1 + 1 = 2. This mathematical statement can be understood as an instruction, an appropriation, or as a declaration of ownership that reduces objects, such as apples, people, and machines, to numerals. The numerals are used to represent something else, which then comes under the control of numbers and calculation. That would have been the view of Martin Heidegger. Ernst Cassirer, who had a discussion with Heidegger during the Davoser Hochschulwochen [International Davos Conference] in 1929, understood mathematical statements not as statements about what exists, which is thereby formalized, but as expressions of constructive competence. A sign is applied to itself and results in a new sign. This can be expanded into a law for forming natural numbers, and hence into a precise description of infinity. This is one formal possibility for criticizing the medieval concept of God – that is how Cassirer interprets the history of modern science. It is one way of thinking about and questioning the self-empowerment of modern humans.
Vilém Flusser participates in different aspects of this project. He agrees with Heidegger’s fear that modern mathematics has formally installed techniques of domination by means of numbers and measurements, by means of quantification. This corresponds with Flusser’s interpretation of the information society – and of the computer that advances it – as a hierarchical, discursive structure. In Flusser’s idea of dialogic structures, a utopian element recurs which Flusser identifies in Cassirer’s philosophy of culture and which he associates with Martin Buber’s philosophy of dialogue: that numbers can be understood as “media of freely becoming” as long as they are not comprehended as denoting substances but as factors of creative activity. This creative activity produces, for instance, the continuum of real numbers, which are subject to innite differentiations. This is dialogic to the extent that a mathematical interval can be produced between two numbers which cannot be definitively derived. This underivability to be derived can be interpreted as indomitability. It thus corresponds to the ethical model of dialogue: There the distance between I and Thou is immeasurable and thus noncontrollable. Flusser’s philosophy makes it possible to conceive relationships in radical ways against the backdrop of Ernst Cassirer’s philosophy.