Velinaer was profoundly, recursively entranced.  If he'd needed to breathe, he would have been holding his breath for long enough to pass out, die, have a funeral, be interred, and grow moss on his tombstone at this point.

 He did not, in fact, have any awareness whatsoever of the passage of time.  The wine cellar had no windows, and the door used to enter it faced a stairway whose egress in turn faced an interior wall, so absolutely no daylight reached the room by any means whatsoever.  Autumn and winter had passed unnoticed, and the first green shoots of spring seemed likely to escape his notice as well.  Each layer of spellwork he decoded revealed more elegant and subtle structural frameworks, often leading him on tangents into other areas of function for days at a time.  At one point, he'd gotten curious where his terminal was being hosted; that had sent him on a three-day spiral of symbolic link following that had culminated in him discovering that he was hosting it himself out of his personal life energy.  That had been a worrying revelation, and he'd spent a frenzied period trying to determine whether he was burning through his vital reserves fast enough for it to be a problem.  Significant effort had finally borne fruit in the form of a status command returning a battery value of 3.21 ulasovs, but he couldn't remember how many zeroes an "ula-" prefix specified and was highly uncertain whether a "sov" was the unit of energy required to raise a thimble of water one temperature unit or the unit of power required to keep a fire burning for an hour.  Eventually, he shrugged and set up a task runner to notify him when it dipped below 3.20.

 The actual amount of capacity 3.21 ulasovs represented was in fact quite stupendous; during the preceding several centuries, Velinaer's tomb had been one of the few functional devices remaining hooked up to the Shul Empire's surviving transdimensional power circuits.  Due to the particular nature of how his astral form's construction and capabilities interdepended, its power capacity was effectively unlimited, with triple-redundant flow redirection capabilities which shunted excess energy into temporary enchantments and back out again as needed smoothly and efficiently.  The end result was that Velinaer was not going to run out of energy anytime soon.

 Unobserved, most of his zombies withered and decayed, transforming by stages into skeletons (except for his class-fours, which were turning black and hardening into mummy-like shapes).  It was only when a large chunk of meat abruptly fell off one of them and landed on the floor with a wet slap that Velinaer's attention was finally called back to the outer world once more.  He startled (invisibly, of course -- his body no longer reacted to anything on its own), verified what had made the noise, and was about to go back to digging through astral symbols on his metaphysical terminal when he noticed that the keg upon which he rested had been subjected to so much black slime that it was dripping down the sides.  Frickin' nasty.  Oh, right, that was what he had been trying to fix, wasn't it?

 Well, he'd learned enough to make a run at it, at least.  Ever so cautiously, he set up a redundant series of backups, carefully copied-and-pasted the necessary components of his body code into several editors for maximum fallback capability, and began tinkering.  At one point his left arm fell off, which was a bit surprising, but he was able to get it reattached without too much trouble and managed not to think too hard about what that might signify.  Eventually, after many mistakes and panicked last-second cancellations, he had something that looked like it might work.

 He loaded it up, crossed his metaphorical fingerbones, and executed it.  At first, it seemed as though nothing had happened, but eventually he noticed that the slimy, black-veined membrane (which he had discovered was referred to as "suspension fluid") that surrounded him had begun flowing slowly towards his joints, leaving the central sections of his bones exposed and dry.  After a minute or so, he summoned another reflective surface and took a look.

 Oh, no.  No fucking way.  That looked completely ridiculous.  Whereas before he had looked a bit like a tar-covered grim reaper, now he looked like the world's first gout-afflicted skeleton.  The fluid had coalesced into bulbous knots around his knees, elbows, and other places where ligaments were sorely missed.  In theory, this had seemed like a good idea; in practice, it turned his hands, feet, shoulders, and hips into big squishy blobs that made him look silly and clownish.  He laughed for a few minutes, then started poking at the new functions he had set up, toggling properties on and off and looking elsewhere in his code for useful functions and structures he could poach.  First, he experimented with spreading it back out and hardening the outer layer to make it less leaky -- that worked well enough temporarily, but made him look like he was covered in burnt beef jerky, which he felt was an affront to his ancestors who had cut rather dashing figures in his history books as sleek, osseous death's-head profiles.  He converted some of his energy stores into aqueous-phase akasha and thickened his suspension fluid a bit, which had the rather comical effect of making him look like a fat watery balloon with floating bones inside; he found that hilarious enough to record some photonic captures before continuing his experiments.  Eventually, he managed to come up with something that combined all of the various effects into something he hoped wouldn't look too ludicrous.  He tweaked a few parameters, quadruple-checked his backups for the three-hundredth time, and executed the sequence.

