Linear Algebra

The mathematics professor was closing his lecture with questions and answers. He was asking the questions, French accent, chalk in hand.

“Tell me how do you imagine a vector space before your mind’s eyes?”

Lenny raised a hand, the prof found him. A nod in his direction, “yes?”

“Like a dough. You can stretch and pull it”.

The professor considered this for a moment, then made an impatient gesture.

“No, that is not enough. No. No, a vector space is not like a dough at all! You are speaking like the washerwomen at the market. You must learn to speak like a nobleman!”

Snorts and giggles, quiet expressions of disbelief. The professor was known to be eccentic, but not to bizarre extremes like this.

“Yes, you?”

Another student answered the question satisfactorily.


In the slanting afternoon light, a sprawl of students on the main stairs. Cool air and warm light on our faces. Someone exhaled a long plume of smoke into the sky. Elbows back on the steps, I closed my eyes at the sun, red veins brilliant across my field of vision.

Discussions about the professor’s strange tirade. Lenny’s voice, “He has a medieval mindset! Noblemen and washerwomen!”

Someone else’s voice. “But aren’t you into magic yourself, Lenny? You were telling us yesterday -”

Back and forth. Lenny explained his views about magic in the modern world, quantum effects and a conscious substrate of reality made up large parts of his model.

Heavy steps shuffling up the stairs nearby, the cold of the stone steps at my elbows. Motor noise from below.

“So you people are looking for a flatmate?”

Cigarette smoke laced with herbal scents, the sound of a bicycle switching gears.

“Bea, are you looking for a flatmate?”

I opened my eyes. Lenny, long eyelashes, gaze lowered at my chest. I sat up and he looked away.

“Yes, want to see? Josh will be in later, but you should meet him, too.”


On our way from the university to the flat, we passed through a section of the old town. Lenny talked about magic, describing a medieval ritual he had read about, but which he would never try because it involved an animal sacrifice, of a black cat, apparently.

I was pushing my bicycle over the cobbled streets, he was walking along, gesturing and explaining. When we arrived, I swung open the little cast iron gate and led the way past the overgrown garden and the bicycle shed.

Lenny nodded with an approving air at what he saw. We entered the house and ascended the creaking stairs. Evening sunlight filtered through the colourful glass windows of the stairwell, painting our faces yellow and red. We reached the landing and I opened the flat’s doors.

“To the right is my room, and Josh’s. Here is the kitchen. Would you like some orange juice?” He stood closely behind me as I poured our drinks and we took them to the kitchen window overlooking the shadows of the little courtyard behind the house. There were a few folded garden chairs and a soggy cardboard box with pots and other gardening equipment on the balcony outside the kitchen.

“Sometimes we get foxes trying to loot the trash cans in the courtyard. They even fought one night, maybe a cat or a badger or something, very noisy.” Lenny showed some interest in the wildlife, and we discussed urban foxes as I led him out into the hall and to the vacant room.

“Sue used to live here. She’s moved out of town, to Italy, so we’re looking for a new flat mate. How do you like it? She will pick up the boxes next week – ” I gestured at a stack of boxes next to the door.

Lenny went to the window overlooking the old city below. “Nice view!” he remarked. I told him about the rent, he had no questions about it. “Let me show you the living room,” I said, walking out.


In the center of the living room there stood a large wooden frame. Thin wires criss-crossed the wedge of space spanned by the frame, and delicately glazed ceramic discs were suspended on them. The discs were in motion from the draught through the open window, spinning and touching the strings and wires, generating scratching and humming noises.

Lenny was captivated by the mobile. “What is this?”

“It’s full of vectors, isn’t it?” I teased him. “Josh will be able to explain it better. He is into magic, like you are.” I paused, but Lenny did not launch into one of his lectures. “Anyway, Josh says it is an entire cosmos of worlds and when he needs energy or whatever for his magic, he stops one of the discs. He says it is always the end of a world when he does that. He gets really upset when someone else touches it.”

