” him. We only know from enciphered code messages received several days ago from our scouting force, now fifty millions astern of us, that he is up ahead. It would take too long here to explain how the scouts secured the information they sent us. The huge system of expanding spirals along which successive patrols searched the half billion cubic miles of dangerous space lying between us and the enemy planet is much too intricate for brief description. It is sufficient for our purposes that the scouts did detect the passage of the hostile cruiser through their web and that they kept their instruments trained on him long enough to identify his trajectory. Being neither in a position to attack advantageously nor well enough armed – for their function is the securing of information, and that only – they passed the enemy’s coordinates along to us. This information is vital to us, for without it the probability of contact in the void is so remote as to be nonexistent.

The ship in which we are rushing to battle is not a large one. She is a bare hundred meters [328 feet] in length, but highly powered. Her multiple rocket tubes, now cold and dead, are grouped in the stern. We have no desire for more speed, having all that is manageable already, for after the few seconds of our coming brush with the enemy our velocity is such that we will far overrun him and his destination as well. It will require days of maximum deceleration for us to check our flight and be in a position to return to base.

Our ship’s armament, judged by today’s standards, will at first sight appear strangely inadequate. Our most destructive weapon is the “mine,” a simple sphere of meteoric iron about the size of a billiard ball, containing no explosive and not fused. The effectiveness of such mines depends upon the speed with which they are struck by the target ship – no explosive could add much to the damage done by a small lump of iron striking at upward of thirty miles a second. Then there will he torpedo tubes amidships, and perhaps a few guns, but it may lie well to postpone a discussion of the armament until we have examined the conditions at the place of battle.

Although we know in a general way where the enemy is and where he is going, before we close with him we must determine his course and speed very accurately, for our ability to hit him at all is going to depend upon extremely nice calculations. Our speeds are such that angular errors of so much as a second of arc will be fatal, and times must be computed to within hundredths of seconds.

This falls within the province of fire-control, a subject seldom if ever mentioned by fiction writers. There is no blame to be attached to them for that, for the problems of fire-control are essentially those of pure mathematics, and mathematics is notoriously unthrilling to the majority of readers. Yet hitting with guns – or even arrows, though the archer solves his difficulties by intuition – requires the solution of intricate problems involving the future positions and movements of at least two bodies, and nothing more elementary than the differential calculus will do the trick. In these problems interior ballistics, for all its interesting physics, boils down to a single figure – the initial velocity of the projectile, while exterior ballistics evaporates for the most part the moment we propel our missile into a gravityless vacuum. In space we are to be concerned with the swiftly changing relationship of two rapidly moving vessels and the interchange of equally swift projectiles between them, the tracks of all of them being complicated curves and not necessarily lying in a plane.

In its simplest statement the problem of long-range gunnery is this: where will the enemy be when my salvo gets there? For we must remember that even in today’s battles the time the projectile spends en-route to its target is appreciable – fully a minute on occasion, at sea, during which the warship fired upon may move as much as half a mile. Under such circumstances the gunner does not fire directly at his target, but at the place it is going to be. That requires very accurate knowledge of where the enemy is headed and how fast he is moving.

At sea that is done by observing successive bearings and ranges and plotting them as polar coordinates, bearing in mind that the origin is continuously shifting due to the ship’s own motion. This work of tracking – the subsequent range-keeping and prediction of future ranges and bearings – is done in our times in the plotting room. This is the most vital spot in the ship, for if her weapons may be likened to fists and her motive power to legs, her optical and acoustical instruments to eyes and ears, then the plotting room is the counterpart of the brain. There all the information is received, corrected, digested, and distributed throughout the ship. Without that co-ordination and direction the ship would be as helpless as an idiot.

Well, hardly that helpless today. Our individual units, such as turret crews, can struggle on alone, after a fashion. But not so with the ship of the future. There the plotting room is everything, and when it is put out of commission, the ship is blind and paralyzed. It will, of course, be located within the center of the ship, surrounded by an armored shell of its own, and in there will also be the ship control stations.

