A ball and a bat cost $1.10, the bat costs $1 more than the ball, how much does the ball cost?
(http://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Baseball.jpg/250px-Baseball.jpg)
(http://upload.wikimedia.org/wikipedia/commons/thumb/3/30/Fourbats.jpg/181px-Fourbats.jpg)
The correct answer is 5 cents, most people (as much as 87% in some studies) answer 10.
This is not a hard question though, any grade school student should be able to answer this correctly. And most people do get the question right when the numbers are less kind to human consumption (two objects total 37 cents, one is 13 cents more than the other), presumably because it is harder to do. No easy answers mean that it must be processed the hard way, instead of the deceptive simple solution to the ball and bat problem.
We latch on to that easy answer too, when presented with the correct answer and the incorrect answer side by side, half of respondents still went with the 10 cent answer to the question. An improvement over the two thirds incorrect in the control condition, but hardly resounding success at removing the bias.
There is I think, a very deep flaw in human reasoning. Once we have that simple solution, we simply stop thinking about the problem. And the ball and bat problem is math, it can be proved, with 100% certainty, that the easy answer is wrong. How much more dangerous are simple and wrong solutions to complex problems, where the simple solution is not so easy to disprove, and there may be no correct answer waiting to replace it?
My brain works pretty straight forward. After reading this I would still answer $.10.
fucking maths :argh!:
Quote from: P3nT4gR4m on June 06, 2010, 05:09:49 PM
fucking maths :argh!:
It's not deep maths.
You have $1.10
You buy 1 item for $1.00
That leaves $0.10 left.
The statement that item 1 costs $1.00 more than item 2 completes the formula.
Not quite. $1.00 more than 10c = $1.10
1+0.1=1.1
That would make both items come in at 1.20 (1.1 + 0.1 = 1.2)
if ball=0.05 and the bat is 1.05 (1+0.05) then both items come to $1.10
Simples!
Quote from: Hawk on June 06, 2010, 06:42:15 PM
Quote from: P3nT4gR4m on June 06, 2010, 05:09:49 PM
fucking maths :argh!:
It's not deep maths.
You have $1.10
You buy 1 item for $1.00
That leaves $0.10 left.
The statement that item 1 costs $1.00 more than item 2 completes the formula.
But then the bat only costs 90 cents more than the ball.
Hawk,
going to go sit in a corner now.
FUCKERS
On a serious note some peoples brains are not wired for math. Mine isn't and never has been. People always tell me math is logical and damned if I can see any logic in it at all. Obviously.
Other things I can grasp easily and some people struggle with them. I wonder why that is.
Can totally relate - I'm okay with arithmetic (which this example is) but maths I'm fucking retarded at. I can add and subtract and, with a bit more head scratching, I can multiply and divide but my power to divide is severely limited with the pitfall happening at the point where you have to employ something called "long division"
Maths is when they introduce letters instead of or as well as numbers and you need to balance and solve. Fuck that shit - I can count but I have no fucking idea what balancing and solving even means, never mind the million and one stupid fucking ways those cunts at school tried to show me how to do it. Common denominators, factors, venn fucking diagrams, cartesian some bullshit or other... and then there was all that sin and cos and tan crap. I swear to this day they were just making shit up to make me feel stupid :argh!:
Funny thing is when I was a carpenter I could just 'see' the solution to a fraction problem in my head. I have no idea how that happened either. Other guys would do the problem on a 2 X 4 after I would just spout the answer.
I even aced algebra in community college without understanding one iota of it.
Meh. When I was at school I could english like a ninja and I could also biology the shit out of pretty much anybody but all the other subjects just confused the piss out of me. Except for history and geography - those struck me as straightforward enough memory tests which I was crap at on account of the amount of hash I went through at school.
Uhh the point isn't that math is hard.
Quote from: BADGE OF HONOR on June 06, 2010, 07:32:51 PM
Uhh the point isn't that math is hard.
