As I was guilty of starting something by hastily and provocatively
writing:-
> The first real computer was the Manchester Mark 1 aka
> the SSEM or the "Baby".

...I had best define "real computer". Apologies for the length of
this mail, it grew whilst I carried on following various paths of
inquiry.
Whilst sorting out my own mind, I came to the conclusion that the
best definition of  "real computer" has to be one where the computer
is capable of running a respected benchmark. Therefore my definition
is that it should be capable of running a primality test, preferably
on a Mersenne :-)

Last but least, it not only should be capable of doing it, but it
should have done it. It is not valid if the hypothetical Left sisters
had belatedly announced that they had built a flying machine, but
never flew it.

Therefore I was just about to award the honour of First Real Computer
to SWAC (built late 1950) which found for Robinson (assisted by D. H.
& E. Lehmer) M521, M607, M1279, M2203 & M2281 in 1952, but...

[Structuring my thoughts chronologically]
In reply to Luke Welsh, Ernst Mayer wrote:-
> The stored-program idea goea back at least to 1805, when Jacquard used
> strung-together sequences of hole-punched wooden cards to control the
> weaving patterns of his famous loom. A few years later, Babbage used
> the same stored-program idea (also with puched cards) for his difference
> engine. Von Neumann himself usually credited the idea to Turing, who
> advocated its use years before.

The Jacquard cards were just an input, not a storage media.
For the loom to be a computer it needed at least a card punch and for
the output to be looped back to the input. Even with a stored programme
this still isn't a real computer. There also needs to be some decision
making that alters the path of execution of the control programme.

Charles Babbage whilst building the Difference Engine in 1832 was
greatly assisted and inspired by Ada Byron, Countess of Lovelace.

Ada was the true visionary who foresaw the magic of viewing the numeric
representation as symbols of operations, where the symbols themselves
could be operated on by the engine.

> "It may be desirable to explain, that by the word operation, we mean
> any process which alters the mutual relation of two or more things,
> be this relation of what kind it may. This is the most general
> definition, and would include all subjects in the universe . . . They
> will also be aware that one main reason why the separate nature of
> the science of operations has been little felt, and in general little
> dwelt on, is the shifting meaning of many of the symbols used in
> mathematical notation. First, the symbols of operation are frequently
> also the symbols of the results of operations . . . Secondly, figures,
> the symbols of numerical magnitude, are frequently also the symbols
> of operations, as when they are the indices of powers [e.g., 2 and 32]
> . . . [In] the Analytical Engine . . . whenever numbers meaning
> operations and not quantities (such as indices of powers), are
> inscribed on any column or set of columns, those columns immediately
> act in a wholly separate and independent manner . . . "

Babbage's Analytical Engine was meant to be a mechanical stored
programme machine, with separate data and programme, but it was never 
built.

Andrew Hodges, author of the book "Alan Turing: The Enigma" and also the
Alan Turing Internet Scrapbook at http://www.turing.org.uk/turing/ wrote

> I wouldn't even call Charles Babbage's 1840s Analytical Engine
> the design for a computer. It didn't incorporate the vital idea
> which is now exploited by the computer in the modern sense, the
> idea of storing programs in the same form as data and
> intermediate working.

Luke Welsh wrote about the Atanasoff Berry Computer from
Why Computers Are Computers: The SWAC and the PC
by David Rutland
> "The machine was not really a general purpose computer as
> it was more like Babbage's Difference Engine than the Analytical
> Engine.  Its control circuits were wired to do one and only one
> important task: the solution of simultaneous algebraic equations.
>
> Although parts of the machine were built and proven, it was never
> put into full operation."

I don't think that this was capable of testing primality, even
though it worked in binary so calculating modulo 2^p-1 is convenient.
Whilst this machine was deemed to be "prior discovery" to Eckert's 
and Mauchly's ENIAC, there were earlier (slower & simpler) automatic 
electronic calculators. The court case did not prove that the ABC was 
the first. There is no legal or commercial motivation for earlier
calculators or later superior designs to debate in a US Court that
they were the first.

Vincent J. Mooney Jr. wrote:-
> the  judge, Earl R. Larsen, ruled "Eckert and Mauchly did not
> themselves first invent the automatic electronic digital computer, but
> instead derived that subject matter from one Dr. John Vincent Atanasoff".

In 1940 George Stibitz demonstrated the Complex Number Calculator.
As I work for them I had best mention Bell Labs. "Bell Labs" -
there I've done it. This has been called the first working Automatic
Electronic Computer, but it had no stored programme.

The intended application for all of these were the calculations for
military ballistics such as bombing tables.

The Zuse Z3 was a relay based electromechanical floating point
calculator - neat! One application for it was ironically anti-aircraft
calculations. It's usefulness (and Zuse's Berlin apartment) was ended
towards the end of the war by an application of American or British
military ballistics. Zuse himself continued with the valve based Z4 
and went on to develop commercial computers for Siemens.

ENIAC was completed on 15th February 1946, but it was basically a
Numeric Integrator, a very very good one, but was barely programmable.
I have recently learnt that at the end of 1948 a programme store was
added but this was not manipulable like data. Before then reprogramming
could take days and involved recabling and even moving cabinets.

Up to and including this point X modulo m was possible, but would have 
been calculated by the inefficient
r := X - ( (X DIV m) * m )

continued.....
Paul Landon
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