The best way to approach the problems our descendants will have to face is to consider a simple problem in tracking that our own warships deal with daily. It is an absurdly simple one compared to the warped spirals to be handled in space warfare, but it will serve to illustrate the principle. In Fig. 1. it is shown graphically, but in actual practice the elements of the problem are set up on a motor-driven machine which thereupon continuously and correctly delivers the solutions of problems that would take an Einstein minutes to state. As the situation outside changes, corrections are cranked into the machine, which instantly and uncomplainingly alters its calculations.

In the figure we have the tracks of two ships, ours the left-hand one. For the sake of clarity and emphasis I have made the ratio of speeds three to one, but the same trends would be shown at the more usual ratio of, say, 20:19

At positions “1,” “2,” “3” and so on, we observe the range and hearing of the target, and plot them. By noting the differences between successive readings and the second differences between those, we soon have an idea of the type of curve the rates of changes would plot into. In a short time we can also note that the rates themselves are changing at a certain rate. This is a rough sort of differentiation – by inspection – and to one familiar with such curves these trends have a definite meaning.

For example, it is apparent that the series of observed angles “Beta” are steadily opening, signifying that we are drawing past the target. Any sudden alteration of the second differences, such as occurs at “8,” at once indicates a change of condition on the part of the enemy. He has either turned sharply away or slowed to half speed, for the bearing suddenly opens nearly two degrees more than the predicted beating. We learn which by consulting our ranges. It could be a combination of changed course and changed speed.

The ranges during the first seven lime-intervals have been steadily decreasing, although the rate of decrease has been slowing up, indicating we are approaching the minimum range. At “8,” though, the range not only fails to decrease, but the rate of change actually changes sign. We know without doubt that the enemy has turned away.

The importance of having the machine grind out predicted bearings and ranges, aside from the desirability of speed and accuracy, is that at any moment smoke, a rain squall, or intervening ships may obscure the target. In that event the gunners need never know the difference – their range and bearing indicators arc ticking away like taximeters, fed figures by the controlling range-keeper. It would not have mattered if sight had been lost of the enemy at “4”; the gun-fire would have been just as accurate up to the time he changed course as if they had the target in plain sight.

As a matter of fact, the guns are not pointed at the target at all, but in advance of it, as is shown in Fig. 1 (a), both range and bearing being altered to allow for the forward movements of the target while the shells are in the air. The projectiles may be regarded as moving objects bandied on a “collision course” with regard to the enemy vessel.

Speaking of collision courses, it is an interesting property of relative bearings that when the bearing remains constant – except in the special case of the vessels being on parallel courses at identical speeds – the vessels will eventually collide, regardless of what their actual courses and speeds are. Hence, from the time the shots of the salvo left their guns – Fig. 1 (a) – until they struck their target, the target bore a constant angle of thirteen degrees to the right of the nose of the shells. (This knowledge has some utility in estimating the penetration of armor at the destination.)

In the example above, all the movement can be regarded as taking place in a plane; the ships follow straight courses and they maintain constant speeds. Our terrestrial problems are in practice much complicated by zigzagging, slowing down and speeding up, but at that they are relatively child’s play compared to what the sky-warrior of the future must contend with.

His tracks are likely to be curved in three dimensions, like pieces of wire hacked out of a spiral bed spring, and whether or not they can be plotted in a plane, they will nowhere be straight. Moreover, whatever changes of speeds occur will be in the form of steady accelerations and not in a succession of flat steps linked by brief accelerations such as we know. Computing collision courses between two continually accelerating bodies is a much trickier piece of mathematical legerdemain than finding the unknown quantities in the family of plane trapeziums shown in Fig. I.

Yet projectiles must be given the course and speed necessary to insure collision.

The gunnery officer of the future is further handicapped by rarely ever being permitted a glimpse of his target, certainly not for the purpose of taking ranges and bearings. In the beginning of the approach the distances between the ships is much too great, and by the time they have closed, their relative speed will generally forbid vision.