There is I think, a very deep flaw in human reasoning. Once we have that simple solution, we simply stop thinking about the problem. And the ball and bat problem is math, it can be proved, with 100% certainty, that the easy answer is wrong. How much more dangerous are simple and wrong solutions to complex problems, where the simple solution is not so easy to disprove, and there may be no correct answer waiting to replace it?I think what we are trying to get at is why our brains tend to work the way Requia has accurately stated they do.
Thoughts on building a better biped:
The problem isn't math, and it isn't exactly easy answers. It's the human tendency to really cogitate as little as possible.
We are much more happy and comfortable when we can simply get through the day on force of habit alone. Having to focus for too long, or too often, wears us out.
A better biped would have a different policy on focus and attention.
Quote from: Sigmatic on June 06, 2010, 09:18:39 PM
Thoughts on building a better biped:
The problem isn't math, and it isn't exactly easy answers. It's the human tendency to really cogitate as little as possible.
We are much more happy and comfortable when we can simply get through the day on force of habit alone. Having to focus for too long, or too often, wears us out.
A better biped would have a different policy on focus and attention.
True enough. If I had $1.10 in front of me I would have arrived at the right answer quickly. As it was I skimmed the statement and formed the answer without thinking deeper.
I wonder how much of life we skim on a daily basis?
Most of it, by my observations.
I like to watch people and get inside their heads. A lot of the time, there's not a lot going on.
We filter out a lot of shit by necessity. If you actually felt the information coming to you from even a quarter of your nerve endings you'd be so overwhelmed you'd be utterly unable to do or concentrate on anything. You'd just roll around on the floor either screaming or cumming at the top of your lungs.
Same with information.
Problem is that it gets all to easy to do everything on autopilot. And it is. Ask someone who's never read a single book (I'd guess most of us have probably met one or two) how much trouble their life has been and you'll get much the same answer as you would from a poet laureate, albeit framed in less rosy language.
If you can get through life, quite comfortably, as an inferior biped and arrive at the same death as someone who really pushed themselves and went the extra mile, why should you bother? Most answers I've heard to this question seem to boil down to "just because" or equivalent. The intellectuals always seem to get indignant about "most people" and their lowest common denominator attitude but the bit most intellectuals never seem to be able to get is that it works for them.
I say fuck the masses. Concentrate on your own development. Take your avatar wherever the hell you want it to go and leave the rest to rot. As far as I'm concerned they're just something for me to hate or laugh at, depending on my mood. Improving them? Two words - how and why?
Good concept Pent. Don't you think the world is 'dumbing down' though? I mean people don't have to think as much anymore. Calculators were not allowed when I was in school for instance. 'Research' now mostly involves Google. Cars even tell you what to do and where to go.
Calculators are still discouraged at the algebra level, but you kind of need it for trig and above.
Tables of trig values are cool and all, but it's just really slow.
As for filtration, yeah that's a part of it. We learn by habit that lots of data doesn't need our attention, but that leads to zealous habituation that can be dangerous. For instance, you get used to driving, and you're bored, so you rubberneck at the scenery a bit and, crunch.
Tough example, but it applies to less deadly scenarios as well.
Yes research involves a lot of Googling, but you still have to go through the stuff to find what you're looking for. You could argue the same for "'Research' now mostly involves card catalogs in libraries." Filtering is required either way.
Anyway, there's a line between too simple/autopilot and what I'd call actually simple.
Too simple: the answer to everything is prayer.
Simple: introspection is a good way to start looking for answers.
Both are simple concepts, but one is probably the better answer than the other.
Probably a bad example, but I'm hoping I got what I meant across. :P
Quote from: Sigmatic on June 06, 2010, 09:57:16 PM
Calculators are still discouraged at the algebra level, but you kind of need it for trig and above.
Tables of trig values are cool and all, but it's just really slow.
As for filtration, yeah that's a part of it. We learn by habit that lots of data doesn't need our attention, but that leads to zealous habituation that can be dangerous. For instance, you get used to driving, and you're bored, so you rubberneck at the scenery a bit and, crunch.
Tough example, but it applies to less deadly scenarios as well.
