Characteristica Universalis

calcmach

“Utile erit scribi \int pro omnia” (Leibniz, 29 October 1675, Paris, now in Gottfried Wilhelm Leibniz, Manuskript Analysis tetragonistica, 1675, Manuskriptseite, GWLB: LH XXXV, 8, 18, Bl. 2.)
A new world was born. If numbers \in \mathbb{Q} are just like stars in the night sky of numbers \in \mathbb{R}, another metaphor is possible. Calculus as devised by Leibniz is just a way to save computational effort (as compared with Eudoxus ‘method of exhaustion’) where the formal symbolic method could be used to compute the integral. Finding a symbolic manipulation (solving an integral analytically, i.e.) is then just like landing in one of the stars, surrounded by the deep dark sky of not-analytically solvable problems. Leibnitz realized that devising a notation (a language) in which the problems could be properly expressed would contribute to their solution, by virtue of the very language struts.
The Step Reckoner was an attempt to reduce an analytical problem to a mechanical algorithm. See Martin Davis, The Universal Computer, the Road from Leibniz to Turing

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