The problem with one right answer
Jan. 27th, 2007 10:50 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
imomusOne of the things that frustrated and perplexed me most at school -- and I think this is the reason I quickly abandoned science and maths subjects -- was the way teachers would set us problems to which they assumed there was only one right answer. Students who solved these problems "correctly" were the ones who framed the question in the same way as the teacher, subscribed to the same assumptions, and shared the teacher's utter lack of imagination.
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The kind of absurd, scary arbitrariness of the supposed "solutions" to maths problems is mocked in satirical show Look Around You: Maths. Here's an example of their logic.
Problem 1: Jean is shorter than Brutus but taller than Imhotep. Imhotep is taller than Jean but shorter than Lord Scotland. Lord Scotland is twice the height of Jean and Brutus combined, but only a tenth of the height of Millsy. Millsy is at a constant height of x minus y. If Jean stands exactly one nautical mile away from Lord Scotland, how tall is Imhotep?
Solution: Imhotep doesn't exist.
The answer is a nice rebuke to our idiotically conformist attempts to solve the problem on the basis of maths, when in fact we should have been looking at the existential and religious realm (Imhotep is an idol from Easter Island).
I spent a while yesterday on the Analytical Problems and Puzzles site, utterly frustrated by its compilers' lack of imagination as, time after time, they proposed just one right answer to their conundrums. Even when some of their "lateral thinking" puzzle solutions showed a freshness of thought almost as daring as Look Around You's, they never acknowledged the plethora of other possibilities thrown up by each scenario. So today I thought I'd add a few solutions of my own. I've decided to act as if this website were one of those science teachers I used to sit in silence and fume at.
Teacher's Problem: There was once a recluse who never left his home. The only time anyone ever visited him was when his food and supplies were delivered, but they never came inside. Then, one stormy winter night when an icy gale was blowing, he had a nervous breakdown. He went upstairs, turned off all the lights and went to bed. Next morning, he had caused the deaths of several hundred people. How?
Teacher's Solution: He was a lighthouse keeper who turned off the light.
I Say: BAH! Come on, do lighthouses really save hundreds in one night, these days, when there's sonar and satellite tracking? Get real, teacher! Here are some more likely scenarios. After turning off all the lights, the recluse went out sleepwalking and killed several hundred people with an axe, chainsaw or machinegun. Alternatively, he just dreamed he killed the people. You just said "caused the deaths of people", you didn't say they had to be real people. Alternatively, the recluse's nervous breakdown reversed his attachment to his own home and attached him, instead, to other people's. He went upstairs in other people's houses (you didn't say the upstairs was his own, after all), having first locked the normal occupants out in the storm, where they perished. Isn't it obvious, with hindsight? Aren't you kicking yourself now I've told you?
Teacher's Problem: Not far from Madrid, there is a large wooden barn. The barn is completely empty except for a dead man hanging from the middle of the central rafter. The rope around his neck is ten feet long and his feet are three feet off the ground. The nearest wall is 20 feet away from the man. There is a puddle of water nearby. It is not possible to climb up the walls or along the rafters. The man hanged himself. How did he do it?
Teacher's Solution: He climbed on a block of ice which has since melted.
I Say: For fuck's sake, you smug git! Do you really think that block of ice is the only possible correct answer? If you can conjure that out of thin air, I can conjure a barn built entirely underground, with the rafters at ground level. The man simply slings his rope over the "floor" and drops down into the basement. The puddle is formed when he weeps a bit before doing this. Don't forget emotion! Alternatively, it's a normal barn but the man has a leaky jetpack.
Teacher's Problem: It was a dark stormy night and a couple were in a car racing madly through a foreign city. The car broke down and the husband had to go get help from someone who spoke his language. He was afraid to leave his wife alone in the car so he pulled up the windows and locked the car before leaving. When he came back, the car was in the same state as he had left it but his wife was dead, there was blood on the floor and there was a stranger in the car. What happened?
Teacher's Solution: The wife was about to have a baby. They were driving to the hospital. The baby was born, and the wife didn't survive the birth.
I Say: You unimaginative moron! Do you really think that's the only possible answer? The car broke down because the husband crashed it, killing his wife. The stranger was a policeman, investigating the crash. The man had been afraid to leave his dead wife alone because the area was a notorious necrophilia black spot. In fact, even the policeman wasn't above suspicion -- he was fumbling with the dead woman's clothes. Isn't it fucking obvious, you dunderhead?
