Quantam Physicists Invent Quantum Car.
Drivers can get to destination by not starting the car.
In the wake of the Quantum computer which can solve an algorithm by not running it, scientists at the University of Illinois at Urbana-Champaign have invented a new Quantum car, which carries passengers to their destination by not driving.
Quantum cars have the potential for getting to certain destinations much faster than classical cars. Speed and efficiency are gained because quantum cars can be placed in superpositions of being both driving and not driving, as opposed to classical cars, which are either driving or not driving.
"It seems absolutely bizarre that counterfactual driving – using driving that is counter to what must have actually happened – could get a passenger to his destination without driving the quantum car," said Paul Kwiat, a John Bardeen Professor of Electrical and Computer Engineering and Physics at Illinois. "But the nature of quantum driving makes this amazing feat possible."
By placing our car in a quantum superposition of driving and not driving the route, we reached the destination even when the car did not drive," said graduate student Onur Hosten, lead author of the Nature paper. "We also showed theoretically how to get to the destination without ever running the car, by using a 'chained Zeno' effect."
Through clever use of beam splitters and both constructive and destructive interference, the researchers can put each car in a superposition of taking two paths. Although a car can occupy multiple places simultaneously, it can only make an actual appearance at one location. Its presence defines its path, and that can, in a very strange way, negate the need for the car to drive
"In a sense, it is the possibility that the car could drive which prevents the car from driving," Kwiat said. "That is at the heart of quantum driving schemes, and to my mind, quantum mechanics doesn't get any more mysterious than this."
Editor's note: upon completion of this article, the author's head exploded from trying to grasp the concepts contained within.
Tuesday, February 28, 2006
Jasonzonbayhoo.com
Haas School: Prof. John Morgan Shows Sellers How to Boost Profits on eBay
Key line: "[The] findings suggest consumers pay less attention or even completely overlook shipping costs when making bids, the professors conclude."
Haas School: Prof. John Morgan Shows Sellers How to Boost Profits on eBay
Key line: "[The] findings suggest consumers pay less attention or even completely overlook shipping costs when making bids, the professors conclude."
Monday, February 27, 2006
Horoscopes.
Every time a bell rings, a tech support consultant breaks down and cries because some idiot has called him.
Aries: (March 21—April 19)
Your inability to follow simple step-by-step instruction in order may cause a choking hazard next Tuesday when the wrapper on your deli sandwich says "1: Remove toothpick. 2: Eat sandwich."
Taurus: (April. 20—May 20)
The Page Up and Page Down toolbar buttons can be used to view the diagram above or below the current selection.
Gemini: (May 21—June 21)
Many of your problems can be solved by taking the manual, putting it on your chair, standing on it so you can see over your cubicle wall, and shouting "does anyone know how to read a manual?"
Cancer: (June 22—July 22)
The stars can't help you understand the complexities of the English language because phrases like "click the 'Add Block' toolbar button to add a new block" baffle them, too.
Leo: (July 23—Aug. 22)
The Page Up and Page Down toolbar buttons still change the view to show the diagram above or below the current selection, just like last time.
Virgo: (Aug. 23—Sept. 22)
It is true that your supplier's delivery date was pushed back by several weeks, but when you evaluate them, the stars recommend you keep in mind that it was you who sent the wrong user requirements document. Unlike the stars, the supplier isn't telepathic, you know.
Libra: (Sept. 23—Oct. 23)
The stars really have to wonder why you think the poor technical consultant really needs to know every detail of your plans for the next 8 months. The snoring coming out of the phone is because you bored him to sleep. Please hang up and try your call again never.
Scorpio: (Oct. 24—Nov. 21)
Y'know what? You can change the view to above or below the current selection by using the Page Up and Page Down toolbar buttons. No, really. It still works that way.
Sagittarius: (Nov. 22—Dec. 21)
A "Standalone" install is for use on a single computer. A "Network" install allows many users access to the software on a network.
Capricorn: (Dec. 22—Jan. 19)
In case you hadn't figured it out from the previous horoscope, a "Network" install is, in fact, more appropriate for a network server.
Aquarius: (Jan. 20—Feb. 18)
The Page Up and Page Down toolbar buttons can no longer be used to change the view. Nah, the stars are just messing with you. Of course they can. Just like the last 50 times you asked how to change the view.
Pisces: (Feb. 19—March 20)
All your calls to the help desk will go unanswered next week because the Technical Support Consultant hung himself on his phone cord.
Every time a bell rings, a tech support consultant breaks down and cries because some idiot has called him.
Aries: (March 21—April 19)
Your inability to follow simple step-by-step instruction in order may cause a choking hazard next Tuesday when the wrapper on your deli sandwich says "1: Remove toothpick. 2: Eat sandwich."
Taurus: (April. 20—May 20)
The Page Up and Page Down toolbar buttons can be used to view the diagram above or below the current selection.
Gemini: (May 21—June 21)
Many of your problems can be solved by taking the manual, putting it on your chair, standing on it so you can see over your cubicle wall, and shouting "does anyone know how to read a manual?"
Cancer: (June 22—July 22)
The stars can't help you understand the complexities of the English language because phrases like "click the 'Add Block' toolbar button to add a new block" baffle them, too.
Leo: (July 23—Aug. 22)
The Page Up and Page Down toolbar buttons still change the view to show the diagram above or below the current selection, just like last time.
Virgo: (Aug. 23—Sept. 22)
It is true that your supplier's delivery date was pushed back by several weeks, but when you evaluate them, the stars recommend you keep in mind that it was you who sent the wrong user requirements document. Unlike the stars, the supplier isn't telepathic, you know.
Libra: (Sept. 23—Oct. 23)
The stars really have to wonder why you think the poor technical consultant really needs to know every detail of your plans for the next 8 months. The snoring coming out of the phone is because you bored him to sleep. Please hang up and try your call again never.
Scorpio: (Oct. 24—Nov. 21)
Y'know what? You can change the view to above or below the current selection by using the Page Up and Page Down toolbar buttons. No, really. It still works that way.
Sagittarius: (Nov. 22—Dec. 21)
A "Standalone" install is for use on a single computer. A "Network" install allows many users access to the software on a network.
Capricorn: (Dec. 22—Jan. 19)
In case you hadn't figured it out from the previous horoscope, a "Network" install is, in fact, more appropriate for a network server.
Aquarius: (Jan. 20—Feb. 18)
The Page Up and Page Down toolbar buttons can no longer be used to change the view. Nah, the stars are just messing with you. Of course they can. Just like the last 50 times you asked how to change the view.
Pisces: (Feb. 19—March 20)
All your calls to the help desk will go unanswered next week because the Technical Support Consultant hung himself on his phone cord.
Friday, February 24, 2006
Pure Pwnage.
Ok, in case you couldn't figure it out from the subliminal links in the earlier post, go to PurePwnage. "Anonymous" first linked to the FPS Doug video in a post a while back, but I don't think too many people saw it. I also stumbled across "WoW is a Feeling" some time ago, too.
