How to Derive a Taylor Series

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

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[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.]

General l’Hopital: Entry 2f

End of the Taylor Series

“Will you please explain to us what the point of all this was?” Ana inquired of her sister.

Elly nodded. “The punctuation that’s been going missing is all connected to numbers. Periods as decimals, dashes as minus signs, exclamation marks as factorials. But there’s no such correlation with question marks, which is why we’re seeing more of them! A question mark fancier must be behind this scheme!”

“Don’t start into Scheme,” groused a large ?, rising up from behind a basic pro-log sign. “With all the parentheses involved in that language, my fort ran better under Al Golle. Though he was never able to seize me a big, oh, notation in math!”

“Awk!” exclaimed Max. “I see Q! And it’s irrational!”

“pFFT, just call me ?,” the ? said. “You know Elly, you didn’t even mention how commas appear in numbers and as french decimals.”

“Right, commatose patients have been sparse too,” Dr. Waterson realized.

“Now this all parses,” Ana remarked. “It’s been a plot designed to amplify appearances of the question mark.”

“With an attempt being made to finger Elly as the cause of some problems, owing to her natural immunity,” Max reasoned. “? wanted her out of the equation!”

“Indeed,” ? stated. “But I was thrown a curve by her discussing with people who could track the problem to this sector of town. I regret that I’ll now have to dispose of each of you… but my principal ideals must continue.”

“Wait, you’re forgetting something,” Dr. Waterson interjected. “The question mark may not appear often in notation but it is of fundamental importance. Without mathematicians asking questions, we would never be where we are today.”

? paused. “There’s a ring of truth to that,” it admitted.

“Consider the following,” Elly stated. “The popular questions that surrounded Fermat’s Last Theorem, the current P versus NP problem, even the 23 Mathematical Problems of David Hilbert.”

“All of it is mathematically important and all of it involves big question marks,” Ana added.

“Don’t go recognition crazy now and put mathematics in Jeopardy,” Max concluded.

“You think maybe I taught all o’… gee,” the ? reflected. “I suppose my role is larger than I suspected.”

“Of course,” Dr. Waterson concluded. “Come on now, let us work to re-solve our differences and put an end to this power struggle.”

“Very well,” agreed ?. “I suppose what I really require is psychological counselling…”


So, as a result of their care, ? overcame a period of monic depression and became unconditionally stable. Electra “Elly” Lysis resumed her duties in the l’Hopital as before, actually being five times as functional. Max Value and Ana Nuther Value took relaxing vacations in Monte Carlo and Las Vegas, prior to accepting a case that involved making Al Gore rhythmic using a horn clause. And Dr. Carrie Waterson carried on with her own work… with no other large problem ever revealing itself.

So the moral of the story is: If you question marks, don’t forget the importance of notation.

Finis II

-Greg “hologrami” Taylor

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[Dr. Waterson suddenly gets a first name. And yes, it’s Carrie Waterson, the same name as the protagonist in “Time & Tied”… recall that I was first writing that story at around this time in 2000/2001 (under the name “Time Trippers”). I don’t think this will be Time Carrie’s eventual occupation though… setting aside how she doesn’t go for puns, and this one looks like Ami Mizuno, I have other plans for Time Carrie.

In other random trivia, the ? was actually italicized as a person in the issue. Also in this issue was “How to Derive a Taylor Series”, an explanation of how I wrote Hopital and Quantum Loop… I will probably include that on this site too, because why not.

So did you realize the question mark was behind things, as Sham alluded to in Entry 4? I did actually sketch l’Hopital out very roughly this time around, so there’s that. Did you have a favourite character from the series at all? Even back then I did seem to prefer largely female casts. Feel free to let me know, or at least share the link around. Since it’s my birthday this coming week, that’d be cool and all.

Thank you for reading!]

General l’Hopital: Entry 2e

Full of questionable content

“What are you doing at the Fourier Factory on this fine night?” Max muttered.

