Quantum Loop: Entry 1f

“An aliquot is a number which can be divided evenly into another number!” shouted Hal and Rick Ursion concurrently.

“OOP!” Sham recalled. He quickly set the detonator’s timing device to a suitably large prime number, giving them time to defuse the situation before the counter hit ‘1’. It was all over in record time.

“Congratulations, Sham,” Hal remarked. “Got out of a heap of trouble with minimal Risc.” He knocked his hand against the calculator as Rick led Lynn Kedlist away.

“What happens to them?” Sham queried in reference to the others.

“Uhmmm, looks like Lynn reveals the identities of some CPU members… the CPU gets locked away… oh, this is good though. Rick Ursion changes the ALU to RAM, Rick’s Amusing Mathematics. Talks a lot about interesting principles and inspires a lot of students.”

“Great!” Sham declared. “… so why haven’t I looped?”

“Well, if you recall, things were already going to work out before you changed them and made them better,” Hal reminded. “Helping the ALU wasn’t your reason for being here.”

“Then what??”

“Uh, we’re still working on it,” Hal admitted.

Sham threw up his hands. “There must be a hex on me.”


The afternoon of July 20th found Sham grading C papers when Hal suddenly appeared. “We’ve figured it out!” he pronounced. His handlink made a noise. “Okay, BigE’s figured it out,” Hal relented. “You know, I think the E stands for Ego, darn computer sent an interrupt as I was having a private moment with Xina…”

“Hal, can we settle arguments after I’ve looped?” Sham pressed.

“Oh, sure Sham. Well, it seems you looped in on a mathNEWS publication day, which should have tipped us off. Maybe you’ve seen it around? Anyway, you just need to include an article which will inspire the whole idea of RAM that eventually leads one student to unparalleled greatness.”

“You’re kidding. Like what, information about divisibility…?”

“No, no, that’s been done to death. Something like… ‘the first number with the letter ‘a’ in it is one thousand’.”

“That will inspire someone to great heights?”

“I’m just reading suggestions off the link. Or how about that the only number with all it’s letters in alphabetical order is for… for…”

“The birds?”

Hal hit the link. “Forty.”

“This is ridiculous.”

“This is mathNEWS. Just write some things down and do some BLACK BOX testing on the third floor. You’ll be inspiring someone to a Nobel Prize in Mathematics!”

“Hal, there is no Nobel Prize in Mathematics,” Sham observed.

Hal shrugged. “You get the idea.”

Sham sighed, pondering for a while before finally jotting down some options. He proceeded downstairs and started dropping paper into the box. Hal watched as ‘8 pints in a gallon’ and ’69 is the same upsidedown as rightside up’ went in. “I hope the last one’s more unique,” he noted.

Sham grimaced, dropped in his final sheet… and looped away in a blue haze. Sitting in the box was a slip of paper containing some simple words: ‘Take a number between 6 and 12. Square it. If the number you have is odd, add one. Add all digits in your number until there is one digit left. Subtract one. Take this number modulus 4. The result is how much sense this series was intended to make.’

–Greg “hologrami” Taylor

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[That concludes the Summer 1998 run of “Quantum Loop” in volume 77 of mathNEWS. This serial would later return in Fall 1999, during volume 81, hence the “Next” option. Hope you enjoyed; I like to think Sham’s departure here was due more to quantity than quality.]

Quantum Loop: Entry 1e

Sham was hurrying through the hall when he heard the imagine chamber door open and saw Hal step through. “Sham, BigE says there’s only a 43% chance this will work now,” he related.

“Well I can’t help that Professor Ursion left on a bus before I could talk to him,” Sham lamented. “Has he bicycled back yet?”

“Yup,” Hal affirmed. “And you have an hour until the detonation in Room 1082 destroys the building.”

“I’ll intercept Ursion in time then,” Sham said confidently. He continued down the hall.