The whole group of 9 shorts (averaging between 15 and 25 minutes each) are quite humorous, and the quality just goes up with each one.
(Mandatory adult language warning.)
Oh, and for those of you who still doubt my DoD abilities and claim that I can only Run 'n' Gun, while real men play rifleman, I say stick it in your ear:
That's some good ol' fashioned one-shot-one-kill bolt-action K98 goodness. (map was dod_donner.)
Boom! Headshot!
I can dance all day! I can dance all day! Try 'n' hit me! Try 'n' hit me!
My heart's beatin', my heart's beatin, and my hands are shakin' but I'm still shootin' and I'm still gettin' headshots!
Ok, in case you couldn't figure it out from the subliminal links in the earlier post, go to PurePwnage. "Anonymous" first linked to the FPS Doug video in a post a while back, but I don't think too many people saw it. I also stumbled across "WoW is a Feeling" some time ago, too.
The whole group of 9 shorts (averaging between 15 and 25 minutes each) are quite humorous, and the quality just goes up with each one.
(Mandatory adult language warning.)
Oh, and for those of you who still doubt my DoD abilities and claim that I can only Run 'n' Gun, while real men play rifleman, I say stick it in your ear:
That's some good ol' fashioned one-shot-one-kill bolt-action K98 goodness. (map was dod_donner.)
Boom! Headshot!
I can dance all day! I can dance all day! Try 'n' hit me! Try 'n' hit me!
My heart's beatin', my heart's beatin, and my hands are shakin' but I'm still shootin' and I'm still gettin' headshots!
Kitty Update.
Well, the kittens have gotten a bit bigger since last time. They're now around 5 lbs. each, as opposed to the 8 ounces or so when we took them home.
As they've gotten older, personalities have begun to emerge.
Isis is definitely a "people cat". She loves to be held and loves to be around us. When we're sitting on the couch watching a DVD, she's usually curled up in between us.
As it turns out, Polly would have been a good name for her as she has taken to perching on shoulders.
Boy do I need to shave!
Her favorite hobbies while sitting on my shoulder include
1) Chewing on my glasses,
2) Chewing on my ears, and
3) Licking my hair
I've decided to stop bathing and will instead have the kitties lick me clean.
Other nicknames she has earned are "The Purry One" and "Six Toes".
Bastet is more of a loner kitty. She likes people, but on her own terms. She likes being in the same room as us, but not being held. She is a little bit of a Freaka-Cat and has earned the nickname "The Sniffy One" because she often intently smells things (especially people), probably trying to decide if they're edible
Both kitties are trouble-makers, but in different ways. Isis is a trouble-makers of the "chewing" variety, as she has grown quite adept at pulling my glasses off my face so she can chew on the stem, and is responsible for the severing of at leastthree four headphone cords.
Bastet, on the other hand, is a trouble-maker of the "exploratory" variety. She has already learned to open doors if they're left ajar, and has defied all attempts we've made at containing her. Initially, we kept them in the kitchen, to keep them out of harms way. First we did this by blocking the entrance with suitcases (which they both quickly learned to climb) and then later with cardboard boxes (which they couldn't climb). When Bastet learned she could jump right over the boxes, it became apparent that corraling kitties is not a simple task, and by that point they were big enough that we decided to let them run around in the living room. Even still, Bastet still gets into trouble by climbing under the couch, then up inside it, despite our sincerest efforts to completely block off the bottom.
Humorously, Bastet learned to climb the suitcases first, and while Isis was trying to figure it out Bastet would stand at the top and step on Isis toes when she got close to the top.
Speaking of off-limits places, one place they don't go is the trash in the kitchen, despite its easy accessibility. Shortly after we first got them, the learned to climb their cage and from there, jump onto the trash in the kitchen. Not wanting them rolling around in the trash, Anne Marie threw a towel over the trash so they would sit on that instead. By the next day, the trash had been emptied and while I intentionally left the towel off the trash can so they could see it was empty, Rie put the towel back over the empty can. I asked her if that was such a good idea, since they might think they could walk on it. As soon as I had said that, we both looked at each other with the same idea. The kitties were both on top of their cage, so we got their attention with one of their favorite toys (a catnip mouse) and dropped the mouse on top of the towel. Both kitties jumped for it and both fell into the empty trash can. Isis calmly jumped out, but Bastet freaked, poofed up, and ran to the other side of the kitchen. Neither cat has jumped on top of the trash can since.
Bastet actually poofs quite easily. One of the funnier incidents was when I dropped their catnip mouse in the kitchen. Bastet jumped for it, which startled Isis, who hissed and turned towards Bastet, which startled Bastet, who hissed and jumped back, landing in their water dish, which startled her even more and made her hiss and poof up.
Now that they run around in the living room, they've both taken to jumping on my desk and "helping" me play games.
They both love the hippogryphs in WoW. I think it's something about the flapping wings.
She knows Claw (Rank 1). 25 Focus, 5 yard range. Claw the enemy, causing 4 to 6 damage.
On more than one occasion, Bastet has blocked my view at a critical time in DoD, causing my pwnage by some n00b.
Boom! Headshot!
In addition to "Kitty Stummy Therapy" Other uses I've found for kitties includes Kitty Scarves and Kitty Earmuffs. So warm and fuzzy!
I'm so glad we got them together, as they're best friends. They usually sleep next to each other, and often play with and groom each other. Sometimes they sweetly try to bite the other one's neck.
Shoelaces: a kitten's second favorite toy (first favorite being the other kitten's tail).
She looks so cute! Kitty with a bow!
She's thinking "this is it. I'm going to kill them."
Awwww. Kitties love curling up with the Murloc.
Well, the kittens have gotten a bit bigger since last time. They're now around 5 lbs. each, as opposed to the 8 ounces or so when we took them home.
As they've gotten older, personalities have begun to emerge.
Isis is definitely a "people cat". She loves to be held and loves to be around us. When we're sitting on the couch watching a DVD, she's usually curled up in between us.
As it turns out, Polly would have been a good name for her as she has taken to perching on shoulders.
Boy do I need to shave!
Her favorite hobbies while sitting on my shoulder include
1) Chewing on my glasses,
2) Chewing on my ears, and
3) Licking my hair
I've decided to stop bathing and will instead have the kitties lick me clean.
Other nicknames she has earned are "The Purry One" and "Six Toes".
Bastet is more of a loner kitty. She likes people, but on her own terms. She likes being in the same room as us, but not being held. She is a little bit of a Freaka-Cat and has earned the nickname "The Sniffy One" because she often intently smells things (especially people), probably trying to decide if they're edible
Both kitties are trouble-makers, but in different ways. Isis is a trouble-makers of the "chewing" variety, as she has grown quite adept at pulling my glasses off my face so she can chew on the stem, and is responsible for the severing of at least
Bastet, on the other hand, is a trouble-maker of the "exploratory" variety. She has already learned to open doors if they're left ajar, and has defied all attempts we've made at containing her. Initially, we kept them in the kitchen, to keep them out of harms way. First we did this by blocking the entrance with suitcases (which they both quickly learned to climb) and then later with cardboard boxes (which they couldn't climb). When Bastet learned she could jump right over the boxes, it became apparent that corraling kitties is not a simple task, and by that point they were big enough that we decided to let them run around in the living room. Even still, Bastet still gets into trouble by climbing under the couch, then up inside it, despite our sincerest efforts to completely block off the bottom.