Since optical instruments are useless except for astrogational purposes, his rangefinders and target-bearing transmitters will have to be something else. For bearings, his most accurate instrument will probably be the thermoscope – an improved heat-detector similar to those used by astronomers in comparing the heat emission of distant stars. It will have a spherical mounting with a delicate micro-vernier. A nearby spaceship is sure to radiate heat, for it is exposed constantly to full sunlight and must rid itself of the excess heat or its crew will die. Once such a source of heat is picked up and identified, it can be followed very closely as to direction, although little can be told of its distance unless something is known of its intrinsic heat radiation.

Ranges will probably be determined by sounding space with radio waves, measuring the time interval to the return of reflected waves. It is doubtful whether this means will have a high degree of accuracy much beyond ranges of one light-second on account of the movement of the two vessels while the wave is in transit both ways.

At long range the need for troublesome corrections is sure to enter.

Such observations, used in conjunction with one another, should give fairly accurate information as to the target’s trajectory and how he bears from us and how far he is away. This data will be fed into a tracking and range-keeping machine capable of handling the twisted three-dimensional curves involved, and which will at once indicate the time and distance of the closest point of approach. Both captains will at once begin planning the action. They may also attempt to adjust their courses slightly, but since the rockets evolve great heat, neither can hope to keep his action from the knowledge of the other owing to the sensitiveness of the thermoscopes.

The rangekeeping instrument suggested, while far surpassing in complexity anything we know of today, will represent a much smaller technical advance than the rockets which drive the ships that house them. We already have similar machines, so that their counterparts of the future would seem much less mysterious to us than, say, the Walschaert’s valve gear to Hero or Archimedes, or the Jacquard loom to the weavers of the Gobelin tapestries.

Assuming we have, by observation and plotting, full knowledge of the enemy’s path and have come almost into position to commence the engagement, we find ourselves confronted once more with the two overwhelming factors of space warfare – great distance and immense speeds – but this time in another aspect. We have come up close to our foe – in fact we are within twenty seconds of intersecting his trajectory – and our distance apart is a mere four hundred miles [643 km]. It is when we get to close quarters that the tremendous problems raised by these lightning-like speeds manifest themselves most vividly.

Look at Fig. 2.

The elapsed time from the commencement of the engagement until the end is less than twenty seconds. Our ship is making forty miles per second, the other fellow is doing thirty-three. We will never be closer than fifty miles, even if we regard the curves as drawn as being in the same plane. If one rides over or below the other, that minimum range will be greater. What kind of projectile can cross the two or three hundred miles separating the two converging vessels in time to collide with the enemy? Shooting cannon with velocities as low as a few miles per second would be like sending a squadron of snails out from the curb to intercept an oncoming motorcycle – it would be out of sight in the distance before they were well started.

Projectiles from guns, if they were to be given velocities in the same relation to ships’ speeds that prevail at present, would have to be stepped up to speeds of three to four thousand miles per second! A manifest impossibility. It would be difficult, indeed, to hurl any sort of projectile away from the ship at greater initial velocities than the ship’s own speed. Such impulses, eighty times stronger than the propelling charge of today’s cannon, would cause shocks of incredible violence. It follows from that that an overtaken ship is comparatively helpless – unless she is in a position to drop mines – for whatever missiles she fires have the forward inertia of the parent ship and will therefore be sluggish in their movement in any direction but ahead.

Another difficulty connected with gunfire is the slowness with which it comes into operation. This may seem to some to be a startling statement, but we are dealing here with astonishing speeds. When the firing key of a piece of modern artillery is closed, the gun promptly goes off with a bang. To us that seems to be a practically instantaneous action. Yet careful time studies show the following sequence of events: the primer fires, the powder is ignited and burns, the gases of combustion expand and start the shell moving down the tube. The elapsed time from the “will to fire” to the emergence of the projectile from the muzzle is about one tenth of a second. In Fig. 2 our target will have moved more than three miles while our shell is making its way to the mouth of the cannon! It looks as if guns wouldn’t do.

