Re: Charles Babbage's "Analytical Engine"

From: Butterworth, Penny (
Date: Wed Feb 16 2000 - 15:27:50 GMT

> Egerland:
> In this classical article from 1842 the Officer of the Military
> Engineers of Turin, L.F. Menabrea, explains the capabilities of the
> first calculating machine which consisted of a memory for variables, a
> punched card control unit and I/O devices. Though being a completely
> mechanical approach this 'Analytical Engine' by Charles Babbage can be
> considered as the first computer in human history. Before pointing out
> the machine's functionality Menabrea gives us an outline about the
> intention why it was built and how it is related to its predecessor,
> the 'Differencing Engine':

(general introduction to the motivation and workings of the Differencing
Engine by Matthias and Menabrea)

> Egerland:
> So far the author dealt with the Differencing Engine from 1822. Now he
> is going to point out what the Analytical Engine from 1833 is about,
> which in fact is a major improvement of the first machine.

> But if human intervention were necessary for directing each of these partial
> operations, nothing would be gained under the heads of correctness and
> economy of time; the machine must therefore have the additional requisite of
> executing by itself all the successive operations required for the solution
> of a problem proposed to it, when once the primitive numerical data for this
> same problem have been introduced. Therefore, since, from the moment that
> the nature of the calculation to be executed or of the problem to be
> resolved have been indicated to it, the machine is, by its own intrinsic
> power, of itself to go through all the intermediate operations which lead to
> the proposed result, it must exclude all methods of trial and guess-work,
> and can only admit the direct processes of calculation.

> Egerland:
> This is the main point about the Analytical Engine. Menabrea says that
> the machine needs to be independent from humans to fulfil its main
> purpose - being a useful tool by improving correctness and time
> efficiency when humans have to deal with complicated mathematics.

> At the same time the author is completely aware of the fact, that this
> machine can not make use of intuition. For solving mathematical
> equations it has to take a completely different approach than an
> 'intelligent' being.

Although the Analytical Engine was completely incapable of intuition, it is
interesting that research into artificial neural networks is now investigating
the impact of machines using what is essentially trial-and-error in order to
learn. Menabrea implies that such methods are at least one property of what
he calls 'a thinking being', so his opinion on our discussions of intelligence
may have been interesting, given new technologies.

> It is necessarily thus; for the machine is not a thinking being, but simply
> an automaton which acts according to the laws imposed upon it. This being
> fundamental, one of the earliest researches its author had to undertake, was
> that of finding means for effecting the division of one number by another
> without using the method of guessing indicated by the usual rules of
> arithmetic.

To what degree ANNs can be described as 'an automaton which acts according
to the laws imposed upon it' may be debatable. Although ANNs have
predetermined rules for learning (such as Rosenblatt's Perceptron learning
algorithm), these could be described as ways in which the network learns
new laws or features of the input, which are not necessarily determined
by the operator.

> Egerland:
> So the main goal was finding a possibility to make the machine
> calculating without 'thinking'. Hence, the machine could only be as
> powerful as its inventor, who had to find this very fundamental way of
> solving mathematical equations.

> One of the major inventions in connection with the Analytical Engine,
> which improved its flexibility very much, came from the textile
> industry. Those days mechanical looms already had been equipped with a
> punched card system which contained information about how to weave the
> particular material. Babbage was the first person who had the idea of
> using a similar system to store information needed for mathematical
> calculations. His second machine used punched cards for two different
> matters:

> Arrangements analogous to those just described have been introduced into the
> Analytical Engine. It contains two principal species of cards: first,
> Operation cards, [...] secondly, cards of the
> Variables,

> This example illustrates how the cards are able to reproduce all the
> operations which intellect performs in order to attain a determinate result,
> if these operations are themselves capable of being precisely defined.

> Observe that we should thus require of the
> machine to interpret a result not of itself evident, and that this is not
> amongst its attributes, since it is no thinking being.

Note that in the above sentence, Menabrea was not really talking in a
general sense about the machines ability to interpret, but simply that
Babbage required his machine to be able to terminate computation at a
certain level of accuracy when evaluating (for instance) the expression
to find pi.

> Egerland:
> To summarize things Menabrea gives the following conclusion:

> Resuming what we have explained concerning the Analytical Engine, we may
> conclude that it is based on two principles: the first, consisting in the
> fact that every arithmetical calculation ultimately depends on four
> principal operations - addition, subtraction, multiplication, and division;
> the second, in the possibility of reducing every analytical calculation to
> that of the coefficients for the several terms of a series. If this last
> principle be true, all the operations of analysis come within the domain of
> the engine.

