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http://www.youtube.com/watch?v=lCJ3Oz5JVKs
"Do you recognize there's a difference between one dollar and one cent?"
"Definitely."
"Do you recognize there's a difference between half a dollar and half a
cent?"
"Definitely."
"Then, do you therefore recognize there's a difference between .002 dollars
and .002 cents?"
"No."
--
- Warp
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"Warp" <war### [at] tag povrayorg> wrote in message
news:498b1a76@news.povray.org...
> http://www.youtube.com/watch?v=lCJ3Oz5JVKs
>
Half of the company that I work for is a call center. I'm not saying that
they are all stupid, and that I'm all that smart, but when it comes to
concepts like fractions or percentages, you will lose most of them.
Unfortunately, t's probably true of a large percentage of the population.
Once, while explaining how much I was putting in my retirement account:
"My wife and I are both contributing 10%."
"Wow, so between the both of you, you're putting in 20%."
"No. We're both putting in 10% of what we make."
"You're putting in 10% or your wife is?"
"Both of us are putting in 10%."
"Well then you're putting in 20% together."
"Ahhhhg!!!"
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"Warp" <war### [at] tagpovrayorg> wrote in message
news:498b1a76@news.povray.org...
> http://www.youtube.com/watch?v=lCJ3Oz5JVKs
>
Here's the entire audio file, if you're bored. I haven't listened to the
whole thing, but the youtube was highly edited. Anyway, this guy was very
patient, and explained this problem multiple times to multiple people, and
apparently never got a single employee to understand the problem.
http://media.putfile.com/Verizon-Bad-Math
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http://xkcd.com/verizon/
- Slime
[ http://www.slimeland.com/ ]
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Warp wrote:
> http://www.youtube.com/watch?v=lCJ3Oz5JVKs
Such a classic!
A friend of mine recently had a similar conversation on the internet:
Ok, this one is too funny and I have to share. I usually don't post
messages to internet forums, but I got an e-mail about Obama's
"change.gov" website where citizens can voice their ideas. I was
browsing through and ran across a posting that I felt I had to correct.
Them:
----------------------------
Wouldn't it have been cheaper to give each verified US citizen (or
household) a one-time grant of $750,000 that could have been used to pay
off or down mortgages, student loans, or school fees, car loans? Of
course, folks would have also spent money on other things, clothes,
cars, vacations, electronics, real estate, investments, savings, health
care, whatever they wanted or desired.
That would have affected everyone, (even those of us who are not
documented),and would have stimulated the economy for everyone. It would
have been been cheaper than giving Bush & his fellow crooks 750 billion
dollars to finish their ransacking of the US economy one last time
before they left office.
[...]
If you give me a $1,000.00 stimulus check, I am going to buy groceries
or pay down the electric /gas bill. Next month I still have to feed my
family and the electric company will only raise their rates, knowing
that the stimulus checks are in the mail.
[...]
Me:
--------------------------
$750,000 x 300,000,000 americans = $225,000,000,000,000
That's 225 trillion. So no, it's not cheaper. Not anywhere close.
To put that number into context, the federal budget (not counting
medicare, medicade, and social security) is 1 trillion.
And if everyone has tons of money, everyone raises their rates (like you
said the electric company will do if you have a $1,000 stimulus check.)
It's called inflation, and the money would become practically worthless.
There's no magical solution, and the government can't just pay
everything off.
Them:
-------------------------
Not to all Citizens,
Children who are still Dependants would not be eligible.
Nor would incarcerated individuals. I am sure that there could be a
formulation that would lower the grant amount those over a certain
income level.
Just open your mind to it for a minute. It's better that giving it to AIG
Me:
-------------------------
Even if you exclude criminals and give the money to households, that's
roughly one out of every ten americans, and the number is $22 trillion.
I can open my mind, but numbers are numbers. You can't just dream up a
magical solution that sounds exciting. You have to back it with facts
and reality because in the end, we want life to get better, not to cause
more problems.
Them:
-------------------------
I AM NOT A MATHEMATICIAN BUT I THINK THAT YOUR MATH MAY BE OFF.
WE HAVE 300 MILLION CITIZENS. IF WE GAVE EVERYONE 1 MILLION DOLLARS
WOULDN'T THAT BE 300 MILLION DOLLARS? HOW DID WE GET 22 TRILLION FROM
750 THOUSAND DOLLARS PER HOUSEHOLD?
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Kevin Wampler <wampler+pov### [at] uwashingtonedu> wrote:
> Them:
> -------------------------
> I AM NOT A MATHEMATICIAN BUT I THINK THAT YOUR MATH MAY BE OFF.
> WE HAVE 300 MILLION CITIZENS. IF WE GAVE EVERYONE 1 MILLION DOLLARS
> WOULDN'T THAT BE 300 MILLION DOLLARS? HOW DID WE GET 22 TRILLION FROM
> 750 THOUSAND DOLLARS PER HOUSEHOLD?