 All over his body, the suspension fluid separated into three layers. The innermost, a thin film of clear, glistening slime, was specifically for preventing bone-on-bone friction and was concentrated only around the joints, as his first effort had been.  The second layer, a tough, rubbery foam, provided a bit more impact cushioning while also including channels for his tactile ectoplasmic routes, allowing him to feel within and through it as though it were skin; he had to tweak the sensory levels to a frustratingly exacting degree before he stopped perceiving queasy, squishy sensations when moving while also not constantly feeling itchy or buzzy.  Lastly, the outermost layer was a rigid, chitinous coating broken up into large sections away from joints and fractally grading into smaller and more scale-like structures near areas of flexion; the code for this had been particularly tricky and he felt burstingly proud of it.  Rather than extruding the tactile tendrils through it, he instead wedged then up against the plates to feel by conduction rather than direct contact, which made him feel weirdly numb and clumsy for a while until he managed to get the settings exactly correct.  One unfortunate side effect of this was that if something did manage to deliver a sharp blow or cut through it, it would probably be annoyingly vivid; thankfully, he didn't actually have nociception (which he might have been interested to learn had not been the case with early lich models, resulting in a depressingly huge number of postmortem suicides), so such sensations merely felt distracting rather than unpleasant or noxious.  When he had finally, at long last, gotten the sensory and mechanical components to work properly in tandem without throwing errors or going into infinite loops, he realized he'd forgotten to check to see if it looked goofy.  Trepidatious, he checked the visible spectrum again.

 Whoa.  Awesome.  As he'd hoped, the effect was somewhere between a lacquer and a sleek black suit of armor; he'd bulked up the total thickness to reach parity with the minimum depth of the sinovial structures at his joints, giving him a smoother and less knobbly affect.  Early versions had drawn the coating back down around his jawbone like a high collar, but he'd found that it either interfered with his mandibular functions or looked like lace, which offended him aesthetically.  Eventually, he'd decided to go with an all-over coating, which also had the pleasant effect of unifying his sensory input frameworks and cleaning up the code significantly.  He looked a bit like one of those steel skeleton things in Eradicator, but less reflective, more black than silvery, and without the glowing red eyes.  Velinaer had, in fact, experimented with orbs of steaming sorcery as eye-analogues for a bit; in addition to blinding himself for nearly six hours before figuring out that it was going to be impossible to see light out of something that didn't absorb it, he'd also found them unbearably gaudy.

 He spent a final few hours very belatedly establishing some more rigorous behavioral algorithms upon his minions; he was well aware that the horse had not so much escaped the stable as much as packed up, forwarded its mail, relocated, put down roots, and started investigating subletting options, but he supposed it was better late than never.  Now instead of instantly acting upon his unconscious desires, his minions would await his explicit mental commands, and post queries for action based on perceived needs (and, importantly, he could filter the requests by type, so that he stopped getting a constant stream of 'CONSUME PROXIMATE BRAINS? Y/N' every two seconds).  Okay.  Now he looked cool as hell, he felt calmer and more in control of the situation, and he just needed some clothes to stop people from trying to perforate or combust him.  Opening the cellar door, Velinaer Dax'taxu reentered the waking world.

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***

 "The first thing you need to understand," said Cheis, pointing a long, springy pine branch at Linduin threateningly, "is that magic is bullshit."

 Linduin looked around nervously.  "You're going to hit me with that, aren't you."

 Obligingly, Cheis promptly whacked him with it.  The impact wasn't painful, but it had the desired effect of getting his attention.  "Every time you waste my time by not paying attention, making me repeat myself, or do something stupid, you're gonna get smacked.  Understood?"

