Some people have wondered how I come up with such serial columns as General l’Hopital (v75, 1997; v85, 2001) and Quantum Loop (v77, 1998; v81, 1999). In fact, creating such Taylor Series’ is not that difficult, and I shall now reveal the appropriate steps in their creation to anyone who cares, or is actually interested in making their own Taylor Series derivative.

1. Select a story arc. Something you can effectively babble about for six issues. If it’s related to math, all the better. You don’t have to stick to said arc the whole time but people will appreciate knowing that the column will eventually stop. This may deter them from coming after you with sharp objects (the operative word being ‘may’). Prior arcs of mine include “mathematical punctuation”, and “why chairs were chained in MC”.
2. Write each column the same week it comes out in mathNEWS. Don’t prepare anything in advance. This way you can slip in any current events as well as give yourself a crash course in stress management. They usually only take between 2 and 4 hours to do anyway.
3. When you write, have a math textbook on hand. Liberally insert terms into the column. As an example, don’t say “You did something wrong”, say “You didn’t log the major factors” or “What you-knit was not a-tribute”. There are actually two ways to do this.
   • Write the column, go back and change the wording. In my case, most often done with QLoop. Classic QLoop comments include “Lynn Kedlist cursed, then recursed”, “My processes have better threads than you, Admiral” and “the CPU will be arrested for making con currency to buy hash”.
   • Pick out some good catch phrases first, or words that you want to use together, and fill in plot elements around them. In my case, most often done with l’Hopital. Classic l’Hopital comments include a paragraph containing words all starting with “ex”, “Gran U. Larity is into cayenne distribution”, “back us now or form”, and the redoubtable “Gram Schmidt ortho gone, Ali Zay’s shun process”.
4. If possible, include some mathematical trivia and words like paraskavedekatriaphobia (fear of Friday the 13th) to maintain reader interest. For QLoop this was required, for l’Hopital it seemed a moral at the end would suffice. Doing this means there’s a chance someone will actually learn something by reading the column. Of course, there’s also a chance they’ll simply be totally confused, but if they miss out on the enlightenment that’s their problem.
5. Finally, make sure to carefully spell and grammar check your work. Whether you have available editors on a production night or not, you don’t want them correcting intentional “kneed” or “monic” errors anyway.

So there you have it. Note that if you have a topic you can only babble about for one issue, it may still be useful (witness Sine Field). I now leave my legacy in the hands of others… but remember, old mathNEWS editors never die. They just get written off.

-Greg “hologrami” Taylor

[This appeared along with the last General l’Hopital, Volume 85, issue 6, March 30, 2001. By this point I had basically already graduated University, though I would contribute a couple columns later, as I did my first year of teaching in Sept 2001.

Did you find this informative? Recall there was also the behind the scenes notes for General l'Hopital Entry 1.5 & 1.6, if you like. Now, if you came here looking for information about Brook Taylor's infinite sums of mathematical terms... sorry about that? Hope you're still entertained, thanks for reading, feel free to drop a comment below.]

A subsidiary of Quantum Loop Enterprises

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.

“Sham, we got problems,” Hal Calalilli asserted as he entered the imagine chamber.

“No kidding!” replied Sham. After dispensing with Elly by sending her on her rounds, Sham had spent the last hour looking about the l’Hopital. “Hal, everyone here is talking in math riddles or doublespeak!”

“Sounds like the joy of lex.”

“Hal…”

“Sham, you’ve handled worse,” Hal said. “Now, back in Stall-Eons Gate, New Mexico we’ve got real trouble! Your parallel hybrid computer BigE is having a mental breakdown. Sushi and Xina can’t fix her, so it’s up to… er, Dr. Geeks.” Hal caught himself before mentioning Sham’s wife Drawna WeeBTree, or Sham’s daughter Shammy Pro Filer.

“So I guess you don’t know why I’m here,” Sham sighed.

