From the USM Southworth Planetarium
“The bronzed guy has trouble viewing Colorado’s border markers. In other words, the tan gent can’t see the CO signs.”
THE DAILY ASTRONOMER
July 11, 2011
The Impossible Assignment
“How is this astronomical?”
“What is she, nuts?”
“To hell with this!”
“And, of course it’s 90 degrees today and we’re in here.”
“What is she, kidding?”
“I don’t think this is possible.”
I made that last statement, to the chagrin and amusement of the receding gray hair (who spoke first), the scraggly beard (who questioned Dr. Evergreen’s sanity), the public radio tote bag (she said ‘Hell’), the bead necklace who told us the temperature, and the Sox Cap who spoke just before I did. (He was also the one who snidely said, “Ya think?” after I made my profound pronouncement.)
All six of us stood dumbfounded in the fourth floor classroom. We had been there for awhile, staring hopelessly at a pyramid of empty boxes arranged neatly in the room’s center. (All the chairs were arranged circularly around them.) It resemled a cardboard wedding cake. We counted five boxes in a stack and each one was slightly larger than the box above it. Altogether, the box pyramid reached five feet, enabling everyone except for the bead necklace to look down at it easily. Two slightly curled-up Post-it-notes, taped together so as to make a larger writing surface, rested on the box stack. The note read, “Fit these in the red box in the corner.” Finding that box wasn’t easy, as it was so infuriatingly tiny: just big enough, or so the Red Sox Cap determined, to accommodate two cigarette packs.
“What do we do?” Bead necklace asked, looking a bit frightened. “We only have half an hour.”
I should explain that this task was an assignment Dr. Evergreen gave to us earlier. Dr. Evergreen was the shape-shifting professor of the newly fashioned “Astronomical Geometry” course. It was one of those fusion courses combining two somewhat-related disciplines. We called her the “shape shifter” because her appearance varied drastically from one class to the next. Not only her clothes (the first class she wore biker chains, the second a gym suit; the next she sported a gingham pinafore), but her hair style, eye color voice and, amazingly, height and weight. Having earned degrees in theatre as well as mathematics, she was passionate about characters and assumed a different one each time. Such alterations required platform shoes, protesthics and a variety of other costume accessories. As she explained to us during the class in which she stood before us masquerading as Hypathia, “living a thousand lives in fragments is the only way to live my life.” And, as Dr. Evergreen was quite good at changing her voice, appearance and behaviour, most of us looked forward to class if for nothing else than for the entertainment value. The amusement almost made up for the exhaustion, as we moved constantly in her class, working out this problem and that one, for she preferred real world exercises and applications to what she called the “droll lecture format.”
We never quite knew what to expect in each class.
A perfect example was, well, the day in which six of us ended up standing around a box pyramid. The entire class had earlier been in the room, impatiently waiting for Dr. Evergreen to arrive. It was actually more crowded that usual. Not a surprise. Some students had recently taken to bringing friends to class to ‘experience Evergreen.’ These visitors seem to increase in number with each class. She was becoming something of an attraction. Yet, she was nowhere to be found when class was supposed to begin. That was a shock, actually, as she promised us she would never be late for class. (So much for professorial promises.) Five minutes later, still nothing but the empty space in front of the chalkboard. We were getting restless and wondering if the day’s session would be cancelled. By the time a few people were preparing to depart, a large, plump-faced man barged into the classroom, causing a few students closest to the door to jerk back in their seats. Without so much as a ‘hello,’ this furious intruder pointed toward the shocked students in the first row. “Room 101!”
“What?” a brave student asked, looking a bit perplexed. The man shouted, “First row students to Room 101!” However, nobody moved, but instead stared frightfully at the quarter-ton terror looming before them. He repeated the command yet again and sounded all the more enraged.
“First row students will report to Room 101 at once!”
At this, another student addressesd the fat man from the safety of the distant corner. “Hello, Dr. Evergreen!”
“His name’s Dr. Bryce, actually,” a young lady said, rising from her seat toward the room’s center. “My former drama coach.”
