The other day, I discussed only one kind of abstraction that Marshall and Eric McLuhan explore in the first sections of Laws of Media. The second kind of abstraction regards our experience of space, and the epistemic effects of Euclidean and Pythagorean geometry. These are the concepts that I would say are the most trippy so far in their analysis of how thought became abstract.
“Trippy. Hm. Is that a technical term?”
Yes, actually, it is.
The son and father describe how people experienced and thought about space before Euclid as acoustic. The primary objects in the world were physical things flying around us, and space was the product of these interactions. Remember, however, that these concepts of space were explained in philosophical poetry, performed testimonials of logos itself that speaker and audience memorized in the act of recitation and listening. There were no mathematics to accompany these concepts.
Euclid and Pythagoras changed all this when they started constructing geometric figures and investigating their properties on paper. They conceived what MuLuhan calls the visual model of experiencing space, where figures stand in focus on a featureless ground that extends infinitely in all directions. Space exists as infinite extension that is the theatre on which objects appear.
This concept of infinite extension was very different from what amounts to the previous equivalent conception, that of boundlessness. The sages of recitation understood the world as ultimately finite, but having no boundaries. It used to be easily understood, but we've lived with the concept of space as infinitely extended for so long that now boundlessness is hard to get our heads around.
Boundless finitude goes like this. Travel in your spaceship as far away from everything else as you possibly can. Literally everything else in the entire universe is behind you. You’ve only travelled a finite distance, but your position now constitutes the most distant point in the universe. Now throw a baseball in front of you.
That's what the boundless finite universe is. It's a bunch of stuff scattered around. There’s no limit to that finitude beyond which you can’t go, as if there was a magic fence around the universe. You’re not throwing that baseball into anything. You’re just throwing it farther away from everything else. The size of the universe is just the distance between stuff and there's no principle that sets any limit on how distant stuff can be from each other.
This is actually really hard to conceive today, because as a culture we’re so accustomed to thinking about the universe as a plane of space, the end of which is literally no-space. If you can throw the baseball, you must be able to throw it into something. This idea that there had to be something that underlay the existence and relationships among objects was weird and difficult to understand in Euclid’s day. His ideas were so innovative that they literally made no sense without long periods of complex study.
Of course, Einstein’s revolution in physics has thrown the Euclidean conception of space into the pile of obsolete ontology. Yet we’ve been thinking according to Euclidean presumptions for so long (or so says the McLuhans) that returning to a conception of space that makes it a function of relative distance from the image of a theatre prior to the objects that appear in it is just as difficult as it was to leave that conception behind in the first place 2500 years ago.
I’m not sure where their conceptual story of how we understand space ends, because I’ve been spending most of my philosophical time editing the manuscript of Ecology, Ethics, and the Future of Humanity. So I had to put Laws of Media down for a while. Only so many hours in the day.