Perhaps, the necessity to calculate has its origin in the beginnings of the abstraction of trade. A simple example: two farmers are trading seventeen geese versus five sheep. The shepherd owns temporally enough geese but is still willing to give away the sheep. In doing so, trust is an important factor. The farmer could still give away the sheep, anticipating that he will receive the seventeen geese whenever he needs them. Modern economics, dealing with consumption, capital, debt and interest as forms of symbolic reproduction, relies on trust, speculation and rhetoric. Thus, many of the foundational economic theories come from moral philosophy rather than from mathematics.

In his book 'Number and Numbers', Alain Badiou sets out how numbers serve, strictly speaking, for everything. They provide a norm for all things. Number governs our conception of the political, of suffrage, of opinion polls, of the majority. What counts, in the sense of what is valued, is that which is counted. Conversely, everything that can be numbered must be valued. Political thought is numerical exegesis. Number governs the quasi-totality of the 'human sciences'. Badiou asks: 'Isn't another idea of number necessary, in order for us to turn thought back against the despotism of number, in order that the subject might be subtracted from it? And has mathematics simply stood silently during the comprehensive social integration of number, over which it formerly had monopoly? In our situation, that of Capital, the reign of number is thus the reign of the unthought slavery of numericality itself. The reverse side of the abundance of capital is the rarity of truth, in every order where truth can be attested to: science, politics, arts, love.

As early as the time of the Pythagoreans, a concept of number for a harmonic relationship between mathematical and musical proportions as constitutional element for an ontology of the cosmos was acknowledged. This idea of music is based on the fact that simple proportions would create the most harmonic intervals from the vibration of a string. In essence, 2000 years of musical history have revolved around the problem of how to minimize numerical paradoxes arising from the desire to make music with multiple fundamentals, or multiple 'Ones'. Around the period of the Pythagoreans, an early second strand in philosophy was formulated by Heraclitus and Lucretius, which we could call the strand of minimal deviation and of continuous change.

Interestingly, it is the problem of the continuum, the dialectic of the discrete and the continuous, which, saturating and subverting the ancient opposition between arithmetic and geometry, compelled mathematicians around the second half of the nineteenth century to rethink the idea of number. The question still remains: is there a concept of number capable of subsuming, under a single type of being and by means of a uniform procedure, at least natural numbers, real numbers and ordinal numbers, whether finite or infinite?

In 1888, Richard Dedekind wrote "Was sind und was sollen die Zahlen?" (What are numbers and what should they be?). A generalization of numbers can be approached by regarding the different number classes as proper parts of sets. Revising Dedekind, Alain Badiou lists three fundamental causes that mark the collapse of Greek thinking about numbers: first, the irruption of the problem of the infinite; second, the problem of the ontology of number, zero, the void; and third, the dislocation of the idea of the One. We find ourselves under the jurisdiction of an epoch that obliges us to hold that being is essentially multiple. Consequently, number cannot proceed from the supposition of a transcendent being of the One.

By discussing the concept of Conway's 'surreal number', he aims to 'limit the glory of number to the important, but not exclusive, glory of being, and thereby demonstrating that what proceeds from an event in terms of truth-fidelity can never be, has never been, counted.' The surreal numbers describe an arithmetic (dis-)continuum containing the real numbers as well as all infinite and infinitesimal numbers respectively larger and smaller than any real numbers. In set theory, surreals are the largest possible ordered field; other ordered fields, such as the rationals, the reals, the rational functions, the superreal and hyperreal numbers, are all subfields of the surreals. Surreals also contain every transfinite ordinal number reachable from within the set theory in which they are constructed. We therefore find the program of unification of the concept of Number (one sole concept which subsumes the natural whole numbers, the negative whole numbers, the rationals, the reals and the ordinals) to be wholly realized, firstly in multiple-being, and then in the operational dimensions. This way, this specific notion of Number mirrors the swirling nature of music.

Exploring the relationship between this world of music and economics becomes evident in the structure of the institution, WDR Studio Akustische Kunst. Where does the world of frequencies end and the world of numbers begin? It was impossible to separate method from result. Here, it could not come down to the production of theory; instead the limits of intuitive understanding are explored. The intelligible and the sensory are inseparably interlaced, but their unity is unattainable.

DEDEKIND CUTS ............

NUMBER AND NEGATIVITY

SPECTRAL DIGITS .........

PRIME FACTORS ...........

COMPLEX NUMBERS ......

RIEMANN'S ZETA FUNCTION

LINEAR CONGRUENCE / INTERCALATION ...........

INTERLUDE: DISSONANCE / DIVERGENCE ................

CARDINAL NUMBERS .....

א0 \ALEPH_0 .............

ONE (UNITY) ................

REFRAIN NUMBERS NEGATION

## References | |||

2023 | Nov 17 | Rome | Italian premiere presented by European Pavilion @Villa Massimo |

2016 | Sep18 | Köln | Photoszene presents Politiken der Frequenz with Greek Choir inside an installation "Volatile Smile" by Geissler/Sann. |

Aug28 | CD | new mix CD by Objekt containing a track from "Politiken der Frequenz" on legendary Technolabel Tresor | |

Apr 09 | Athens | Borderline Festival presents Politiken der Frequenz with choir in Greek language | |

2015 | Mar 07 | Los Angeles | Noise and the Possibility for a Future conference at Goethe Institut LA. |

2014 | Apr 14 | Release | Marcus Schmickler/ Julian Rohrhuber 'POLITIKEN DER FREQUENZ' ( Tochnit Aleph / editions Mego ) |

Apr 10 | Berlin | Politics Of Frequency - Record Release Presentation at KW Kunstwerke for Contemporary Arts | |

2013 | Apr 28 | MusikTexte 138 "Sonification in the Context of Composition" by Marcus Schmickler (German) | |

Apr 20 | Providence | Performance and Talk at Brown University | |

2012 | Dec 14 | Radio | ORF presents 'Politiken der Frequenz' as performed at Steirischer Herbst, Graz |

Oct 5 | Graz | Concert Performance Musikprotokoll im Steirischen Herbst | |

May 25 | Frankfurt | "Politiken der Frequenz" Lecture at Hochschule für Musik und Darstellende Kunst. | |

Jan 19 | Bielefeld | Kunstverein: Presentation/Talk: Politiken der Frequenz / Concert | |

2011 | Nov 4 | Köln | Premiere of Politics of Frequency, WDR3 Radio |

Nov 3 | Radio | MACBA webradio Mix: Interruptions 6 / Ontology of vibration : economics, music and number. |