Re: Babbage/Menabrea: Analytical Engine

From: Hindle Thomas (
Date: Thu Mar 01 2001 - 01:06:45 GMT

Sketch of the Analytical Engine invented by Charles Babbage. 1842

This paper is translation of an overview of Charles Babbages Analytical
Engine by Menabrea. Ada Lovelace did the translation. It explains the
Analytical Engine not in term of how it works but in terms of the
processes one has to under take to operate it. This paper attempts to
perform mathematical analysis of the Analytical Engine. The paper also
makes statements about the importance of the engine.

> The Analytical Engine is an embodying of the science of operations,
> constructed with peculiar reference to abstract number as the subject of
> those operations.

The above paragraph is a summary of what the Analytical Engine does. Too
use the Analytical Engine one takes the mathematical combination of
symbols which you want to evaluate and split them up into individual
symbols which represent a numeric value. One then converts the symbol
relationships into a series of simple operations, in the form of
cards. Submitting these cards to the Engine would allow the Engine to
produce the result in one of its columns.

> The Analytical Engine, on the contrary, is not merely adapted for
> tabulating the results of one particular function and of no other, but
> for developing and tabulating any function whatever. In fact the engine
> may be described as being the material expression of any indefinite
> function of any degree of generality and complexity

This is Menabrea claim of what the Analytical Engine is capable of. I
think that he has-over hyped the situation. I dont believe that he really
meant that a real Analytical Engine could express any function of any
degree of complexity. I believe he was referring to a hypothetical
Analytical Engine that you could build if you had infinite space and time.

> The power of repeating the cards reduces to an immense extent the
> number of cards required. It is obvious that this mechanical improvement
> Is especially applicable wherever cycles occur in the mathematical
> operations, and that, in preparing data for calculations by the engine,
> it is desirable to arrange the order and combination of the processes
> with a view to obtain them as much as possible symmetrically and in
> cycles, in order that the mechanical advantages of the backing system
> may be applied to the utmost. It is here interesting to
> observe the manner in which the value of an analytical resource is met
> and enhanced by an ingenious mechanical contrivance. We see in it an
> instance of one of those mutual adjustments between the purely
> mathematical and the mechanical departments, as being a
> main and essential condition of success in the invention of a
> calculating engine.

In the above paragraph Menabrea points out that the order of the
mathematical arrangement of the operation cards with relation to the
inner-workings of the engine has an important effect on how quickly the
engine produces its result. In todays terminology this is akin to
reordering ones software code so it will run quicker on the given
hardware. Hence Menabrea has stated that the order of the software
instructions has an effect on how long the program takes to run. On a
single-processor system this would not be correct, as Menabrea does not
say that the number of instructions changes. Therefor I conclude that
Babbages Analytical Engine must operate in a similar way to how a parallel
processor system works. Obviously we must excuse Menabrea for not making
this clear as he didnt have many other engines (or computers) to compare
this too.

> It is desirable to guard against the possibility of exaggerated ideas
> that might arise as to the powers of the Analytical Engine. In
> considering any new subject, there is frequently a tendency, first, to
> overrate what we find to be already interesting or remarkable; and,
> secondly, by a sort of natural reaction, to undervalue the true state
> of the case, when we do discover that our notions have surpassed
> those that were really tenable.

Perhaps people, any one who had an option on the subject, had too great
expectations about the power of computation. Menabrea proclaimed a warning
here in 1842. He most probably anticipated the hype that was going to be
associated with computation i.e. that it alone would lead to the
production of machines with human level intelligence. Now that it looks
unlikely that the hypnosis of computation reproducing human intelligence
looks to be false, then it may now be time to take heed to the second part
of the paragraph. We perhaps now hold a too low opinion of the power of

> The Analytical Engine, on the contrary, can either add, subtract,
> multiply or divide with equal facility; and performs each of these
> four operations in a direct manner, without the aid of any of the
> other three. This one fact implies everything; and it is scarcely
> necessary to point out, for instance, that while the Difference Engine
> can merely tabulate, and is incapable of developing, the Analytical
> Engine can either tabulate or develop.

The Earlier Engine called the Difference Engine had one instruction and
that was ADD. All other operations were built up from that
instruction. The Analytical Engine had 4 Instructions. However if the
implementation of the machine changed and it had only one instruction
e.g. ADD then that instruction could be used to generate the other
necessity instructions, without changing the capability of the engine. The
only thing that would likely to change is the processing time to compute
calculations. Therefor I think Menabrea is wrong to claim that this
accounts for the increased power of the Analytical Engine over the
Difference Engine . How can the number of instructions have any effect on
the power of the engine if by using the reduced number of instructions one
is able to generate the missing instructions?

> The bounds of arithmetic were however outstepped the moment the idea
> of applying the cards had occurred; and the Analytical Engine does not
> occupy common ground with mere "calculating machines." It holds a
> position wholly its own; and the considerations it suggests are most
> interesting in their nature. In enabling mechanism to combine together
> general symbols in successions of unlimited variety and extent, an
> uniting link is established between the operations of matter and the
> abstract mental processes of the most abstract branch of mathematical science.
> A new, a vast, and a powerful language is developed for the future use
> of analysis, in which to wield its truths so that these may become of
> more speedy and accurate practical application for the purposes of
> mankind than the means hitherto in our possession have rendered
> possible. Thus not only the mental and the material, but also the
> theoretical and the practical in the mathematical world are brought into
> more intimate and effective connection with each other. We are not aware
> of its being on record that anything partaking in the nature of what is
> so well designated the Analytical Engine has been hitherto proposed, or
> even thought of, as a practical possibility, any more than the idea of a
> thinking or of a reasoning machine.

In the above Paragraph I believe that Menabrea has captured the key point
between the difference between mathematical calculation and
computation. He has identified that the meaning inferred in the order of
the operations is what makes the Analytical Engine so powerful. The
intelligence is the generating of the order of the operations, not in the
operations or the order of operations themselves. Unfortunately the
ordering of the operations or programming has to be done by a Human and so
the machine itself is not intelligent. Menabrea does then seem to suggest
the possibility of a thinking machine being made from an expanded
Analytical Engine. By thinking machine I take him to mean an intelligent
machine. This is where I think he makes a mistake, he suggests that an
intelligent machine could be make from computation alone. To his credit he
did present this idea as speculation rather than as a theory. In my
opinion, his flawed reasoning when something like this; he thought that
since intelligence was present in the programming, or ordering, of the
operations then if he could build a machine which was capable of ordering
the operations it would be intelligent or a thinking machine. What I think
he failed to grasp was that if he built a machine capable of ordering the
operations then the intelligence would be in the ordering of the
operations of that particular machine. This is closely related to the
frame problem, only instead of the meaning of objects being in question,
the problem lies with the meaning of the ordering of operations.

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