Humorously, Bastet learned to climb the suitcases first, and while Isis was trying to figure it out Bastet would stand at the top and step on Isis toes when she got close to the top.
Speaking of off-limits places, one place they don't go is the trash in the kitchen, despite its easy accessibility. Shortly after we first got them, the learned to climb their cage and from there, jump onto the trash in the kitchen. Not wanting them rolling around in the trash, Anne Marie threw a towel over the trash so they would sit on that instead. By the next day, the trash had been emptied and while I intentionally left the towel off the trash can so they could see it was empty, Rie put the towel back over the empty can. I asked her if that was such a good idea, since they might think they could walk on it. As soon as I had said that, we both looked at each other with the same idea. The kitties were both on top of their cage, so we got their attention with one of their favorite toys (a catnip mouse) and dropped the mouse on top of the towel. Both kitties jumped for it and both fell into the empty trash can. Isis calmly jumped out, but Bastet freaked, poofed up, and ran to the other side of the kitchen. Neither cat has jumped on top of the trash can since.
Bastet actually poofs quite easily. One of the funnier incidents was when I dropped their catnip mouse in the kitchen. Bastet jumped for it, which startled Isis, who hissed and turned towards Bastet, which startled Bastet, who hissed and jumped back, landing in their water dish, which startled her even more and made her hiss and poof up.
Now that they run around in the living room, they've both taken to jumping on my desk and "helping" me play games.
They both love the hippogryphs in WoW. I think it's something about the flapping wings.
She knows Claw (Rank 1). 25 Focus, 5 yard range. Claw the enemy, causing 4 to 6 damage.
On more than one occasion, Bastet has blocked my view at a critical time in DoD, causing my pwnage by some n00b.
Boom! Headshot!
In addition to "Kitty Stummy Therapy" Other uses I've found for kitties includes Kitty Scarves and Kitty Earmuffs. So warm and fuzzy!
I'm so glad we got them together, as they're best friends. They usually sleep next to each other, and often play with and groom each other. Sometimes they sweetly try to bite the other one's neck.
Shoelaces: a kitten's second favorite toy (first favorite being the other kitten's tail).
She looks so cute! Kitty with a bow!
She's thinking "this is it. I'm going to kill them."
Awwww. Kitties love curling up with the Murloc.
Friday, February 10, 2006
Mathematics can solve everything.
The Science Creative Quarterly » A GAME THEORETIC APPROACH TO THE TOILET SEAT PROBLEM
The Science Creative Quarterly » A GAME THEORETIC APPROACH TO THE TOILET SEAT PROBLEM
From the Gamestop front page.
Gamestop.com - Home:
"Star Wars: Empire At War
Free Death Star* with Pre-Order!
In a galaxy between Episode III and Episode IV become a galactic commander as you choose to either battle the Empire or to crush the Rebellion at its roots. Collector's Edition also available.
*Death Star is a desktop ball."
Oh, and I so much wanted a real Death Star.
Gamestop.com - Home:
"Star Wars: Empire At War
Free Death Star* with Pre-Order!
In a galaxy between Episode III and Episode IV become a galactic commander as you choose to either battle the Empire or to crush the Rebellion at its roots. Collector's Edition also available.
*Death Star is a desktop ball."
Oh, and I so much wanted a real Death Star.
Whadya know, Roger Ebert Can Be Funny.
Roger Ebert - Final Destination 3
As a lover of the morbid and macabre, I took a grim appreciation of the first two FD movies, as they were just essentially movies about unpleasant ways to die. They primarily consisted of improbable Rube Goldberg devices that ended in someone's death. For instance, in one of the movies (I think the first one) a woman pours coffee into her mug which, unbeknownst to her, cracks and begins to leak. She then walks from the kitchen to the den, where she places the mug on top of her computer monitor. A few minutes later, she comes back and turns on the computer when the monitor, which has been short-circuited by dripping coffee, explodes, sending shards of glass flying into her neck, which begins to squirt blood everywhere, and starts a fire. She then proceeds to run around the house, blood spurting everywhere, things catching on fire as if her entire house had been built out of Kingston Quick-Lighting Charcoal. She runs in to the kitchen to get the phone, but slips on a coffee spill and lands on the floor next to the counter. She can still barely reach a towel which is dangling off the counter and as she pulls it from the counter, a knife, which had been sitting on top of the towel, falls and impales her, killing her.
Cinema at its finest.
Roger Ebert - Final Destination 3
As a lover of the morbid and macabre, I took a grim appreciation of the first two FD movies, as they were just essentially movies about unpleasant ways to die. They primarily consisted of improbable Rube Goldberg devices that ended in someone's death. For instance, in one of the movies (I think the first one) a woman pours coffee into her mug which, unbeknownst to her, cracks and begins to leak. She then walks from the kitchen to the den, where she places the mug on top of her computer monitor. A few minutes later, she comes back and turns on the computer when the monitor, which has been short-circuited by dripping coffee, explodes, sending shards of glass flying into her neck, which begins to squirt blood everywhere, and starts a fire. She then proceeds to run around the house, blood spurting everywhere, things catching on fire as if her entire house had been built out of Kingston Quick-Lighting Charcoal. She runs in to the kitchen to get the phone, but slips on a coffee spill and lands on the floor next to the counter. She can still barely reach a towel which is dangling off the counter and as she pulls it from the counter, a knife, which had been sitting on top of the towel, falls and impales her, killing her.
Cinema at its finest.
Thursday, February 9, 2006
Angst, the Musical
Good news, everyone! The archives of Angst Technology are finally back online!
InkTank.com - Angst Technology
If you have never read this funny web comic, I highly recommend it. I think it is my favorite web comic, easily beating out PVP. Too bad the artist is no longer creating it. /cry.
If I wasn't so gosh darn lazy, I'd link to my favorites, so those of you who are gosh darn lazy can just read the best ones.
Good news, everyone! The archives of Angst Technology are finally back online!
InkTank.com - Angst Technology
If you have never read this funny web comic, I highly recommend it. I think it is my favorite web comic, easily beating out PVP. Too bad the artist is no longer creating it. /cry.
If I wasn't so gosh darn lazy, I'd link to my favorites, so those of you who are gosh darn lazy can just read the best ones.
Frabjous Day, Kaloo, Kalay.
Telltale Games - Sam and Max
Also be sure to check out the Sam 'n Max web comic.
Telltale Games - Sam and Max
Also be sure to check out the Sam 'n Max web comic.
Wednesday, February 8, 2006
The Adventures of Ion, Intergalactic Milk-Man.