Hal tapped at his TI-85 calculator. “No, but we know the woman in the fating room is Dr. Waterson,” he offered.

“Doctor! Doctor Waterson!” called out Electra Lysis as she rejoined her associate. “Sir Cul wants to transcend dental work and eat pie. There’s also trouble with Jacob, Ian and May tricks. Oh, and Zeke wants help tracking down new classical records, but I just told him ‘Stop playing Haydn, Zeke’.”

Sham winced. “Stop speakin’ like that,” he pleaded.

“Like what?” Elly inquired. “I didn’t mean to go off on a tangent. Though I often strike a chord when not aligned with the story arc. But my maxim is, ‘If you’re cut, seek aunts’!”

“Sham, I was wrong,” Hal sympathized. “No matter what it takes, we’ll get you out of here.”

*

However, it was a few days before Hal could return with good news. “You won’t believe this, Sham,” he revealed at last. “The underlying situation here is a peculiar punctuation problem.”

“You positive?” Sham mused. “Because the Hopital logs show even their elementary operations involve calculations that are way off base.”

Hal flinched. “You’ve been here too long, Sham.”

“The trouble is I can’t project the point of origin for these errors!” Sham looked up. “Uh, Hal, can’t you wear proper ties?”

“Sham, what you need to do is make sure Dr. Waterson and Elly Lysis team back up with Max Value and his wife Ana. Elly’s presence is necessary to crack this missing punctuation case.”

“But what about the stats here? The error vectors on this scale are—”

“Stop it, you’re going dotty!” Hal interrupted. “Just get Elly to the Fourier Factory!”

“Wait, that’s it,” Sham realized. “Decimals and periods are both dots! There’s the connection, it even explains the missing cases of colon cancer. Brilliant, Hal!”

“Oh. Well, it was adjoint effort—” Hal stopped himself. “Anyway, just get that clique of people I mentioned back together so you can loop out of here.”

Sham quickly co-ordinated things. “But Hal,” he realized even as he left for the Fourier Factory. “I haven’t im-parted any mathematical information yet, like how there are 43,252,003,274,489,856,000 possible positions for a Rubik’s cube. How can I loop?”

Hal shrugged. “General l’Hopital is just less educational.”

Indeed, Sham did loop upon his arrival at the factory. However, the story did not end there.

*

Still going…

-Greg “hologrami” Taylor

[Was this worth it, to hear about Shammy ProFiler? Or about Hal's properties? Well, here's something more random: Sham's "stop speakin' like that" line was a direct reference to FASS 2001, the February 2001 show for which I was CSW (chief scriptwriter). I'd written in a character who constantly spoke in music puns - a role I was ultimately cast into. In Act II scene iv, s/he was told to "stop speakin' like that". Weird that I still remember that 20 years later.

Anyway, that concludes Quantum Loop's bonus episode of 2001. Two more parts remain in the Hopital!]

“That went well,” Hal acknowledged. Sham was returning from the police office, where he had left a well documented statement. After all, once Sham looped, Ray Toobe would likely have no memory of the pivotal events.

“It’s remarkable that Millie came quietly,” Sham markedly remarked.

“I don’t think she really believed you could expose the truth,” Hal observed. “She seemed unphased.”

Sham shrugged. “I just figured that Millie’s encoding was going to have something to do with 357,686,312,646,216,567,629,137,” he pointed out. “No matter how you decapitate that number, you end up with another prime.”

“I don’t know how your swiss cheesed memory can recall stuff like that but forgets terms like the ‘lucky numbers’ or the ‘weird numbers’.”

“The weird numbers are abundant numbers without being the sum of any set of it’s own divisors. Like 70,” Sham noted.

Hal rolled his eyes. “If only you’d remembered that last loop…"

“So, what happens to Millie Niem anyway?” Sham continued.