“I’m wondering if we’ll see Lynn again,” Hal mused. “She had a nice set of…”


“…polygons. Could use a new array of jewelry though…”

“We don’t have time to get graphic about a newed Lynn Kedlist,” Sham interrupted. “Though if I’m right she will play a part in this. I just hope I can catch Rick Ursion off guard.”

As it turned out, the two professors collided at the next corner. Lynn, who was also there, dropped a stack of papers.

“Rick!” Sham gasped. “No time for password semantics – you need to authorize a cancellation of the current ground floor ALU project.”

“What? Why?”

Sham paused. “It’s pointless,” Sham hedged, glancing at Lynn. “Computer Science is CS, right? But CS can also be Customer Support. That means work on a Helpdesk. Which implies answering phones. But if something is phoney, then it’s not real, so neither is CS. QED! And if Computer Science isn’t real, why waste time on it?”

Rick Ursion paused. “That seems to follow logically,” he said slowly.

Lynn gaped. “You CAD! I object!” she cried.

Rick turned. “Don’t be object oriented,” he admonished. “You’re acting even odder than you were the day under the larch tree.”

Sham quickly processed this. “I think she’s upset because she’s a secret member of the CPU,” he revealed. “I’ve suspected her ever since she identified what sociable numbers were.”

“Sociable numbers?” Rick wondered.

“Like friendly numbers,” Sham explained. “Three or more numbers whose divisors add up to the next in a closed loop. Such as 12496, 14288, 15472, 14536 and 14264, the divisors of one add up to the next and the last ones sum to the first number. Lynn must have seen some when she read up on divisibility, as all ALU passwords have something to do with that subject. But no normal person would know about these numbers.”

“Clever, Sham!” Hal realized. He paused. “So I guess you really can study too much.”

Lynn cursed, then recursed. “Well, you haven’t foiled my Scheme yet!” she shouted, producing a black box and an assembly of switches. “I can set off the explosion from here! The chairs will released from their confines whether you like it or not!”

Sham hadn’t counted on this. “The explosion will also destroy the building…” he began. But Lynn had lost control.

“I’m setting it to go off when the countdown reaches an aliquot of 360!” she shouted. She flipped a switch… but the flip flopped.

“Sham, now the whole University is going to be wiped off the map!” Hal shouted.

Rick quickly blocked Lynn’s escape as Sham grabbed her black box. “Set a different aliquot!” Rick Ursion proposed.

Sham’s memory swiss-cheesed. “What’s an aliquot?” he asked.

Will Sham remember in time to save the University of Mizuloo? Find out in the epic conclusion next issue…

–Greg “hologrami” Taylor

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[None of this was scripted ahead of time, can you tell? We’re at entry 5 of 6.]

Quantum Loop: Entry 1d

Al Locute watched as Professor Late walked out of the Reflex Angle Cafe and dropped his food. “Hal!” the Prof said.

Al felt puzzled by Cal’s server error and subsequent mispronunciation, not sure how to account for it. “Hot container?” he asked.

“Uhhhh… yes,” the professor quickly agreed. “And I just remembered an engagement. Can I go over the marks with you another time?”

“Okay…” Al agreed. “If you’re sure you’re all right?”

“Aside from starvation I’m fine,” Cal mumbled. He hurried off.

Once back in his office, Cal (actually Sham Breakit) turned to talk to his holographic observer. “Can you ever not pop up so suddenly?” he asked.

“I’m sorry Sham, I can’t do that,” Hal intoned absently, worriedly punching calculator keys.

Sham caught the concern in Hal’s voice. “Has there been some change with respect to time?”

“Oh, mega delta, beta believe it,” Hal revealed. “You’ve blown up the math building after all!”


“It’s going to happen in two weeks!” Hal paused. “On the plus side, we can log the major factors now.”

“How will I blow up the math building??”

“Indirectly. See, Professor Rick Ursion is part of the ALU; they’re the Additional Labs Union. You might have noticed scarcity in terminals as enrollment increases. This group is trying to find a way to fix the labs, add more units… the problem is a lack of space.”