Teacher's Problem: A man was driving alone in his car when he spun off the road at high speed. He crashed through a fence and bounced down a steep ravine before the car plunged into a fast-flowing river. As the car slowly settled in the river, the man realised that his arm was broken and that he could not release his seat belt and get out of the car. The car sank to the bottom of the river. He was trapped in the car. Rescuers arrived two hours later, yet they found him still in the river, but alive. How come?
Teacher's Solution: The water in the river only came up to the man's chest.
I Say: Oh for Christ's sake! Is that the best you can do? The car might have had a watertight passenger compartment, and had air trapped inside it, enough to breathe for two hours. Or -- much more likely -- there was a snorkel and oxygen tanks on the back seat, because the man was going diving. Or, who knows, there was a drought and the river chose that moment to dry up. It happens.
Teacher's Problem: A man lives in the penthouse of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. Upon his return, however, he can only travel halfway up in the lift and has to walk the rest of the way - unless it's raining. What is the explanation for this?
Teacher's Solution: The man is a dwarf. He can't reach the upper elevator buttons, but he can ask people to push them for him. He can also push them with his umbrella.
I Say: You apart-height-endorsing, politically-incorrect fascistic mongol! If the dwarf had this problem reaching the top buttons, why couldn't he carry a stick with him every day, or keep one stowed in the lift somewhere? Why didn't you say "unless there are other people in the lift", in which case the dwarf could just have said "Could you press penthouse please?" And anyway, how come this dwarf owns the best apartment in the building, you idiots? Dwarves are inadequate losers who never have any money and have to join the circus. Haven't you thought this scenario through at all?
But, given the parameters of the problem as you've set it, your pathetic answer is still not the only solution. He suffers from vertigo. The lift is glass walled. He doesn't mind approaching the earth, but does mind leaving it behind. When it's raining and misty, he can't see the earth, so he can go the whole hog. Or... or... it's an open-topped mechanical elevator which you operate under your own power, with a pulley system. Going down is easy, but a small man or a child can only pull the thing up half way. But a bucket of water hangs as a counterbalance. If it's raining the bucket fills up, making the dwarf's task easier.
Isn't it obvious, you cretin? I knew this stuff in first grade.
[Error: unknown template video]
The kind of absurd, scary arbitrariness of the supposed "solutions" to maths problems is mocked in satirical show Look Around You: Maths. Here's an example of their logic.
Problem 1: Jean is shorter than Brutus but taller than Imhotep. Imhotep is taller than Jean but shorter than Lord Scotland. Lord Scotland is twice the height of Jean and Brutus combined, but only a tenth of the height of Millsy. Millsy is at a constant height of x minus y. If Jean stands exactly one nautical mile away from Lord Scotland, how tall is Imhotep?
Solution: Imhotep doesn't exist.
The answer is a nice rebuke to our idiotically conformist attempts to solve the problem on the basis of maths, when in fact we should have been looking at the existential and religious realm (Imhotep is an idol from Easter Island).
I spent a while yesterday on the Analytical Problems and Puzzles site, utterly frustrated by its compilers' lack of imagination as, time after time, they proposed just one right answer to their conundrums. Even when some of their "lateral thinking" puzzle solutions showed a freshness of thought almost as daring as Look Around You's, they never acknowledged the plethora of other possibilities thrown up by each scenario. So today I thought I'd add a few solutions of my own. I've decided to act as if this website were one of those science teachers I used to sit in silence and fume at.
Teacher's Problem: There was once a recluse who never left his home. The only time anyone ever visited him was when his food and supplies were delivered, but they never came inside. Then, one stormy winter night when an icy gale was blowing, he had a nervous breakdown. He went upstairs, turned off all the lights and went to bed. Next morning, he had caused the deaths of several hundred people. How?
Teacher's Solution: He was a lighthouse keeper who turned off the light.