“Oh… it looks like she gets off with a light sentence but they confiscate her viral device,” Hal answered, tapping at his calculator. “So everything’s back on track at the Project because of that… she doesn’t try it again. And hey, Sham, it looks like you accomplished your mission too!”

“What? I thought it was to provide room for terminals.”

“Yeah, well it looks like Millie’s son, Tita Niem, was going to prevent some initiative by the University of Mizuloo this year… that is, in the year 2000. But due to this disruption in her life, now Millie never has kids. And without the hinderance to the Mizuloo space program, it seems there is no longer a need for you to renovate the original MC design!”

“Oh.” Sham paused. “But then if I’ve fixed Y2K and accomplished what I was supposed to do here, why haven’t I looped yet? Am I supposed to prevent your alien invasion in the year 2000 too?”

“Oh… that turned out to be a hoax. It was a scam run by some cracked group of PCs,” Hal admitted. “And… it seems you’re still here because you need to render your art.”

“My art? Do I have to make a mosaic?”

“Hmmm… if ice in act, I've…" Hal smacked his calculator. “Sorry, you’re here to render your artifice inactive. BigE is playing with parsing…"

“My artifice?”

“You know, the thing you used to broadcast your mapping? It’s going to cause problems for some guy named Sine Field who ends up living on the sixth floor.”

Sham shrugged and detoured back to where he’d left his equipment. Arriving promptly at his destination, Sham Breakit switched off his device and began to dismantle it. “So, I guess that even though this wasn’t a routine loop, it at least has a good end,” Sham concluded.

“Uh oh… wait a minute,” Hal abruptly broke in. “It looks like there’s still a lot of unexplained Y2K problems in the future.”

“Pardon?” Sham mused, putting away his circuits and wires before looking back at his friend.

“Sham -- someone else has a Y2K Bug!” Hal declared, shocked. “And… oh man, Sham, it’s…”

Sham looped.

Finis

--Greg “hologrami” Taylor

[Thus ends "Quantum Loop" as a serial, in December 1999. I hope you enjoyed it. In the issue's mastHEAD, I was pleased with myself for avoiding coffee to that point in my life. I’m pleased to say the trend has continued over 20 years later.

That said, there was ONE more entry, as part of the "General l'Hopital" serial in 2001. Once it's published, I'll switch the "Next" to link out to it. Beware, there's no returning from that. Alternatively, you can look up the standalone "Sine Field" entries (a column about nothing), referenced above, of which there were four. Seems I loved to multiverse my stories even back then.]

Hal looked up from his calculator. “The lucky numbers? They’re similar to the prime numbers. You start by striking out all the even numbers. Then after 1 you have a 3, so you strike out every third number. That gets rid of 5, 11, 17, etc. Now after 3 you have a 7, so take out every seventh number, and so on.”

“Oh, right,” Sham recalled. “13 is the fifth lucky number then, isn’t it?”

“Oddly enough, yeah,” Hal confirmed. “But you don’t have triskaidekaphobia, do you?”

Sham blinked. “That’s like paraskavedekatriaphobia, isn’t it?”

Hal shrugged. “Not quite. Look it up.” He punched at his calculator. “But it doesn’t look like that will work either. Your higher dimensions on the sixth floor are never used as extra space for terminals. You’ll have to try something else.”

Sham frowned. “Would the odds improve if I provided the mapping information directly?”

“We have zip on that,” Hal indicated.

“There’s that big room right in the middle - how about I just place some sort of device near that location which will activate in 1999?”

“Well, it would be difficult constructing it with the technology of this decade,” Hal said, nonplussed.

“It’s better than restarting,” Sham insisted. “Go get the Quantum Loop staff and BigE to work on it.”

“I think you’re using fuzzy logic.”

“Just open the imagine chamber door, Hal.”

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

“Pardon?”

“It’s going blooie again…" Hal smacked his calculator and the door opened. “There we go. Wish we could thrash the originator of this Y2K bug.” Sham sighed, stacking some papers as Hal popped off.

