He swung down from the bottom branch. "Hi, I'm Nathaniel," he said, reaching out to shake their hands.

  "Harrumph," said one. "Our math-doubter is named Nathaniel, Tick. Not Nate or Nat or Nathan. No, three syllables. Ain't that fancy."

  "That means Nathaniel might slip on a banana peel, Tock."

  "But not if we change his name to Nate, then it would be Nate the Great."

  "Which do you prefer? A banana peel or greatness?"

  "How about a great banana peel?" Nathaniel replied.

  "That doesn't make sense, you can't convert that. We'll have to take the length of his name into account in our calculations. Let's see..." he counted on his fingers, "nine letters."

  Tock threw his hands in the air. "Nine letters? That's an odd number! That messes up everything!"

  "So it does," Tick said.

  "You would think his name would be three letters or six, but nine?"

  "How is that a possible conversion?"

  "Forget his name, how about his hair?"

  "That would take too long and be unfair."

  "Um... sorry." Nathaniel interrupted.

  "Eh, not your fault." As if noticing Nathaniel’s hand for the first time, they reached out to shake it... simultaneously. "We're the McReady brothers," Tick said.

  Nathaniel saw that they were indeed twins; they stood a little shorter than him, and appeared to be about the same age. He immediately liked them. "So, where do you two come from?" he asked.

  "We're from the Northern Country, at the foothills of the mountains," Tock said. "We normally don't travel this far south, but since the map has been expanded, we decided to come take a look for ourselves — to see if we can make a conversion."

  "A conversion?"

  "Sure, why not? We can convert anything to seconds or minutes or hours, but mostly we like converting things to seconds. Go ahead, name something," said Tick.

  "Name something? Like what?" Nathaniel looked around for something cool to convert. "Oh — can you convert my backpack?"

  Tock replied, "You just have one backpack with what looks like four pockets. If we knew what was inside we could convert it, but we're not going to. We don't convert backpacks."

  "But you just said…"

  "We can convert anything we want and nothing we don't — at least, I don't. Do you, Tock?"

  "It's a trick conversion anyway. You have one backpack with four pockets so the obvious answer is 1,500 seconds for the backpack alone, but what we don't know is how much stuff you have in the backpack. There could be anything in there, even backtime items. Until we know the contents and can get an exact count, it would only be speculation, and we Clockmaticians don't speculate. At least, I don't. Do you, Tick?"

  "Not once in my life. Yes, the obvious answer is 1,500, but without knowing what's in the pack, we would be unable to give the precise conversion."

  "How in the world did you get 1,500 seconds from my backpack?"

  "Well, you do know you can take any given number except the number one — "

  "Or zero," Tock interrupted.

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  " — and multiply it with any other number except the number one, and the total will be greater than the total you started with?"

  "Huh?"

  "You have one backpack and four pockets which makes five, multiply that by three hundred, and you have 1,500 seconds just like we said. There would be no use in multiplying each pocket by the number of backpacks you have, which is one times four, which is still four, or one if you multiply them individually so you have to add them together, not multiply them, and only then can you multiply that by three hundred, so like I said, the obvious answer is and always will be 1,500," Tock concluded.

  And then the two just went on and on with their numerical gibberish like Nathaniel wasn't even standing there. As he listened to them talk, he realized they were both filled with truckloads of cow manure. Their conversations were completely ridiculous in nature, filled with pointless jargon and pointless mathematics. Everything was weighted down with meaningless information, interrupted by spontaneous laughter that could break out on any given equation. This drew Nathaniel into the living Inkworld in a whole new way — a hidden new world filled with interesting characters, even if their "clockematics" were conversations centered on the circles of time and making conversions.

  After a dreary discussion dealing with derivatives and debating decimals, during which they descended into a discourse of diabolical deductions, which disclosed the determination of both delinquents and their detailed distractions about fractions and abstractions and how it related to decoding long division, Nathaniel became desperately despondent and decided to discontinue the dissonance he was discerning by declaring above their dissension: "Hey guys, have you seen any black birds flying around?"

  "Black birds?" Tock tapped his chin. "Half the birds in the world are black. The rest are white or gray. Any ideas, Tick?"

  "Maybe he means the ones with all the eyes, Tock."

  "Oh, those dumb things… they come from the Dark World, shudder, a place with no time or clocks, let alone any conversions. Shudder."

  "What do you know about the Dark World, Tock?" asked Tick. "You've never been there." Tick turned toward Nathaniel. "He's always talking about the Dark World, and how there's no time or space in there. Always throws in a shudder or two for effect. I don't know where he even gets his information, because we spend all our time together."

  "What is the Dark World?" Nathaniel asked.

  "There is no Dark World…" said Tick, rolling his eyes.

  "Is too!" Tock shot back.

  "Is not!"

  "There is. I should know, I've been there."

  "No you haven't."

  "Okay, well, if I had, I know it would be dark. Convert that!" Tick shut up and shook his head.

  Clearly, "covert that" meant "shut up, this conversation is over" in McReady language. As Nathaniel learned later, it meant several other things too, depending on the context and the way it was said. He could see the twins had a unique relationship and an interesting way of speaking to one another.

  "So those nasty black birds with the eyes — do they really come from a Dark World?" Nathaniel asked.

  "Heck, no one really knows, Nate. Can I call you Nate? There are only rumors about that, and as Clockmaticians, we do not speculate, we only calculate, never to deviate or insinuate what is or isn't and what can convert and what cannot." Tick glowered at his brother. "Or at least that's how it should be. We know for sure those birds are soulless — which makes them impossible to convert. Our conclusion is that they must be drawn from some Dark World that exists on the other side of this one, but again it's not a clockematical certainty… just a rumor. A hunch."

  "You're kind of talking in circles," Nathaniel said.

  Tick and Tock both looked shocked. "We never talk in circles!" they protested at the same time. "But maybe you're just listening in circles, Nate," Tock said. "Go ahead, make that conversion. Besides, Nathaniel, we don't tell everything we know to perfect strangers."

  "That kind of makes sense."

  "And we don't tell everything perfectly strange to people we know," Tick added.

  "So is there a Dark World?" Nathaniel belted in when he had a chance.

  "Yes, and also a funny one — dark and funny. That's all we know; dark and funny," said Tock. "It's all in the… yes, the cube — three of six... yes, that's right, three of six," he added.

  "Oh yes, you're right, Tock… three of six," Tick agreed. "You can't forget the cube."

  "Two sides to everything, and three sides to that, so that makes six."

  "Yes, but remember: if you multiply it out you will always get thirty-six," cautioned Tick.

  "And if you multiply it the other way, you will still get thirty-six."

  "Divide that by three and you get twelve. The total distance of one is twelve."

  "But the sides are six."

  "That's right, three of six."

  "And you have to multiply twelve by six, not just three of six, so the total distance of the twelve is compounded to seventy-two and seventy-two is the actual total distance of everything."

  "Yes, that’s right, but we are only familiar with three of six."

  "And more directly two of six, because the third of six is too dark for us to count."