I Say: BAH! Come on, do lighthouses really save hundreds in one night, these days, when there's sonar and satellite tracking? Get real, teacher! Here are some more likely scenarios. After turning off all the lights, the recluse went out sleepwalking and killed several hundred people with an axe, chainsaw or machinegun. Alternatively, he just dreamed he killed the people. You just said "caused the deaths of people", you didn't say they had to be real people. Alternatively, the recluse's nervous breakdown reversed his attachment to his own home and attached him, instead, to other people's. He went upstairs in other people's houses (you didn't say the upstairs was his own, after all), having first locked the normal occupants out in the storm, where they perished. Isn't it obvious, with hindsight? Aren't you kicking yourself now I've told you?
Teacher's Problem: Not far from Madrid, there is a large wooden barn. The barn is completely empty except for a dead man hanging from the middle of the central rafter. The rope around his neck is ten feet long and his feet are three feet off the ground. The nearest wall is 20 feet away from the man. There is a puddle of water nearby. It is not possible to climb up the walls or along the rafters. The man hanged himself. How did he do it?
Teacher's Solution: He climbed on a block of ice which has since melted.
I Say: For fuck's sake, you smug git! Do you really think that block of ice is the only possible correct answer? If you can conjure that out of thin air, I can conjure a barn built entirely underground, with the rafters at ground level. The man simply slings his rope over the "floor" and drops down into the basement. The puddle is formed when he weeps a bit before doing this. Don't forget emotion! Alternatively, it's a normal barn but the man has a leaky jetpack.
Teacher's Problem: It was a dark stormy night and a couple were in a car racing madly through a foreign city. The car broke down and the husband had to go get help from someone who spoke his language. He was afraid to leave his wife alone in the car so he pulled up the windows and locked the car before leaving. When he came back, the car was in the same state as he had left it but his wife was dead, there was blood on the floor and there was a stranger in the car. What happened?
Teacher's Solution: The wife was about to have a baby. They were driving to the hospital. The baby was born, and the wife didn't survive the birth.
I Say: You unimaginative moron! Do you really think that's the only possible answer? The car broke down because the husband crashed it, killing his wife. The stranger was a policeman, investigating the crash. The man had been afraid to leave his dead wife alone because the area was a notorious necrophilia black spot. In fact, even the policeman wasn't above suspicion -- he was fumbling with the dead woman's clothes. Isn't it fucking obvious, you dunderhead?
Teacher's Problem: A man was driving alone in his car when he spun off the road at high speed. He crashed through a fence and bounced down a steep ravine before the car plunged into a fast-flowing river. As the car slowly settled in the river, the man realised that his arm was broken and that he could not release his seat belt and get out of the car. The car sank to the bottom of the river. He was trapped in the car. Rescuers arrived two hours later, yet they found him still in the river, but alive. How come?
Teacher's Solution: The water in the river only came up to the man's chest.
I Say: Oh for Christ's sake! Is that the best you can do? The car might have had a watertight passenger compartment, and had air trapped inside it, enough to breathe for two hours. Or -- much more likely -- there was a snorkel and oxygen tanks on the back seat, because the man was going diving. Or, who knows, there was a drought and the river chose that moment to dry up. It happens.
Teacher's Problem: A man lives in the penthouse of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. Upon his return, however, he can only travel halfway up in the lift and has to walk the rest of the way - unless it's raining. What is the explanation for this?
Teacher's Solution: The man is a dwarf. He can't reach the upper elevator buttons, but he can ask people to push them for him. He can also push them with his umbrella.
I Say: You apart-height-endorsing, politically-incorrect fascistic mongol! If the dwarf had this problem reaching the top buttons, why couldn't he carry a stick with him every day, or keep one stowed in the lift somewhere? Why didn't you say "unless there are other people in the lift", in which case the dwarf could just have said "Could you press penthouse please?" And anyway, how come this dwarf owns the best apartment in the building, you idiots? Dwarves are inadequate losers who never have any money and have to join the circus. Haven't you thought this scenario through at all?
But, given the parameters of the problem as you've set it, your pathetic answer is still not the only solution. He suffers from vertigo. The lift is glass walled. He doesn't mind approaching the earth, but does mind leaving it behind. When it's raining and misty, he can't see the earth, so he can go the whole hog. Or... or... it's an open-topped mechanical elevator which you operate under your own power, with a pulley system. Going down is easy, but a small man or a child can only pull the thing up half way. But a bucket of water hangs as a counterbalance. If it's raining the bucket fills up, making the dwarf's task easier.