At the mere mention of this name, Cari and Tom are probably recoiling in horror and have collapsed in drooling siezures. But as much as we all hated Dr. Mrs. Salter at the time, in retrospect, I realized I learned more in her classes than in any others. Additionally, the stories of Ion are very interesting studies in the concept of infinity and I thought that those readers of FU-News who are mathenatically inclined but haven't had the love/hate experience of a class taught by Dr. Mrs. Salter (Mom and Dad B, Mrs. Pickles, The Blue Fox) might find these stories interesting.
Ion was first introduced to me by a certain professor of mathematics. While I had only swerving loyalty towards the professor in question, after just a brief amount of time talking with Ion, I discovered he had a wealth of humorous anecdotes and tales of mathematical intrigue.
It was during one of our many conversations that followed that he related to me the tales of his friend Calvin Q. Lator, owner of a very interesting chain of hotels. Cal, as Ion referred to him, was the owner of the "Inn of the Infinite Happiness" chain of hotels (slogan: "We've got a room for you, guarenteed"). What made this chain so notable, was that not only were there an infinite number of hotels in the chain, but each hotel had an infinite number of rooms. The actual mechanism that accomplished this is something of a trade secret, but it is known to involve poison gas, a closed box, and a cat that may or may not be dead (perhaps both). Cal kept his secret from absolutely everyone, except his own mother, Seeia.
So after one particularly taxing milk delivery run, Ion stopped at Cal's hotel near the Horsehead Nebula to get a good night's sleep before heading home. It was with a feeling of great relief that he entered the hotel's lobby, looking forward to some relaxation, and headed to the front desk.
"Hello," Ion said to the receptionist. "I'd like a room for tonight."
"I'm sorry sir, but we're full," came the receptionist's reply.
Ion's feeling of relief gave way to an even greater sense of confusion. "How can you be full? There are an infinite number of rooms?" asked Ion.
Upon hearing the elevated volume of his good friend's voice, Cal emerged from the office behind the front desk. He was a short, rotund man, scarcely five feet tall, and having a weight-to-height ratio of at least 36 lbs./ft. His balding hair gave one the impression that a tiny man with a tiny lawn mower had started cropping Cal's hair, but had gotten up to get a lemonade half-way through, with the job still unfinished. He was also exceptionally well dressed, wearing a nicely pressed suit jacket and pants, with a striped neck tie sporting the two-tone blue colors of the hotel chain. A gold watch chain hung from his pocket; Ion knew that on the back was inscribed "Cal, thanks for keeping one of your infinite doors open for me. G." Who 'G.' was, Ion didn't know, but the rumor was it was a famous actress or model, of the gorgeous persuasion. Cal wouldn't answer any questions on the subject prefering to keep people guessing. The reality was much tamer than the rumors, and Cal liked it that way.
Cal was quite the rich man, as being the owner of the Universe's largest hotel chain is prone to make one. He also had far more wrinkles than a man his age should have, and much of his remaining hair was grey, as having to manage an infinite number of hotels and rooms is prone to make one look older than one's peers.
"Ion! I'm both happy and sad that you have come to my hotel today," said Cal, as he greeted Ion with a firm handshake and a slap on the back. "Happy to see my friend once again, but sad because you have come at the one time where it seems I can't accomodate you."
Ion's puzzlement had not subsided. "How can that be? I don't understand how a hotel with an infinite number of rooms could possibly be full."
"One would not think it possible, but yet it has happened. You see," Cal began explaining, "the Association of Infinite Members has chosen this hotel for their convention this year. Since there are an infinite number of them, they have completely booked up my hotel! Every room is currently occupied by one of the convention-goers. Thank goodness no one else has come to get a room tonight. I'm afraid this could ruin my reputation."
"But surely, you can squeeze me in somewhere," pleaded Ion. "I mean, with an infinite number of rooms there's got to be an empty one."
"Not a one," Cal responded, upset that he had to turn away his good friend.
"Can you move a guest to another room?" asked Ion.
"Quite easily, but as I mentioned, all rooms are full. To what room would I move the guest?" Cal said, not really understanding where Ion was going with his question.
"Well then, I'll wager that you do have room for me. I'll wager you a lifetime supply of milk for an unlimited number of free hotel stays."
"That sounds reasonable," said Cal. "Now what room shall I put you in."
"Simple," said Ion. "Room 1."
"But Room 1 is occupied," said Cal. "I would have to move the occupant to another room."
"Yes, you shall move him to Room 2."
"But Room 2 is also occupied. Where shall I put him?"
"Room 3," replied ion. "You see, all you have to do is move the guest staying in Room N to Room N+1. There is still room for everyone in your infinite hotel. Should anyone else come into the hotel asking for X number of rooms, you just simply need to put them in Rooms 1 through X, and move every other guest to Room N + X."
"Astounding, Ion! I hadn't thought of that. Eegads, man, you're a genius."
"It's all part of the job of an intergalactic milk-man," replied Ion.
And so Ion was checked in and given the key card to access his room. Ion remarked that for a hotel with so many rooms, it was ironic that they only had one door. The rooms themselves didn't exist within normal space, but were instead accessed by sliding your room's key card through the control panel of a teleporter. When you opened the one hotel room door, you would be transported to your own private room. As Cal explained it to Ion, the process of moving a guest from one room to another was actually quite simple, and in fact, the guest didn't even know he was being moved. All that was done was the guest's key card was changed so that when he activated the teleporter, he was ported to Room N + 1, instead of Room N.
Ion had just gotten comfortable in his hotel room and was flipping through the infinite number of channels on the Hotel TV, when his phone rang. He hadn't told anyone where he was staying for the night, so it was with a small amount of curiosity that he answered the phone, wondering who it was.
"Hello?" queried Ion of the unknown caller on the other end.
"Ion! You must help me!" the caller said in a frenzied panic. It took Ion a moment to recognize the voice as belonging to Cal.
"What's the matter, Cal?" asked Ion.
"Oh, you must help me, Ion. You are the only one I could think to turn to, after you solved my last problem. You see, we've had a problem with double-booking. The Infinite Membered Consortium has booked this hotel for their convention also! We have an infinite number of rooms, so we didn't think to check for room availability. But I don't know what rooms to assign the infinite number of people who have just come into my hotel. I thought about using your suggestion of assigning them rooms 1 through X, and moving everyone else to Room N + X, but I can't move someone to Room N + ∞! There is no such room!" Ion was taken aback not by the problem, but by Cal's ability to somehow speak all that without ever stopping for a breath.
"Well," said Ion, "that certainly is a pickle. On the one hand, you have an infinite number of rooms, so you should be able to fit them in, but on the other hand, how do you fit an infinite number of people into a hotel that is already full?"
"My dilemma exactly. I fear it cannot be done," came Cal's nervous reply.
"Oh, of course it can be done!" said Ion. "And quite simply, too."
"Then please, enlighten me. Where can I put the guests who are waiting in my lobby?"
"Well, the first person should be assigned to Room 1, the second person to Room 3, the third to Room 5, and so forth."
"Yes, yes, but what of the people in those rooms?"
