Category Theory and Mathemes

'For a working mathematician, when he/she is concerned at all, “foundations” is simply a general term for the historically variable set of rules and principles of organization of the body of mathematical knowledge, both existing and being created. From this viewpoint, the most influential foundational achievement in the 20th century was an ambitious project of the Bourbaki group, building all mathematics, including logic, around set-theoretical “structures” and making Cantor’s language of sets a common vernacular of algebraists, geometers, probabilists and all other practitioners of our trade. These days, this vernacular, with all its vocabulary and ingrained mental habits, is being slowly replaced by the languages of category theory and homotopy theory and their higher extensions. Respectively, the basic “left-brain” intuition of sets, composed of distinguishable elements, is giving way to a new, more “right brain” basic intuition dealing with space-like and continuous primary images, both deformable and deforming.'

(Yuri Manin, Truth as value and duty: lessons of mathematics)

'After three thousand years of explosion, by means of fragmentary and mechanical technologies the Western world is imploding.'

(Marshall McLuhan, Understanding Media)

'...the greatest compatibility, the greatest coordination, the liveliest possible affinity [indeed, let us call it what it is: Continuity] appears to be imposing itself today between what seems the most alive, live, and différance or delay, the delay in the exploitation or diffusion of the living.'

(Jacques Derrida, Echographies of Television)

'...we may forget that a written word IS AN IMAGE and that written words are images in sequence that is to say MOVING PICTURES. So any hieroglyphic sequence gives us an immediate working definition for spoken words. Spoken words are verbal units that refer to this pictorial sequence.'

(William Burroughs, Electronic Revolution)

'...the evolution of the technical synthesis implies the evolution of the spectatorial synthesis.'

'...life (anima – on the side of the mental image) is always already cinema (animation – image-object).'

(Bernard Stiegler, Echographies of Television)