We watched Dr. Evergreen, completely unrecognizable as a ‘visitor’ with a black wig, move from the desk to the front of the classroom. “Apart from being ruggedly handsome,” Dr. Evergreen announced cheerfully as she approached and then hugged the large man, “Dr. Bryce is a bit of a devil. Loves to go around different classrooms, making students think he’s me. We’re hard to tell apart, you see.”
She moved away from grinning Bryce and addressed the classroom. “You will find different challenges scattered around the building today. Your job is to use your brain to defeat these challenges and perhaps learn something in the process.” She turned to the students in the first row. “As Dr. Bryce hinted, your challenge is in Room 101. Everyone on the first row go there now and follow the instructions you find. Row Two students, please report to Room 201. Row Three, proceed to Room 301. And, you guys in Row Four…”
“401?” Gray hair asked.
“417,” Dr. Evergreen answered. “Kill me if I ever become predicatable.”
So, there we were in Room 417 looking at the box pyramid. After another tense moment, Gray hair walked to the chalkboard. “We might as well try to work it out.”
“How?” Sox cap snapped.
“Geometry, I assume,” Gray hair said softly. “After all, geometry is the point of this class, isn’t it? Certainly isn’t much astronomy in it..”
“What are you going to write on the board for?”
“Making measurements,” Gray replied matter-of-factly. “Let’s just measure the boxes and then see what we can do.”
That is precisely what we did. Well, all except for the public radio tote bag who lingered in the corner looking disgruntled. We brought the little red box over next to the boxes. That made us feel all the worse, of course, for we truly saw how large the pyramid was relative to the red box. Using our rulers, we determined that the largest box was 18 inches along the side; the second was 14; the third was 12, the fourth was 9 and the fifth was 7 inches. The red box measured four inches by two by 1.5.
Gray hair wrote all these numbers on the chalkboard and though his columns were admirably straight, it didn’t seem to help much. As we stood there in despair, Bead Necklace had an inspired idea. “Let’s break the boxes down!” We discovered that, fortunately, the boxes were all empty and could easily be opened. With nothing else for it, we all pulled apart the boxes. Scraggly beard became suddenly elated. He pulled a calculator out of his shirt pocket and hopped to the chalkboard.
“The volume of each box, assuming they’re perfectly cubical,” Scraggly beard interjected pedantically, “is equal to the cube of its side. So, the first box is 5832 cubic inches, the second is 2744; the third 1728; the fourth 729 and the fifth 343. Now, I could add those volumes together, but that would be tedious. Let’s just say that by breaking down the boxes, we’ve eliminated thousands of cubic inches from the problem. They are all now flat, so it’s no longer an issue of volume, but surface area. We have reduced the problem from a cube to a square, for, as you know, the area of a plane is proportional to the square of the side.”
“It won’t help,” Tote Bag protested. ” The cardboard has thickness, so you have to add that to the surface area and to stuff it into the small box, you have to fold it repeatedly. It’s still a volume problem.”
Shraggly Beard shrugged, “Well, maybe in reality it is, but on paper…”
“Look!” Sox Cap said, pointing to the broken-down boxes on the floor. “There’s no way we’re going to fit those into the small box.” He looked over at Shraggly Beard. “Hey, Einstein. Tell us the volume of the small red box.”
“Twelve cubic inches,” he replied proudly as he didn’t require a calculator for that calculation.
Sox Cap looked at us and seemed to deflate. “Twelve cubic inches! Someone explain to me how that will work!”
A minute passed without a reponse, until Bead Necklace stepped forward, her face bright with a sudden fervor. “I have an idea. What do we know about the boxes?” She didn’t wait long for the answers that we didn’t offer. “They’re empty space!”
“Not now that you’ve broken them down,” Gray hair said.