Tough example but it illustrates another almost absolute truth - human beings learn things best the hard way. The guy who loses the use of his body from the waist down cos he was rubbernecking and ploughed into a bridge stanchion? Bet that fucker never gets nonchalant about watching the road after that :lulz:
Quote from: Hover Cat on June 06, 2010, 10:01:16 PM
Yes research involves a lot of Googling, but you still have to go through the stuff to find what you're looking for. You could argue the same for "'Research' now mostly involves card catalogs in libraries." Filtering is required either way.
Anyway, there's a line between too simple/autopilot and what I'd call actually simple.
Too simple: the answer to everything is prayer.
Simple: introspection is a good way to start looking for answers.
Both are simple concepts, but one is probably the better answer than the other.
Probably a bad example, but I'm hoping I got what I meant across. :P
No, I get it. There is definitely a bias against simplicity in this culture, which I find erroneous. There's a corresponding bias in favor of complexity. Someone may be unpleasable and indecisive, but what they say is "I'm complicated". Like it's some kind of desirable trait.
Simple stuff often works best,
in the right frame. Salmon with pepper, butter, and lemon is simple and magnificent. Using a hammer and duct tape to fix everything is probably too simple.
(Probably.)
The idea is to find out what level of simplicity is required. Which often requires a certain amount of profundity. Which leads back to the "don't make me think" syndrome.
Quote from: P3nT4gR4m on June 06, 2010, 10:02:23 PM
Quote from: Sigmatic on June 06, 2010, 09:57:16 PM
Calculators are still discouraged at the algebra level, but you kind of need it for trig and above.
Tables of trig values are cool and all, but it's just really slow.
As for filtration, yeah that's a part of it. We learn by habit that lots of data doesn't need our attention, but that leads to zealous habituation that can be dangerous. For instance, you get used to driving, and you're bored, so you rubberneck at the scenery a bit and, crunch.
Tough example, but it applies to less deadly scenarios as well.
Tough example but it illustrates another almost absolute truth - human beings learn things best the hard way. The guy who loses the use of his body from the waist down cos he was rubbernecking and ploughed into a bridge stanchion? Bet that fucker never gets nonchalant about watching the road after that :lulz:
By the same token, a moment's careful consideration can spare you having lessons burned into your brain.
"Time is the greatest of teachers, but it kills all its students".
Quote from: Sigmatic on June 06, 2010, 10:12:50 PM
Quote from: P3nT4gR4m on June 06, 2010, 10:02:23 PM
Quote from: Sigmatic on June 06, 2010, 09:57:16 PM
Calculators are still discouraged at the algebra level, but you kind of need it for trig and above.
Tables of trig values are cool and all, but it's just really slow.
As for filtration, yeah that's a part of it. We learn by habit that lots of data doesn't need our attention, but that leads to zealous habituation that can be dangerous. For instance, you get used to driving, and you're bored, so you rubberneck at the scenery a bit and, crunch.
Tough example, but it applies to less deadly scenarios as well.
Tough example but it illustrates another almost absolute truth - human beings learn things best the hard way. The guy who loses the use of his body from the waist down cos he was rubbernecking and ploughed into a bridge stanchion? Bet that fucker never gets nonchalant about watching the road after that :lulz:
By the same token, a moment's careful consideration can spare you having lessons burned into your brain.
"Time is the greatest of teachers, but it kills all its students".
Experience is the most effective and most merciless teacher of all.
Same diff. :)
Monkey learn: Fire bad, oww, very bad.
Correct answer: the store is having a "buy a bat for a dollar, get a ball free" sale, and the local sales tax is 10%. (That math problems about buying things always leave out tax unless they were specifically about tax / percents really bugged me as a kid. Bobby has a five-dollar bill, and he wants to buy a $4.99 toy - what happens when he gets to the checkout register? Fucking despair, that's what.)
I suspect part of the problem with that question is that if you try to answer it as you're reading it, you come up with $1 before you get to the word "than":
"A ball and a bat cost $1.10, the bat costs $1 ... " <- right here you're thinking, okay, the bat is a dollar and the ball is the remaining 10 cents, then you get back to the question just in time to hear " ... how much does the ball cost?" (okay, that's probably not what really happens, but it sounds believable.)