"I was getting to that. The person in Room 1 should be moved to Room 2; the person in Room 2 should be moved to Room 4; the person in Room 3 should be moved to Room 6, and so on," said Ion, smuggly. "You see, a guest staying in Room N should be moved to Room 2N. That way, only the even-numbered rooms are occupied leaving the odd-numbered rooms, of which there are an infinite number, available for the newcomers."
"Ah! I see! Thank you once again, Ion! You have saved my reputation."
Ion was barely able to get out the "You're" of "You're Welcome" before Cal, in a frenzy to begin accomodating his infinite number of patrons waiting in the lobby, hung up.
Much time passed by after that night (I say "much time" and not "many months" or "years" because depending on where in the galaxy you were, the orbital frequency of a planet's moons or of the planet itself changed dramatically). Ion and Cal had been corresponding in the time since they had last seen each other, but as all things of that nature go, the frequency of their correspondence waned with the passage of time. Then one moment, (I say "moment" because "day" is a very relative term depending on which planet you are on and what direction the side you are on is facing) Ion received an IGE-mail (inter-galactic e-mail) from Cal pleading for his help. The letter stated:
'Ion,
'You must help me. The Intergalactic Business Regulatory Commission is complaining that I have a monopoly on infinite-roomed hotel chains and forcing me to close all of my hotels but one and consolidate my guests to that one hotel. I can easily move guests from one hotel to another, but at the moment, all my hotels are completely full with an infinite number of conventions of societies with infinite members. I don't know how I can move an infinite number of guests from an infinite number of hotels into only one hotel, even if there are an infinite number of rooms. I fear this cannot be done, but I cannot afford to reimburse an infinite number of guests. I would be ruined! Please help me.
'Your friend,
Cal L.'
Ion had to think for quite a bit, but eventually offered Cal the following solution.
'Cal,
'It is, in fact, possible, so you needn't worry about going bankrupt. The answer is not trivial, and may take some explanation.
'What you need to do is come up with a function that, given a guest's hotel number and room number, will give you a new number for their room in your one remaining hotel. To begin, let's start making a list of all the rooms and all your hotels. Such a list would start out looking something like this, where the rows (m) correspond to the hotel and the columns (n) correspond to the rooms:
'Now we need to come up with a numbering system so that each hotel/room combo is counted. We can accomplish this by numbering the rooms in diagonals, as such:
'Now to come up with a function to figure out the new room numbers based on the old hotel/room combination.
'Note that for any hotel/room (M/N) combination, the number of the hotel at which the diagonal it lies on ends is M + N - 1. For instance, Hotel 2, Room 3 lies on the diagonal ending at Hotel 4. 2+3-1=4. Another way of looking at this might be that each diagonal corresponds to all hotel/room combinations that add to a given number. We can use this to our advantage.
'Now, let's take a look at a hotel/room combination's value in the list of all rooms. Remember this list value is the room number in the one remaining hotel that the guest will be assigned to. This list number is equal to the list number at the end of the diagonal above it, plus the position of the combination on the diagonal it is on. For instance, the list number of Hotel 2, Room 3 is equal to the list number at the end of the diagonal above it, 6, plus its position along its diagonal, 2. 6+2=8, which is the list number associated with Hotel 2, Room 3.
'A combination's position on the diagonal is just equal to its row number (M), and the hotel number at the end of the diagonal above it is (M + N - 1) - 1, or M + N - 2. Now to come up with a function relating the list value at the end of a diagonal to the hotel number at the end of the diagonal. A list of these hotel numbers and corresponding list values looks something like this:
1: 1
2: 3
3: 6
4: 10
5: 15
6: 21
'We can re-write the list values (new room numbers) as such:
1 = 1+0
3 = 2+1
6 = 3+3
10 = 4+6
15 = 5+10
21 = 6+15.
'The first addend is just the hotel number. The second addend (and this is trickier to see) is equal to half the difference between the hotel number and its perfect square. 1^2=1, half the difference of 1 and 1^2 is 0. 2^2=4, half of 2^2 - 2=1. 3^2=9, half of 9-3=3. 4^2=16, (16-4)/2=6, etc. Generally speaking, the second addend can be expressed as:
'So the whole value is:
'Now, this just relates the hotel number to the value next to it. To calculate the new room number based on the current hotel and room number, we substitute the hotel number at the end of the diagonal above the one our hotel/room combination lies on (M+N-2) into the above equation and add the position on the diagonal that the hotel/room combination lies upon (M). So the function to calculate the new room number of a guest staying at Hotel M, Room N is as follows:
'Which simplifies to:
'Your friend,
Ion
'P.S. Perhaps a simpler way of expressing this is as a piece-wise defined function. If instead of listing the new rooms in a diagonal fashion, we use a square numbering method like such:
'Then we can define the new room function as:
Cal was quite thankful for Ion's reply. He was most thankful, however, that he was able to "stick it to the man" and avoid bankruptcy, despite a very stern commissioner for the Intergalactic Business Regulatory Commission who seemed intent on closing Cal's hotels down. Cal thought that perhaps he must have inadvertantly offended the commissioner's mother.
Eventually, the commissioner was fired in a scandal whose details were not widely know, but it involved a weasel, a chainsaw, and a watermelon. As this commissioner was not well-liked among the businessmen of the intergalaxy, a group of them decided to throw a party to celebtrate their good fortune. Cal was hosting the party and in a particularly good mood, as it was mere seconds after the commissioner's dismissal that he was allowed to re-open the rest of the hotels in his chain. Cal had asked Ion to provide the milk for the party, and so he did, saying "it's what I do best."
It was at this party that Ion was hastily pulled aside by Cal. Cal had been having a very intense, yet friendly, argument with his business manager, Warren, after they had both had a few too many glasses of milk. Cal had been extolling the praises of Ion and how he'd saved him from bankruptcy and humiliation countless times (which is not necessarily an exageration if you are the manager of an infinite number of hotels). Warren agreed that this Ion fellow must be pretty smart, but wagered that he couldn't solve the hotels' every problem. In truth, he was feeling a bit threatened that Cal so frequently had to go to Ion for help, completely skipping over his manager.
"Nonsense," said Cal. "If anyone can solve one of the hotels' problems, Ion can. I'd wager the secret to my infinite hotels on it!"
"I will have to take you up on that," said Warren. It was then that Cal pulled Ion into the conversation and explained to him the stakes.
"I've wagered the secret of my infinite-roomed hotels against an infinite supply of the best wine with Warren here that if anyone can solve a problem about my hotels, you can," explained Cal.
"You have quite a lot of confidence in me, Cal," Ion said, just a bit nervous about being put on the spot. Then turning to Warren he said, "expain the problem to me."
Warren said, "I have a problem that's been nagging at me for a bit. It has to do with maintenance and assigning cleaning staff to one hotel. I would like to have a list of all possible configurations of the rooms in the hotel. Each list of this entry should state whether each room is occupied or vacant and the list in its entirety would contain every possible combination of occupied and vacant rooms. This list would be very useful for assigning cleaning personnel and for booking purposes. Do you think you can make such a list, Ion?" Warren had a very smug expression on his face.