Lenny had been leaning closer to the sculpture, hand extended towards one of the spinning, humming slivers of ceramic, but he backed away now, eyes wide. “What does Josh do? I mean, is he a student?” he asked.

“Biology,” I nodded. “He is in one of the labs where they do vivisection. He has this method of dissecting a mouse where he first fixes it to a board” – I made a cruciform with my arms to illustrate – “and then injects formaldehyde into a major blood vessel. That way, the heart circulates the formaldehyde … I think it’s horrible, too. But he once told me he gets power from that as well.”

I laughed at Lennys expression. “No, really. Josh is nice! Just don’t talk to him when he comes home before he has a chance to stop the mobile. He is much more relaxed when he can do that.”

Steps and the sounds of the door opening. I called a hello to Josh, who muttered something as he came into the living room. His long, thin hair was hangig in strands to his shoulders, and his broad face seemed slack and tired. He wore a black t-shirt with a band’s name in grotesquely overdone gothic lettering.

I did not speak, and neither did Lenny. After pausing and giving us a look for a moment, he held the biggest disc with the fingers of his left hand, until the mobile quieted down. Then he nodded at us and left wordlessly. Lenny had not moved. After a few moments, running water and the sounds of drops on a shower curtain could be heard through the hallway.

“He’ll be more talkative after taking a shower!” I beamed at Lenny. “Do you want to stay? It’s going to be pizza, I’m afraid.”

But Lenny was leaving, saying some vague things about letting me know. I let him out.


As we were putting our pizzas in the oven, Josh asked, “So who was that just now? Didn’t even want to say hello?”

I shrugged. “Lenny. Looking for a room. From the Algebra course.”

“You know I’m not big on conventions, but not saying hello is a red light. I get enough of that kind of attitude in the computer science lab all day, I don’t want it all evening as well.”

“He is a bit strange, but we need to find someone for Susan’s room.” I set the alarm for the pizzas.

Josh shook his head. “We will find someone else a bit higher on the social aptitude scale. Speaking of social aptitude, when is Susan going to get her stuff? That mobile is driving me insane! Can’t we just put it out on the balcony?”

Our Fundamental Mode of Being

The Spell of the Sensuous, by David Abram
The Spell of the Sensuous, by David Abram.

In The Spell of the Sensuous (1997) ecologist and philosopher David Abram examines how our minds have become severed from sensory experience, and – consequently – our bodies disconnected from the natural world.

The blame for our current ecological plight he allocates predominantly to alphabetic writing, which destroyed the link between meaning and its basis in our physical participation in the processes and qualities of the natural world.

When linguistic signs become based on arbitrary vocal sounds (in contrast to pictographic symbols), then: “the larger, more-than-human life-world is no longer a part of the semiotic, no longer a necessary part of the system” (1997: 101). Consequently,

our organic attunement to the local earth is thwarted by our ever-increasing intercourse with our own signs […] Human awareness folds in upon itself, and the senses […] become mere adjuncts of an isolate and abstract mind bent on overcoming an organic reality that now seems disturbingly aloof and arbitrary. (1997: 267)

Specifically, it was the ancient Greeks who led us into this sorry state. “Socrates forced his interlocutors to separate themselves, for the first time, from their own words” (1997: 109). Myths and stories formerly provided a union with nature, which Plato’s writings undermined and destroyed. In an oral culture, a term such as “Justice” always has a context: it is expressed in stories as a specific occurrence, as an event that actually took place. Yet “Socrates attempts to induce a reflection upon the quality as it exists in itself” (1997: 111), and so we arrive – via Plato – at the sense of Justice as a thing-in-itself, an abstract entity with an existence somehow independent from the physical world. There is now scope for belief in a realm of ideas separate from nature, and Abram’s complaint is that we have become increasingly lost in this Platonic invention.

Abram’s book has been influential. His evocation of the role of sensation and perception in human cognition is powerful and compelling. He offers a philosophical foundation for shamanistic and ecological magicks. Yet I am troubled by his demonisation of Platonism, and his privileging of the body and nature above soul and intellect.