Sometime later, Sham was prepared to put his plan into action. But Hal still didn’t have high hopes. “Sham, BigE has calculated a 90% probability that activating your device will only delay the 1999 reconstruction in the Red Room by 4 months. People will actually have LESS terminals to work on.”

Sham sighed. “Well, currently I have no alternative so let’s try the direct route. Here goes nothing.”

Sham switched on his abstract device. And Hal blinked. “Sham, in tracking your signal, BigE has picked up an analogous analog object!”

Sham blinked. “How do you account for that?”

“Someone else has an assembly!” Hal addressed Sham. “And… it looks like the other one is actually responsible for Y2K?!?”

“What??”

“I’m trying to get a fix… but it’s looking like the Y2K Bug that hit us in 2000 was actually a virus initiated by someone named Millie Niem here in the 60s. That’s why even Y2K approved computers were affected!”

“I knew Quantum Loop was compliant,” Sham muttered.

“Sham, you can repair our problems in the future if you catch the person in the field nearby!” Hal finally declared.

“Would a net work?” Sham wondered, hurrying towards the location.

But as it turned out, a net was unnecessary. The person was Millie Niem herself, and she stopped willingly when Sham confronted her. However, she was not very forthcoming (or even thirdcoming).

“A virus to truncate dates to two digits in the Year 2000?” Millie retorted, laughing. “How fantastically fantastic! I’d like to see you validate such a claim.”

“You can prove it if you crack the encrypting of her device,” Hal assured Sham. “Unfortunately we don’t have a starting point.”

Sizing up the situation, Sham reached down and grabbed a bit of paper that had been left on the ground. “‘Use largest known truncatable prime’?” Sham read. “I think this will provide enough information to substantiate my statements.”

“That won’t help you,” Millie stated defiantly.

“On the contrary -- I think everything can be determined now,” Sham retorted in satisfaction.

What has Sham figured out? Will all this really solve the problems with Y2K? And what about Sham’s mission to provide Mizuloo’s terminals? Find out when the story concludes in issue six…

--Greg “hologrami” Taylor

[This issue also had more "Cynic's Corner", and the results of my survey on Saskatchewan. I'd needed some filler in the prior episode. I was kind of clever in my youth. Maybe I still am.]

Hal walked into the Central Processing Room of Project Quantum Loop. “Any news?” he asked.

Sushi, the head programmer, stood up from behind the centre dais. “Dr. Geeks was looking for you earlier,” he replied. “That Katho guy in the fating room asked for some punched cards to toy with, and she doesn’t think he’s playing with a full deck.”

Hal nodded. “Well, I’m still trying to convince the nozzles who want to shut us down that we could fix Y2K better than their aliens.”

“As long as I don’t have to interface with all the infected computers,” the omnipresent BigE reminded. “It would cause hard wear.”

Hal nodded. “I’m currently working on just the right angle for my next presentation.”

“Then will things get back to normal?” Sushi mused.

“It may result in some basis of normality,” Hal shrugged. “So, anything else I should know before I see Sham?”

“The only people still reading this column are the ones looking for the occasional mathematical number theory,” BigE offered.

Hal blinked. “BigE, sometimes your statements don’t make a heap of sense,” he accused.

“This from someone in a lime green tinted suit. My processes have better threads than you, Admiral.”

Hal frowned, while Sushi patted a console, consolingly. “There, there. We’ll get to the root of this,” he assured.

Just then, Drawna WeeBTree entered the room. “Hal! How’s Sham?” she inquired.

“Haven’t checked on him yet, but I’m sure he’s doing fine,” Hal said with confidence.

Drawna nodded. “Xina was telling me that this looked like an easier loop.”

“Awk!” muttered Sushi, having gone back to his calculations. “Well, debugging this Y2K isn’t easy - I’m starting to think someone planned all this two-digit-bug business from the start.”

“I’m sure you’ll pull through when the chips are down,” Drawna comforted.