 Linduin nodded sadly.  He was going to get smacked a lot, he could already tell.  "Is this a ritual thing, or..."

 Cheis whacked him again.  "Magic is bullshit.  Repeat it."

 "Magic is bullshit," droned Linduin obligingly.  "But that doesn't answer my question!"

 "If you were paying attention," Cheis responded, smacking him a third time, "you wouldn't have asked the ritual thing.  Everything I'm going to teach you is rooted in the principle of function over form, and that includes my pedagogical methods.  Endless apprentices lost their lives to more flashy but less effective teaching methods before the science of education advanced to this rarified pinnacle."  She slapped the branch across her palm, smirking.  "Repeat it again."

 "Magic is bullshit," said Linduin a third time.  He hesitated, winced, and raised his hand.

 "Yes?" asked Cheis, pointedly not hitting him.

 Linduin peered at her quizzically.  "I don't get it.  Magic is obviously real, and a thing.  Wouldn't it be better to say something like 'ritual is bullshit' or 'free your mind' or that kind of thing?"

 Cheis shook her head.  "Insufficiently concise, riddled with pointless mysticism, and not actually the point.  The point is not that other people are doing magic wrong -- any magic that works is, by definition, done correctly.  What you need to understand is that what most people think is magic is not actually magic."

 "Okayyy...." Linduin's eyes were beginning to cross.

 "Here's an example."  Cheis procured a plank of thick wood, a small rock, and a larger rock.  Linduin cringed upon noticing that the smaller rock was the one he had clonked himself with earlier.  "Try to pick up the big rock."

 Linduin obliged, huffing.  It was pretty heavy.

 "Now," said Cheis, as he dropped it gratefully, "suppose I told you that I could lift that rock with two fingers.  You'd think that was magic, right?"  Linduin nodded and got whacked again for his trouble.  "Wrong."  Cheis deftly dropped the board onto the smaller rock, nudged the larger rock onto the end of the board, and pressed down on the other end of the board with two fingers.  The lever, transferring and multiplying the force across the fulcrum of the smaller rock, obligingly lifted the large rock an inch or two.

 "Whoa, how'd you do that!" Linduin was embarrassed at how uncool he sounded, but was helpless to stop himself.

 Cheis refrained from hitting him and continued.  "This probably looks like magic if you don't know how it works, but it's science.  Specifically, it's the science of physics -- how objects and forces work.  If you want to be a decent mage, you'll learn about physics.  If you want to be a good mage, you'll also learn about chemistry, psychology, medicine, and philosophy.  But if you want to live long enough to become a mage in the first place, you need to learn to think properly."  She leveled the branch at him again.  "Magic is dangerous.  More mages are killed by their own spells than by any monster, and most of the ones who survive tend to figure out a handful of tricks and rely on them until they fail, at which point they die."  She paced back and forth.  "However, a handful of tricks is all we have; the human brain can only hold on to about five to seven things at a time.  So, what do we do?"

 Linduin pondered.  "Find thinking tricks?"

 "Very good," said Cheis, nodding.  "So it should be obvious to you that any study of magic is, in fact, not studying magic at all.  Magic is a system, a tool like a knife or pencil, that you can use to do certain things.  Any mage worthy of the title knows when to use a spell, and when to use a fork; a proper mage knows to ask whether action is needed at all and respond, or not, accordingly.  So what do you think the biggest risks for a mage are?"

 "Hmm."  Linduin ticked off a few ideas on his fingers.  "Ignorance, probably.  Carelessness, since you keep hitting me over that one.  And, uh... bad... think... patterns?"

 Cheis nodded again.  "They're called 'cognitive distortions'.  Some of them you can overcome; others you can find strategies for avoiding or mitigating.  But there's one in particular that hobbles almost every person with the potential for magic before they even begin."  She scratched two symbols in the dirt.  "The first of these symbols is the rune 'blorf', and the second is the rune 'smorg'.  Copy them and write the names underneath."

