His family’s ancestral dungeons were every bit as welcoming and hospitable as Fabian remembered. Which is to say, they weren’t. The tiny cell was damp and mostly empty, with a few pitiful pieces of ancient straw for bedding. It was also chokingly pungent, thanks in large measure to a chamber pot in one corner that probably hadn’t been emptied since Fabian had last graced these apartments.
The dungeons were as hospitable as he remembered
He sat in the gloom and tried to be grateful for the flickering torch in the corridor, and for the small barred window that let the meager light into his cell. He tried to be grateful that his brother hadn’t just executed him on the spot.
He tried—not very successfully—to be grateful for the limp, battered twig he held in his hand. It was the same twig that Basil had given him just a few hours earlier, and his master’s advice still echoed in his ears.
Just picture it in your head, and when you start sketching, believe.
“Just like that,” Fabian said softly. He shook his head. He’d been trying to get the illusion spell to work almost since the moment they locked him in this cell, and he was no closer now than he was an hour ago. He was obviously missing something, still. There was something fundamental that he wasn’t understanding.
He was reminded of something his father had liked to say whenever a particularly thorny problem tripped him up. It might be the family accounts, or a dispute between two villagers who’d come looking for mediation. It really didn’t matter. He’d stand there, scratching his head, considering, and then he’d shrug and say, “Well, Fabian, that’s cows for you.”
Fabian had never really understood that, either.
Footsteps suddenly sounded in the hall, faint, but growing louder. Guards? Or even Fergus himself? Fabian’s stomach went into crisis mode and decided that ‘nausea’ was absolutely the best bet for survival just now. He was terrified of his brother—more so since seeing him today than ever before. He had no idea why that little prank of his—done years ago, and more out of cowardice than any real malicious intent—would have so angered Fergus, but it definitely had. Even now, his brother still seemed murderous.
He wondered if he’d leave these dungeons alive. At this point, he decided he’d even settle for mostly alive.
The footsteps grew closer. Louder. There were at least two people coming, he realized. They seemed to be moving deliberately. Fergus, with a guard? Or would Fergus even bother to come down here himself? Maybe whoever it was, was down here for something else entirely. Maybe they’d just walk on by his cell, unaware of this tortured soul mere feet from their carefree smiles. Maybe—
The footsteps stopped just outside his door, and Fabian’s heart sank. A mumbled word, a jingling of keys, and then the door squealed open slightly, swinging outward.
“Thank you, Captain,” said a familiar voice. “I’ll just pop in and give the, ah, prisoner his food. I’ll call for you when I’m done, then, shall I?”
A brief hesitation. “Of course, Doctor. I’ll be down the hall, in the guardroom. If you call, I’ll hear you.”
The door squealed loudly again as it was pulled open further, and there, silhouetted against the flickering torchlight, was Basil Smockwhitener, holding a tray in one hand.
‘I’ll just pop in and give the prisoner his food.’
“Sir!” Fabian gasped in relief. “What—what are you doing here?”
“Bringing you dinner, you UNGRATEFUL MISCREANT.” The insult was oddly emphasized.
Fabian flinched. “Sir? What—?”
“I’LL ASK THE QUESTIONS,” Basil boomed again, head turned as if shouting down the hall. “IT’S MORE THAN YOU DESERVE…BUT…but…” He paused, still staring down the hall, and then turned to face Fabian. “There, the Captain’s gone.”
“Sir?”
“Had to make the fellow think I was here to scold you,” Basil said. “It was all I could think of to get down here. And, I say,” he added, wrinkling his nose and eyeing the chamber pot in the corner. “That is a remarkably zesty bouquet.” He paused, sampling the air. “Hmm! Yes. It has some bite.”
Fabian could only gape.
