From: Hindle Thomas (th598@ecs.soton.ac.uk)
Date: Tue May 01 2001 - 03:44:58 BST
Thomas Hindle's Skywritting Second Assignment.
> MENABREA:
> “Those labours which belong to the various branches of the mathematical sciences,
> although on first consideration they seem to be the exclusive province of
> intellect, may, nevertheless, be divided into two distinct sections; one of which
> may be called the mechanical, because it is subjected to precise and invariable
> laws that are capable of being expressed by means of the operations of matter;
> while the other, demanding the intervention of reasoning, belongs more specially to
> the domain of the understanding. This admitted, we may propose to execute, by means
> of machinery, the mechanical branch of these labours, reserving for pure intellect
> that which depends on the reasoning faculties”
Hindle:
The paper is concerned with the production of a mathematical machine,
rather than the production of a machine that might contain intelligence.
The paper begins by distinguishing between the too branches of
mathematics, one which it calls mechanical and one which is says to
belong to the domain of understanding. Here Menabrea states there is a
clear difference between intelligence (pure intellect) and things which
can be achieved by a mechanical (rule following) process. The
Implication from this statement is that Menabrea believes that things,
which simply follow rules, can not be intelligent. Although this is not
backed up by evidence, except experimental evidence i.e. no machine
currently built can generate new reasoning, this is akin to current
theory on this subject, that a symbolic system alone can not produce an
intelligent system. It may however be possible that Menabrea meant
something much stronger, that no rule following machine is capable of
intelligence because it follows rules. This is an example of a granny
argument.
> MENABREA:
>"The chief drawback hitherto on most of such machines is, that they require the
> continual intervention of a human agent to regulate their movements, and thence
> arises a source of errors; so that, if their use has not become general for large
> numerical calculations, it is because they have not in fact resolved the double
> problem which the question presents, that of correctness in the results, united
> with economy of time."
Hindle:
Here Menabrea comments on the fact that all machines, which came before
Charles Babbages Analytical Engine, were not useful as they could not
guarantee the correctness of their results because they required human
intervention to continually assist them during their 'processing'. The
reasoning being that humans may make mistakes, because of their
inability, to follow rules correctly all of the time and so mistakes may
be made whilst the results are calculated. Through out this paper
Menabrea sees the time saving ability together with the guaranty of
correctness as the main breakthroughs of Babbage's machine.
> MENABREA::
>"… 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"
Hindle:
Menabrea for some reason feels the need to add the stipulation that the
machine during its processing does not use any guesswork or iterations
to determine the result of the calculations. Therefore the machine can
use no numerical methods. The machine must entirely use algebraic
techniques to perform its calculations. I think that the reason Menabrea
insisted on this stipulation is because, in his viewpoint the main aim
of the Analytical Engine was the correctness of results. Since numerical
methods only produce an answer correct to some specified tolerance the
result may not be totally correct.
> MENABREA:
>" It is necessarily thus; for the machine is not a thinking being, but simply as
> automation which acts according to the laws imposed upon it."
Hindle:
Menabrea correctly states that to achieve the aim, of both the time
saving and the correctness of the result of the calculation the machine
does not have to be intelligent (thinking being) but only has to be able
to follow blindly a set of laws. By implication Menabrea states that
(intelligence) is something more than the ability to follow
instructions. Unfortunately he does not tells us what else is needed too
produce an intelligent machine.
> MENABREA:
>"To take another point of view: the use of the cards offers a generality equal to
> that of algebraically formulae, since such a formula simply indicates the nature
> and order of the operations requisite for arriving at a certain definite result,
> and simply the cards merely command the engine to perform these same operations;
> but in order that the mechanisms may be able to act to any purpose, the numerical
> data of the problem must in every particular case be introduced. Thus the same
> series of cards will serve for all questions whose sameness of nature is such as to
> require nothing altered excepting the numerical data. In this light the cards are
> merely a translation of algebraical formulae, or, to express it better, another
> form of analytical notation."
Hindle:
Its is remarkable the similarities of Babbages Analytical Engine to
today's Computers. Babbages Engine contains an instruction set of four
operations, addition, subtraction, multiplication, and division. The
cards that were used to program the Machine make references to these
operations in the same way modern a program work by referencing the CPUs
instruction set. Menabrea correctly recognised that these cards were
merely a translation of the algebraic statement, which the Machine was
to perform. I find it somewhat surprising that at this point Menabrea
does not identify the potential problems impacting on the correctness of
the calculation whilst the Machine is being programmed. I.e. A mistake
could be made in the translation of the algebraic statement to the
associated Card State.
> MENABREA:
>"Considered under the most general point of view, the essential object of the
> machine being to calculate, according to the laws dictated to it, the values of the
> numerical coefficients which it is then to distribute appropriately on the columns
> which represent the variables, it follows that the interpretation of formulae and
> of results is beyond its province, unless indeed this very interpretation be itself
> susceptible of expression by means of the symbols which the machine employs. Thus,
> although it is not itself the being that reflects, it may yet 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. 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 translations of allegorical 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.
Hindle:
Menabre realises that the power of Babbage's machine is because of the
ability to re-program it with a different ordering of cards. He realises
that the difficult part in using the Analytical Engine is the
translation of the algebraic formula to the cards that tell the machine
how to perform the calculation. He does however realise that this
translation can be performed be following a set of rules. He envisages a
machine which as its input will take the algebraic formula and as its
output produce the ordering of the cards which would could be given to
the Analytical Engine and so it could produce the result of the
algebraic formula for given numbers. This surely has to be the world's
first use of a meta-program. (A meta-program is a program that creates
as output another program.).
>Menabre
>"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. Again, who
> can foresee the consequences of such an invention? In truth, how many precious
> observations remain practically barren for the progress of the sciences, because
> there are not powers sufficient for computing the results! And what discouragement
> does the perspective of a long and arid computation cast into the main of a man of
> genius, who demands time exclusively for meditation, and who beholds it snatched
> from him by the material routine of operations!"
Hindle:
With Babbage's Analytical Engine together with his envisioned upgrade of
a machine which will do the translation of the algebraic formulae,
Menabre was very optimistic about what these machines were going to be
able to achieve. He saw them as tools, which would be intelligence
enhancing by removing repetitive operations.
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