Gilles ChĆ¢telet, graphic reason (mathematics)

"ā¦ some contemporary research ā¦ completely renews _the very notion of indexation_. No explicit intuition accompanies the āclassicalā behaviour of calculations: in formulae of the type āįµ¢ = , the set of indices is neutral and the indexation remains completely external to the development of these calculations, behaving like a ānotationā which is completely indifferent to that which it notes. These formulae remain captive to a linear successiveness, xā then xā then xā etc., an artificial sequence a little analogous to the chain of verbs _veni, vidi, vici_ where the temporal order of the processes of enunciation ā¦ replicate exactly the order of the processes of the statement ā¦ The contemporary point of view makes the notation _concrete_ by identifying it with a diagram already used in an _a priori_ foreign domain ā¦ This domain thus 'evokesā gestures which are classical for it, but completely new in the domain when it is imported as ānotationā ā¦ This upsets the very notion of indexation which becomes _bi-dimensional_ in freeing itself from the successive: it is very much a victory of the hand that comments on itself, the indexation no longer being delivered by an external āsetā, but by a process of deformation and modification of diagrams."