If you make the mistake of misinterpreting the question as "the set costs a dollar more than the just the ball" or "buying the bat on top of the ball costs you an extra dollar" - which is what people are a lot more likely to actually say, then the "correct" answer for you to come to is 10 cents. Nobody who pays $1.05 for one item and $.05 for another item announces that they paid a dollar more for one than the other. For that matter, it's pretty uncommon to buy two different items where one is 20x the other without the smaller one being a small snack object because you got hungry while shopping. That, and you can't buy anything for a nickel - it screws with your intuition to have such a tiny amount be relevant. I (and I think most people) solve practical arithmetic problem by just doing approximations until you get close enough - which is a lot more efficient than digging around for pencil and paper and doing algebra. For this problem it might go something like this (which is basically what I did):
Approximate bat at at $1 (since the bat has to be at least a dollar, and one dollar is a nice round number) and ball at the remaining $.10.
Then here, it forks:
The more intuitive heuristic method says, $1 and $.10 together make a dollar and a $1 is a dollar more than a dime - because the question asked about real quantities, and every American knows that a dime all by itself is worth approximately nothing. It's this tiny little coin, whereas dollars are bills. And to be honest, I can't fault people who think this way. They're within 5% of being correct of the price of an item that costs less than $1.25 - the error is insignificant, or at least it is anywhere except on a math test.
The "correct" method then says, but wait, then the bat would have to be $1.10, and they'd total $1.20, I've got an extra ten cents, so I take half of 10 cents off of both of them, and I get one-ten minus zero-five is one-five, and ten minus five is five again, so $1.05 for the bat and $.05 for the ball. Quite a bit more mental math.
The error remains when you talk about a transaction totaling 1.1 million as well, so the dime being next to nothing doesn't seem to be a contributing factor.
Quote from: P3nT4gR4m on June 06, 2010, 10:02:23 PM
Tough example but it illustrates another almost absolute truth - human beings learn things best the hard way. The guy who loses the use of his body from the waist down cos he was rubbernecking and ploughed into a bridge stanchion? Bet that fucker never gets nonchalant about watching the road after that :lulz:
Depressingly, this is not the case - real statistics show that people are more cautious for a while after an accident (either themselves or someone they know, although the effect is weaker if it doesn't happen to them personally) but that after a few months or so they're right back doing whatever it is that got them injured in the first place. In fact, once you get injured, you're statistically more likely than the general population to have the same general sort of injury happen to you, because you're still the type of person who got injured in the first place. For example, people who get into serious car accidents are more likely than the general population to be people who have greater "risk factors" - like poor driving skills, casual treatment of road regulations, people who routinely drive with a lot of distractions, or just ADHD - and so after they've gotten over the shock of the accident they're right back where they started. At least I think this is based on real statistics - a psych prof told our class this, but not being a real science teacher she didn't have cited sources at the ready for at least a third of the alleged facts she presented. :argh!:
Quote from: Requia ☣ on June 06, 2010, 10:28:12 PM
The error remains when you talk about a transaction totaling 1.1 million as well, so the dime being next to nothing doesn't seem to be a contributing factor.
Stay away from my just-so stories! :argh!:
Quote from: Hawk on June 06, 2010, 09:49:56 PM
Good concept Pent. Don't you think the world is 'dumbing down' though? I mean people don't have to think as much anymore. Calculators were not allowed when I was in school for instance. 'Research' now mostly involves Google. Cars even tell you what to do and where to go.
Calculators, I'll give you. I see college kids who can't do basic mental arithmetic because of this, and it blows my mind. I TA'd for a special section of general intro physics, where all of the students were education majors, and I had this conversation happen during a study/review session:
"So how do you find the momentum of the block?"
"Times the mass and the velocity together."
"Right. And what is the block's mass?"
"2."
"Yes, 2 kilograms. And the problem says that the block is stationary, so what is its velocity?"
