Irrational Numbers: Sonification and Intervention

ALOGOS — Research Summary

ALOGOS is an ongoing research and compositional project on the sonification of irrational numbers and the politics of the unmeasurable. The Greek alogos names a double meaning: "without ratio" and "unspeakable." When the Pythagoreans discovered that the diagonal of the unit square cannot be expressed as a ratio of whole numbers, incommensurability entered the world as both a mathematical fact and a political problem — a wound in the order of measure that, according to legend, cost Hippasus his life and was bound under a vow of secrecy.

The project takes this double meaning seriously. It treats the irrational not as a technical curiosity to be tamed by rational approximation but as a sonic, perceptual, and social figure. Continued-fraction expansions of π, e, √2, and φ are realised as real-time SuperCollider sonifications: each irrational carries its own rhythmic and spectral signature, audible as a structure that approaches without arriving. Alongside the sonifications, the research develops a reading apparatus drawn from Theophanidis on the alogos, Esposito's communitas as the absence of common measure, Anders's Promethean gap, Blanchot, and Badiou — situating incommensurability as a name for everything that resists being brought to a common standard: qualitative difference, embodied knowledge, ecological time, lives that refuse equivalence.

Two happenings, developed for the !RRATIONALE festival (Bauhaus-Universität Weimar, 8–12 June 2026), test the research in public form.

I. The Ear as Limit: Mathematics, Sound, and the Unmeasurable

Class · Tuesday 9 June 2026, 14:00–15:00 · Klanglabor

A short public class drawing together strands of mathematics, sound, and listening. It moves from Pythagorean ratio and the discovery of the alogos through the continued-fraction expansions of π, e, √2, and φ — each made audible in real time via SuperCollider — and toward the threshold of measure in perception itself: psychoacoustic non-linearities, distortion-product otoacoustic emissions, the edge between the rational and the irrational as it surfaces in the ear. A brief reading of Theophanidis on the alogos alongside Esposito's image of community as the holding-open of a wound frames the technical material politically. Open to the public, no mathematical background assumed; the live sonifications carry the conceptual weight.

II. Procession of the Unutterable

Workshop and public-space intervention · Thursday 11 June 2026, 15:00-17:00 · Bauhaus campus

A morning workshop in the Klanglabor prepares the materials: megaphones and portable speakers loaded with continued-fraction sequences of π, e, √2, and φ as spoken digits, processed voice, and percussive pulses; large-format banners carrying the digits of irrationals, fragments of ancient sources on alogos, and chant text; a libretto built from mathematical definitions, anti-equivalence slogans, and the unspeakable names of Hippasus's discovery. A parallel stratum goes out live on Radio Lotte and Bauhaus FM, picked up on portable FM radios carried in the procession.

The afternoon intervention moves across the Bauhaus campus and into the adjacent public space. Each device broadcasts a different irrational; the procession is therefore polyphonic and structurally non-converging — the sources never agree, never resolve to a common pulse, never arrive. This is the auditory shape of incommensurability. The route itself traces a convergent sequence of rational approximations to a point that is never reached: the procession approaches a square or courtyard, stops short, withdraws, returns closer, withdraws again — staging Dedekind's cut as a choreography of refusal. Voices recite, chant, and spell out the unutterable; banners declare what cannot be measured. The intervention closes back in the Klanglabor with a collective listening session on the field recordings made along the route, returned to the room as a final document.