“Anyway,” Basil said, setting the tray down carefully in front of Fabian and joining him on the floor. “I got what I could from the kitchens after dining with your brother, but it’s not much, I’m afraid. Leftover meatloaf, mostly.” He paused, stroking his mustaches thoughtfully. “Seems terribly inhospitable to serve meatloaf to guests, but I suspect Fergus might be making a statement.”
“I—thank you,” Fabian finally managed. He eyed the tray curiously. “And actually, sir, meatloaf was always kind of a staple at our table. The cook’s repertoire was…limited.”
“Really? Yet you kept him on?”
“He did make an exquisite meatloaf.”
Basil nodded in understanding, and suddenly spied the twig in Fabian’s hands. He smiled and gestured to the stick. “Ah!” he said. “You’ve been practicing, I see! Very good. How’s it coming?”
Fabian shrugged, dropping the stick on the ground in front of him. “It’s not. I’ve been trying that illusion spell ever since Fergus threw me down here. It’s hopeless, sir. I… I can’t do it.”
Basil raised an eyebrow. “I see.” He stroked his mustaches and nodded thoughtfully. “Well. I’ll admit, I don’t know everything. Not yet, at least. Still learning, you know, every day. But do you know what, Fabian? The more I learn, the more I’m convinced that there is nothing that can’t be learned.”
“But sir—”
“Yes, yes, I know,” Basil said, gesturing impatiently. “You’ve tried and you’ve tried, and it isn’t working. How very tragic for you. How soul-crushingly disappointing. My heart, it is bleeding profusely for you.” He shook his head, setting his enormous mustaches waving. “Bah! Shall I tell you something truly tragic?”
Fabian hesitated, debating whether to protest again or not. He decided the opportunity had passed. “What, sir?”
“People who tell themselves that they can’t,” Basil said. “That is tragic, because then they generally try so hard to prove themselves right. All that effort, wasted.”
“But sir,” Fabian said, hurt. “I was trying. I’ve been trying almost non-stop for hours, and haven’t made any progress at all!” He hung his head, disgusted. “You’re just wrong about me, sir. Not everyone is cut out to be a wizard.”
Basil didn’t respond. After some moments, Fabian hesitantly raised his head to see what was causing the silence and found Basil staring back at him, stroking his mustaches, brows drawn down in stern concentration.
When the wizard finally spoke, it was in a dangerously soft voice that Fabian had seldom heard before.
“You’ve been my manservant for several years now, yes?”
Fabian eyed his master uncertainly. “Yes, sir.”
“But my apprentice, now… You’ve only been my apprentice for—what? Eight hours, maybe?”
“Something like that.” Fabian shrugged uncomfortably. “Feels like years.”
“Eight hours,” Basil insisted. “Eight. Hours. And in that span you have come to be able to see the situation clearly enough to decide what you are capable of?”
Fabian only cast his gaze downward and sighed, shaking his head in exasperation.
Basil pursed his lips for a moment. “I usually prefer to wait more than eight hours before I introduce the Second Great Secret of Wizardry, but it seems particularly germane just now.”
Fabian shrugged. “I don’t know that I got all that much from the First Secret, sir.”
An odd intensity entered Basil’s voice as it dropped almost to a whisper. He wielded the sound like a dirk, pointing it tip-first at Fabian and thrusting. His eyes were cavernous in the dim light. “The Second Great Secret is a contradiction,” he said, “somewhat like the first secret, in fact. It’s this: Nothing is merely what you think it is.”
Fabian raised an eyebrow, trying hard to not be impressed by his master’s change of countenance. “I’m telling you, sir—”
“It has many corollaries,” Basil continued, just as intensely. “Here’s one of them. You are more than what you think you are.”
Fabian paused a moment, hoping for some clarification, but none was forthcoming. “I—” he said. “That…makes absolutely no sense, sir. I’m sorry.”
“On the contrary,” Basil said, sitting back and sounding suddenly weary. “It makes a great deal of sense. But you have to be willing to look for it. Just like anything. How willing are you to learn that illusion spell, Fabian? Willing enough to work at it for days and days and days? Willing enough to endure hours of practice without visible improvement? Or will you just give up?”
