Severus Snape and the Order of the Potions

In Harry Potter and the Sorcerer’s Stone, just after the bit where the Scooby Gang Hogwarts Three (Harry, Ron, and Hermione) discover that evil forces are after the titular stone and before the bit where Harry vanquishes the face of Voldemort with the power of love (to the rejoicing of Huey Lewis fans everywhere), there is the bit where the kids must best a sequence of chambers guarded by homicidal three-headed dogs, homicidal shrubberies, homicidal flying keys, homicidal chess pieces, and a logic puzzle involving bottles.

If you don’t remember this last challenge, that’s probably because it didn’t make it to the movie, partly because watching someone solve a logic puzzle is only slightly less boring than reading about someone solving a logic puzzle, but mostly because the problem, as described in the book, is incomplete.

“Dude, Wizard Sudoku sucks.”

In the book, after the giant chess match, Harry and Hermione enter a room that immediately seals up both entrances with magical fire, purple flames on the door leading back out they way they came, and black flames on the door leading forward to the hiding place of the Sorcerer’s Stone.  The room is empty except for a table with a line of seven potion bottles and a note that reads as follows (the line numbers are included by me):

(1) Danger lies before you, while safety lies behind,
(2) Two of us will help you, whichever you would find,
(3) One among us seven will let you move ahead,
(4) Another will transport the drinker back instead,
(5) Two among our number hold only nettle wine,
(6) Three of us are killers, waiting hidden in line.
(7) Choose, unless you wish to stay here forevermore,
(8) To help you in your choice, we give you these clues four:
(9) First, however slyly the poison tries to hide
(10) You will always find some on nettle wine’s left side;
(11) Second, different are those who stand at either end,
(12) But if you would move onward, neither is your friend;
(13) Third, as you see clearly, all are different size,
(14) Neither dwarf nor giant holds death in their insides;
(15) Fourth, the second left and the second on the right
(16) Are twins once you taste them, though different at first sight.

So one potion of the seven provides a means to exit through the black fire; one provides a means to exit through the purple fire; two do nothing; and three will kill you.  However, as it turns out, the only way to know if the potion you’ve picked will work is to actually walk through the magic fire in question, so you risk char-broiling yourself if you pick the wrong potion (assuming, of course, you don’t straight-up die from the poison).

Hermione quickly realizes it’s a logic puzzle devised by the school’s resident potions master and all-around dick Severus Snape, and sets out to to use the clues to figure out which bottle will send her back through the purple fire (to alert the school officials) and which will send Harry forward through the black flames (to battle with He-Who-Had-Not-Yet-Become-Ralph-Fiennes).

“At least in this move I got to have a nose!”

I did the same thing, only to be befuddled by the fact that at no point does the novel tell the reader anything about the sizes of the bottles, which seems like a rather crucial piece of information what with it being the whole point of third clue in the poem.

Interestingly enough, though, on the assumption that Snape’s clues do, in fact, specify a unique solution to his potion puzzle, it is nevertheless possible to solve it — that is, to determine the precise locations of the Go-Back and Go-Forward potions!

Why don’t you give it try, and then I’ll show you the solution after the jump.

Continue reading

Posted in nerdify | Leave a comment

Pi filling

In deference to the recent Super Pi Day, in 2010 the students and teachers of Southern California’s Salem Lutheran Church built an enormous globe out of paper mache.

According to the Guinness Book of World Records, this makes it both the largest paper mache sculpture on Earth (at 2.27 meters tall and 8.55 meters in circumference) as well as the biggest \pi on Earth (at \pi = 3.77).

Posted in mathify | Leave a comment

Pi-partisian legislation

WASHINGTON | In an address to the nation, President Barack Obama declared Saturday, March 14, 2015 as Super Pi Day.  “My fellow Americans,” the president said, “today is a chance to reflect on one of the most important constants in all of mathematics and science, \pi.  For on this once-in-a-century morning of 3/14 of the 15th year at 9:26 and 53 seconds, we find the first 10 digits of \pi‘s decimal expansion: 3 point 1 4 1 5 9 2 6 5 3.”

