I shuffled into Ginnn He's class barely on time, which meant five minutes early. It had taken me some time to learn to track the time via my scryer rather than from the sun and shadows, but that had been one of the easier cultural lessons to learn.

In many ways, my hexmage lessons were much easier to learn. Much of it was based on areas of mathematics I had already taught myself, though much of it was cloaked in confusing language. Once I had grasped what hexing actualy was it had become vastly simpler. At the same time, many aspects of the subject had become incredibly frustrating.

Ginnn He was engaged in animated discussion with a trio of students near the front of the class. I chose an empty seat near enough to easily listen, but not so close as to impose, or to be easily drawn in myself. A couple of carers who served as teaching assistants were circling the periphery of the array of desks, watching for students who might need assistance. There were about thirty in this class, and it looked as though I was among the last to arrive. Everyone else had hall's scryers out and ready to take notes or perform exercises.

The conversation between Ginnn and the students turned out to be of little importance. Hall were only going over some minor details of the turtle counter assignment. The details were so beside the actual point of the excercise that I wondered whether those students were really suited to hexmagery. Everyone should be fluent in those basic details by now, so hall could concentrate on higher level issues. Those smaller details were little more than repetitive busywork. That was actually one of my big problems with hexmagery as a whole. It seemed bizarre to me that so much time and brainpower was lost on such trivialities when the entire point of hexmagery was to...

"A pleasant evening to you, students," Ginnn He said from the front of the classroom. Ginnn wore he's violet hair in three long six-stranded braids, one to each side of he's head and one behind. He was quite tall and narrow-framed, and he's wise, expressive eyes were adorned with long purple-tinted lashes which I could not help but envy. Most importantly, he was quick-witted and generally quite sensible. Ginnn was my favourite teacher, most of the time.

"Tonight's lesson covers a very exciting topic," Ginnn continued. "You've heard at length about how to craft hexes to perform specific tasks. But that is not all there is to hexing. A hex exists as part of a greater world, functioning within an ecosystem. To be properly understood as part of that ecosystem, a hex must begin with certain nonfunctional components, which act as 'labels' and 'flags'. Understanding these parts of a hex will help you to evaluate and fix a malformed hex, and to comprehend the purpose and operation of hexes that you did not fashion yourself. This journey starts with the step of grasping the magic number 7f454c46. Can anyone tell me what 7f454c46 means?"

My hand shot up immediately, as I had been trained to do instead of blurting out the answer. Despite following procedure, this earned me a glare from the closest blue-collared mage, whose name was Thade.

"Anyone except Chloe?" Ginnn added. A nod of approval in my direction told me that Ginnn rightly though it was obvious that I knew the answer. I'd answered similar questions quite often in past lessons.

A few students tentatively raised their hands.

"Yes, Mmegg?"

"Uh, it represents ancient writing symbols," Mmegg said. Mmegg was a clever student but had to be encouraged to speak up.

"Very good. Aedda, can you tell us what the symbols are?"

"The first signifies the end of a sentence, which is odd considering that it is the start of the hex stream. And the other three are in the uppercase range. Is this an example of the TLA phenomenon?"

"Correct. It is believed that these symbols were pronounced 'elf', and..."

I struggled not to yawn. The pronunciation, origin, and meaning of the 'magic number' was of zero practical use to any hexmage. Because the number appeared at the start of every existing functional hex, there wasn't really any need to go to the trouble of memorising it. No hexmage should ever need to manually enter it into he's scryer. But Ginnn had now wasted multiple minutes involving the class in the process of explaining it. Most of the young hexmages would go home believing hall had been blessed with secret knowledge that would enhance their careers and lives. The remainder of us were probably bored out of our minds.

"Chloe?"

Oh. Ginnn had called my name, and I had failed to respond. Again. "Hmm?"

"Are you reading ahead, or did you drift off again?"

"I... Well... Sorry, what was the question?"

"What magic numbers might a hexmage working with an artistic conjurer need to know?"