Isn't it obvious, you cretin? I knew this stuff in first grade.
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Glaswegian Rhapsody
Date: 2007-01-27 10:03 am (UTC)Is this the real life, is it the methodone?
Stuck in Govan, "two bob fur the telephone?"
Open yer wine an' talk wi' a whine like me.
Um just a weeji, gie us yer Sunny D.
Cos I'll chib yer pal, rip yer Da; slash yer dug, ride yer ma!
Any way the Clyde flows Disnae really mater tae me......tae me.
Haw Maw, just chibbed a radge,
Buckie bottle tae the heid,
An noo the fuckin' bastard's deid!
Haw Maw, Um just oan parole,
An noo I'm headin straight back tae Bar-L.
Haw Maw, ooh oohooh ooh,
Never meant tae steal yer purse,
But if I'm no fu' o' smack this time the morra'.
Carry oot, carry oot!
An we'll go oot oan the batter!
Too late, the bailiff's here,
Sends shivers doon ma spine,
Gubbed 10 jellies just in time.
Goodbye all ye dobbers, I've got tae go,
Got tae go and rip some wank fae up the scheme.
Haw Maw, ooh oohooh ooh
I'm a jakey bam, I sometimes think I've never been washed at all.
I see a little silhouetto of a bam,
Adidas! Adidas! "Can ye get us a kergo?" .
Thunderbird, White Lightning, very very frightning to me!
Twenty Mayfair, Twenty Mayfair, Twenty Mayfair and some skins,
Magnifico oh oh oh oh!
I'm just a vat boy, nae buggar loves me,
He's just a vat boy fae a vat family!
"Spare us a pound fur a wee cup o tea'?"
Get tae fvck, skanky slob, will ye get a job?
Forfucksake, No! I will no' get a job! - Get a job!
Forfucksake, I will no' get a job! - Get a job!
Forfucksake, Will you get a job? - Get a job!
Will no' get a job, get a job!
Will no' get a job, get a job!
No, no, no, no, no, no, no.....
Oh gonorrhoea! gonorrhoea! gonorrhoea and the clap!
Then doon the pub, has the barman put aside for me?
For me, for meeeee!?
So you 'hink you can slash me and pish in my eye?
So ye 'hink ye can chib me an' leave me to die?
Haw bawbag, can't dae this tae me bawbag!
Just wait till I'm oot, just wait till I'm right oot ma nut!
Fuck all really matters,
Any cvnt can see,
Fvck all really matters, fvck all really matters to me!
Any way the Clyde flows.....
(no subject)
Date: 2007-01-27 10:15 am (UTC)Solution: Imhotep doesn't exist."
If Imhotep doesn't exist, how can it be said that he/she/it is taller/shorter than anything elese?
(no subject)
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Date: 2007-01-27 10:49 am (UTC)(no subject)
Date: 2007-01-27 10:57 am (UTC)I didn't lay down any rules, but you CHEATED!
(no subject)
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From: (Anonymous) - Date: 2007-01-29 01:26 am (UTC) - Expand(no subject)
Date: 2007-01-27 10:50 am (UTC)Your problem here doesn't seem to be with the underlying reasoning or the communal framework of assumptions it requires, but with the graceless, heavy-handed exposition of "practical context" around it, which is characteristic of current science and maths teaching (since we decided logic and nature had to have an application if they were to have a place in the curriculum).
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Date: 2007-01-27 11:32 am (UTC)My answer was "10", my explanation being that Sam was pretty certain that I could be trusted, as he was a friend of mine for more than a few years, so he simply asked me. Also, the fact that I was in 4th grade kind of gave it away anyway.
My teacher told me that I'd never be in a single math problem of hers ever again.
(no subject)
Date: 2007-01-27 11:33 am (UTC)(no subject)
From:Inconsiderate old men are ruining the world.
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From:"tap door run"
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Date: 2007-01-27 11:57 am (UTC)The mechanical lift is a problem, because you can only have one passenger at a time. Otherwise it becomes too heavy. What then happens to people on the middle floors, waiting to go down? You can't just send the lift up to them. They'd have to go down and bring it up, which would make no sense.