> Since the engine has a mode of acting peculiar to itself, it will in every
> particular case be necessary to arrange the series of calculations
> conformably to the means which the machine possesses; for such or such a
> process which might be very easy for a calculator may be long and
> complicated for the engine, and vice versā.

> So the way how the Analytical Engine has to be instructed to solve a
> particular problem corresponds to a programming language. Nowadays
> there exist dozens of different programming languages, each with
> particular advantages and disadvantages. According to the equivalence
> theorem the power of all these languages is the same, because the task
> solved by a program in any language can be simulated by a turing
> machine. Therefore a machine would be optimal if it was able to choose
> always the most efficient approach to solve a problem. Unfortunately it
> already has been proven that there is no such algorithm which can
> determine whether a program is optimal or not.

> Thus, although it is not itself
> the being that reflects, it may yet be considered as the being which
> executes the conceptions of intelligence. The cards receive the impress
> of these conceptions, and transmit to the various trains of mechanism
> composing the engine the orders necessary for their action.

Again, Menabrea implies a particular understanding of the word
'intelligence', such that he can separate reflection and the execution of
'the conceptions of intelligence'. It is likely that many people would
understand or agree with this description, but it is difficult to define
logically this distinction, even for as simplistic a machine as the
Analytical Engine. Perhaps this in itself is a property of human

> When once the
> engine shall have been constructed, the difficulty will be reduced to the
> making out of the cards; but as these are merely the translation of
> algebraical formulae, it will, by means of some simple notations, be easy to
> consign the execution of them to a workman. Thus the whole intellectual
> labour will be limited to the preparation of the formulae, which must be
> adapted for calculation by the engine.

> Here Menabrea says explicitly that the only intelligence in conjunction
> with this machine has to be in the head of the designer of the cards,
> who can be considered as the 'programmer'. Neither the workman nor the
> machine itself need to have a (high level) of intelligence.

and the job of the workman has now been automated, in an abstract sense,
by compilers and interpreters, so only the designer or programmer remains.

> it will afford the following advantages: - First, rigid accuracy. [...]
> Now the engine, by the very nature of its mode of acting, which
> requires no human intervention during the course of its operations, presents
> every species of security under the head of correctness: besides, it carries
> with it its own check; for at the end of every operation it prints off, not
> only the results, but likewise the numerical data of the question; [...]
> Secondly, economy of time: to convince ourselves of this, we need only
> recollect that the multiplication of two numbers, consisting each of twenty
> figures, requires at the very utmost three minutes. [...]
> Thirdly, economy of intelligence: [...]
> Now the engine, from its capability of performing by itself all these purely
> material operations, spares intellectual labour, which may be more
> profitably employed. Thus the engine may be considered as a real manufactory
> of figures, which will lend its aid to those many useful sciences and arts
> that depend on numbers.

> Egerland:
> According to the first point, in my opinion it would make less sense to
> verify every calculation with the help of the printout, because then
> one could nearly have done the work without the machine right from the
> beginning. On the other hand if it is only wanted to check some
> particular results, then the output of course is of great help.
> Furthermore, assuming that printing the input values and possibly some
> provisional results should not be too difficult, there is no reason not
> to implement this security feature. Secondly, as long as we deal with
> the creation of large mathematical tables it is of course more time
> efficient to use a machine to calculate them. On the other hand from
> our point of view nowadays we can say, that there will never be enough
> computation power and memory capacity, because the complexity of the
> tasks we want to cope with rises at least as fast as the performance of
> our computers.

> In my opinion Menabrea's interpretation of the third point - economy of
> intelligence - is quite interesting. Though he already pointed out that
> the machine does not have any intelligence itself, according to his
> point of view it still rises the amount of intelligence available. It
> does so by not bothering an intelligent human being with monotonous
> tasks which can be fulfilled automatically. The question is just if
> human beings really use their intelligence to think about more complex
> problems than the ones that the machine can work on, or if it rather
> prefers to use the regained time for recreational matters.

I think I disagree with Matthias here, as in my opinion Menabrea's
comment does not necessarily imply that the introduction of the machine
increases the amount of intelligence available. I think what he was
trying to say was that the intelligent human engineers/scientists etc had
been wasting their time doing menial mathematical tasks which did not
really require their intelligence, only their time. With the machine
doing these tasks for them, their time could be used more fruitfully (in
whatever way).

Primary: Egerland, Matthias <>
Respondant: Butterworth, Penny <>

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