3.14 AND CHANGE!

“As I’ve said before,” the two-term president continued, “Americans must move back to the top of the pack in mathematics and science, and there’s no better place to start than with an appreciation of this much better approximation of one of nature’s most profoundly important constants.  It’s certainly much better than last century’s old 3.14.”  President Obama then unveiled an executive order to adopt 3.141592653 as the national approximation for the irrational, transcendental number \pi.

While Obama’s actions met with support from both Democrats and the nation’s two largest mathematical groups (the American Mathematical Association and the Mathematical Association of America), Republicans in both houses of Congress are unified in their opposition to the better approximation of \pi.

Representative from the Tea Party Caucus.

GOP Representatives in the House were outraged at the president’s perceived power-grab.  “I can’t believe the President is suggesting we give out more pi to every American!” Louie Gohmert (R-TX) announced in a press release.  “It’s just another handout from Big Government!”  Representative Dave Brat (R-VA) agreed. “Who’s going to pay for these extra digits?  We’re stealing digits from our grandkids’ numbers to pay for this bloated left-wing, socialist, mathist agenda.”

Other Representatives expressed concerns regarding religious freedom. Renee Ellmers (R-NC) declared “Once again, Christianity is under attack by this President.  The Bible very clearly says in I Kings 7:23 that the alter font of Solomon’s Temple was ten cubits across and thirty cubits around in compass… therefore, according to the Bible, the bedrock of our Judeo-Christian laws, God says that \pi is 3.  Not 3.14 or 3 point 666 or whatever.”

We must stop being the party of stupi— ah, never mind.

Speaker of the House John Boehner (R-OH) also expressed his dissatisfaction with Obama’s choice of approximation.  “Time after time, this president has chosen to re-write federal law on his own without a vote of Congress,” Boehner noted in a press conference, “and now he’s lawlessly rewriting the digits of \pi!”  Boehner has already instructed his Republican caucus to repeal Obama’s extra digits of \pi, although when asked with what digits he planned to replace them, remarked that the reporter could “kiss his ass.”

This is really Boehner’s response to a repeal question…

Republican members of the Senate expressed similar sentiments.  Ted Cruz (R-TX) cited Obama’s executive order as another example of his unlawful executive overreach.  “This isn’t what the Founding Fathers would have wanted,” he preached on the Senate floor.  “They wanted a limited central government, where the individual states could decide for themselves what the value of \pi ought to be.”

…and this is really a page from Ted Cruz’s official coloring book.

Senator Cruz, together with 45 other Senators, added their names to an open letter from Senator Tom Cotton (R-AK) to President Obama providing the commander-in-chief with a basic civics lesson.  In it, Cotton writes “We will consider any assignment of value to \pi that is not approved by the Congress as nothing more than an hot air.  The next president could rewrite the digits of \pi with the stroke of a pen, and future Congresses could modify the definition of \pi at any time.

Senator Jim Inhofe (R-OK) also took the floor to cite evidence that \pi was a hoax perpetrated by a cabal of left-leaning mathematicians and scientists.  “I ask the chair, do you know what this is,” Inhofe said to Sen. Bill Cassidy (R-La.), who was presiding over the Senate’s debate, as he removed a calculator from a plastic bag.  “It’s a mechanical abacus. And when I push the “pi” button, it says 3.141593 each and every time!”  Inhofe then threw the calculator at Cassidy before concluding with “We hear how \pi has all these digits from all these mathy-magicians, but look: that machine says it has only 6.  Six!”

Don’t get me started on climate change or that hippity-hop music…

Senate Majority Leader Mitch McConnell was unable to be reached for comment regarding the new \pi controversy, being on vacation at his winter home in the Swamp of Sadness.

…’cause McConnell looks like a turtle, see?