Fabian shook his head. “No offense, sir, but you don’t understand.”
“Don’t I?” Basil said. “I think, Fabian, that it is you who does not understand. You don’t understand how powerful you are. You can learn anything. Anything at all. But you have to be willing to balance the scale with effort.”
Fabian made no response.
“Anyway,” Basil said. “Something to think about, I guess.” He sighed, grimacing at the smell, and looked around the cell. His gaze settled on the wall beside the door, and he raised an eyebrow. “What’s this?” he asked, gesturing at the wall.
Fabian glanced up. “Oh,” he said. “Just…something I tinkered on while taking a break from practicing that spell.”
Basil got up and walked to the wall. He ran his fingers over the joints where the mortar held the bricks together. Beginning near the floor, some of the joints had been recently cleaned, dirt and grime painstakingly prised out, resulting in a kind of branching path that moved vertically up the wall.
“It’s a tree, isn’t it?” Basil asked, considering. “You made this?”
Fabian nodded. “Yes, sir. It was just something to take my mind off my frustration. And the cracks reminded me of trees, somehow.”
‘It’s a tree, isn’t it?’
Basil smiled. “And well they should, Fabian! You’ve stumbled onto a fundamental principle of mazes, here. Look.” He pointed at a junction where the mortar joint branched into three different directions. “You’ve got an intersection here, haven’t you? You could follow the path any of those three ways.” He stepped back and gestured to the tree as a whole. “And see, there is only a single path that goes from any point in that tree, to any other.”
Fabian smiled crookedly. “Yes, sir, you’re right. It’s—what did you call it? It’s a ‘perfect’ maze, isn’t it?”
Basil pointed at Fabian and smiled broadly. “Exactly so! As a matter of fact, a ‘tree’ is another name for these ‘perfect’ mazes. What you have here—this tree you’ve constructed—is simply another way to represent a maze.”
Fabian scratched his chin thoughtfully. “But sir,” he said. “It’s not a very good maze, is it? I mean, it all kind of goes the same direction, doesn’t it? Bottom to top?”
“That’s a good observation,” Basil said, nodding. “However, given any perfect maze, you can convert it into this kind of representation easily, and non-destructively. They’re the same thing.” Basil paused and stroked his mustaches. “But maybe I should back up a bit, first.”
He pointed to one of the junctions where multiple bricks met. “Some vocabulary, then. Let’s call this a ‘vertex’, shall we?”
“‘Vortex’? Sounds…ominous.” Fabian scooted a few nervous inches farther from the wall.
“No, no, no. Vertex. A point where two or more line segments intersect. Sometimes it’s also called a ‘node’. It’s just a location in our maze. A place.” He tapped the junction again. “Fair enough? I’m just giving it a label. ‘Vertex.’”
Fabian nodded. “Yes, sir.”
Basil pointed at the mortar joints that connected to the junction he’d indicated. “These paths,” he said. “They run along the edges of the bricks, so let’s just call them ‘edges’. They are simply paths that link two locations—nodes, or vertices—in our maze. Right?”
Fabian nodded again. “Vertices and edges. Yes, sir.”
Basil rubbed his hands together and blew out his mustaches. “Excellent. Now, true, or false? In a perfect maze, every vertex must be connected by at least one edge.”
Fabian thought a moment, and then nodded. “True, sir. Because you’ve already said that a perfect maze has exactly one path between any two locations. Or vertices, I suppose. Thus, there must be a path leading to every vertex.”
“Precisely. Now, imagine a maze where one of the paths—one of these edges, as I’ve called them—gets removed. Maybe a hedge topples over and blocks the path. Or a tunnel caves in.” Basil reached over and hid one of the mortar joints with his hand. “Is it still a maze?”
Fabian considered. “Well, parts of it are, right? Removing that edge kind of split the maze into two separate—and smaller—mazes.”