Ion stopped to think about it for a moment, rubbing his hand across his chin. After a minute he looked Warren straight in the eye and said without any emotion. "No, I can't."
Cal, who had been waiting for Ion with an increasing sense of nervousness, suddenly stared agape at Ion. "Ion! You can't let me down now. Are you telling me that I'll have to tell my secret to Warren?"
"Quite the opposite, actually," said Ion. "You've won the bet and he owes you an infinite supply of the best wine."
"But you yourself admitted you couldn't make such a list, Ion," interjected Warren. "How have I lost the bet?"
"The wager was that if anyone can do it, I can. But such a list cannot be made, not because I am incapable of it, but because it is impossible. As such, Cal has won the wager."
"A-ha! But I have you there," said Warren. "I have such a list! I made it myself. The way I accomplished this was as such:
"Each of my cleaning supervisors is assigned ten rooms to care for. Of course there are an infinite number of maintenance supervisors. I asked each supervisor to make a list of all possible combinations of his ten rooms, using 0 for vacant, and 1 for occupied. Each of these lists, therefore contains 1024 entries.
"I then combined each of these lists together, in every possible combination, into one master list, giving me a super-list of all possible configurations of vacant and occupied for the hotel."
"That's an very impressive attempt," said Ion. "But I can think of a configuration that isn't on your list."
"Oh yes? Please tell," said Warren, with an air of over-confidence.
"Well, it's very similar to your first entry, but it differs in the first digit. So if the first entry on your list begins with 1, my configuration begins with 0."
"Nonsense," said Warren. "I have that configuration somewhere else in my list. It's probably the second entry."
"No, it's not the second entry, either," said Ion. "My configuration differs from your second entry in the second digit."
"Then it's the third entry," said Warren.
"I don't think so either," said Ion. "My configuration differs from your third entry in the third digit. Actually, it differs from your nth entry in the nth digit."
"Well, even if your configuration is not on my list, I'll just add it to the list, and then I'll have a complete list."
"It's not that simple," said Ion. "You would have to add it as the nth entry, and then I would just create a new configuration that is not like it because it differs in the nth position. You see, no matter how many configurations you have, I can create a new configuration that differs from all your others in the nth digit. That is the first digit is different from the first entry, the second digit from the second entry, and so on. Such a list of all possible configurations cannot be made because all possible configurations are uncountably infinite which, by the very definition of such, cannot be listed, that is, put into one-to-one correspondence with a list that is countably infinite."
"Eegads, man, you're right!" proclaimed Cal. Warren just stood with a dumbfounded look on his face, trying to piece together what Ion had just said.
The rest of the party passed without any further incedent, except for the maid getting tipsy on the milk Ion had brought. In the end, Cal gave half his winnings from the bet to Ion, and still had an infinite amount of wine for himself. "That's the wonderful thing about infinity," Cal was known to say. "It doesn't matter how much you take out of it. You still always have an unending supply leftover."
At the mere mention of this name, Cari and Tom are probably recoiling in horror and have collapsed in drooling siezures. But as much as we all hated Dr. Mrs. Salter at the time, in retrospect, I realized I learned more in her classes than in any others. Additionally, the stories of Ion are very interesting studies in the concept of infinity and I thought that those readers of FU-News who are mathenatically inclined but haven't had the love/hate experience of a class taught by Dr. Mrs. Salter (Mom and Dad B, Mrs. Pickles, The Blue Fox) might find these stories interesting.
Ion was first introduced to me by a certain professor of mathematics. While I had only swerving loyalty towards the professor in question, after just a brief amount of time talking with Ion, I discovered he had a wealth of humorous anecdotes and tales of mathematical intrigue.
It was during one of our many conversations that followed that he related to me the tales of his friend Calvin Q. Lator, owner of a very interesting chain of hotels. Cal, as Ion referred to him, was the owner of the "Inn of the Infinite Happiness" chain of hotels (slogan: "We've got a room for you, guarenteed"). What made this chain so notable, was that not only were there an infinite number of hotels in the chain, but each hotel had an infinite number of rooms. The actual mechanism that accomplished this is something of a trade secret, but it is known to involve poison gas, a closed box, and a cat that may or may not be dead (perhaps both). Cal kept his secret from absolutely everyone, except his own mother, Seeia.
So after one particularly taxing milk delivery run, Ion stopped at Cal's hotel near the Horsehead Nebula to get a good night's sleep before heading home. It was with a feeling of great relief that he entered the hotel's lobby, looking forward to some relaxation, and headed to the front desk.
"Hello," Ion said to the receptionist. "I'd like a room for tonight."
"I'm sorry sir, but we're full," came the receptionist's reply.
Ion's feeling of relief gave way to an even greater sense of confusion. "How can you be full? There are an infinite number of rooms?" asked Ion.
Upon hearing the elevated volume of his good friend's voice, Cal emerged from the office behind the front desk. He was a short, rotund man, scarcely five feet tall, and having a weight-to-height ratio of at least 36 lbs./ft. His balding hair gave one the impression that a tiny man with a tiny lawn mower had started cropping Cal's hair, but had gotten up to get a lemonade half-way through, with the job still unfinished. He was also exceptionally well dressed, wearing a nicely pressed suit jacket and pants, with a striped neck tie sporting the two-tone blue colors of the hotel chain. A gold watch chain hung from his pocket; Ion knew that on the back was inscribed "Cal, thanks for keeping one of your infinite doors open for me. G." Who 'G.' was, Ion didn't know, but the rumor was it was a famous actress or model, of the gorgeous persuasion. Cal wouldn't answer any questions on the subject prefering to keep people guessing. The reality was much tamer than the rumors, and Cal liked it that way.
Cal was quite the rich man, as being the owner of the Universe's largest hotel chain is prone to make one. He also had far more wrinkles than a man his age should have, and much of his remaining hair was grey, as having to manage an infinite number of hotels and rooms is prone to make one look older than one's peers.
"Ion! I'm both happy and sad that you have come to my hotel today," said Cal, as he greeted Ion with a firm handshake and a slap on the back. "Happy to see my friend once again, but sad because you have come at the one time where it seems I can't accomodate you."
Ion's puzzlement had not subsided. "How can that be? I don't understand how a hotel with an infinite number of rooms could possibly be full."
"One would not think it possible, but yet it has happened. You see," Cal began explaining, "the Association of Infinite Members has chosen this hotel for their convention this year. Since there are an infinite number of them, they have completely booked up my hotel! Every room is currently occupied by one of the convention-goers. Thank goodness no one else has come to get a room tonight. I'm afraid this could ruin my reputation."
"But surely, you can squeeze me in somewhere," pleaded Ion. "I mean, with an infinite number of rooms there's got to be an empty one."
"Not a one," Cal responded, upset that he had to turn away his good friend.
"Can you move a guest to another room?" asked Ion.
"Quite easily, but as I mentioned, all rooms are full. To what room would I move the guest?" Cal said, not really understanding where Ion was going with his question.
