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?”

Divination and the Holy Guardian Angel

A prerequisite for working with the Holy Guardian Angel (HGA) is to attain its Knowledge and Communication. The HGA has been defined in various ways: as the true or higher self; as a dualistic representation of the non-dual; or as the future magickal self. Despite the various methods for attaining the HGA and the diverse definitions of what it is, one characteristic remains constant and implicit: it is wiser than I am.

Recently, I confronted a life-changing choice. I had to decide between two courses of action. The first offered radical change, freedom from what I had long wished to escape, but a risk of serious material hardship. The second entailed biding my time, enduring the limitations on personal freedom I had already tolerated for so long, but remaining materially secure.

An angel with properties.
Box Angel, by Chickie456. From the Deviant Art website.

I was most inclined towards the first, the direction my heart wanted to take me, but this was not entirely free of anxiety and fear. The second seemed more sensible, yet contemptibly so; I had been wasting my life for too long already, and if now were not the time to break free, then when?

Loved ones expressed concern over what I was proposing to do. In response, I flared up in anger. Did they not understand I had put up with enough already? How little they knew about what I was feeling! As the days passed and I wrestled with the decision, I fell into depression. I was losing sleep and feeling ill. Finally it occurred there was only one way through: I would have to consult my HGA.

I do this rarely and never take it lightly, because experience has shown that my HGA is never wrong. By definition, it cannot be wrong; it is my true or higher self, after all. So I banished the temple space and invoked the angel with a ritual so simple it barely deserved the label: inwardly I recited his name, until I felt his presence. Then I asked my question and drew three runes from a pouch.

The runes provided a response resoundingly pertinent and clear, but it was not the answer I wanted. The message instructed me in no uncertain terms that the time to act was not quite yet. It would not be long, but I had to wait. Things would remain tough, but I had to suck it up. My preferred option would only make things worse in the long run.

An infallible and precise message: NIED, EIHWAZ, ISA.

This was not what I needed to hear, and it hurt like hell, but soon I started to feel better. How odd, that advice I would not tolerate from loved ones, I could accept from a discarnate being with no material existence! My HGA is never wrong, so there was no question whether this was the right course. Things could indeed be nothing other than shitty for a while, but now I had the backing of my HGA and I knew my interests were – by definition – safeguarded. If this was what the HGA said was best, then I could and would endure it.

There is something special about divination by HGA that sets it apart from a run-of-the-mill tarot spread or I Ching reading. The message received is known to be faultless advice, because its source is tailored specifically to the interests of the questioner. But there is also the sense that, on our part, we are obliged to follow it; to pursue another course would be grossly self-deceiving and self-destructive.

Having access to an infallible oracle makes particular demands upon the magickian. Omniscience is a precious resource and requires protection. Should you wish to develop an oracle with similar properties for your own use, you might like to consider the following:

  • If the response is always correct, then it is pointless to consult the oracle on questions we could answer for ourselves. This oracle should never be consulted on questions answerable by another means. For issues on which the questioner cannot decide, but which demand an infallible answer, then consult the HGA. For anything else, another oracle will do. Or try Google.
  • If the response is always correct, then it must be adhered to. It is not a “possibility” or a “suggestion”; the answer that comes back is binding. If the response is not treated in this way, then it has the status of merely an option or opinion. And what kind of HGA would provide you with only its best guess?

To any skeptical objections, concerning whether this is merely an exercise in self-delusion, and whether it is conceivable that the HGA could have any sort of objective existence, let alone “infallibility”, I make the following reply: these comments are not arguments for or against such things either being or not being the case, but a recipe for creating a certain experience.

“Infallibility” is an experience of such, and to arrive at that experience a certain attitude requires cultivation, in the way I have suggested. That attitude could be described as retreat into delusion, or as a calculated alteration to perception with discrete psychological benefits.

If you feel you might occasionally find it useful to draw on an unfailing and faultless source of guidance (and I have certainly found it helpful down the years) then these are some thoughts that may perhaps enable you to find a means to do so.

A Response to Fascism within the Chaos Community

Recently I unfriended several occultist Facebook contacts. I do not regard unfriending as a particularly significant gesture, but their posts sickened me: calls for racial segregation; eugenic purging of the poor and the “stupid”; the economic futility of educating women; alleged conspiracies of Moslems and Jews… Accuse me of living in an echo chamber, but I cannot have this trash in my newsfeed. By all means suggest that I am rejecting “alternative viewpoints”, but my considered rejection of these views makes me what I am, and I will do all I can to stand apart from ideas like these.

The most upsetting aspect was not the views themselves – their reasoning was risible – but how they were being spread by people whose company I have enjoyed.

Young men operating a mortar wearing t-shirst with an eight-rayed motif.
Neo-Eurasianist fascists in Russia, led by Aleksandr Dugin, have unfortunately adopted an eight-rayed motif as their emblem.

So did I call them out in public? Have I expressed my feelings in person? The answer in both cases is “no”.

The activities of the magickal organisation to which they and I belong are private. Any political differences between members – if these existed, or, indeed, the lack of them – remains also a private matter between individuals. Chaos magick by definition is a broad church. But I have noticed how the reaction from the chaos community to these posters on-line is frequently a seemingly deliberate silence.

This ought to tell the posters something important about the on-line friends they are so fortunate to have. Refusing to challenge noisily such extreme views might seem at first disingenuous, or an abdication of responsibility, but it could also be seen as allowing the poster some space to immerse themselves fully in the belief-system they have chosen.

Typically, a chaos magickian would not engage in magickal action against a sibling – indeed, I imagine that many would not engage in magick “against” anyone – but contradicting a magickian’s choice of belief would be tantamount to this. If the principles of chaos magick teach us anything, it is that we do not adopt beliefs without experiencing their consequences or results. For instance, believing that a minority or ethnic group is conspiring to make your life a misery will simply ensure an experience of this being the case. It should be considered carefully by the magickian adopting such a view whether this is really the kind of reality he or she wishes to inhabit.

It can be no accident that the people I unfriended were male, white, and may have been finding life recently – for all sorts of reasons – difficult. Opportunities for living a comfortable and meaningful life are shrinking across the board and young, white men are confronting perhaps a sharper check to their aspirations, because formerly those aspirations were disproportionately accommodated in relation to other social groups. Regardless of who we happen to be, a question that faces us all is how we deal with frustration and disappointment. Finding an object outside ourselves to hate offers psychological relief, but at the harsh price of stranding us in a world populated by those hated objects.

Perhaps, like me, you sometimes feel powerless. Perhaps, like me, you consider yourself a magickian. If so then your life, like mine, is a means of manifestation by which beliefs can come to be realised in the world. In that case, what beliefs will most effectively transform your reality into the world you want? First, a chaos magickian contemplates this, and then makes his or her choice.