“Yes, that’s it,” Basil said. “We no longer have a single maze. Instead, we have two. Two mazes—two trees.”
“Practically a forest,” said Fabian with a grin.
“Well, yes, actually,” Basil said. “That’s actually the proper term for what we’d have: a forest. And if you split those trees further, you’d have more trees in your forest. But does our forest grow any bigger as we divide our mazes?”
Fabian thought a moment. “Well, there are more trees, but we aren’t really adding any new vertices to it. I suspect you’re wanting me to say ‘no’, sir.”
“Very good, Fabian. Right. Our forest is increasing in trees, but the trees are growing smaller. The number of vertices is constant, because it is limited by the underlying graph.” He gestured at the wall as a whole. “A graph is simply a collection of vertices and edges, with no particular rules about how they are connected. Or, for that matter, not connected! A single graph can contain multiple trees, or one tree, or no trees at all.”
Fabian was nodding, so Basil went on. “Now, if a single graph happens to contain a single tree that includes all of the graph’s vertices—if you were to make this entire wall a tree, for instance—you’d have what is called a spanning tree. A tree that spans the entire graph. Do you understand?”
Fabian nodded. “Yes, sir. That makes sense.”
“So, when I talk about mazes, what I’m generally referring to are these spanning trees. Graphs that contain no cycles, and where every vertex is connected. Your tree here”—he gestured to the wall—“is not a spanning tree, because it doesn’t incorporate the entire graph, or wall, but it is still a tree. Got it?”
Fabian nodded again. “I understand, sir.”
“Excellent. Excellent! Now, back to what I was saying before, about your tree being the same as a maze, and vice versa. Can you imagine a way to preserve all the connections in your tree, but move the vertices around? To change its shape, without changing how each vertex is connected to its neighbors?”
Fabian thought for a moment, and then smiled. “I think so, sir. Yes. Here.” He stood up and walked over to the wall, where he pointed at one of the junctions. “If this intersection were to bend down instead of up, this whole branch would follow suit.” He gestured at one half of his tree.
“Very good, Fabian. Very good. Yes, that’s the idea. Now, I’m going to show you a little trick.” He pulled his pencil from his lab coat and held it above one of the junctions. “Watch this.”
Fabian, for once, forgot to be nervous about the pencil, and looked eagerly at what his master was doing. Basil tapped the bottom-most vertex of the tree on the wall, and then dragged it up. The rest of the tree followed, changing shape as vertices and edges were pulled along messily behind like a sheet being dragged over the ground. Basil finally lifted the pencil. “Voilà!” he said, gesturing.
The tree was now most definitely a maze, complete with twists and turns and dead-ends.“Watch, again,” Basil said, grinning, and once again tapped a vertex in the maze and dragged it back down the bottom. Fabian watched closely, noting how every vertex remained attached to its same neighbors, even as the entire maze seemed to reshape itself back into a tree. “Just like that! From tree, to maze, and back again. They’re the same thing!”
Tap the “switch” button to convert between tree and maze!
Tap a vertex to change the selection.
Tap the selected vertex in “maze view” to change the root.
Darker squares are further from the “root” than lighter squares.
Fabian grinned, too. “Yes, sir! I see it, now!”
For a moment, they both stood and grinned at the wall, until Fabian’s face suddenly crumpled. He sat down, his back to the tree pattern on the wall. “But it’s useless to me here, sir. Fergus is probably planning to have my head soon, anyway.”
Basil considered his servant for a moment in silence, before seating himself next to Fabian. “I think,” he said gently, “that it is time for you to tell me what happened between you and your brother.”
Fabian glanced over at the wizard. “Fergus didn’t tell you?”
“Well,” Basil said, stroking his mustaches. “He hinted at things. Apparently, you ‘meddled’. And at dinner, Lady Curmudgeon suggested that this whole ‘mess’ is your fault, somehow. But—”
“Wait.” Fabian sounded surprised. “Did you say, ‘Lady Curmudgeon’?”