"... zero?" (Whenever you ask students an easy question, they think you're trying to trick them. Always.)
"Right! So if its mass is 2 kilograms and its velocity is zero, then what is its momentum?"
At this point the student pulled out a calculator and I very nearly flipped my lid. Yes, this college student who plans on teaching impressionable young children pulled out a calculator to multiply 2 and 0, and then in all seriousness announced that the answer was, in fact, zero. There was no "How silly of me! I just used a calculator to multiply a number by zero without even realizing it!" She saw nothing wrong using a calculator to solve 2 x 0.
Research, no. The point of intelligence in research comes in understanding and interpreting the information you find, not finding it in the first place. This is definitely a case where the means are largely irrelevant as long as you get the information you're looking for. And skill, or at least know-how, is there too - people don't check the discussion page on controversial Wikipedia articles, they don't look at the cited sources to find more information (or even to confirm that it says what the wiki says it says.) If they're looking for scholarly info, they don't check the list of references at the end of the book or article. (Protip: if you check the references on a couple of related books/articles, and then look up the works that are in the overlap of the references list, you're almost guaranteed to find the most cited/referenced works on the subject you're looking for, which is probably one that you want.)
Quote from: Golden Applesauce on June 06, 2010, 11:33:37 PM
Quote from: Hawk on June 06, 2010, 09:49:56 PM
Good concept Pent. Don't you think the world is 'dumbing down' though? I mean people don't have to think as much anymore. Calculators were not allowed when I was in school for instance. 'Research' now mostly involves Google. Cars even tell you what to do and where to go.
Calculators, I'll give you. I see college kids who can't do basic mental arithmetic because of this, and it blows my mind. I TA'd for a special section of general intro physics, where all of the students were education majors, and I had this conversation happen during a study/review session:
"So how do you find the momentum of the block?"
"Times the mass and the velocity together."
"Right. And what is the block's mass?"
"2."
"Yes, 2 kilograms. And the problem says that the block is stationary, so what is its velocity?"
"... zero?" (Whenever you ask students an easy question, they think you're trying to trick them. Always.)
"Right! So if its mass is 2 kilograms and its velocity is zero, then what is its momentum?"
At this point the student pulled out a calculator and I very nearly flipped my lid. Yes, this college student who plans on teaching impressionable young children pulled out a calculator to multiply 2 and 0, and then in all seriousness announced that the answer was, in fact, zero. There was no "How silly of me! I just used a calculator to multiply a number by zero without even realizing it!" She saw nothing wrong using a calculator to solve 2 x 0.
Research, no. The point of intelligence in research comes in understanding and interpreting the information you find, not finding it in the first place. This is definitely a case where the means are largely irrelevant as long as you get the information you're looking for. And skill, or at least know-how, is there too - people don't check the discussion page on controversial Wikipedia articles, they don't look at the cited sources to find more information (or even to confirm that it says what the wiki says it says.) If they're looking for scholarly info, they don't check the list of references at the end of the book or article. (Protip: if you check the references on a couple of related books/articles, and then look up the works that are in the overlap of the references list, you're almost guaranteed to find the most cited/referenced works on the subject you're looking for, which is probably one that you want.)
So if you were going to do a paper on architecture in your town you would go to the internet. Research like that used to involve getting the bottom of your shoes dirty.
There's nothing wrong with using the internet for research.
A good paper would require both actually visiting the buildings and doing research online. I'd add that there's places on a building you can't get a good look at from the ground or that you can't see from inside for one reason or another. Example: If I were to to a paper on one of our few cool buildings here, it would be an old bank building in downtown. Most of the upper floors are cut off from public access, not to mention the back vault itself, which is really cool (I got to go down there when I was at a wedding in the ballroom - we weren't supposed to be down there, but we went anyway). Online research would give me more information than just a pair of binoculars and my text book on the subjecct.
Whatsname said it best.
The internet isn't a replacement medium, it's ANOTHER medium.
Quote from: Hover Cat on June 06, 2010, 11:57:10 PM
There's nothing wrong with using the internet for research.