“Anyway, I’m off to the imagine chamber,” Hal declared. He grabbed his TI-85 and headed up the appropriate slope. Hal arrived holographically back in the 1960s shortly after, where he found Sham computing an inverse in verse. “Hey, Sham, how go the Harshad numbers?” Hal intoned.

Sham paused in his singing. “I decided that a number divisible by the sum of its own digits wouldn’t work for the mapping,” Sham responded. “But I think everything is finally in place now.”

Hal peered down at the schematics. “Sham, this floor labelling makes no sense,” he protested. “You’ve even labelled the potential elevators on each floor. 1101, 2079, 3093, 4115, 5220, 6312… where’s the pattern in that?”

“They all sum to numbers divisible by 3, except 4115.”

Hal tapped at the calculator in his hands. “Sham, no one figures this encoding out. There’s still the space problem in Mizuloo. Maybe you need to apply a mapping using the lucky numbers.”

Sham paused. “How do you define those again?” he inquired.

Can Sham still save the day? Are lucky numbers important? Do you feel lucky? Then keep reading when this series next continues…

--Greg “hologrami” Taylor

[Happy New Year 2022! I still chuckle at 'My processes have better threads than you, Admiral.' Yes, we needed a scene set in the far future of 2000 to see the Drawna character. For those who don't know, we now have the following Quantum Leap (Quantum Loop) name associations: SAM BECKETT (Sham Breakit); AL CALAVICCI (Al Calalilli); ZIGGY (BigE); TINA MARTINEZ (Xina); DR. "GOOSHIE" GUSHMAN (Sushi); DR. VERBENA BEEKS (Dr. Geeks); DR. DONNA ELEESE (Drawna WeeBTree). If you're puzzled about Calalilli that's a self-referential joke for hardcore Leap fans. Make sense?]

Mr. Aba Cuss shook his head. “The fact that an abundant number is a number less than the sum of its factors (excluding itself) changes nothing. The first number of that form is 12 and I cannot present such a design to the architects. It’s too much.”

“I suppose such an abundant number of floors would be odd,” Sham admitted.

Aba stared. “An odd abundant number? There’s no way we could build a structure of 945 floors!”

“No, no! That is… well, can’t we add just one more floor?” Sham continued worriedly.

“Not a floor or a ceiling,” Ada responded. “Don’t you remember how our original design for the MC was that big castle structure…? Some people had real math news issues with that.”

Sham pondered for a moment, trying to determine what to do. “How about enlarging the floors we already have?” he proposed.

“Won’t do. Anyway, it’s all out of our hands now, our feat was merely working out the dimensions,” Aba reminded.

“And it’s too late to change them?” Sham verified. This loop was becoming infinitely more complex.

“Yes,” Aba declared firmly. “Though if you’re this concerned I can send along the schematics when they come in.”

Sham nodded. “Please do,” he requested.

A few days later, Sham found himself on a plane, observing cubism as he grappled with a tesseract. Indeed, he had managed to work out a diabolical plot on his graph paper. “You’re looking well co-ordinated,” Hal observed, stepping into the imagine chamber.

Sham jumped and fell, almost fracturing his spline. He spun to face the hologram. “Where have you BEEN?” he demanded. “And what are you WEARING?” he continued.

Hal’s pink tie was clashing with his plaid suit. “Aw, Sham, you don’t remember?” he chided. “I wore this tie last time you were in Mizuloo. Remember how my fifth wife graduated from here? …or maybe it was the fourth…"

“Nevermind,” Sham sighed.

“Anyway, sorry about the loss of contact. BigE is better but we’ve had our hands full in the year 2000 what with the aliens.” Sham stared. Hal continued. “See, they seem to be negotiating with the President about fixing the whole Y2K Bug using superior alien technology. But they’re asking for a lot of money. Thus the government is considering rerouting the funds currently going to Quantum Loop.”

