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Logic, Reason and Critical Thinking, Class 10: Period 4, Thursday, November 12

"This week," Miss Bennet said, "we are going to discuss another tool that will aid us in problem-solving: one that starts at the very beginning and can immediately set us upon the right track. This technique is deceptively simple: we define the problem. We restate it methodically, examine the hidden assumptions and unspoken concerns, and address the exact dimensions of the current difficulty. When properly defined, the problem will lead us toward possible solutions.

She lifted a piece of chalk and headed towards the blackboard. "Let us take a simple hypothetical. Let us say that a certain teacher wished to have office hours on Tuesday, but discovered that the town was filled with vicious, sentient plants." Miss Bennet did, in fact, think she was amusing. "In describing the problem, said teacher might express her frustration in the following manner:"

I cannot go to my office; there are killer vegetables on the loose.

Miss Bennet underlined the sentence before turning back to her students. "This is a rather natural response to the situation, but it is not a well-defined problem, for our purposes. Let us make it into one, then. Where shall we start? Cannot is a rather strong term; in many cases, 'cannot' would be more accurately replaced with 'would rather not.' Similarly, the word 'killer' is quite loaded, and we would do well to replace it with a more accurate and less emotional word. Very well; there are menacing plants about, and the instructor would rather not go to her office. The connection between the two statements is left unspoken. It seems a natural deduction that the teacher is fearful of the dangers presented by those plants, which is a rather more specific problem. Reshaped, the problem now appears to be:"

Dangerous vegetables may harm me if I go to my office today.

"In this form, the dilemma quite readily lends itself to suggestions. For one, perhaps the instructor should not go to her office today. These vegetables may present only a temporary difficulty; perhaps there is nothing in the teacher's office which cannot wait until tomorrow. Another alternative is for the lady in question to arm herself before leaving the house, if she is confident in her abilities. If she is not, she may do well to ask a gentleman to escort her, or to fetch whatever is so urgent from her office that it mustn't wait a day.

Satisfied, Miss Bennet set the chalk down and brushed the dust from her hands. "When we fully understand a problem, we will have an easier time discovering its solution."

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Miss Bennet took the liberty of writing a few other potential problems on the board:

I cannot go to the party on Friday.

I will never finish this paper in time.

I want to but my parents said no.

Rephrase one of them (feel free to make up relevant information where it is missing) or state your own problem, and allow your classmates to help you in phrasing it more helpfully.

Edited 2009-11-12 12:17 (UTC)

"This paper's not going to be finished on time cause I'm too busy doing other stuff?" Rose tried, figuring she'd go for the one that applied.

"That's a useful start," she laughed. "So are you choosing to place other priorities before the paper? That's an acceptable trade, so long as you acknowledge it as such."

//My parents have forbidden me from going to th'party on Friday, unless I finish my paper on time.//

Yes, Jono occasionally thought he was clever.

"I know how to solve that problem," Calvin grinned. "You just need to build a time machine, go to the future where you've already done the paper, bring it back to show your parents, go to the party, then do your paper afterwards."

He wasn't joking.

The sad thing was, Jono had heard stranger solutions for far simpler problems in the past.

//And yer've got experience with that sort of thing, do yer?//

"Sure I do," Calvin replied. "Got an A-plus for that assignment too."

Just because he'd only gotten that mark for the story past-Hobbes and future-Hobbes had written while past-Calvin and future-Calvin had gone back in time to beat up intermediate-Calvin for not actually doing the assignment was no reason not to count it a success in Calvin's eyes.

//Must've been one hell of a paper,// Jono decided, bemused. //Remind me to keep that solution in mind for th'next time I want to have a social life of some sort.//

He'd probably just write the paper before Friday anyhow.

"It was the most vile slander," Calvin muttered darkly, before smiling magnanimously. "I'm just happy to pass my wisdom on."

"Or you just sneak out," Rose said. "So much less work."

Calvin thought about it. "I like my solution better. It uses science."

"Yeah, but I suck at science," she said, trying hard not to grin. "So does that mean you'll do all my science for me?"

Calvin liked science. It went 'Bonk!'.

"Maybe? What's in it for me? I'm not cheap." Unlike Hobbes, who was anybody's for a tummy-rub and a tuna-fish sandwich.

Eww, tuna fish. It always left your hands smelling funny.

"And I'm not easy," she ~~lied~~ said. "What d'you want?"

Calvin had never actually been bribed to do someone else's homework for them. Finally, people were ~~completely unaware of~~ realising his genius.

"I'm sure you can think of something."

Edited 2009-11-12 14:05 (UTC)

"Well, yeah, but where's the fun in that?" Rose teased. She tossed her hair back over her shoulder. "Get back to me when you know how much you're worth, Calvin."

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Miss Bennet was going to clear her throat, and smile generously at both students.

"That is quite an amusing topic for conversation," she said. "It's fortunate that I realize that neither of you are in earnest, as I know full well that you would not tolerate academic dishonesty. A less observant teacher might mistake your playfulness for sincerity, and that might have dire consequences, indeed."

"Nicely done," Miss Bennet smiled. "One would say that you should then work to finish your paper before Friday, or else see how flexible your parents are willing to become."

//I suppose that'd make sense, wouldn't it?// Jono gave a nod of his head, crossing his arms over his chest. //Consid'ring I'm away at boarding school,// and that his parents were a bit of a moot point in the first place, //I can't see them holding too much sway over what I do and don't do. Though I prefer t'get my work done on time regardless.//

Kiss-up.

"Then it seems you need only budget your time properly, make the right assurances to your parents, and you've solved three problems at once," she said, her eyes sparkling with amusement. "Quite clever of you."

//And then th'biggest concern I've got is what in th'world to wear,// Jonothon mused. //I suppose all of the cleverness I have at my disposal doesn't change th'fact that there'll always be more decisions to be made once the first ones are out of the way.//

Okay, what to wear was easy enough. Bandages and black. But he was kind of having fun with this assignment, now. So there.

"No, it doesn't," Miss Bennet teased. "But there again, we define the problem. Whatever shall I wear isn't nearly so helpful as I detest all of my clothes and wish to buy new ones for the party."

And what a happy solution that presented! Especially if you were someone like Lizzy's sister Lydia, who never met a shop she didn't like.

Well, it was a happy solution if you didn't have any sort of aversion to fitting rooms.

//There's one option,// Jono decided. //Or, perhaps it's even more complex. Perhaps the issue is that all of my laundry is dirty, and I have time to either finish my paper by Friday, or else do the wash.//

A predicament! Oh no!

"One might suggest you enlist help in washing your clothing," Miss Bennet laughed. "Or that you work on your paper while the clothes are tumbling in one of those machines. Which brings us around to time-management again."

//Trust me,// Jono replied, his own voice sitting somewhere on the edge of a chuckle, //nobody wants to get anywhere near my laundry. Time-management it'll have t'be.//

His pants were scary.

Pants, of course, in that very British sense of the word. Jonothon's trousers were just fine.

Re: Discussion #2: Other Problems

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