I can understand that most people don't have a good grasp of very large
and very small numbers. Heck, even I have hard time grasping the magnitude
of something like "10^20 kilometers". From an astronomical point of view,
is that a very large distance or a very small distance? How large is it?
However, some people seem to get completely lost with even the simplest
of equations when numbers get out of the 0.01 - 10^6 boundaries. It seems
that they can more or less grasp concept of that magnitude, but immediately
when numbers get out of that range, they are completely lost, and units and
magnitudes get hopelessly mixed.
I find it curious how those people at Verizon don't seem to have a
problem in understanding the concept of (and difference between), for
example, 0.1 dollars and 0.1 cents, but when they see "amount of money
per unit equals 0.001" they immediately lose all grasp of the concept
of *units*, and only seem to see that *number* alone, without the context
of the unit. "There's no difference between 0.001 dollars and 0.001 cents.
They are the same number." Like the unit stopped mattering when we go out
of the safe boundaries.
--
- Warp
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Warp wrote:
> I find it curious how those people at Verizon don't seem to have a
> problem in understanding the concept of (and difference between), for
> example, 0.1 dollars and 0.1 cents, but when they see "amount of money
> per unit equals 0.001" they immediately lose all grasp of the concept
> of *units*, and only seem to see that *number* alone, without the context
> of the unit. "There's no difference between 0.001 dollars and 0.001 cents.
> They are the same number." Like the unit stopped mattering when we go out
> of the safe boundaries.
I heard of some study once which looked at what the poorest and best
students had learned in a math class. It turned out that the worst
students had actually learned *more* concepts. For instance, they
learned the equation for the area of a square, the area of a rectangle,
the area of a right triangle, etc. The best students, however, only
learned a few concepts, like "area" which they could than apply to solve
many different problems.
I wonder if what's going on here is something like that where people
have learned the concept of "multiply small numbers" without ever really
grasping the meaning of "multiply" in general (or many even "number" in
general).
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Kevin Wampler <wampler+pov### [at] uwashingtonedu> wrote:
> I heard of some study once which looked at what the poorest and best
> students had learned in a math class. It turned out that the worst
> students had actually learned *more* concepts. For instance, they
> learned the equation for the area of a square, the area of a rectangle,
> the area of a right triangle, etc. The best students, however, only
> learned a few concepts, like "area" which they could than apply to solve
> many different problems.
> I wonder if what's going on here is something like that where people
> have learned the concept of "multiply small numbers" without ever really
> grasping the meaning of "multiply" in general (or many even "number" in
> general).
It probably is indeed a big problem that some people seem incapable of
seeing the big picture, the generic rules behind the specific examples,
when dealing with certain subjects. They only see (and often memorize)
the individual examples, but are incapable of making the connection to
a more abstract, more generic rule behind them.
What I find strange in this particular example is that several people
at that company had the exact same misconception about numbers and monetary
units. (Deducing from the unedited recording those were not the first two
persons he was talking with about the subject.)
I suppose that in their mind it goes something like this: Any monetary
amount which is larger or equal to 1 is in dollars, and anything smaller
than 1 (but larger than 0) is some amount of cents, ie. not dollars. Thus
for example a price of 10 is "dollars" (ten of them), while a price of
0.1 is "less than a dollar, ie. cents". Now their mind just tells them
that it's an amount in "cents", but fail to conceptualize exactly how
many cents. They just understand that it's "cents". Thus it becomes
"0.1 cents". Consequently "0.1 dollars" doesn't make sense to them because
0.1 is less than 1 dollar, and there can't be anything "less than a dollar".
Something less than a dollar is in cents, and thus it must be "0.1 cents".
Of course where this becomes very confusing is what their brain is
telling them when they encounter something like "10 cents". They understand
that "10 cents" is *not* the same thing as "10 dollars", that 10 cents is
actually less than a dollar, but... Well, my logic fails to follow exactly
what goes through their mind at this point.
Perhaps they can grasp the concept of integral amounts in different
units, but have hard time understanding the concept of fractional amounts
in different units. 10 is a nice integer, easy to count, so maybe they
understand "10 cents", because you can have physically 10 coints of 1 cent
each. However, when it becomes "0.1" it immediately becomes impossible
to grasp because you can't have 0.1 of a coin. At this point their brain
switches to a completely different "0.something is cents" mode.
Maybe there's a connection failure between integers and decimals less
than 1. The general rule which applies to both is not there.
--
- Warp
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Warp wrote:
> It probably is indeed a big problem that some people seem incapable of
> seeing the big picture, the generic rules behind the specific examples,
> when dealing with certain subjects. They only see (and often memorize)
> the individual examples, but are incapable of making the connection to
> a more abstract, more generic rule behind them.
I find it problematic that a great number of subjects in school are taught
this way, too. "Here's 30 examples. See if you can deduce what we're trying
to teach you by showing these things." Possibly because the teacher himself
can't verbalize what he's trying to teach.
Even math classes do this sometimes.
--
Darren New, San Diego CA, USA (PST)
"Ouch ouch ouch!"
"What's wrong? Noodles too hot?"
"No, I have Chopstick Tunnel Syndrome."