“What on earth on you talking about?”

“No, they’re not from Earth, that’s the point. But anyway, what are you up to here?”

Sham decided to ignore Hal’s aliens for now. “I’m fixing the Math & Computing building’s problem,” he explained. “It seems like I ended up getting here too late to alter the three dimensional construction - so I’m adding a few extra dimensions to the sixth floor.”

Hal blinked. “How would anyone know to look in n-space to install extra computers??”

“There are mathematicians in the building, right? I figure I just have to introduce the proper labelling system for the doors and people will be able to work out a mapping from that. Access follows.”

Hal looked dubious. “Access at Mizuloo is not known for it’s reliability,” he stated. “What are you going to be basing this mapping on?”

“Probably something to do with Harshad numbers. What do you think?”

“I think I have no clue what you’re talking about,” Hal concluded.

What is Sham up to now? Is he as spaced out as the aliens in the future? Are you as lost as Hal? Then look for the continuation in two weeks time…

--Greg “hologrami” Taylor

[A prior issue of mathNEWS had featured a castle structure as cover art. Access was the University's unreliable software program for co-op. With the inside jokes out of the way, I'll just mention that the previous Loop entry fit very nicely into one column. This entry, not so much. The joys of layout, when one is the editor.]

“Ah, there we go!” Hal declared.

“4,294,967,297 worked, did it?” Sham verified.

“Yeah… pretty big for being only the fifth Fermat number,” Hal commented.

“Well you’d expect that for 2 raised to the power of powers of 2,” Sham argued. “I’m sure it wasn’t that easy for Euler to find that 641 divided into 2^32 + 1.”

“Whatever. Now that Sushi, the head programmer, has access… well, we should be able to get you some data,” Hal offered optimistically.

“So, what’s it like in the Year 2000 anyway?” Sham inquired.

“Pretty bad,” Hal observed, being the observer. “Almost all the computers have failed - even ones that were supposed to be Y2K compliant. Businesses are failing because no supervisors can do arithmetic without calculators. The stock market is crashing, the economy is plummeting and there’s looting and pillaging in the streets.”

“What?! How are people taking it?” Sham gasped.

“Some haven’t noticed the difference,” Hal said, shrugging. “But at least it’s not that bad yet in Stall-Eons Gate, New Mexico… Hey, maybe you looped in as Ray to convince everyone to use four digit dates?” he mused, amused. Suddenly the calculator in his hand let out a squeal, and he glanced down at it. Picking up the squeal, he then turned his attention to the display. “Oh here we are… Sham, it looks like you’re here to get supple.”

“Well, I thought I was in pretty good shape…"

Hal smacked the device he held. “Sorry, get supplementary space. There’s a Math & Computing building that’s going to be constructed shortly, but it won’t have enough room in it for computers by the end of the century.”

“Computers that won’t work anyway because of Y2K?”

“That’s not the point. You just need to talk to the people designing the building and tell them to add more floors,” Hal reasoned. “According to BigE, the MC building now has six floors. With relative ease you can make MC^2.”

“Actually, someone was asking me about floors just a little while ago,” Sham recalled.

“Could be Mr. Aba Cuss - apparently he’s supervising the design.”

“I’ll try to find him,” Sham decided.

“I’ll see if any of BigE’s drives need reFermating,” Hal resolved.

As Hal disappeared, Sham hurryied out of Ray’s office. Unfortunately, tracking down the MC design head from his current sector proved difficult. And after the seek time, Sham had to wait for a block of available discussion time. Then finally, when Sham presented his case to Mr. Cuss, he met with immediate opposition.

“I don’t understand,” Aba protested. “I thought you agreed earlier that we had an abundant number of floors.”

Sham paused. “Actually, if you go by the actual definition of an abundant number, a six floor building falls just short of the mark,” he countered.