Posted in komplexify | 1 Comment

The dog days of winter

The Queen B uses a technique called Love and Logic to psychologically manipulate empower the Butterfly to make good decisions.  I have watched it enough to have some sense of how it’s done.  For example, suppose it is time for the Butterfly to go to bed because either (a) it’s almost 8 o’clock and she needs her sleep or (b) it’s the seventeenth time she’s rolled her eyes and stomped out of the room and her parents need her sleep.  Rather than simply assert “Go to bed!” to the child and deal with the arguing, negotiating, or crying that invariably comes after, the Queen B uses a two-prong technique to “guide” the Butterfly to the right decision.

The first step is what I call “Buttering her up,” in which the Queen B gets the Butterfly excited about something… something that will arise as a consequence of going to bed.  For example:

Queen B: Oh my gosh!  Tomorrow do you want to help me make hard-boiled eggs!

Butterfly: Awesome!  I can’t wait.

This provides a segue into the task at hand

Queen B: Me either.  But that’s something we need to do tomorrow, and I’m going to need you awake and alert to help me in the kitchen, so I guess that means you’ll need to go get some sleep soon.

Butterfly: But… but… but

Now that the trap has been sprung, the Queen B moves to the second step: the “Sucker’s Choice.”  That is, she offers the Butterfly a choice of actions, both cleverly designed give the Butterfly a sense of control but which have absolutely no effect on the actual outcome of events:

Queen B: I’ll tell you what.  I let you stay up a little bit longer, but then you have to go to sleep.

Butterfly: Oooo… okay.

Queen B: Would you like to stay up for five more minutes… or SIX more minutes?

Butterfly: SIX MORE MINUTES!

Queen B: Sounds good.  We’ll go to bed in six minutes.

Six minutes later, the Butterfly is in bed and almost asleep before she realizes she’s been played.

Which brings me to a week prior to Valentine’s Day, when the Queen B sent me a text:

“This is not a trick” is precisely the thing you’d say if it WAS a trick, isn’t it? Checkmate, wife!

I knew something was up, and I let her know.

Ironically, it was not ME who got sent to the dog-house for this.

“It’s not a trap, I swear,” she texted back.  Then she spent the next seven days asking me a  questions…

If you had a pet, would you want a sweet, likeable dog, or a mean, evil cat?

If you had a dog, would you want an outside dog or a hypoallergenic inside dog?

If you had a inside dog, would you want a medium-sized dog or a small-sized dog?

If you had a medium-sized indoor dog, would you want dark fur or light fur?

If you had a medium-sized, dark-furred indoor dog, would you want a puppy or an older dog?

If we were going to pick up a medium-sized, dark-furred indoor puppy right now, would you want it to sit in the front seat or the back seat?

It wasn’t until we were driving back to Rapid City with a medium-sized, dark-furred indoor puppy seated between the Ladybug and the Butterfly that I realized my wife had just Love-and-Logicked me into getting a dog.

Without further ado, meet the newest member of the Komplexify clan, our dog Cauchy.

A bug and her dog.

So why call him Cauchy?

Because he leaves a residue around every pole! [ Rimshot! ]

Additionally, the name “Meromorphic function” wouldn’t fit on the dog’s collar.

Cauchy is a 3-month-old puppy who weighs about 2 pounds, most of that being a coat of soft but thick brown-black fur.  The dog breeder said that we should expect him to grow to “medium-sized” 25 pounds, although the vet we took him to afterwards politely suggested that this estimate was off by an order of magnitude.  Said differently, Cauchy will always look like a wire frame to which someone added back wool.

The dog is cute, almost irritatingly so.  It doesn’t hurt his overall “cutesy” factor that his breed is something called a Labradoodle, a portmanteau that is supposed to communicate the fact that the dog is a crossbreed between a Labrador Retriever and a Poodle, but in actuality merely sounds like a three-year-old’s description of dog urine.  In fact, Cauchy is a crossbreed between a Labradoodle and a Poodle, which I suppose technically makes him a Labradoodleoodle and, consequently, Ned Flander’s dog.