The correct answer was that hexmages shouldn't need to see or consider these numbers at all. Unfortunately, that wasn't the answer Ginnn wanted. Fortunately, I knew the offcial answer. "474946383961, FFD8 and 45786966, and also 89504E470D0A1A0A are relevant for image manipulation. 4D546864 for control of musical instruments," I recited.

"Very good!" Ginnn said, as if knowing any of that made me a more useful hexmage. It didn't, in my well-considered opinion. "Now I'll explain some of the finer points of 'elf description'. In most cases, only one value is considered correct in any practical sense as all other potential values refer to hex substrates which are no longer in existence. For example, the next value must be a 3 because all known substrates have 128 fliplines and the concept of a hex spanning only 64 or 32 fliplines is not supported. Also the following value must be a 1 because all recovered hardbrain segments ever recovered have hexical ecosystems assuming only smolwayayix flipgroup arrangement."

Some of that was worth knowing about in general. Practically it all boiled down to 'put a 2 and then a 1, except you should never need to do this manually'.

I knew it would take Ginnn several minutes to get to anything nontrivial, and even then it was all material I already understood, so I let my mind drift back to a much earlier lecture that had been far more profound.

Flashback: A Further Four Months Prior

I sat at a desk in the centre of the classroom, surrounded by near strangers. This method of group learning was both unusual and familiar to me, like meeting a complete stranger I also felt I knew well. While I had regularly heard the clerics give exposition at the weekly convocation, all my deeper learning had been done alone with the help of technical books and occasional guidance from my father or a brother. Learning alongside an unruly group of students was a new experience. The convocation had been a time of solemn listening. The young hexmages interrupted with questions and comments at unpredictable intervals, and sometimes chatted and joked amongst heemselves. Maintaining my focus had required weeks of practise and still took great effort.

Before me, Ginnn He spoke with certainty and clarity about the finer points of hex construction. I listened with no certainty or clarity as to why I was in this class. On the one hand, Skids told me that I 'thought weird enough' to be a hexmage, and a set of recruitment tests seemed to indicate that I would be a good fit for this role. On the other hand, I didn't understand the point of hexmagery, and its close connection to demons made me quite uncomfortable. But the second hand didn't really count for much, especially since I was already stuck living with a demon. I might as well learn what made it tick, so to speak. That had been my logic, but so far none of the confusing streams of incantations and arcane symbols had comforted me at all.

On the wall behind Ginnn, a shifting grid of tiny lights painted lines of letters and numbers. These symbols were the components of part of the hex he was explaining. In response to he's gestures, certain clusters of symbols changed colour and were marked with arrows and explanatory labels.

"The binding phrase marked in blue, which you see repeated in these four locations, is an order to retrieve a fact from linear memory. Not a conceptual fact, but a numerical fact. The set of symbols following this binding phrase are understood numerically to be the linear distance in aethermagical memory storage to that fact. In three of those cases, the next phrase happens to be the same. I've marked those in red. That is a directive to consider the previously retrieved numeric fact and make a decision depending upon whether the value of that fact is zero. Under normal circumstances, the immediate next set of symbols would be ignored and the set of symbols after than would be interpreted and followed in the regular fashion. However, if and only if the value is zero, a radical change occurs. Under such circumstances, the following symbols are used as a redirection to change which part of the hex is considered next."

Ginnn then proceded to explain the concept again in slightly different words for anyone who didn't get it the first time. It all sounded very dry and confusing. But it wasn't. This was significant.

Though I was now counted among the mages, I had grown up as a Pure child. I had spent years memorising and reciting the Codex of Purity. Over and over, it had passages with very similar structure. 'As part of such and such a procedure, perform the following evaluations for each household in the town: consider the number of goats owned by that household. If and only if the number is zero, skip forward to page twenty-five, paragraph five. Otherwise...'

I knew the Codex like the back of my left hand: I hadn't seen it in a few months but it still felt like an integral part of me. I had trained in readiness to be a secretary to a cleric. That meant being able to follow the dictates of the Codex like a well-oiled machine. Tracing the logical flow of instructions and calculations line by line and page by page was like breathing to me. It was only natural that I would use the structure of hte Codex as a metaphor for framing my understanding of this concept of hex operation.