“I don’t mean that,” Necklace answered testily. “I mean that cardboard itself. It is mostly empty space, isn’t it? I mean, microscopically or quantumly, or however you want to say it. There’s hardly any matter there. In fact, if we could squeeze all the matter out of it, like what happens to neutron stars, the boxes would fit. In fact, they’d fit with plenty of room to spare. I even heard that the Empire State Building would be a small marble if all the empty space within its material were removed. Now, if the Empire State Building could fit inside that little box, this cardboard should.”
“And, how,” Gray Hair inquired with a determined calm, “do you propose to produce the forces necessary to compress the boxes down to that small a volume?”
“I saw some bricks outside,” I interjected.
“Neutron stars form because big stars collapse in on themselves,” Beard remarked disdainfully. “You can’t replicate that kind of force with bricks.”
“They’re those large concrete bricks,” I said.
“In theory, your idea could work,” Gray hair gently told Bead Necklace. “But, I am afraid we can’t do it in practise.”
“Unless we find a collapsing star out in the parking lot,” Sox Cap suggested, smirking in response to Necklace’s dark scowl.
Tote Bag stepped forward “What if we can reduce its volume another way?”
Gray hair looked at her. “In what way?”
“Burning,” Tote Bag said, taking a lighter out of her, um, tote bag.
“What is she, nuts?” (Yes, that was Scraggly Beard who said that, yet again.)
“We burn the boxes, reducing it to ashe and then pour the ashes into the small box. We will have made the boxes fit by chemically reducing the cardboard’s volume. Dr. Evergreen encourages us to be creative.”
“Yes,” Sox Cap seethed. “but not to commit arson.”
“We’ll take it outside and burn it. Collect the ashe and bring it back into the classroom. Simple as that.”
“But that won’t fulfill the requirements. The burning will turn some of the cardboard into ashe, but some will become smoke, which we cannot put into the box as it will float away into the atmosphere.” Scraggly beard proved rather insightful about physics.
Tote Bag rounded on him. “Do you have any better ideas?”
Nobody did. We also realized that our time was almost up, so three of us gathered the cardboard boxes into our arms while the others helpfully stood by the treshhold incase the door spontaneously slammed on its own accord. Dr. Evergreen met us in the corridor just outside the classroom.
“May I ask where you genuiuses are taking that?”
“Outside.”
“And why, may I ask?”
Silence. None of us were quite sure how to dress up the phrase “to burn it.”
Finally, Beard said, “We have an idea how to put the boxes into the small box.”
“Really?!” Dr. Evergreen answered, sounding genuinely impressed.
Beard brightened. “Yes!”
Evergreen’s face darkened. “Let’s go back in the classroom and discuss this.”
As though on a death march, we followed Dr. Evergreen into the classroom. She watched us all file back inside. Those of us carrying boxes held onto them while the professor walked into the room’s center. While we observed her fearfully, she picked up the post-it-notes and the small red box from the floor. “Can somebody remind me what these notes said?”
“Aren’t you actually looking at them now?” Beard asked. He then looked down ashen faced in response to Dr. Evergreen’s withering stare.
“It says, ‘Fit these in the red box in the corner.’ Are you sure you read this note carefully?”
“Yes,” Gray hair replied. “I assure you we did.”
“And we’ve spent the last thirty minutes trying to fit these into that small box,” Sox Cap said sharply, as he slapped the boxes.
Dr. Evergreen raised the post-it-notes above her head. “THESE!” She then slid the two post-it-notes into the small red box. “You were supposed to place those two taped notes into the box, not the pyramid of boxes. I was going to use those for something else, but seeing as my brilliant students have torn them up and are hellbent on torching them, I’ll have to find others.”
“You meant the notes?!” Sox Cap shouted, dropping the boxes.
“It’s admirable the way you can grasp the meaning of plainly phrased statements. You all just assumed I meant the boxes. That’s the trick about indefinite pronouns. Never quite sure what they mean. You could have asked, because sometimes creative thinking involves knowing when to ask the right question.”
After letting this soak in, she said. “The secret to success in geometry and astronomy is the same as the secret to success in marriage.” With a wink, she concluded, “Follow directions.”