For twenty eight years, during the nineteenth century, an English school teacher, William Shanks, spent his evenings computing the first 707 digits of the number π ... and made an error in the 528th place. It took years - and he made an error. He had used multiplication tables and tables of logarithms; each table had taken years to generate - and were filled with errors. The people who generated the tables, and indeed Shanks himself, were "computers" in the original sense of the word.

Shanks used the series π/4 = 4 tan-1(1/5) - tan-1(1/239). Shanks' error was uncovered in 1944 when D.F. Ferguson discovered that Shanks had omitted two terms in the series!%#$&@* In fact, it was noticed (even in Shanks' time) that there was a suspicious shortage of 7's in the last 707 digits. After the correction, the sequence of digits passed all statistical tests for randomness.

Speed and reliability were the bane of "computers" ... and would be for another century.

In the seventeenth century, mechanical calculators for performing addition/subtraction (and multiplication/division, with some help from the operator) had been devised by the German astronomer and mathematician Wilhelm Schickard. The French mathematician Blaise Pascal later built such a device and later still, in 1673, the German mathematician Wilhelm Leibniz (who, with Isaac Newton, co-invented the Calculus: see Newton & Leibniz) built a mechanical multiplier.

Leibniz was to write of Pascal's device: "... it facilitates only additions and subtractions, the difficulty of which is not very great ..."

---

In the early nineteenth century the eccentric Cambridge mathematician Charles Babbage (1791-1871) employed two human computers to generate mathematical tables for the Astronomical Society, checking the work of one against the other in order to identify errors. There's an old mariner's adage that goes something like: "Never take 2 chronometers; either take 1 or 3." About 1820, frustrated by the time necessary and the inevitable errors, he conceived of a "Differential Engine" which would compute the values of functions for equally spaced values of the independent variable, using the Method of Differences.

Charles Babbage

Part of the "Engine"

It was a mechanical device replete with wheels, gears and levers and a crank which would successively generate the function values automatically - without human intervention except to turn the crank - once the function definition had been set into the machine. Errors in navigation tables had been the cause of ships running aground, astronomical observations required accurate tables, so Babbage's Differential Engine was of great importance ... and the British government funded the project.

By 1833, ten years after the project had begun, there was little to show for their investment so the government withdrew funding and all work on the Engine ended. Undeterred, Babbage designed a more ambitious, more versatile "Analytic Engine".

It would consist of three parts:

• The STORE where numbers were stored, or "remembered".
• The MILL where arithmetical operations on numbers taken from the STORE would be performed.
• The SEQUENCE MECHANISMS which would select the proper numbers from the STORE and instruct the MILL to perform the proper operations.

It was, indeed, an automatic, general purpose, programmable computer complete with CPU and input/output and programs and conditional (IF ... THEN) branching and micro-programming - and it printed its answers. Further, it took its instructions from punched cards!

Punched Cards

Punched cards was an idea Babbage extracted from the textile industry where Joseph M. Jacquard, in 1805, used punched cards to control which threads of warp were lifted above and which below the shuttle. In 1886 a U.S. statistician, Herman Hollerith, would also used punched cards in statistical and accounting machines, to expedite the taking of the U.S. census. (It had taken seven years to perform the clerical work for the 1880 census.) For Babbage, "Operation" cards identified the operation to be performed and "Variable" cards located the operand in the STORE.

Charles Babbage was a well known scientific and political figure and held parties ... often! His guests might include Darwin or Dickens or Longfellow.

Apparently, Babbage would read Tennyson (among other things). When he read the lines "Every moment dies a man. Every moment one is born." he wrote Tennyson to inform him that "... this calculation would keep the world's population in perpetual equipoise." Babbage suggested: "Every moment dies a man. And one and a sixteenth is born."

His guests would come, be entertained ... and ignore his partially completed Engine.

Countess of Lovelace

In 1833, one guest alone understood: the Princess of Parallelograms, the seventeen year old daughter of Lord Byron, destined to become the Countess of Lovelace, Babbage's Enchantress of Numbers, the world's first computer programmer, the beautiful and brilliant Augusta Ada. We owe to her a detailed account of both the hardware and software for the Engine.