"Well then, I'll wager that you do have room for me. I'll wager you a lifetime supply of milk for an unlimited number of free hotel stays."
"That sounds reasonable," said Cal. "Now what room shall I put you in."
"Simple," said Ion. "Room 1."
"But Room 1 is occupied," said Cal. "I would have to move the occupant to another room."
"Yes, you shall move him to Room 2."
"But Room 2 is also occupied. Where shall I put him?"
"Room 3," replied ion. "You see, all you have to do is move the guest staying in Room N to Room N+1. There is still room for everyone in your infinite hotel. Should anyone else come into the hotel asking for X number of rooms, you just simply need to put them in Rooms 1 through X, and move every other guest to Room N + X."
"Astounding, Ion! I hadn't thought of that. Eegads, man, you're a genius."
"It's all part of the job of an intergalactic milk-man," replied Ion.
And so Ion was checked in and given the key card to access his room. Ion remarked that for a hotel with so many rooms, it was ironic that they only had one door. The rooms themselves didn't exist within normal space, but were instead accessed by sliding your room's key card through the control panel of a teleporter. When you opened the one hotel room door, you would be transported to your own private room. As Cal explained it to Ion, the process of moving a guest from one room to another was actually quite simple, and in fact, the guest didn't even know he was being moved. All that was done was the guest's key card was changed so that when he activated the teleporter, he was ported to Room N + 1, instead of Room N.
* * * * *
Ion had just gotten comfortable in his hotel room and was flipping through the infinite number of channels on the Hotel TV, when his phone rang. He hadn't told anyone where he was staying for the night, so it was with a small amount of curiosity that he answered the phone, wondering who it was.
"Hello?" queried Ion of the unknown caller on the other end.
"Ion! You must help me!" the caller said in a frenzied panic. It took Ion a moment to recognize the voice as belonging to Cal.
"What's the matter, Cal?" asked Ion.
"Oh, you must help me, Ion. You are the only one I could think to turn to, after you solved my last problem. You see, we've had a problem with double-booking. The Infinite Membered Consortium has booked this hotel for their convention also! We have an infinite number of rooms, so we didn't think to check for room availability. But I don't know what rooms to assign the infinite number of people who have just come into my hotel. I thought about using your suggestion of assigning them rooms 1 through X, and moving everyone else to Room N + X, but I can't move someone to Room N + ∞! There is no such room!" Ion was taken aback not by the problem, but by Cal's ability to somehow speak all that without ever stopping for a breath.
"Well," said Ion, "that certainly is a pickle. On the one hand, you have an infinite number of rooms, so you should be able to fit them in, but on the other hand, how do you fit an infinite number of people into a hotel that is already full?"
"My dilemma exactly. I fear it cannot be done," came Cal's nervous reply.
"Oh, of course it can be done!" said Ion. "And quite simply, too."
"Then please, enlighten me. Where can I put the guests who are waiting in my lobby?"
"Well, the first person should be assigned to Room 1, the second person to Room 3, the third to Room 5, and so forth."
"Yes, yes, but what of the people in those rooms?"
"I was getting to that. The person in Room 1 should be moved to Room 2; the person in Room 2 should be moved to Room 4; the person in Room 3 should be moved to Room 6, and so on," said Ion, smuggly. "You see, a guest staying in Room N should be moved to Room 2N. That way, only the even-numbered rooms are occupied leaving the odd-numbered rooms, of which there are an infinite number, available for the newcomers."
"Ah! I see! Thank you once again, Ion! You have saved my reputation."
Ion was barely able to get out the "You're" of "You're Welcome" before Cal, in a frenzy to begin accomodating his infinite number of patrons waiting in the lobby, hung up.
* * * * *
Much time passed by after that night (I say "much time" and not "many months" or "years" because depending on where in the galaxy you were, the orbital frequency of a planet's moons or of the planet itself changed dramatically). Ion and Cal had been corresponding in the time since they had last seen each other, but as all things of that nature go, the frequency of their correspondence waned with the passage of time. Then one moment, (I say "moment" because "day" is a very relative term depending on which planet you are on and what direction the side you are on is facing) Ion received an IGE-mail (inter-galactic e-mail) from Cal pleading for his help. The letter stated:
'Ion,
'You must help me. The Intergalactic Business Regulatory Commission is complaining that I have a monopoly on infinite-roomed hotel chains and forcing me to close all of my hotels but one and consolidate my guests to that one hotel. I can easily move guests from one hotel to another, but at the moment, all my hotels are completely full with an infinite number of conventions of societies with infinite members. I don't know how I can move an infinite number of guests from an infinite number of hotels into only one hotel, even if there are an infinite number of rooms. I fear this cannot be done, but I cannot afford to reimburse an infinite number of guests. I would be ruined! Please help me.
'Your friend,
Cal L.'
Ion had to think for quite a bit, but eventually offered Cal the following solution.
'Cal,
'It is, in fact, possible, so you needn't worry about going bankrupt. The answer is not trivial, and may take some explanation.
'What you need to do is come up with a function that, given a guest's hotel number and room number, will give you a new number for their room in your one remaining hotel. To begin, let's start making a list of all the rooms and all your hotels. Such a list would start out looking something like this, where the rows (m) correspond to the hotel and the columns (n) correspond to the rooms:
'Now we need to come up with a numbering system so that each hotel/room combo is counted. We can accomplish this by numbering the rooms in diagonals, as such:
'Now to come up with a function to figure out the new room numbers based on the old hotel/room combination.
'Note that for any hotel/room (M/N) combination, the number of the hotel at which the diagonal it lies on ends is M + N - 1. For instance, Hotel 2, Room 3 lies on the diagonal ending at Hotel 4. 2+3-1=4. Another way of looking at this might be that each diagonal corresponds to all hotel/room combinations that add to a given number. We can use this to our advantage.
'Now, let's take a look at a hotel/room combination's value in the list of all rooms. Remember this list value is the room number in the one remaining hotel that the guest will be assigned to. This list number is equal to the list number at the end of the diagonal above it, plus the position of the combination on the diagonal it is on. For instance, the list number of Hotel 2, Room 3 is equal to the list number at the end of the diagonal above it, 6, plus its position along its diagonal, 2. 6+2=8, which is the list number associated with Hotel 2, Room 3.
'A combination's position on the diagonal is just equal to its row number (M), and the hotel number at the end of the diagonal above it is (M + N - 1) - 1, or M + N - 2. Now to come up with a function relating the list value at the end of a diagonal to the hotel number at the end of the diagonal. A list of these hotel numbers and corresponding list values looks something like this:
1: 1
2: 3
3: 6
4: 10
5: 15
6: 21
'We can re-write the list values (new room numbers) as such:
1 = 1+0
3 = 2+1
6 = 3+3
10 = 4+6
15 = 5+10
21 = 6+15.