“Dr. Waterson connected our series of errors to your punctuation problem,” Elly explained.

“Did I?” Dr. Waterson worried.

“Sounds like a quick sort of decision,” Ana admitted. “But is merging really a heap of trouble, Max?”

“I suppose not,” he huffed. “But can we keep things proper, prim and kruskal?”

“NP. Complete control is yours,” endorsed Elly.

The four characters advanced into the factory a bit testily, making their way past a Campus Crew pram, a fortuitously full adder, and some touring machine pumping lemma meringue on the floor.

“Who Kleenes this place?” Waterson whispered.

“I think it’s a con cave, does the con vex you?” Max mused.

“I feel like a mime-on-the-road,” Elly enunciated erroneously.

“Would that make you the LIFO the party?” Ana articulated.

“Can we hash this out without getting to the use of PCP?” winced Waterson.

“Look, would UNIX all the talk now?” Max mumbled.

“Or what, you’ll deque someone?” asked Ana.

“But then wouldn’t the odds be stacked against us?” Waterson warned.

“Hey, either you back us now or form a rival group, right?” Max maintained.

“Wait!” Elly exclaimed. They all reached a halting state. “Your language is irregular,” Elly elaborated. “It’s currently all in the form of questions.”

“She’s right, isn’t she?” Ana asserted.

“Who am I, the Confused Mathie?” Max moped.

“Could there be interference from the CFL?”

“No, Doctor,” Elly expressed. “There is no field goal and the context is sensitive. In fact, I’m starting to realize that the complexity of the situation is a sham.”

“If so, doesn’t this sham rock?” mentioned Max.

“Could you not make this an ire ish?” Waterson wondered.

Elly exhaled. “Enough!” she soothed. “I think I now know who’s behind both the punctuation trouble AND the numerical mystery PLUS the reason they’ve been doing it!”

“What??” the others observed.

“Is this finally a terminal case?” Max marvelled.


Have you come by-nary a solution to this column? Then make sure to read the conclusion in two weeks time!

-Greg “hologrami” Taylor

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[This appeared on the same mN page as “The Confused Mathie”, including a picture of me. I’d forgotten about that filler, though of course it was referenced by Max. Find it here:

Did you spot the descriptives synching with the names? I’d forgotten about that too. And if only I could remember what “mime-on-the-road” was a reference to. Ah well, as it says above, last part in two weeks! Can you see where this is going?]

General l’Hopital: Entry 2d

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.”


“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

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[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!]

General l’Hopital: Entry 2c

Why won’t that place just die?

“Your ex claimed exclamation marks!” exclaimed Max Value.

“Exactly, extraordinary exchange,” expressed experienced Expo executive Exeter excitedly. “Except extremely expensive experiment, exporting extracted exam exclamations! Excerpts exited existence exponentially!”

“Excellent extra example,” Max said, hanging up the external extension.

“Explain what function that call served?” Ana asked the PI.

“I can add it to my composite,” Max revealed. “I now have many prime cases with odd factors.”

“Are you positive?”

“Naturally.” Max proceeded to pull several files. “There is just one common thread I’ve seen running through all these processes. Observe the following cases! Colonel Space spoiling nachos. Jordan missing cannon nickel forms. The Gram Schmidt ortho gone, Ali Zay’s shun process—”

“Enough!” Ana interrupted. “What is the common factor?”

“Its identity,” Max said, “Is… punctuation! Or more precisely a lack thereof.”

Ana frowned. “But Electra’s case involved no missing punctuation, it had to do with lopped off decimals,” she recalled.

“Ah, unfortunately I’ve discovered that connection has time doubt,” Max remarked. “So while the decimation of her numbers does occur within the same time period, I must set her case aside temporarily to concentrate more closely on the punctuation caper.”

“But while we caper and bandy about, who is left to orchestrate how l’Hopital Central conducts itself?” Ana noted. “This is the pits!”