What, though, if there's a monkey lift operator? He brings the lift up to the middle floors, then gets out, lets the people in, and runs back downstairs. Problem solved. Unless the monkey and the dwarf fight, I add, anxiously.
"No!" shouts Hisae, "I want them to be friends!"
(no subject)
Date: 2007-01-27 12:12 pm (UTC)Thomas S.
(no subject)
Date: 2007-01-27 02:03 pm (UTC)(no subject)
Date: 2007-01-27 02:23 pm (UTC)They're like jokes from little kids, where they just wait for the answer telling you "no.... no.... no.... no...."
(no subject)
Date: 2007-01-27 02:51 pm (UTC)I am quite close, but not physically at this moment, to someone very much from a science background, whereas I'm much more arts and humanities, and I feel a certain friction in our world views sometimes.
He once told me that he never liked the humanities subjects at school because there wasn't any one right answer. Interesting. He did make the very reasonable point, though, that if there wasn't any right answer, how could the teacher ever presume to be in a position to mark one person higher than another? I think that dilemma is at the very heart of everything that's wrong with our current education system.
Here's an extract from Viz:
Armed Robber: No nonsense. Just give me all your money.
Mr Logic: I shall commence by pointing out to you that my demeanour is not one which could be described as nonsensical. Consequently I can attest you have no cause to reprimand me on your first point. On to your second point: Bearing in mind the potentially lethal situation in which I find myself, to wit: your presence in conjunction with the presumably loaded firearm which is presently levelled at my cranium, I will comply with your request comprehensively, albeit reluctantly. Here, twenty-seven pence.
Armed Robber: Twenty-seven pence? Fuck off. There's more than that in the till.
Mr Logic: Indeed, undoubtedly so. However your request was for *my* money. The currency in the till belongs to a third party and is therefore not "my money". However, if you are still desirous of said money I would suggest that you re-phrase your original statement to recognise and incorporate this important distinction.
(no subject)
Date: 2007-01-27 02:58 pm (UTC)(no subject)
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Date: 2007-01-27 04:32 pm (UTC)height of silliness (attempt #2)
Date: 2007-01-27 04:53 pm (UTC)Imhotep is usually depicted sitting down (even if, on occasion, his throne has been stolen) which can't help.
***
I was expecting some comment on the Japanese Triumph shopping
bra-sket (although Nihonese with No! branding on their pants
can't be that great a selling point for the convertible
garments).
http://www.timesonline.co.uk/article/0,,8122-2565920_2,00.html
(bottom of p2; the Currant Bun had pix & melon gags,
but not the Japanese for "shopping bag")
http://www.thesun.co.uk/article/0,,2-2006520033,00.html
with more of the pink mannequin in this pic:
http://www.impactlab.com/modules.php?name=News&file=article&sid=9750
very eco, to use only one actual woman in the promo
(no subject)
Date: 2007-01-27 06:00 pm (UTC)This would explain your always generous use of arguments you don't understand, pulled out of unlit areas of your anatomy (or google), to support your flight of fancy de jour. Always talking about Gini, never caring whether it lives in a bottle or under a Lorenz curve.
der.
(no subject)
Date: 2007-01-27 06:04 pm (UTC)Solution: Flush. Thus making the problem go away.
However, I used another solution which involved washing my hands afterward.
(no subject)
Date: 2007-01-27 07:14 pm (UTC)(no subject)
Date: 2007-01-27 11:55 pm (UTC)Just because you're bad at something doesn't make it irrelevant. You're worse than the 'Americans' you hate for lashing out at what they don't understand. The truth is you are a pig-ignorant bigot of viewpoints different than your own, and yet you try to cloak your contempt as some sort of pluralism.
Seriously, why would you attack math?
(no subject)
Date: 2007-01-28 08:56 am (UTC)Apparently, even Scientists Agree...
Date: 2007-01-28 12:19 am (UTC)Discipline!
Date: 2007-01-28 08:32 pm (UTC)You're joking, right? <nervous laugh>
Date: 2007-01-29 03:21 am (UTC)Re: You're joking, right? <nervous laugh>
Date: 2007-01-29 04:38 pm (UTC)I've just finished giving a press conference here in Palma and I spent most of the event telling local journalists that you should "never trust the narrator". Maybe I have the maths teacher to thank for that lesson.