'The first addend is just the hotel number. The second addend (and this is trickier to see) is equal to half the difference between the hotel number and its perfect square. 1^2=1, half the difference of 1 and 1^2 is 0. 2^2=4, half of 2^2 - 2=1. 3^2=9, half of 9-3=3. 4^2=16, (16-4)/2=6, etc. Generally speaking, the second addend can be expressed as:
'So the whole value is:
'Now, this just relates the hotel number to the value next to it. To calculate the new room number based on the current hotel and room number, we substitute the hotel number at the end of the diagonal above the one our hotel/room combination lies on (M+N-2) into the above equation and add the position on the diagonal that the hotel/room combination lies upon (M). So the function to calculate the new room number of a guest staying at Hotel M, Room N is as follows:
'Which simplifies to:
'Your friend,
Ion
'P.S. Perhaps a simpler way of expressing this is as a piece-wise defined function. If instead of listing the new rooms in a diagonal fashion, we use a square numbering method like such:
'Then we can define the new room function as:
* * * * *
Cal was quite thankful for Ion's reply. He was most thankful, however, that he was able to "stick it to the man" and avoid bankruptcy, despite a very stern commissioner for the Intergalactic Business Regulatory Commission who seemed intent on closing Cal's hotels down. Cal thought that perhaps he must have inadvertantly offended the commissioner's mother.
Eventually, the commissioner was fired in a scandal whose details were not widely know, but it involved a weasel, a chainsaw, and a watermelon. As this commissioner was not well-liked among the businessmen of the intergalaxy, a group of them decided to throw a party to celebtrate their good fortune. Cal was hosting the party and in a particularly good mood, as it was mere seconds after the commissioner's dismissal that he was allowed to re-open the rest of the hotels in his chain. Cal had asked Ion to provide the milk for the party, and so he did, saying "it's what I do best."
It was at this party that Ion was hastily pulled aside by Cal. Cal had been having a very intense, yet friendly, argument with his business manager, Warren, after they had both had a few too many glasses of milk. Cal had been extolling the praises of Ion and how he'd saved him from bankruptcy and humiliation countless times (which is not necessarily an exageration if you are the manager of an infinite number of hotels). Warren agreed that this Ion fellow must be pretty smart, but wagered that he couldn't solve the hotels' every problem. In truth, he was feeling a bit threatened that Cal so frequently had to go to Ion for help, completely skipping over his manager.
"Nonsense," said Cal. "If anyone can solve one of the hotels' problems, Ion can. I'd wager the secret to my infinite hotels on it!"
"I will have to take you up on that," said Warren. It was then that Cal pulled Ion into the conversation and explained to him the stakes.
"I've wagered the secret of my infinite-roomed hotels against an infinite supply of the best wine with Warren here that if anyone can solve a problem about my hotels, you can," explained Cal.
"You have quite a lot of confidence in me, Cal," Ion said, just a bit nervous about being put on the spot. Then turning to Warren he said, "expain the problem to me."
Warren said, "I have a problem that's been nagging at me for a bit. It has to do with maintenance and assigning cleaning staff to one hotel. I would like to have a list of all possible configurations of the rooms in the hotel. Each list of this entry should state whether each room is occupied or vacant and the list in its entirety would contain every possible combination of occupied and vacant rooms. This list would be very useful for assigning cleaning personnel and for booking purposes. Do you think you can make such a list, Ion?" Warren had a very smug expression on his face.
Ion stopped to think about it for a moment, rubbing his hand across his chin. After a minute he looked Warren straight in the eye and said without any emotion. "No, I can't."
Cal, who had been waiting for Ion with an increasing sense of nervousness, suddenly stared agape at Ion. "Ion! You can't let me down now. Are you telling me that I'll have to tell my secret to Warren?"
"Quite the opposite, actually," said Ion. "You've won the bet and he owes you an infinite supply of the best wine."
"But you yourself admitted you couldn't make such a list, Ion," interjected Warren. "How have I lost the bet?"
"The wager was that if anyone can do it, I can. But such a list cannot be made, not because I am incapable of it, but because it is impossible. As such, Cal has won the wager."
"A-ha! But I have you there," said Warren. "I have such a list! I made it myself. The way I accomplished this was as such:
"Each of my cleaning supervisors is assigned ten rooms to care for. Of course there are an infinite number of maintenance supervisors. I asked each supervisor to make a list of all possible combinations of his ten rooms, using 0 for vacant, and 1 for occupied. Each of these lists, therefore contains 1024 entries.
"I then combined each of these lists together, in every possible combination, into one master list, giving me a super-list of all possible configurations of vacant and occupied for the hotel."
"That's an very impressive attempt," said Ion. "But I can think of a configuration that isn't on your list."
"Oh yes? Please tell," said Warren, with an air of over-confidence.
"Well, it's very similar to your first entry, but it differs in the first digit. So if the first entry on your list begins with 1, my configuration begins with 0."
"Nonsense," said Warren. "I have that configuration somewhere else in my list. It's probably the second entry."
"No, it's not the second entry, either," said Ion. "My configuration differs from your second entry in the second digit."
"Then it's the third entry," said Warren.
"I don't think so either," said Ion. "My configuration differs from your third entry in the third digit. Actually, it differs from your nth entry in the nth digit."
"Well, even if your configuration is not on my list, I'll just add it to the list, and then I'll have a complete list."
"It's not that simple," said Ion. "You would have to add it as the nth entry, and then I would just create a new configuration that is not like it because it differs in the nth position. You see, no matter how many configurations you have, I can create a new configuration that differs from all your others in the nth digit. That is the first digit is different from the first entry, the second digit from the second entry, and so on. Such a list of all possible configurations cannot be made because all possible configurations are uncountably infinite which, by the very definition of such, cannot be listed, that is, put into one-to-one correspondence with a list that is countably infinite."
"Eegads, man, you're right!" proclaimed Cal. Warren just stood with a dumbfounded look on his face, trying to piece together what Ion had just said.
The rest of the party passed without any further incedent, except for the maid getting tipsy on the milk Ion had brought. In the end, Cal gave half his winnings from the bet to Ion, and still had an infinite amount of wine for himself. "That's the wonderful thing about infinity," Cal was known to say. "It doesn't matter how much you take out of it. You still always have an unending supply leftover."
Monday, February 6, 2006
Take this Parental Fitness Exam!
Would you entrust your children to this man?
ftp://24.96.118.140/pub/TreasureIslandFunCenter.wmv (3.6 MB)
If you answered yes, you fail. Seriously, I think this place is just a front for child services, and as soon as you walk in the door they take your kids away. (you might have to right-click on the link and click 'Save As...' to download the file)
Would you entrust your children to this man?
ftp://24.96.118.140/pub/TreasureIslandFunCenter.wmv (3.6 MB)
If you answered yes, you fail. Seriously, I think this place is just a front for child services, and as soon as you walk in the door they take your kids away. (you might have to right-click on the link and click 'Save As...' to download the file)
Friday, February 3, 2006
For all the Tolerance we're supposed to show them, they certainly don't grant us a whole lot.
Anger over Mohammad cartoons spreads | Reuters.co.uk
Anger over Mohammad cartoons spreads | Reuters.co.uk
Thursday, February 2, 2006
Subscribe to:
Posts (Atom)