A good paper would require both actually visiting the buildings and doing research online. I'd add that there's places on a building you can't get a good look at from the ground or that you can't see from inside for one reason or another. Example: If I were to to a paper on one of our few cool buildings here, it would be an old bank building in downtown. Most of the upper floors are cut off from public access, not to mention the back vault itself, which is really cool (I got to go down there when I was at a wedding in the ballroom - we weren't supposed to be down there, but we went anyway). Online research would give me more information than just a pair of binoculars and my text book on the subjecct.
I couldn't agree more. Using BOTH would make good research.
While the net has largely replaced library research (and given the quality of the nonfiction in the county library system here, good riddance), I don't see how it would change something like going and visiting a given building. If that was relevant before its still relevant now.
I'm not really sure what good it would do in the first place though, unless you're already well versed in architecture how would you know how to describe what you see around town? and if you are at that level, you probably have access to far better resources than can be found on the public internet.
Quote from: Golden Applesauce on June 06, 2010, 11:33:37 PM
Quote from: Hawk on June 06, 2010, 09:49:56 PM
Good concept Pent. Don't you think the world is 'dumbing down' though? I mean people don't have to think as much anymore. Calculators were not allowed when I was in school for instance. 'Research' now mostly involves Google. Cars even tell you what to do and where to go.
Calculators, I'll give you. I see college kids who can't do basic mental arithmetic because of this, and it blows my mind. I TA'd for a special section of general intro physics, where all of the students were education majors, and I had this conversation happen during a study/review session:
"So how do you find the momentum of the block?"
"Times the mass and the velocity together."
"Right. And what is the block's mass?"
"2."
"Yes, 2 kilograms. And the problem says that the block is stationary, so what is its velocity?"
"... zero?" (Whenever you ask students an easy question, they think you're trying to trick them. Always.)
"Right! So if its mass is 2 kilograms and its velocity is zero, then what is its momentum?"
At this point the student pulled out a calculator and I very nearly flipped my lid. Yes, this college student who plans on teaching impressionable young children pulled out a calculator to multiply 2 and 0, and then in all seriousness announced that the answer was, in fact, zero. There was no "How silly of me! I just used a calculator to multiply a number by zero without even realizing it!" She saw nothing wrong using a calculator to solve 2 x 0.
That kind of thing was normal in physics long before calculators showed up.
Quote from: Requia ☣ on June 07, 2010, 12:08:47 AM
While the net has largely replaced library research (and given the quality of the nonfiction in the county library system here, good riddance), I don't see how it would change something like going and visiting a given building. If that was relevant before its still relevant now.
I'm not really sure what good it would do in the first place though, unless you're already well versed in architecture how would you know how to describe what you see around town? and if you are at that level, you probably have access to far better resources than can be found on the public internet.
Let me bring this discussion back to the point I was trying to make.
That which makes us weaker just makes us weaker.
Look at a car that can now parallel park itself. A car that has rear sensors that will stop your car. I know these CAN be good things once in a while but what is it really doing to us as humans? At what point are we going to say enough, we have to rely on our own efforts, our own thoughts?
While I agree with you on things like car sensors (though god knows I could use them, since I suck at parking), the internet has not, imo, made us weaker like you're suggesting. If anything, it has sharpened my BS detection when filtering information.
And, as I said before, you could make the same argument by saying that library catalogs were making our predecessors weaker. It's just a tool.
Quote from: Hover Cat on June 07, 2010, 12:16:52 AM
While I agree with you on things like car sensors (though god knows I could use them, since I suck at parking), the internet has not, imo, made us weaker like you're suggesting. If anything, it has sharpened my BS detection when filtering information.
And, as I said before, you could make the same argument by saying that library catalogs were making our predecessors weaker. It's just a tool.
Clarification:
If I wanted to write about China I would go there. NOT VIRTUALLY. I would get off my ass and go to China. I would mingle with the people. I would shop their markets. I would eat their food and drink their drinks. I would (gasp) TALK with them.