“Er, yes,” Basil said. “Your brother’s wife. You…you didn’t know?”
Fabian shook his head in amazement. “No, I’d not heard anything about it! When did this happen?”
Basil scratched his chin. “Hmmm. I think he said it was about five years ago?”
Fabian gasped and slapped himself on the forehead. “Five years? Five years!?” He looked like he’d been punched in the stomach. “I— Zounds. It kind of makes sense, now. I—I must have nearly ruined it. No wonder…!”
Basil looked on, bemused. “Would you mind sharing your little epiphany with me?”
Fabian exhaled noisily and ran a hand through his tousled hair. He finally nodded. “It was about five years ago. You remember Anathema, that woman from the village that I was so smitten with?”
“Ah, yes,” Basil nodded. “‘She who must not be named.’”
Fabian rolled his eyes. “Very good, sir. That never gets old.” He shook his head. “Anyway, I was trying to find some way to get her attention. I spent a lot of time with her, even went dancing”—Fabian blushed furiously at the memory—“but I wanted to do something really memorable, so I, um…I kind of borrowed Fergus' thesaurus and wrote a love note to her.”
“And he got upset about that?”
“Well, it was his best thesaurus. And, well…I also kind of signed the letter in his name.”
“I kind of signed the letter in his name.”
“What? Why on earth would you do that?”
Fabian shook his head. “I know. I know! It makes no sense, now, but after writing the letter, I got panicky. I was a few years younger than she was. What if she thought it was presumptuous? What if she didn’t like it? What if…what if she laughed? So in a moment of weakness I signed it with Fergus' name, figuring it would be good for a laugh if nothing else, and sent it off.”
Basil nodded. “Well, yes. Love makes us all a bit dotty at the best of times. So you signed this love note as your brother. What then?”
“Well, the next thing I know, Anathema shows up at the door, asking to speak to Fergus, and suddenly I’m being thrown into the dungeon! Fergus wouldn’t speak to me. He barely fed me! I was down there for two or three weeks before the captain of the guard took pity on me and helped me escape. Only, I couldn’t just escape, could I? Because suddenly there were all these mazes, now, where the pastures used to be. I wandered for another few days trying to find my way out. And once I got out, I just wandered town to town doing what I could to find food and shelter—”
“And making the good people of a certain village quite angry with you in the process, as I recall.”
Fabian shrugged uneasily. “Well, yes, you know the rest of the story. But don’t you see? Fergus must have been secretly engaged to someone else, and this whole thing with Anathema must have threatened it all! No wonder he was so angry with me. I nearly ruined everything.”
Basil sighed and shook his head. “Fabian, Fabian, Fabian. You poor fool. Why didn’t you ever just tell me this? Why let me believe you were just a wandering vagabond?”
Fabian shrugged again. “Would you have taken me as your manservant if you’d known who I really was? A noble? In name, if not in deed.”
It was Basil’s turn to shrug. “Maybe not. And maybe I’d have tried to send you home—”
“Which would have been a death sentence, as you can see,” Fabian said, gesturing at his accommodations.
“Yes, well. I was going to say, though, that while being a wizard’s manservant is probably beneath you, being a wizard’s apprentice is generally considered quite acceptable, even for blue bloods like yourself. We could have made it work.”
Fabian sighed. “Yes, you’re probably right. But I was so afraid…”
Basil nodded and patted Fabian on the shoulder. He straightened up and cleared his throat. “Well, there’s no shame in being afraid. It’s only what fear can make us do, that we ought to beware of. So, learn from the past, and let’s move on.”
“Move on?” Fabian asked, incredulously. “I’m in a dungeon cell. Where do I go from here?”
“Out!” Basil said heartily. “‘Nothing is merely what you think it is’, remember? It’s mostly up to you, but if you’re interested, I’ve got a plan…”