But it wasn't a metaphor. And it wasn't just this one concept. It was everything I had learned about hexes, and it was the same exact thing. Hexes weren't like a list of instructions to follow, with conditions saying to skip a few steps under certain circumstances. That was what they were, to the highest degree of rigorous specification. A hex was a set of precise instructions to be carried out with exact mathematic precision, but it wasn't designed to be understood or followed by a human. Hexes were for controlling demons, or more specifically for the nonliving components of demon brains that were harvested by hunting parties of casters.

I resumed staring at the coloured words on the wall behind Ginnn. The groups of letters and numbers — there were sixteen possible symbols, each one representing a quartet of fliplines — were very easy for a magical machine to read. But humans were not machines. It took a very slow process of annotation for a human to be able to read and comprehend their meaning, as they all looked like part of a formless mess of symbols at first glance. Perhaps after years of memorisation and drilling, a typical hexmage might become fluent in reading hexes, but it seemed like an inefficient use of brainpower to me. There had to be a better way.

"Chloe, are you with us?"

I belatedly realised that everyone was staring at me. "Er..."

"Am I boring you? Did you drift off again?"

Ginnn did not like it when students failed to pay attention, but he did like it a lot when students asked insightful questions. "Sorry, I was just thinking, why don't we write out hexes in a format that we can understand? Learning all these command phrases seems... well it isn't very intuitive." I hoped that made heem think I was actually engaged in the lecture.

"You are of course welcome to write down the design of your hexes in any format you wish, but you need to know how to turn that into a working hex. There's no point in knowing what operations you wish to be done if you can't specify those operations. I thought I made that clear in the first few lectures."

I saw pitying looks on the faces of my fellow students. They thought I had said something dumb. Hall thought I had displayed a lack of understanding. I felt my cheeks flushing, and was glad for not the first time that my embarrassment was easily noticed. "I mean, does it have to be that way? Demons can be hexed to follow written commands, and even spoken commands. Why not mak—"

"Those sorts of instructions are at a completely different scale. Hardbrains can perform billions of mathemetical operations in only a second. The process of recognising and responding to the description of a mathematical command would take many hundreds of such operations per actual operation. Hexes are designed to be swiftly obeyed. Hexmages are taught to overcome the difficulties and create such efficient hexes. Do you understand?"

"Well... I... But..."

"I understand that this must be very confusing to someone as new as you, but I assure you that the way we do it is the best way. You are not the first person to think about this. Now, back to the difference between these two commands, marked red and orange. The first one is a mere redirection, while the second one stores a memory of where the current command is located, so normal command flow can resume later. Now you might wonder what the point of that is. Why follow some other chunk of commands for a while and then resume where it left off? Why not include all those commands in between this one and the next one? Can anyone make a guess?"

I knew the answer immediately. The implications of the orange-marked command were actually a lot larger than Ginnn's casual tone might imply. I didn't raise my hand to answer. My mind was already elsewhere.

Ginnn was right that using a hex written in human words would be inefficient. It would take a lot more time and it would take a lot more symbols to write it down. Hexmages seemed to be content to turn their designs into compact symbolic hexes that were not meant for human understanding, by hand. I saw a better solution. If the readable design for a hex was expressed in a carefully specified rigid format, then the steps for turning it into a proper, usable hex could be exactly determined. Performing those steps would be repetitive drugery for a human, who would have to slowly read through a very long list of instructions, consult tables, and keep notes on their progress throughout the process. Or...

I smiled privately. Such a process of decoding one set of symbols and encoding them into a different set of symbols according to specific rules of mathematics and logic, that was the perfect job for a hex. To put an end to the manual writing of hexes, I would need to create an extremely complicated hex by hand.

This might take a few weeks.

Four months had passed, and I was still working on the hex-making hex.

Four minutes had passed, and Ginnn was still talking about elfs.

I switched my scryer from my lecture notes to my design notes. This time might as well go towards something productive.