If, as Abram suggests, the invention of phonetic writing sealed us within a world of human signs, excluding the other in the body, in non-human species and the natural environment, then our conception of soul or spirit is a harmful, autistic delusion.

However, surely by coincidence, the very next book I read after Abram’s makes a similar but opposite argument. In The Primitive Edge of Experience (2004), psychoanalyst Thomas Ogden writes of a basic mode of human experiencing that he names “the autistic-contiguous position”:

Sequences, symmetries, periodicity, skin-to-skin “molding” are all examples of contiguities that are the ingredients out of which the beginnings of rudimentary self-experience arise. (2004: 32)

The elements of this level of experience, which first appears in early infancy, are perceptual sensations of bodily contact, hardness or softness, being rocked, rhythms of appearances and disappearances, all of which: “have nothing to do with the representation of one’s affective states, either idiographically or fully symbolically. The sensory experience is the infant” (2004: 35).

The Primitive Edge of Experience, by Thomas Ogden
The Primitive Edge of Experience, by Thomas Ogden.

Yet whereas Ogden concurs with Abram that the use of language or symbolisation detracts from experience at this autistic-contiguous level, in Ogden it lacks the Edenic quality evoked by Abram’s writing. For Ogden, the autistic-contiguous is “preparatory for the creation of symbols” (2004: 59), and to dwell exclusively within it presents a dilemma of becoming “entrapped in sensory experience” (2004: 78). For Abram, the sensory is primary and language is an autistic detraction. For Ogden, sensation attracts the label of “autism”, yet without any sense of pathology, because this type of non-reflective experience provides an essential “bounded sensory ‘floor’ […] of experience” (2004: 45), “the beginnings of qualities of who one is” (2004: 54).

For Abram, the turning in upon human signs results in alienation from the body. But for Ogden, the turning in upon sensory experience results in a basic sense of self on top of which further maturational developments may accrue. Both writers are exploring similar territory, but from opposing points of view. Placing these authors beside one another, perhaps we start to see how this “autism”, the reflexive turning in upon oneself, is perhaps not by definition detrimental. And perhaps neither is sensation or symbolisation necessarily malign or benign. Increasingly, it may seem that we are labouring beneath a false opposition between the body and spirit.

Abram himself recognises a flaw in his privileging of the sensory and those indigenous means of apprehending the world that are deeply rooted in it. “If our primordial experience is inherently animistic,” he wonders, “how can we ever account for the loss of such animateness from the world around us?” (1997: 90). The argument that x is our primary mode of being, but that x has been forgotten, contains a glaring contradiction that the forgetting of x is evidently more primary than x itself. In that case, perhaps the ecological crisis is not a consequence of the invention of writing so much as the forgetting of nature because our (even more) primary mode of being is, perhaps, forgetfulness. Indeed, for Ogden, the autistic-contiguous is a “position” (2004: 11), a kind of stance or attitude that may be lost, or into which we may fall at any time, if more sophisticated levels of being are placed under stress. Our fundamental mode of being is maybe neither sensory nor cognitive, neither bodily nor spiritual. Perhaps our fundamental mode of being consists in not having a fundamental mode of being.

Enlightenment traditions present themselves as the antidote to habitual forgetfulness. Techniques for realising the absence of a fundamental self rely on cultivating a turning inwards, a kind of intentional autism that contrasts with the reactive type that both Abram and Ogden evoke. Within enlightenment traditions, it does not appear to matter what the objects of that turning inwards might be, whether sensations, thoughts or meritorious actions. The intention is to realise how whatever fills experience is not fundamentally what we are, because it is not invulnerable to forgetting.

Applying this to magickal practice, my view is that magick is wherever we find it. There are body magicks and shamanistic nature magicks. But there are also word and number magicks, and magicks of abstract contemplation. They are not of equal value, but neither is one of them necessarily of greater value than all the rest.


Abram, D. (1997) The Spell of the Sensuous: Perception and Language in a More-Than-Human World. New York: Vintage.

Ogden, T.H. (2004) The Primitive Edge of Experience. London: Karnac.