It looks like you hi-diddly-doodled all over the carpet again.

I’ve been trying to come up with a less infantile-sounding name with which to describe Cauchy.  I thought Poodrador had a fierce, vaguely Spanish-explorer-y sound to it, until the Butterfly cheerily noted that this required saying Poo first and promptly cracked up.  I shant even go down the rabbit hole into which Poobrador leads.  I have since decided to simply refer to Cauchy’s breed as Mutt.

When people ask “What is he?” I just say “A dog.”

Personality-wise, Cauchy is very much a puppy. He only likes to do three things: bite, eat, and pee, although not necessarily in that order.  We wanted to prevent the dog from both chewing up and eliminating in our house, so to help him to ignore the carpet we got him food to eat, toys to chew on, potty-pads to pee on.  Unfortunately, whatever software Cauchy runs on has an Off-By-One error in it, because at run-time the dog invariably ignores the food, eats the toys, chews on the potty-pads, and pees on the carpet.

Cauchy is also remarkably hyper, to the point that when he gets too excited he quite literally stops existing in ordinary space-time and instead becomes a quantum distribution of fur and puppy teeth distributed across the current room.  He also can be in the process of peeing in any instant at which it is not being unobserved.  What I’m saying is that when it came time to choose an animal to exemplify quantum counter-weirdness, Erwin Schrödinger picked the wrong one.

Schrodinger’s cat walks into a bar. AND DOESN’T.

While Cauchy can be (and is) out and about while the family is home, during the school hours he is corralled in a largish dog pen in our kid’s playroom, partly to keep him from hurting himself, but mostly to keep him from turning our house into a composter.  The Queen B and I set up an octagonal corral lined by metal fencing and equipped with both a cozy pillowed kennel for naptime and a waterproofed tarp flooring for craptime.  When we left for school on Monday morning, we placed him in his kennel with food and toys; when we returned home Monday afternoon, we found Cauchy waiting impatiently for us in the kitchen sitting in a puddle of his own labdradiddle. Apparently, he took his six hours of unsupervised free time to teach himself how to pull his barely-foot-long canine self up and over the two-foot-tall corral fence.  Indeed, he taught himself so well that when we placed him in the corral that evening to see how he did it, he obliged… in just under two minutes.

Over the next two weeks, the dog and I engaged in an incarceration arms race, with me trying to find ways to make his corral escape-proof and he trying to Andy-Dufresne his way out to freedom. In fact, he escaped so often that we considered changing his name from Cauchy to Hairy Houndini.

After viewing the surveillance footage, I also briefly considered renaming him “Goddamitdog.”

I tried putting chicken wire around the fence to prevent him from getting his paws in-between the rungs of the fence; he learned to climb with just his claws like a poochified Peter Parker.  I tried building an inverted “sneeze guard” along the top of the fence to prevent him from getting his paws over it; he learned to climb with this teeth.  I put in an alligator-filled moat around the corral; he learned to swim and alligator-wrestle.  I replaced the original 2-foot-tall fence with a four-foot-tall one; he built a grappling hook out of some rope and chew toy and scaled his ass up.  We’ve currently reached an impasse: his corral now has four-foot-high walls covered with  a tough but flexible plastic netting for which Cauchy has yet to devise an counter strategy, although he does seem to spend a lot of time with that Reta Hayworth poster he asked to be hung up in his kennel….

It always comes down to two choices: get busy living, or get busy dying.

I think the prison time has hardened Cauchy too.  The last time he escaped, he straight-up murdered our robot vacuum MO with a shiv he’d whittled out of a piece of bone.  Okay, in point of fact, he only chewed through MO’s power cord, but still…. coldbloodedmurder.

Behold the face of evil… EEEEEEVIL!!!

Welcome to the family, dog. Please don’t kill us all in our sleep.

Posted in komplexify | Leave a comment

The Star Wars/Predator mash-up you never knew you needed. Because you didn’t.

Posted in flixify, nerdify | Leave a comment