The History of Mathematics: A Brief Course

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  1. MECHANICAL METHODS OF COMPUTATION 153


further than Babbage had envisioned. Babbage's assistant Augusta Ada Lovelace
(1815-1852) had written that Babbage's analytical engine could do only what it
was told to do, but Turing believed that the difference between human intelligence
and a computer was not so stark as that. He considered it possible that what
appeared as human creativity might be the result of some information delivered at
an earlier time, and that computers might mimic this apparent creativity.
The other mathematician was John von Neumann (1903-1957), who was at
Princeton in 1936 when Turing came there as a graduate student.^7 Von Neumann
became involved in the development of the computer while working as a consultant
at the Aberdeen Proving Grounds in Maryland. There, in August 1944, he met Her-
man H. Goldstine (1913-2004), who told him about ENIAC. From our perspective,
two generations on, ENIAC looks like the brontosaurus of computing technology.
Here is a description of it from a website devoted to its history:^8


When it was finished, the ENIAC filled an entire room, weighed
thirty tons, and consumed two hundred kilowatts of power. It
generated so much heat that it had to be placed in one of the
few rooms at the University [of Pennsylvania] with a forced air
cooling system. Vacuum tubes, over 19,000 of them, were the
principal elements in the computer's circuitry. It also had fifteen
hundred relays and hundreds of thousands of resistors, capacitors,
and inductors. All of this electronics was held in forty-two panels
nine feet tall, two feet wide, and one foot thick.

Despite its size, ENIAC had very little memory—only 1000 bits of RAM! More-
over the use of vacuum tubes (thermionic valves) meant frequent breakdowns—one
every 8 minutes on the average, until the operators reduced the voltage and current
to the minimum; after that, breakdowns occurred only once every two days on the
average. Most seriously, it could not be programmed in the present-day sense of the
word. It simply had to be set up for each particular computation. Von Neumann
and the builders of ENIAC collaborated on the construction of EDVAC (Electronic
Discrete Variable Automatic Computer), which had the ability to read stored pro-
grams. Of course, those programs had to be written in machine language, a serious
drawback for human interaction, but von Neumann's basic idea was sound. We
have engineers to thank that the vacuum tube has been replaced by the transistor,
that transistors can now be etched onto tiny computer chips, and that production
methods have made it possible to produce for a very modest price the machines
that everyone now uses with such ease.

9.3. The effects of computing power. A crystal ball can be very cloudy, even
in relation to the eternal truths of mathematics. A book of mathematical tables
and formulas (Burington, 1958) purchased by the author nearly half a century ago
confidently assured its readers in a note from the publishers that

the subject matter [of this book] is not ephemeral but everlasting—
as true in the future as it has been in the past. By all means, retain

(^7) According to Heppenheimer (1990), von Neumann offered Turing a position as his assistant,
but Turing preferred to return to Cambridge.
(^8) http: //ei. cs. vt. edu/~history/ENIAC. Richey. HTML.

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