In the 1970s, the U.S. Defense Department contracted for a programming language to permit all of its computers to "talk" to each other ... a precursor to the Internet. The language was called ADA.

Alas, lack of funds prevented the completion of Babbage's Analytical Engine.

On October 18, 1871, Charles Babbage died, disappointed, frustrated, embittered.

During the years 1935 - 1945, the word "computer" took on its modern meaning of a device which computes rather than a person which computes.

In the early 1930s, in Berlin, a Civil engineering student named Konrad Zuse, in typical student fashion (!), was too lazy to perform the endless calculations necessary for his studies. He designed a machine based upon the binary number system using telephone relay switches as on-off devices. Earlier machines had been decimal, incorporating the digits 0 through 9 on toothed wheels. For years, computers would be decimal. (see Zuse)

It took four switches to add 1+1, in binary. Zuse's machine filled a small room - his parents' living room! By 1939 he was the world's leading computer designer.

Later, in a TV interview, Zuse said, "I was too lazy ... so I invented the computer."

Punched Tape (movie film?)

Then came World War II and he received unlimited funds from the German military. Yet, to overcome war-time shortages, his "programs" were on punched tape made from discarded movie film. By 1941 he had built Babbage's dream machine: an automatic, programmable, general purpose computer, using binary arithmetic and, unfortunately, electromechanical relays. They were slow, taking up to five seconds to perform a simple multiplication.

A friend visiting his laboratory suggested using a switch from the new electronics industry: the vacuum tube. As his successors in computer science would do, to the present day, Zuse made up a proposal for government funding: it would be a two-year project and would result in a computer 1000 times faster than the earlier version.

Two years? Hitler knew the war would be won in less than two years - so the project wasn't funded. It would be many more years before the world knew of these developments in Germany.

Zuse managed to sneak his latest model, the Z4, out of Germany, accompanied by rocket scientist Wernher von Braun. He later started a computer company that was bought out by Siemens.

In 1939, the Bell Telephone Laboratories (using a design of Bell mathematician George Stibitz who invented floating point arithmetic), had built a binary calculator which they called a "Complex Computer" (to perform the troublesome arithmetic associated with complex/imaginary numbers). A 1940 demonstration, in New York, had the user sending problems from New Hampshire via teletype.

When the U.S. entered the war, one of the most distressing problems was the time necessary to supply the latest weaponry. There was a drastic shortage of human computers to calculate the trajectory of shells. "Firing Tables", incorporating the effects of wind, temperature, angle of elevation, etc. came from test firings at the Aberdeen Proving Grounds in Maryland. Hosts of female computers were employed; it took 30 - 40 minutes with a desk calculator to compute a single trajectory. It would take four years for a single female computer to compile one Firing Table, incorporating 1800 trajectories!

Shell Trajectories

Howard H. Aiken of Harvard, inspired by Babbage's ideas, worked with International Business Machines to build, in 1944, the Harvard-IBM Automatic Sequence-Controlled Calculator (ASCC, or Harvard Mark I). It was a decimal machine with 73 storage registers handling 23 decimal digits and performed additions in 1/3 second, multiplications in 6 seconds and worked 24 hours a day solving urgent military-computation problems ... but it contained gears and wheels and relay switches and failed to take full advantage of the speed inherent in vacuum tubes. Four years later, on January 27, 1948, IBM was to demonstrate the Selective Sequence-Controlled Electronic Calculator (SSEC) with 13,500 tubes ... and 21,400 electromechanical relays!

In a 1981 book, R. Morceau (IBM-France) claims the SSEC to be the world's first computer. Earlier machines, including the ENIAC, he calls universal calculators.

The problem of speed was taken up by John W. Mauchly, a physicist, and J. Presper Eckert, a young engineer, during the war years from 1942 to 1946. Both were at the Moore School of Electrical Engineering, University of Pennsylvania. With army funding, they designed a fully electronic computer with some 18,000 vacuum tubes. In spite of the unreliability of vacuum tubes (they burned out - rapidly!) and a prediction that their computer would break down every five seconds (the old reliability problem), the army was desperate.