Hawk,
Sooooooooooooooooo last century.
And how many people did that last century? Last century people would have read other people's books about China. Original research, like you're talking about, hasn't changed much. It's the secondhand research (which is all most people have the resources to do) is what the net changed.
I give up.
Quote from: Hawk on June 07, 2010, 12:12:12 AM
Quote from: Requia ☣ on June 07, 2010, 12:08:47 AM
While the net has largely replaced library research (and given the quality of the nonfiction in the county library system here, good riddance), I don't see how it would change something like going and visiting a given building. If that was relevant before its still relevant now.
I'm not really sure what good it would do in the first place though, unless you're already well versed in architecture how would you know how to describe what you see around town? and if you are at that level, you probably have access to far better resources than can be found on the public internet.
Let me bring this discussion back to the point I was trying to make.
That which makes us weaker just makes us weaker.
Look at a car that can now parallel park itself. A car that has rear sensors that will stop your car. I know these CAN be good things once in a while but what is it really doing to us as humans? At what point are we going to say enough, we have to rely on our own efforts, our own thoughts?
I meant to talk about GPS since you tangentially mentioned it earlier. I own a GPS unit, and I have owned one for longer than I've had a car (strictly speaking, I still don't technically
own a car) and it makes navigation possible. I have a terrible sense of space and no sense of direction. I have trouble finding my way back to the waiting room after a doctor's appointment. But even for people with a normal sense of direction, there is one huge benefit of the GPS: you can miss turns. If you're traveling in an unfamiliar area with just a list of directions, which turns to make and when, and you make a wrong turn or miss one, you're screwed. You either have to backtrack until you're back on your old route headed in the right direction (which can be devilishly tricky with lots of one-way streets, or if you have to make an additional detour for construction on the way back) or pull over somewhere, get out your map, and figure out where on that map you are. With a GPS that plots routes for you, it automatically notices when you've made a wrong turn and re-plots a route that gets you back on track. This means you can miss turns with impunity: if you're in the wrong lane and can't turn safely, rather than being forced to choose between cutting through lanes of traffic and being hopelessly lost, just keep going! The handy GPS will uncomplainingly find you a new path, no matter how much you need to detour around something.
Quote from: Requia ☣ on June 07, 2010, 12:11:34 AM
Quote
<snip>
Yes, this college student who plans on teaching impressionable young children pulled out a calculator to multiply 2 and 0, and then in all seriousness announced that the answer was, in fact, zero. There was no "How silly of me! I just used a calculator to multiply a number by zero without even realizing it!" She saw nothing wrong using a calculator to solve 2 x 0.
That kind of thing was normal in physics long before calculators showed up.
Really? Did they get out a slide rule and then announce that the problem was unsolvable because there is no logarithm of zero?
edit for I suck at quote tags.
No, but physics people didn't generally know what to do when it came to solving simple arithmetic. (Einstein was famous for this). In that particular case the answer would (even today sometimes), be listed as m*v, without any attempt to determine what that is.
Quote from: Hawk on June 07, 2010, 12:22:23 AM
Quote from: Hover Cat on June 07, 2010, 12:16:52 AM
While I agree with you on things like car sensors (though god knows I could use them, since I suck at parking), the internet has not, imo, made us weaker like you're suggesting. If anything, it has sharpened my BS detection when filtering information.
And, as I said before, you could make the same argument by saying that library catalogs were making our predecessors weaker. It's just a tool.
Clarification:
If I wanted to write about China I would go there. NOT VIRTUALLY. I would get off my ass and go to China. I would mingle with the people. I would shop their markets. I would eat their food and drink their drinks. I would (gasp) TALK with them.
Hawk,
Sooooooooooooooooo last century.
You're not as behind as you think - if I wanted to write about China, I'd just talk to my roommates. Okay, right now I'm at home for summer break and they're still staying near the university, but I can still IM them. (with the magic of the internet!) If I wanted to get a sample of the news articles being published in the various provinces in China (and I could read Chinese)
I could read local news articles from sources distributed across the largest country in the known universe from my laptop an ocean away. With the internet, you can start a real-time conversation - potentially with voice and video - with anyone in the world who has an internet connection.
