Two signals of varying frequency and phase result in a perpetual infinity (figuratively and literally as it actually constructs itself in the shape of the infinity sign given the right starting values), drawing and redrawing itself over and over, a picture of timing and sequence in the center of the screen. The familiar resulting shapes are known as Lissajous curves after French mathematician Jules Antoine Lissajous and his “beautiful machine” of 1855.
Devised to draw a picture of two superimposed systems falling into and out of phase, Lissajous’ machine was constructed of a pair of tuning forks placed facing at right ...

This publication presents Peter Eisenman’s Biozentrum project, an expansion of Goethe University in Frankfurt am Main, from 1987.
In the competition brief, the program of the complex included biotechnology, molecular biology and biochemistry research laboratories and support spaces. The design process used biological concepts and procedures to generate the geometrical pattern that establishes the location, dimension and form of the complex. The iterations of DNA molecules in the production of the protein collagen were at the base of the fractal geometry guiding the project design. These pairs of figures, with a gap in between them, were the base forms Eisenman adopted ...

This issue doubles as a catalog-of-sorts to Ecstatic Alphabets/Heaps of Language, a group exhibition curated by Laura Hoptman at The Museum of Modern Art, New York, from May 6 to August 27, 2012. It is a *pseudo*-catalog in the sense that, other than a section of images at the back, it bears no direct relation to the works in the exhibition. Instead, the bulletins extend in different directions from the same title, and could be collectively summarized as preoccupied with the more social aspects of Typography. In this way we hope to throw some *glancing* light on the exhibition. For ...

This issue loops around NUMBERS and was produced in the ambient glow of a reprogrammed electronic scoreboard clock which first appeared in Venice one year ago. Bulletins this time arrive from Angie Keefer, John Dewey and James Mclellan, James Langdon, Rosie Cooper, Mathew Kneebone, Philip Ording, David Foster Wallace, David Reinfurt, Cory Arcangel, Justin Warsh, Perrine Bailleux, Byron Cook and Tauba Auerbach, Dan Fox, Katherine Pickard, and Vincenzo Latronico.

Kolmogorov’s axioms present an abstract conceptual formalisation of probability that runs counter to our intuitive image of randomness and its concrete instances. But are the relations between concept and intuition, concrete and abstract, so straightforward? And does the revolutionary historical sequence leading from set theory and measure theory to abstract probability occlude a deeper, conceptual order of priority? Elie Ayache takes the true measure of this revolution in our understanding of randomness and probability, and its as yet unthought ramifications.

In Ursula Le Guin’s 1971 novel The Lathe of Heaven, a seemingly unassuming young white male begins effective dreaming. Desperate to stop altering realities by night, George Orr borrows other people’s pharmacy cards (the world is overpopulated, resources heavily rationed) to obtain more than his share of dexedrine and barbiturates. Landing himself in the hands of an oneirologist, he becomes a tool—a proxy to make the doctor’s megalomaniacal utilitarian fantasies real. The doctor suggests, and George dreams. “This was the way he had to go; he had no choice. He had never had any choice. He was only a dreamer”…
Editorial
Editors
Homeland ...

To mark the publication of a new translation of Jean Cavaillès’s On Logic and the Theory of Science, Robin Mackay is joined by Knox Peden and Matt Hare to provide an introduction to Cavaillès’s philosophical project for the uninitiated, and to examine what is at stake in On Logic’s confrontation with Kantianism, logicism, and Husserlian phenomenology.
Among the many subjects covered in this wide-ranging conversation: optimism, extreme protestantism, and Spinozism; Heidegger and Cassirer’s Davos debate; mathematics as a necessary dynamism; the virtues and vices of phenomenology; philosophical style and the ethics of concision; foucault, archaeology, and the historical a priori; life ...

Easily mistaken for the infinity sign, a circle, or any number of more complex pretzels and knots, the Lissajous figure is a picture of compound harmonic motion named for French physicist and mathematician Jules Antoine Lissajous (1822–1880). The shape is drawn by plotting a two-variable parametric equation as it iterates itself over time — the resulting figure is the picture of two systems falling into and out of phase.
These two varying signals produce a perpetual infinity (figuratively and literally as it will actually construct itself in the shape of the infinity sign given the right initial values). Any figure may ...

In this record of a 1939 meeting, two great philosophers of mathematics, Jean Cavaillès and Albert Lautman, attempt to define what constitutes the ‘life of mathematics’, between historical contingency and internal necessity, describe their respective projects, which attempt to think mathematics as an experimental science and as an ideal dialectics, and respond to interventions from some eminent mathematicians and philosophers.

This short introduction to the 2012 discussion event with Giuseppe Longo and Benedict Singleton sketches out the theoretical positions of the two contributors and the common threads of the discussion.

To mark Urbanomic and Sequence Press’s publication of a new translation of On Logic and the Theory of Science, we present a young Jean Cavaillès’s report on the Second Davos University Conference, Easter 1929—the setting for a now legendary confrontation between Ernst Cassirer and Martin Heidegger.

In this introduction to Albert Lautman’s mathematical philosophy, Jean Petitot reaffirms the importance of a neglected thinker, and outlines Lautman’s extraordinary rearticulation of platonism, realism, dialectics, and the history and phenomenology of mathematical creativity.