Sham frowned. “Then the schematics I got were to help me find an additional terminal room?”

“I suppose. It’s all being done somewhat undercover too, because the ALU doesn’t want the CPU to know what they’re doing; CPU being the Chair Protection Union.”

“Oh, are they the ones who chain the chairs to the terminals?” Sham inquired.

“Actually, they’re the reason the chairs are tied up. It’s a protection racket run by ‘Pa’ Scal and ‘Ma’ Dula III. If the chairs weren’t bolted, they’d be paying cache to keep the chairs ‘safe’.” Hal frowned. “Not that the chairs seem to be worth stealing… but the ALU can’t afford to get new locks when they install new chairs. Hence the secrecy.”

“But how does this lead to the building’s demise?”

Hal tapped more keys. “In the original history, the ALU just tried to redesign the sixth floor to accommodate more students. They gave up because no one could think in sixth-floor dimensional space; the additional terminal problem was left to professionals. And this August, the CPU will be arrested for making con currency to buy hash, thus these groups weren’t supposed to affect Mizuloo.”

“Uh-oh, I did change that,” Sham realized. “Last week when Professor Ursion came by asking about the sixth floor I said it was probably best to keep as far away from there as possible. I didn’t know what he meant.”

“Well, it seems he took your advice. The ALU is now going to try blasting an extra underground floor! Except someone in the CPU alters the circuit to try and shake all the chairs loose too; the resulting charge destroys the entire structure. It’s a mess, Sham.”

Sham frowned. “Well, not for two weeks. So I’m going to go see Professor Ursion now and prevent it!”

But upon arriving at Ursion’s office, Sham found only Lynn Kedlist, the professor’s assistant. “Where’s Rick?” Sham asked.

Lynn eyed him for a moment. “1,184,” she said.

Sham sighed. “1,210,” he responded. It was a similar friend number code to 220 and 284 from another day, whereby each number had divisors that summed up to the other. “You might consider changing to codes other than prime or friendly number sequences,” Sham added. “To really baffle the CPU we could use sociable numbers.”

Will Sham save the building form destruction? Does anyone really care about sociable numbers? More answers next time…

–Greg “hologrami” Taylor

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[Nothing to add this time; enjoy the CS references. We’re at entry 4 of 6.]

Quantum Loop: Entry 1c

Sham tossed the dart at the board at the same time as Hal Calalilli appeared. The dart flew through Hal’s head to land on double 10. Hal blinked. “Want to watch where you’re tossing those things?”

“Hal!” Sham shouted. “Finally – please tell me you have some sort of new information.”

“Well, no quick sort,” Hal admitted. “We’re still checking into these private operators on campus.”

“It’s June 12th. I think I felt my brain going numb last week.”

“Well, all we’ve had to go on is your identifier code: 333,333,331. Plus the other professor’s confirmed identity, Rick Ursion.”

Sham shrugged. “Well, as I said, he began making declarations when I observed it was that number in his sequence that was divisible by 17. Then for a switch he gave me that case.”

Hal nodded, absentmindedly leaning over to put his head through the referenced briefcase. “And you don’t know why he’d give you schematics for the math building?”

“None. With all the red marks, maybe they’re trying to blow it up… I really need more information!”

Hal tapped his calculator. “BigE says the building is still here in the Fall.”

“Very funny, Hal.”

Hal continued tapping. “Here’s something though – a new objective! The secret society may not be why you’re here. There’s some kid named Chip D. Ip in your class, who’s under ten.”

“TEN? I don’t recall anyone so young…”

“Tension,” Hal corrected, slapping his link. “He’s under tension. Stress. According to BigE, he’s going to fail your midterm, lose hope, sink into depression, drop out, and end up bottling soft drinks in a C-Plus Plus Factory…”

“From a MIDTERM?”

“…but he’s going to be coming to your office, so you can monitor his condition, make sure it won’t become terminal.”

“The midterm is not that hard, Hal.”