(no subject)
Date: 2007-01-30 01:10 am (UTC)we've never met, but I was directed here by a friend.
I think you've missed something very important about maths and maths teachers: The point of maths lessons is to teach you maths. To elaborate, that means teaching you mathematical language, mathematical techniques, and mathematical ways of thinking. You don't have to use those things at every second in your life. They are merely intellectual tools which you might find handy. In a similar vein, you don't need to know how to use a screwdriver to get through life, it's merely a tool and a technique you might find handy.
Since the point of maths lessons is to teach you mathematical technique, the questions given to you need to be phrased in such a way that to answer them you need to apply mathematical technique. At lower levels, this means problems will only have one answer. At higher levels, there might be more or none, but in order to check that you have thought the problem through correctly, the number needs to be known to the teacher.
"One of the things that frustrated and perplexed me most at school ...framed the question in the same way as the teacher, subscribed to the same assumptions, and shared the teacher's utter lack of imagination."
So anyone that has skill with numbers is unimaginative? Thanks. Now that you've gratuitously insulted most of the people you'll ever meet, perhaps you could make a sensible point? As I said above, the point of maths lessons is to teach you maths. It's necessary that you solve the question USING MATHS to demonstrate that you understand.
"The kind of absurd, scary arbitrariness of the supposed "solutions" to maths problems..."
The problems are deliberately set up to have a known number of solutions which requires a simplicity that the real world often lacks.
A maths problem having a maths solution does not render the solution invalid in concept, so your use of " marks is like saying that anything maths related is instantly wrong.
"...Look Around You: Maths. Here's an example of their logic.
Problem 1: Jean is shorter than Brutus but taller than Imhotep. Imhotep is taller than Jean but shorter than Lord Scotland. ...
Solution: Imhotep doesn't exist."
The problems internal consistancy lasts until line two, when Jean is stated as being shorter than Imhotep (after line one states Jean is taller than Imhotep). Since the question relates to the height of imhotep, there are a number of acceptable mathematical/logical answers, including "The stated information contains a contradiction", "Not enough information supplied", and "There's an error in this test paper". Since we have no information enabling us to judge any one of the stated facts to be superior to any other, it is illogical to say that Imhotep does not exist. In fact, that's one of the infinitely many wrong answers.
"The answer is a nice rebuke to our idiotically conformist attempts to solve the problem on the basis of maths, when in fact we should have been looking at the existential and religious realm..."
Why would looking at the existential and religious realm help? Imhotep may be a lump of stone, but lumps of stone still have a height. Analysed with pure logic the question is revealed as nonsense. No need to bring religion in at all. I mean, we can call someone a witch and set fire to them if you like, but will it really help?
Having said all that, I took a look at the site you linked to, and the questions you posted later, and I agree with you that those are a crock of something unpleasant. However, an important point here is that those questions do not involve any maths. Mostly they involve faulty logic and an incomplete set of information. Don't dismiss a massive and very useful discipline just because some idiot set up a website full of crap and you mislabelled it.
(no subject)
Date: 2007-01-31 01:12 am (UTC)I don't know what kind of school you went to, but in the maths/science classes at mine they would ask us questions directly pertaining to the subject material. In maths, for example, they might ask "what is the solution to this differential equation?", a question which has one correct answer. Or in my physics class they might have asked "what is the resulting vector of momentum from the collision between these two objects?", another question which has one correct answer.
The subjects of Maths and Physics were taught to me from base principles, where we were free to question why various approaches were taken, and encouraged to prove the theorems we were being taught. (For example, in Physics I can remember measuring the refractive indexes of various substances to prove Snell's Law, measuring the speed of sound, proving that "momentum is always conserved", etc. In maths, everything was built up from basic addition, with nothing left a mystery.) Those teachers never asked us to put our faith in their word, because we could see the truth for ourselves in our own experiments and work books.
The only class in which I can remember being asked to solve the kind of ambiguous "lateral thinking puzzles" you've dissected above was, funnily enough, English. At the time the teacher even acknowledged that, in most cases, there was more than one answer to satisfy each question.
If you were discouraged from maths and sciences by teachers who posed ridiculous, ambiguous puzzles then that's a shame. I don't think that was the case, though, and I suggest that your using them as a means of dismissing a scientific education is rather disingenuous.