THE PRINCIPLE OF HOPE

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survives in an extremely elementary form even in the diverse calculating machines; though not in order to discover new truths but, as the so­called Maniac (Mechanical
and Numerical Integrator and Calculator) has succeeded in doing, in order to multiply two ten­figure numbers in less than a thousandth of a second. Pascal had
constructed the first mechanical calculator, with rotating wheels, and today Lull's arithmeticized dream has been turned into a whole intellectual industry, with speed as
witchcraft. Even the newest American mechanical engineering, which has culminated for the moment in Norbert Wiener's ‘Cybernetics’, still incorporates a portion of
Lull's mechanical idea. His plan never aimed at such automatisms though, even a mathematical ‘alphabet of ideas’ still lay beyond the horizon of the Lullian art, in view
of the time at which it arose. Instead, Lull originally had a — missionary purpose with his machine; the invention was planned as a kind of deductive apostle of the faith.
Thus Lull had intended to convince all unbelievers of the truth of the Christian religion by means of the irrefutable demonstrations of his machine, free of every error in
reasoning. This aim is of course also as remote as possible from Francis Bacon and his ‘natural magic’, even more remote than it is from Leibniz. Bacon thus speaks
almost contemptuously of Lull, and not only because of the scholastic mythology itself, but also because of the curious deduction and subsumption in which its
machinery moves. Nevertheless, because of its technical nature Lull's invention would also have cut quite a good figure in Bacon's ‘Ars inveniendi’, and especially in his
utopian hall of instruments (Theatrum mechanicum). Not even the passionate praise of induction stands in the way of this; for even Bacon's induction still seeks to
explore ‘the basic form of things’ and finally, although the word deduction is deliberately absent, permits ‘descending’, namely from the law of forms to the experiment
of their self­application in appearance. Only in this, in contrast to purely flat empirical progress, is the regulated art of the inventor completed for Bacon: ‘But after this
store of particulars has been set out duly and in order before our eyes, we are not to pass at once to the investigation and discovery of new particulars or works … For
our road does not lie on a level (neque in plano via sita est), but ascends and descends; first ascending to axioms, then descending to works’ (‘Novum Organum’ I,
Aph. 103). In this ‘descendendo ad opera’ the ‘Ars inveniendi’ was for Bacon a portion of Lull's ‘Ars magna’ as well; directed against the method of testing, failure,
and renewed testing (trial and error method) of the philistines, — not just the superstitious ones. But the goal of knowledge for the English project­maker was not
knowledge for its own