“Maybe Chip’s paranoid. There are time constraints too. Just give him some memory pointers.”

Sham nodded. “Of course I will – but I have a feeling that our main process still involves Professor Ursion’s group.”

“BigE hasn’t picked up any major problems though, so whatever they’re going to do either won’t work or be will be very subtle… maybe poisoning the water or something?”

“Hal, have you tasted some of the water already in the area?”

“I’m a hologram,” Hal reminded. “I can’t touch anything in your time.” A knock at the door interrupted the conversation, along with the sound of a big ‘OH!’. “That would be Chip,” Hal commented out loud. “Good luck.”


Outside, in the shadows of a larch tree, two figures spoke quietly.

“You sure Cal can come up with a plan of attack? You said he looked odd.”

“He’s not stringing us along. He’ll come up with a method.”

“Still, next time test him with the friendly numbers password. We can’t afford any error.”

“He knows the drill,” Rick Ursion assured. “We’ll find a way to fix the building’s computer labs once and for all…”


Will Sham pass the new password? Just what are these people plotting? Check back next time…

–Greg “hologrami” Taylor

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[No other columns this time, but this was actually Issue 4 (of Volume 77), as Issue 3 was “The Toronto Numb”. A massive parody special. Hence Sham’s comment about his brain.]

Quantum Loop: Entry 1b

Sham sank into his – or technically Professor Cal Q. Late’s – office chair. The only thing he’d been able to say when he’d seen the size of the class he had to teach was “Oh Boy”. Fortunately, Hal had been able to discover what his lecture had been about in time, so things weren’t off to that bad of a beginning.

“Okay Sham – I think we’ve got it!” Hal piped up, appearing behind Sham and walking forwards through the desk.

“At last,” Sham breathed.

“Perfect numbers are not just number whose divisors add up to the number itself, they’re even the sum of a series of consecutive integers … (Hal paused to tap his calculator, his link to the parallel hybrid computer running Quantum Loop) … and BigE says that the number 2^216,090 X(2^216,091 – 1) is a perfect number.”

Sham cast a look at Hal. “So is 6, but that still doesn’t explain why I’ve looped here.”

“I’m just trying to lighten the mood,” Hal defended himself. He punched a few buttons on the calculator and took a puff of his cigar. “Well, right now it looks like the object of this loop is to improve Professor Late’s record.”

“The record with his class?” Sham wondered.

“Yeah, well, it seems that the person you looped into really lives up to his name; he’s rarely on time. Also he’s missing assignments, losing files, memory errors, stack overflow…” Hal blinked at the readout. “Geez, I told Sushi not to do that programming upgrade!”

Sham cut off Hal’s grumbling with a wave of his hand. “I get the idea. So I teach a few classes, attend a few meetings and thus keep Professor Late from getting fired? Sounds almost too routine.”

“Well, this character appears to be some type of absentminded genius, too wrapped up in work to even recall his address. Knows his stuff though. Anyway, we’ll keep working on scenarios,” Hal assured. The white doorway appeared behind him again. “In the meantime, just consider this loop a break.” Hal stepped through the doorway and was gone.

“If I got a break during a loop, I’d exit,” Sham mumbled to no one in particular. He turned back to his desk, deciding it was time to familiarize himself with his new schedule.

Two weeks later, Sham had the schedule down pat. But he didn’t seem closer to looping, and Hal hadn’t been able to identify any critical section of the loop. They appeared to be deadlocked. “And it’s getting frustrating,” Sham murmured, tossing some darts at the dartboard he’d found in Professor Late’s office.

“What’s frustrating?” came an unexpected statement.

Sham turned to see another professor in his doorway. “Uhhh, can’t hit the bull’s eye,” he said, hoping the darts in the treble twenty would go unnoticed. His colleague had other things on his mind though.

“So, Cal – you haven’t come by for any Java the last couple of weeks.”

“Uhm, I’ve been busy,” Sham ventured. Drat, he didn’t know the other person’s identity, but apparently he should have been making routine calls.