The machine was built, filling a 50 x 30 foot room with tens of thousands of electrical components in addition to the 18,000 tubes, and some half million soldered joints ... and they called it an Electronic Numerical Integrator And Computer (ENIAC).

They demonstrated ENIAC's awesome computing power (with its panel of flashing lights specially wired to impress the cameras of the world) by calculating the trajectory of a shell that would take 30 seconds to reach its target - and they did the calculation in 20 seconds.

Alas, it wasn't finished until 1946, after the war ended.

"Programming" required setting some 6000 switches and incorporating hundreds of cables, effectively rebuilding the machine for each problem. Unfortunately, ENIAC was required for the war effort so building the machine according to this early design had to continue unabated. Before it was put into service, Eckert and Mauchly realized the need for stored program computers and they left the University of Pennsylvania to start the first commercial enterprise to build computers: The Eckert-Mauchly Computer Corporation. They had in mind a stored program Electronic Discrete Variable Automatic Computer, the EDVAC.

John von Neumann, a Hungarian who came to Princeton in 1930 (and perhaps the most distinguished mathematician of the day), learned of ENIAC/EDVAC, visited Eckert and Mauchly and wrote a 101 page First Draft of a Report on EDVAC, laying the theoretical groundwork for how such a machine should be built.

Eckert-Mauchly were not happy! Who really invented the computer? Who really had patent rights? E-M applied for a patent in 1947. Battles ensued for years, between E-K, Neumann, Moore School and, later, patent infringement battles with IBM and CDC and Honeywell and Sperry Rand and etc. etc. The ENIAC patent was finally awarded in 1964. In 1972, a Judge named Earl Larson, being of sound mind and in possession of some 40,000 documents (including a copy of von Neumann's infamous Report), ruled that the computer was invented by (are you ready for this?) John Vincent Atanasoff ... but that's another story.

However, it would be years before the first stored program Eckert-Mauchly computer would be available. Desperately short of funds, their corporation was absorbed by Sperry Rand and, based upon their EDVAC design, the Universal Automatic Computer (EDVAC) was built.

The first EDVAC production model was used by the U.S. government for the 1950 census. Grace Hopper was the premier programmer for Eckert-Mauchly and, subsequently, the Univac division of Rand.

In July, 1948, the Manchester University Computer (M.U.C.) was unveiled. The innovative memory, using cathode ray tubes, was designed by a British radar engineer Freddie Williams, freed from wartime activities. Although small, it was the first fully electronic stored program computer. It took 25 minutes to decide whether 2127 -1 was a prime number ... a problem clearly designed to impress the public!? The newspapers were delighted, yet there was rampant scepticism as to what a no purpose computer could do. A machine to calculate shell trajectories? Okay. A machine to generate star maps? Okay. But a machine without a specific purpose?

Headlines

A problem: whenever a tape was read the subroutine may not go to the same memory locations so certain memory addresses had to be changed. (Each instruction involved an operation to be performed and a single memory address identifying the location of the operand. Later, multiple address instructions would become popular.) This problem was overcome by preceding each piece of code with a set of "coordinating orders", making it self-relocatable. Later, the Cambridge team devised symbolic addresses whereby the programmer used some label and the computer assigned the memory locations (avoiding the need to change any explicit addresses which might appear in the code).

But Wilkes found few who appreciated the problems in programming ... until he visited the U.S. in 1950 and met Grace Hopper's group. (On the way he stopped off at the University of Toronto to give a talk at Kelly Gotlieb's invitation.) During his U.S. trip he also argued with Howard Aiken (of Harvard-IBM ASCC fame) re the advantages of a binary computer. (Recall that the ASCC was a decimal machine).

Although EDSAC solved a variety of problems (including a nonlinear differential equation proposed "in characteristically barbed fashion" by the distunguished statistician R.A. Fisher ... much to Fisher's surprise), in order to avoid the suspicions associated with analog machines, EDSAC spent some time computing prime numbers (which no analog machine could do). It impressed at least one skeptic: the distinguished number theorist L.J. Mordell (who later obtained an honorary degree at the University of Waterloo).

In 1951, Wilkes co-authored the first book on computer programming. Feeling that such a book would be risky, Addison-Wesley offered no royalties until 1000 copies were sold. They were, by the following year.