I come to that conclusion very reluctantly, for I am quite partial to guns as amazingly flexible and reliable weapons, but when we consider that both powders and primers vary somewhat in their time of burning, there is also a variable error of serious proportions added to the above slowness. It is more likely that the rocket-torpedoes suggested by Mr. Willy Ley in a recent article on space war will be the primary weapon of the future. They have the advantage of auto-acceleration and can therefore build up speed to any desired value after having been launched.

The exact moment of their firing would have to be computed by the tracking machine, as no human brain could solve such a problem in the time allowed. But even assuming machine accuracy, great delicacy in tube-laying and micro-timing, the chances of a direct hit cm the target with a single missile is virtually nil. For all their advanced instruments, it is probable that all such attacks will be made in salvos, or continuous barrages, following the time-honored shotgun principle. For the sake of simplicity, only two such salvos are shown on the diagram, but probably they would be as nearly continuous as the firing mechanisms of the tubes would permit. Any reader with a flair for mathematics is invited to compute the trajectories of the torpedoes. The ones shown were fired dead abeam in order to gain distance toward the enemy as rapidly as possible.

It is desirable that these torpedoes should vanish as soon as practicable after having overrun their target. To that end their cases are made of thin magnesium, and between the head and the fuel compartment is a space filled with compressed oxygen and a small bursting charge The tip of the head is loaded with liquid mercury.

Such a massive projectile would penetrate any spaceship with ease, but if it missed it would burst as soon as the fuel supply was spent and then consume itself in brilliant flame, thus avoiding littering the Spaceways with dangerous fragments.

Spotting, as we know it, would be impossible, for the target would be invisible. Hits would have to be registered by the thermoscope, utilizing the heat generated by the impact. The gunnery officer could watch the flight of his torpedoes by their fiery wakes, and see his duds burst; that might give him an idea on which side of the enemy they passed in the event the thermoscopes registered no hits.

If there were guns – and they might be carried for stratosphere use – they could be brought into action at about “15,” firing broad on the starboard quarter. The shells, also of self-destroying magnesium, would lose some of their forward velocity and drift along in the wake of the ship while at the same time making some distance toward the oncoming enemy. These guns would be mounted in twin turrets, one on the roof and the other on the keel, cross-connected so that they would be trained and fired together. It the ships center of gravity lay exactly between them, their being fired would not tend to put the ship into a spin in any direction. What little torque there might be, due to inequalities in the firing charge, would be taken care of by the ship’s gyro stabilizer, an instrument also needed on board to furnish a sphere of reference so that the master could keep track of his orientation.

If upon arriving at point “16” the enemy were still full of fight and desperate measures were called for, we could lay down mines. These hard little pellets would be shot out of mine-laying tubes clustered about the main driving jets. They would be shot out at slight angles from the fore-and-aft line, and given a velocity exactly equal to the ship’s speed, so that they would hang motionless where they were dropped. Being cheap and small, they could be laid so thickly that the enemy could not fail to encounter several of them. If she had survived up to this point, the end would come here.

The end, that is, of the cruiser as a fighting unit. Riddled and torn, perhaps a shapeless mass of tangled wreckage, she would go hurtling on by, forever bound to her marauding trajectory. The first duty of our cruiser would be to broadcast warnings to the System, reporting the location of its own mine-field, and giving the direction taken by the shattered derelict. Sweepers would be summoned to collect the mines with powerful electromagnets, while tugs would pursue and clear the sky of the remnants of the defeated Martian.

______________________________

Illustration by Hubert Rogers, for “Second Stage Lensman – Part I“, by Edward E. Smith, PhD., from Astounding Science Fiction, November, 1941, page 35. (Cover, below, also by Rogers.)

____________________

Illustration by Hubert Rogers, for “Children of the Lens – Conclusion“, by Edward E. Smith, PhD., from Astounding Science Fiction, February, 1948, page 122. (Cover, below, by Alejandro Canedo)

______________________________