“Been doing any work on our project?”

“When I’ve had time…”

“And what about that unusual prime number sequence?” the visitor pressed, now looking a bit concerned. “The one that goes 31, 331, 3331, 33331, 333331 …”

“Oh that!” Sham said hurriedly. “That’s… that’s actually going to fail when you have a certain number of 3’s,” Sham realized. “A later number in the sequence isn’t prime.”

Which number breaks the sequence? Who is this person quizzing Sham? Check back in two weeks…

–Greg “hologrami” Taylor

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[This old mathNEWS issue – volume 77, issue 2 – also featured my first “Sine Field” entry… a column about nothing. And another “Cynic’s Corner”, back when it wasn’t supposed to be a regular column.]

Quantum Loop: Entry 1a

Theorizing that one could time travel within their own lifetime, Doctor Sham Breakit stepped into the Quantum Loop accelerator… and vanished. He awoke to find himself trapped in the past, facing mere images that were not his own, and driven by unknown source code to arrange history for the better. His only guide on this journey is Hal, an observer at run-time, who appears in the form of a hologram that only Sham can see and hear. And so Dr. Breakit finds himself looping through life after life, striving to put right what once went wrong, and hoping each time that his next loop… will be the loop Home.

As the blue glow faded, Sham found himself in a corridor. He wondered where and when. At least there didn’t seem to be anything going on, so he might as well look around. Sham proceeded down the hall, only to find that it dead-ended in a doorway. He backtracked and took another passage. But a few doors later he discovered the same problem.

Sham stopped. Time to think logically. He looked up and started following the Exit signs. He turned down a couple more corridors, glanced behind himself and saw another exit sign pointing in the opposite direction in which he was heading. Sham frowned – wherever he was, it seemed to defy all logic. So maybe he had a map?

Sham turned out the pockets of the suit he was wearing and started looking over the contents. He was interrupted by the appearance of a white door in the middle of nowhere. Hal, decked out in a green jacket and pink tie, stepped through. “Sham! You’ll never guess where you are!”

“In an experiment gone wrong?”

“Close, it’s the sixth floor of the Mathematics and Computer Science Building at the University of Mizuloo. You know, I think my fourth wife graduated from here… or maybe it was the third…”


“Right, sorry. Your name is –“

“Professor Cal Q. Late, and it’s around Friday, May 15th, 1998 according to this speeding ticket I found. Hal, just skip to why I’m here.”

“I’m sorry, Sham. I can’t do that,” Hal intoned.

“You know, you’re about as funny as a statistics class.”

“Well, we had trouble signing and cosigning the new parts for your parallel hybrid computer, BigE. Had to seek out our csc head who was tanning on a cot.”

“Sounds like you have all the angles covered,” Sham said, arcing an eyebrow.

“A cute line, Sham. But one thing we do know is that your main duty right now is to tea.”


“Errr…” Hal slapped the TI-85 calculator in his hand. “Oh, teaching. Your class was supposed to start five minutes ago.”

“What? Where?”

“Two floors down.” Hal glanced around. “You know, it would be a lot easier to get out of here if you could walk through walls…”

“What subject am I teaching?”

“Beats me,” Hal shrugged. “But with all your degrees I’m sure you can come up with something.”

Sham sighed reflexively – Hal was being obtuse again. He hoped that his mission for this loop wouldn’t fall flat, and that whatever he did would be right. “Maybe I’ll give a talk about perfect numbers,” Sham proposed.

“Perfect numbers?” Hal mused. “What are those?”

What are perfect numbers? What is Sham doing in Mizuloo? Look for an answer next issue…

–Greg “hologrami” Taylor

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[This column originally appeared in the University of Waterloo’s mathNEWS publication, Volume 77, issue 1, from 1998 – Sham gives an accurate date. Also in that issue by me were “Cynic’s Corner” and “Everything One Needs to Know in Life Can be Learned by Reading mathNEWS”.]