Indeed, back at the l’Hopital, things were hardly peachy. “I’m plum tired,” Electra remarked gingerly to Dr. Waterson. “Earlier I saw a man go by with the key we needed for a pre-cot storage area. I’m so berried in work I was nuts enough to let the seedy guy leave.”

“Work is a mixed bag,” Dr. Waterson agreed. “Even my breakfasts of late are not Special K-complete.”

“Do you think there’s any angles or incidents we can pursue to help with Max’s investigation?” Elly reflected.

“Perhaps. But we should look before we leap or something may throw us for a loop,” Dr. Waterson stated.

Suddenly, the form of Dr. Waterson was encompassed in a wash of blue light, accompanied by a tingle of static energy. Unnoticed by anyone, she had just been replaced by Dr. Sham Breakit of mathNEWS Quantum Loop fame.

“WHILE I think I got that, could you REPEAT UNTIL I know FOR sure?” Elly asked.

“Oh boy,” Sham concluded.


To be improved…?

-Greg “hologrami” Taylor

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[How’s that for a teaser? Continuity-wise, this takes place after all previous Quantum Loops. And how many mathematical references are you catching, amid the random wordplay? I feel like it was a goal of mine to get the Gram-Schmidt Orthogonalization Process in there. Oh well, hope you’re enjoying the twenty-year-old rerun… feel free to let me know!]

General l’Hopital: Entry 2b

The nonspecific continuation

“These events do form an unusual sequence,” Max Value stated, a bit nonplussed.

“Don’t react negatively,” Dr. Waterson advised. “You must discover the cause so that we can limit such occurrences before they increase without bound.”

Having met with Ana and Max Value, Dr. Waterson and Elly were now persuading the PI to assist them in their investigation of errors at l’Hopital Central.

“Well, my case volume is low and your arguments seem solid on the surface,” Max yielded. “So I’ll get to the point. Electra, any line on people in the area out to wreck your reputation?”

“No, I don’t hang out in circles containing such squares,” Elly replied.

“Are you certain there’s no one, in any shape or form? Perhaps a platonic relationship?”

Elly sighed. “Read my ellipse: Try angles other than your wrecked angle. Maybe contact the Pentagon?”

“Or heck, Saigon,” Max retorted. “After all, I have an informant over there, Gene Etic. He’s my link for criminal confinement cases…”

“Dear,” Ana phrased, moving forwards. “This case has nothing to do with jail cell divisions.”

“AIe!” Elly yelped. “Get off my toe, sis!”

“So who might be involved in this business then?” Max mum-bled, scanning some files. “Someone in marketing? Apparently Eko Nomics decks people… hey, where’s DECA gone?”

“If I may,” Dr. Waterson cut in. “The trouble is primarily financial with the added dimension here including lopped off decimals and negative numbers which were dashed off. It will lead to positive chaos.”

“Aha!” Max realized, raising a digit. “That’s why your number’s up! Figures. But you can count on me.”

“You’re acting a bit irrational about the whole thing,” Elly remarked.

“Max has been dealing with complex cases, it’s only natural,” Ana soothed. “Leave everything in our hands, I’ll even foot the bill.”

“Give us a heads up then if you kneed more info,” Dr. Waterson stated. “We’ll keep in touch as friends and family. But right now me and Elly should start trekking the long distance back to work.”

There was a pause after the two Hopital workers departed. “Well, their case doesn’t seem very arresting,” Ana finally piped up to Max. “How much attention do you think it warrants?”

“Quite a lot,” Max countered, producing a table he put on his desk. “Because I think some of my other cases here are connected! Mark my words Ana, there’s something deep going on here. But it’s not so deep that I can’t get to the bottom of it!”


Not to be discontinued…?

-Greg “hologrami” Taylor

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[If it’s not about polygons, it’s about mitosis. The 2001 hospital saga continues, as more familiar characters return. What do you think? It was actually somewhat planned out in advance this time.]