This very forum is that. We have active members from every country in North America, and at least the UK, Germany, the Netherlands, and I think Israel and Australia. There's at least one guy from Brazil who periodically stops by. We can get first hand accounts of events on three continents - and this is a pretty niche forum. I've probably played chess with people from five, if not six, continents. I can play video games with people who spell "hahaha" "jajaja" or "kekeke" or with characters my computer doesn't even recognize. (Koreans are
murderous at StarCraft, btw, which was developed by Canadians and then played pretty much everywhere - I learned about it from my Brazilian neighbors.)
Heres a thought:
I'm a biologist, a professional scientist. I'd say I'm pretty intelligent, and I think most people here would agree.
I am currently unable to wrap my head around why the ball in the op isn't $.10 and I don't think it's that I just got up a few minutes ago.
Would you say now that I'm stupid?
Maybe someone can explain it to me, but as long as that person is taking a holier than though stance because their mind works better with mathematical logic than mine I wouldn't care to hear it. In the same way people wouldn't like it if I took a holier than thou stance when it comes to gestalt on the spot identification of organisms.
Actually, the better your brain naturally works at math, the more likely you are to get it wrong. What happens is there are easy ways and hard ways to process the answer, when an easy answer pops up, the other processes never trigger. Getting it right relies on checking your answer.
Do it in reverse, if the ball is 10 cents, and the bat is $1 more than the ball, the bat is $1.10, so the bat and ball total $1.20.
I think the main problem is that english sucks, when it comes to math. Bat is one dollar more than ball, both together equal 1.10.
X+(1+X)=1.10
so,
X+X=.10
so,
X=.5
There you go with that fucking 'X' thing! That's exactly my problem with maths :argh!:
It's a metaphor, silly.
Bat is one dollar more than ball. That means [the cost of ball] added to [one dollar plus the cost of the ball], is 1.10.
so,
Ball + (1+Ball)=1.10
so,
Ball + Ball=.10
so,
Ball =.5
Quote from: LMNO on June 07, 2010, 04:14:01 PM
It's a metaphor, silly.
Bat is one dollar more than ball. That means [the cost of ball] added to [one dollar plus the cost of the ball], is 1.10.
so,
Ball + (1+Ball)=1.10
so,
Ball + Ball=.10
so,
Ball =.5
STFU!!! :argh!: :argh!: :argh!:
For the record, when I read the original post, my first instinct was to say the ball cost ten cents.
I knew that I could do the maths, I was just lazy; and so, I got it wrong because the answer was not "intuitive" to me.
Prolly cos my maths is the suck or something I got it right almost straight away (although I did want to try 10c first) I saw the words "more than" so I knew I had to add the bat and ball price together then add the ball again and compare to the total. Straight away I got 1.20 and figured it must be a different price.
A Five cent ball and a dollar and five cent bat are gonna be pretty shitty toys... that's like Dollar General quality there.
If you buy your kid a bat and ball at those prices, you are a terrible parent. They probably came from China and are full of lead, asbestos or some other horrible thing... not to mention the Baseball Sweat Shops that they were manufactured in!!!
The question is from the 60s, inflation has made it a bit obsolete.
Repackaged for the modern age:
A bat and ball set are on ebay with a - buy it now - price of $29 if the Bat is $15 more than the ball and the ball is $1.50 then WTF????
ETA: Okay maybe someone with a better grasp of math should attempt this :oops:
Ten Bucks! ... no wait ... :argh!:
Quote from: Requia ☣ on June 07, 2010, 03:03:29 PM
Actually, the better your brain naturally works at math, the more likely you are to get it wrong. What happens is there are easy ways and hard ways to process the answer, when an easy answer pops up, the other processes never trigger. Getting it right relies on checking your answer.
Do it in reverse, if the ball is 10 cents, and the bat is $1 more than the ball, the bat is $1.10, so the bat and ball total $1.20.
Ah, I get it now. :)