In 1954, IBM had completed the Naval Ordinance Research Computer (NORC) which performed additions in 15 microseconds and multiplications in 31 microseconds. It handled numbers in the form of "words" consisting of 16 decimal digits: 13 for the number, 1 for the sign, 2 for the exponent. It had eight magnetic tape units with 1200 feet of tape at 510 characters per inch, feeding information to the central computer at 70,000 characters per second. "Words" were available, from memory, in 8 microseconds.

In 1953 the UNIVAC was practically the only computer available to a commercial firm. Within two years IBM would sell more than half the computers in the U.S. and within another two years the computer industry would be known as IBM and the Seven Dwarfs.

Sperry-Univac was the first dwarf. Some Sperry-Univac people jumped ship and created the second dwarf: Control Data Corporation. One who jumped ship was Seymour Cray who built the CDC 1604 - the world's most advanced large computer. Eventually, Cray left CDC to build his own computers.

The CDC people who had left Univac had designed the Univac 1103. CDC's headquarters were at 501 Park Ave. 1103 + 501 = 1604 I hate to show my age, but the 1604 was the computer that churned out the numbers for my PhD thesis. I spent many a night, just me, alone with the 1604 ...

Computers could now perform complex calculations with both speed and reliability.

One of the most forward thinkers of the day thought scientists had missed the point. To use computers for arithmetic was a waste.

Alan Turing

A. M. Turing had published a paper in 1936: "On computible numbers with an application to the entscheidüngsproblem". In it he had defined a "theoretical machine" (to become known as a "Turing Machine") which, in principle, could compete with a human in performing cerebral (logical) tasks. During the war, Turing put these ideas to work; he was engaged in breaking the German codes at the highly secret Bletchley Park.

(Bill Tutte, a distinguished professor at the U of Waterloo, worked at Bletchley Park during WWII.)

In particular, Turing was put in charge of breaking the ENIGMA which encoded messages concerning daily German troop movements not by a fixed transformation from message to code, but by continuously altering the characters using rotated toothed wheels. Although Turing devised a strategy for deciphering the messages, there was too little time ... so an electronic, special purpose computer, the COLOSSUS, was built according to Turing's design. It began operation in 1943 when work on ENIAC had just begun. It was highly successful, some believing that "COLOSSUS won the war". Secrecy prevented any knowledge of its capabilities for some thirty years.

My 1960 Colliers Encyclopedia identifies the 1944 Harvard-IBM Mark I as the first general purpose automatic digital computer.

Turing was convinced that computers could do far more than carry out a sequence of instructions, far more than perform mere arithmetical operations: computers could learn!

After the war he built the ACE computer to simulate human thought. The ACE "Pilot" model was completed in 1950 and was regarded by many as the world's most advanced computer. Alas, the ACE was used solely for scientific number crunching. Turing was disgusted with this and with the bureaucracy ... and joined the University of Manchester where he designed a machine to work in conjunction with the Manchester University Computer (M.U.C.) to do "creative word processing", including love letters!

M.U.C. Poem

In 1950, Turing proposed a test of intelligence: for five minutes you ask questions of an unknown "device", either machine or human (presumably intelligent). If you are not 70% sure that the device is a machine then you must concede that the device has some intelligence. Turing predicted that machines would pass such a test of intelligence by the year 2000..

Mamma mia! That's NOW ... as I type this history! Gotta do some Net surfin' to see what's happened in this regard! (See the Loebner Prize)

Math & Computer building U of Waterloo

By 1957 (when the CS dept. at UW begins) there were dozens of suppliers of computing devices, all designed to perform rapid and accurate calculations. In addition to "automatic digital computers" there were, at that time, a variety of other machines, not digital computers, which could handle one of bookkeeping, data sampling, radar fire control, file searching, flight simulation, machine control, telephone switching, navigation, music generation, game playing ...

Alas, Turing never lived to see the myriad uses to which today's fully electronic, automatic, general purpose, stored program computers ^* are put ... including all of the above!

* It's necessary to stress this description of the beast since arguments concerning "who invented what?" - and they contunue unabated to this day - might be circumvented by just such elaborate prefixes ... as well as a clear definition of the word "computer".