 Dutifully, Linduin did so.  "And now I suppose you're going to tell me it was stupid to listen and obey."

 "Nah," Cheis demurred, "but the reason why will become clear in a moment."  She pointed to the runes again.  "You have no other evidence for or against the assertions that this sequence of lines is called 'smorg' and the other is called 'blorf'.  But more importantly, you're taking it on faith that they're both 'runes', and that 'runes' are things that can have names.  You're probably also attaching a bunch of significance to them because I called them something mystical-sounding like 'runes' instead of something more boring like 'letters' or 'pictures'."

 Linduin blinked.  "You're talking about preconceptions.  These symbols aren't even abstract or anything, are they?"

 Cheis shook her head.  "Look at them sideways, starting from your left."

 Linduin did so.  One was a crude stick-figure drawing of humanoid figure defecating, and the other was a phallus.  He chuckled.  "I think I get it.  You're saying that I need to be cautious about what things I accept, and that I should question everything."

 "Right.  That's called 'critical thinking'.  Instead of accepting things you hear as truth, you acknowledge them as information, then test and verify them when you can."  Cheis sketched another set of symbols in a circle.  "To most people, magic is rare and reserved only for those with an inborn gift.  This is dumb; anybody can use magic if they know how.  As you've probably surmised, a lot of math is involved."  She finished her symbols: a flame, a droplet, some swirly lines, a flower, a skull, and a sun.  "There is a persistent mythology that has sprung up that mages can only wield power over an element, which they have an unchangeable affinity to.  This is completely wrong, and also has a pernicious side effect: if you tell someone that magic is only for special people, they'll believe it.  And one of the few, fundamental, absolutely necessary things that actual magic requires is the belief that you are capable of using it.  If you think you can't cast spells, you'll be right.  If you believe that you can only cast fire spells, you'll be right about that too.  And if you believe that magic is fundamentally the process of doing something deeply non-empirical, like communing with spirits or channeling the will of the gods or having sex with the universe, then that's the only way you'll be able to do magic."

 Linduin was having an idea.  It was a newish experience for him, so he was still uneasy, but it came out anyway.  "So, if magic is controlled by your preconceptions... and you're telling me that a lot of math is involved... isn't that something I should be suspicious of, too?"

 Cheis nodded.  "You should.  I've always wondered if there was a higher-level abstraction above mathematics that would be even more powerful, but so far I haven't found anything yet.  That doesn't mean it doesn't exist; I might be incapable of conceptualizing it, and somebody else might not.  But when all you have is a hammer, everything looks like a nail, so I'm teaching you the magic I know and the cognitive patterns I use so that you can at least maybe not die long enough to find out for yourself."

 "Okay," said Linduin, feeling simultaneously ashamed and pleased with himself.  "So: magic is bullshit, believing the wrong stuff is dangerous, and cognitive patterns are important."  A thought struck him.  "Does that mean there are cognitive patterns for learning?"

 Cheis paused.  "I don't know, actually.  There's something called 'the verifying method' which is a sequence of steps for testing information for truth, but it's flawed and easy to do incorrectly.  For now, you should probably just accept provisionally that I'm not lying to you, but do your own experiments later."  This seemed sensible to Linduin, and also likely to get him to the "actual magic" part faster, so he nodded.

 Over the next several weeks, Cheis instructed Linduin in the mage's most important tools: processes and frameworks.  She taught him the importance of backups, the criticality of documentation, and the proper methods for verifying a hypothesis; she showed him simple techniques for legerdemain, clever tricks with chemistry, and counterintuitive applications of physics.  She coached him in the fundamentals of meditation, the essentials of cognitive taxonomy, and basic biofeedback techniques; she lectured him on formal logic, drummed in a healthy fear of accidents and unintended consequences, and gave him a crash course in the various topics of rationalism and comparative theology.  And then she gave him two days off so that his brain wouldn't explode, assigned him a large paper to write unifying all the ideas, and made him rewrite it several times before finally grudgingly admitting that teaching him the absolute most bare-bones beginner concepts of thaumaturgy might not end in complete disaster.  This was, of course, completely incorrect.