Leibniz: 'What a watch is to time, this engine is to thought.' Daniel Waterhouse: 'Sir! You show me a few gears that add and multiply numbers – well enough. Bu

Leibniz: 'What a watch is to time, this engine is to thought.' Daniel Waterhouse: 'Sir! You show me a few gears that add and multiply numbers – well enough. But this is not the same as thought !' 'What is a number, Mr. Waterhouse?' Daniel groaned. 'How can you ask such questions?' 'How can you not ask them, sir? You are a philosopher, are you not?' 'A Natural Philosopher.' 'Then you must agree that in the modern world, mathematicks is at the heart of Natural Philosophy – it is like the mysterious essence in the core of the snowflake. When I was fifteen years old, Mr. Waterhouse, I was wandering in the Rosenthal – which is a garden on the edge of Leipzig – when I decided that in order to be a Natural Philosopher I would have to put aside the old doctrine of substantial forms and instead rely upon Mechanism to explain the world. This led me inevitably to mathematicks.' 'When I was fifteen, I was handing out Phanatiqual libels just down the street from here, and dodging the Watch – but in time, Doctor, as Newton and I studied Descartes at Cambridge, I came to share your view concerning the supreme position of mathematics.' 'Then I repeat my question: What is a number? And what is it to multiply two numbers?' 'Whatever it is, Doctor, it is different from thinking .' 'Bacon said, ‘Whatever has sufficient differences, perceptible by the sense, is in nature competent to express cogitations.' You cannot deny that numbers are in that sense competent – ' 'To express cogitation, yes! But to express cogitations is not to perform them, or else quills and printing-presses would write poetry by themselves.' 'Can your mind manipulate this spoon directly?' Leibniz said, holding up a silver spoon, and then setting it down on the table between them. 'Not without my hands.' 'So, when you think about the spoon, is your mind manipulating the spoon?' 'No. The spoon is unaffected, no matter what I think about it.' 'Because our minds cannot manipulate physical objects – cup, saucer, spoon – instead they manipulate symbols of them, which are stored in the mind.' 'I will accept that.' 'Now, you yourself helped Lord Chester devise the Philosophical Language, whose chief virtue is that it assigns all things in the world positions in certain tables – positions that can be encoded by numbers.' 'Again, I agree that numbers can express cogitations, through a sort of encryption. But performing cogitations is another matter entirely!' 'Why? We add, subtract, and multiply numbers.' 'Suppose the number three represents a chicken, and the number twelve the Rings of Saturn – what then is three times twelve?' 'Well, you can't just do it at random, ' Leibniz said, 'any more than Euclid could draw lines and circles at random, and come up with theorems. There has to be a formal system of rules, according to which the numbers are combined.' 'And you propose building a machine to do this?' 'Pourquoi non? With the aid of a machine, truth can be grasped as if pictured on paper.' -- Quicksilver, Baroque Cycle (#1), Neal Stephenson