What is Sham talking about? What is an abundant number? Does anyone really care? Find out next issue…

--Greg “hologrami” Taylor

[My solo edit of mathNEWS continues. I’d forgotten about my Polkamon cover here. It would be my 8th, and was the only one I drew for Volume 81.]

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.

Sham found himself sitting at a desk, facing an unknown person. Of course, everything was unknown to him at this point - he’d just looped into a new situation. He would now have a certain amount of time to fix whatever needed fixing, and when his quantum was up he would loop to his next assignment. At least his life was predictable that way.

“So, what’s your answer?”

Now if only he could predict an answer to that. “Oh boy?” Sham ventured.

The man across from him rolled his eyes. “It’s not that complex, be rational,” he pressed. “Do you think there’s a real need for another floor?”

“Uhmmm… no,” Sham decided. He hoped Hal would show up soon.

“Fine. Then we have the whole thing?”

“Naturally,” Sham continued, feigning nonchalance.

The man stood, picking up and closing a briefcase. He then grabbed an extendedcase and stated, “All right, I’ll send the schematics in. Thanks, Ray.” And after a quick handshake, Sham’s unknown visitor departed.

Sham looked around the office he was in. It seemed fairly spartan, and poking around through a couple of sheets didn’t enlighten Sham as to why he was here, nor did any pieces of paper. It seemed to be sometime back before 1970 but no year leapt out at him. So it was a relief when Sham heard the imagine chamber door open, signifying the presence of Hal Calalilli. At least, it was a relief until Hal walked out onto one of the walls.

“Hal, stop acting irrationally,” Sham sighed.

“I’m sorry, Sham. I can’t do that,” Hal intoned, punching at his TI-85 calculator with a vexed look on his face.

“Why? What’s going on?” Sham wondered, twisting his head to the side in an attempt at viewing an upright version of his friend.

“It’s this Y2K bug!” Hal declared. “BigE, your parallel hybrid computer is going nuts! You really should have made Project Quantum Loop Y2K compliant, Sham.”

Sham boggled. “I thought it was. Is it really the year 2000?”

“Whoops. Uh, yeah,” Hal admitted. “At least it is where we are, but there’s very limited data on where you are.”

“That’s normal,” Sham pointed out.

Hal made a face, as he was growing edgy. “You’re in Mizuloo,” he revealed. “At the University of Mizuloo to be precise.”

“Hm. Haven’t I been in Mizuloo before?” Sham wondered.

“Yes actually, but it won’t be for about 30 years,” Hal confirmed. “Right now it’s the 1960s and your name is Katho D. Toobe. But everyone just calls you “Ray”.”

“I see. Anything else?”

“Actually, yes. BigE has locked out all but the backup systems under a strange numerical password, and we were hoping you knew how to figure it out.”

“Strange? How so?”

“We have to enter the first composite Fermat number. But no one at the project recalls exactly what that is or even how to figure it out.”

“Oh, I can give you the answer,” Sham assured reassuringly.

What is the answer? Will Sham figure out what he has to do? Will the Project survive Y2K? Find out next time…

--Greg “hologrami” Taylor

[This was Sept 24, 1999, leading up to Y2K. When we were worried all the computers would think '00 meant 1900. Also in this issue were “Cynic’s Corner”, “Everything One Needs to Know in Life Can be Learned by Reading mathNEWS”, and the flippin’ mastHEAD itself because I was the sole editor (HoloEd) for the first time. I have no idea why I decided to run a serial on top of all that responsibility back then... maybe to fill space.

In somewhat related news, between my last post to the mathtans blog and this one, Dean Stockwell passed on. The main "Holo" of my HoloEd (Voyager's doctor aside). That was a gut punch, but 85 years is a good run. This "Loop" retelling is for you, Dean. Rest in peace.]

“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

[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.]

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…"

“Hal…"

“…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

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

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!”

“What??”

“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

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

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

[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.]

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

[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.]

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…"

“Hal…"

“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.”

“Pardon?”

“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

[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”.]