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Number and NumeralIn his essay Thinking Colours and/or Machines Kittler hints at a key point in the emergence of modern European culture: the point at which ‘letters and numbers no longer coincide’. In this essay - first published in 2003 as Zahl und Ziffer - Kittler traces the split between numerals and numbers in sweeping historical detail. This is part of a much larger project, the aim of which is to think about technology, history and culture anew by considering the ways in which ‘letters, numbers, images and tones’ have been differentiated and re-integrated by developing notation systems and media technologies. In this present essay, Kittler is concerned specifically with the question of number. His argument is that numbers and numerals have not always stood apart. In Old Hebrew and even nursery rhymes, for example, numbers are in fact words. This might seem like a banal observation, but for Kittler it is crucial as historically, mathematics proper only developed ‘in cultures in which numbers are present as numerals’, a development which entailed the transformation of numbers from signifiers (‘a matter of hearing’) into signifieds (‘a matter of reading and writing’) and which rested on the emergence of storage and transmission media that Kittler calls ‘the media of mathematics’. This connection between media and mathematics is explored through a wide range of philosophical sources: Plato, Philolaus, Aristotle and Aquinas, to name but a few. Kittler is fascinated by the inscription technologies that make mathematics possible, and which at the same time structure cultural forms as well as our bodily experience of them. As he puts it in a programmatic aside, ‘media studies only make sense’ if they focus on how ‘media make senses.’ Hence his focus on the Greek phonetic alphabet: for Kittler, its superiority has less to do with its ability to reproduce the spoken words of any language, than with the fact that at one point it was used to handle language, music, and mathematics - that is, one and the same set of signs was used to encode letters, tones and numbers. This, however, was not an abstract undertaking but developed in constant feedback with specific instruments or media, especially the lyre and the bow. It was here that fundamental concepts such as logoi were first developed that were subsequently distorted, misunderstood and deprived of their musico-technical origins by philosophers such as Aristotle. Kittler’s essay is thus also part of a larger cultural project, indebted in particular to Martin Heidegger, whose aim it is to ferret out the different, as yet unrevealed beginning of occidental culture. Moreover, while it was necessary for the evolution of modern mathematics that numbers receive a notation system of their own that will allow for ratios and decimals, among others, it is obvious that Kittler sees the computer (as first envisaged in Alan Turing’s mathematical modelling) as a return of universal alphabet that operates in constant feedback with a medium that shapes our senses: ‘In the Greek alphabet our senses were present - and thanks to Turing they are so once again.’
Key Words: history of mathematics • Kittler • numbers • notation systems References
Theory, Culture & Society, Vol. 23, No. 7-8,
51-61 (2006)
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