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Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> > It probably is indeed a big problem that some people seem incapable of
> > seeing the big picture, the generic rules behind the specific examples,
> > when dealing with certain subjects. They only see (and often memorize)
> > the individual examples, but are incapable of making the connection to
> > a more abstract, more generic rule behind them.
> I find it problematic that a great number of subjects in school are taught
> this way, too. "Here's 30 examples. See if you can deduce what we're trying
> to teach you by showing these things." Possibly because the teacher himself
> can't verbalize what he's trying to teach.
> Even math classes do this sometimes.
Can it be that even some elementary school math teachers don't themselves
fully understand the generic rules, and instead just blindly repeat the
examples of the textbooks?
--
- Warp
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Warp wrote:
> What I find strange in this particular example is that several people
> at that company had the exact same misconception
This reminds me of a story told by my high school physics teacher about
a survey done to test people's understanding of basic science concepts
which contained the question:
"is there gravity on the moon"
A large number of people got this wrong, which is odd but maybe not so
surprising. What's more surprising is that the they were then asked:
"You've seen the videos of people walking on the moon, if there's no
gravity how do they do that?"
Some people changed their answer at this point, but aparently a large
number responded:
"Because they have heavy boots!"
I completely fail to understand the reasoning that would give rise to
such a conclusion.
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Warp wrote:
> Can it be that even some elementary school math teachers don't themselves
> fully understand the generic rules, and instead just blindly repeat the
> examples of the textbooks?
I'm firmly convinced that is indeed the case. In the US at least, you get a
degree in "teaching", not in a specific subject. It's usually not until high
school that you even meet someone with an advanced degree in the field
they're teaching. (Of course, college and university is different.)
--
Darren New, San Diego CA, USA (PST)
"Ouch ouch ouch!"
"What's wrong? Noodles too hot?"
"No, I have Chopstick Tunnel Syndrome."
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Kevin Wampler wrote:
> I completely fail to understand the reasoning that would give rise to
> such a conclusion.
Movies where people walk in weightlessness using magnetic boots? And lacking
enough science to understand the boots are magnetic?
--
Darren New, San Diego CA, USA (PST)
"Ouch ouch ouch!"
"What's wrong? Noodles too hot?"
"No, I have Chopstick Tunnel Syndrome."
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On Fri, 06 Feb 2009 21:43:37 +0100, Kevin Wampler
<wampler+pov### [at] uwashingtonedu> wrote:
>
> "is there gravity on the moon"
Of course, just not as much of it.
http://basicinstructions.net/?p=875
--
FE
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Kevin Wampler <wampler+pov### [at] uwashingtonedu> wrote:
> "is there gravity on the moon"
When I was in high-school I had a friend who didn't quite understand
correctly the concept of forces, in particular the attracting force of
gravity. (Simpler times were those, in high-school, where the world was
purely Newtonian, but that's not important here...)
In particular, it seemed that he didn't quite understand that a force
acting on an object does *not* necessarily imply movement. After having
been taught in physics class that actually *all* masses attract each
other, no matter their size (only the magnitude of the attracting force
depends on it), he seemed to think that for example given that two
mountains attract each other, they will eventually collide.
No he was not a stupid person. In fact he was quite clever. It just
seemed that he didn't quite fully grasp the concept of forces and what
it actually means. (His reasoning would have been correct if the mountains
were in vacuum, but he seemed to seriously think that since mountains
attract each other because of gravity, they also move towards each other,
even though they are sitting firmly on the surface of the Earth.)
It's difficult to explain. It made much sense in the situation.
--
- Warp
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Warp <war### [at] tagpovrayorg> wrote:
> It probably is indeed a big problem that some people seem incapable of
> seeing the big picture, the generic rules behind the specific examples,
Then there's the other extreme of people, who are really good at it.
Like that mathematician (I forget his name, but one of the famous ones)
who was in grade school and the teacher told the students to sum all the
numbers from 1 to 100, to keep them busy for at least half an hour, and
practice summation. This guy gives the correct in far less than a minute,
and the teacher is amazed.
I suppose the kid's reasoning was something like: "Hmm, actually if I
take the *average* of all the numbers, and multiply it by the amount of
numbers, I should get the correct result, because summing the average
100 times should be the same as summing all the original 100 numbers.
Now, what is the average of all the numbers between 1 and 100? It must
be (100+1)/2. Now multiply that by the amount of numbers, ie. 100, and
we have the answer."
Unfortunately not many people have that kind of deduction power at
that age (or at any age).
--
- Warp
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Warp wrote:
> Then there's the other extreme of people, who are really good at it.
> Like that mathematician (I forget his name, but one of the famous ones)
> who was in grade school and the teacher told the students to sum all the
> numbers from 1 to 100, to keep them busy for at least half an hour, and
> practice summation. This guy gives the correct in far less than a minute,
> and the teacher is amazed.
I have a vague recollection that might be Galios. And the teacher set
the problem to keep specifically him quiet.
> Unfortunately not many people have that kind of deduction power at
> that age (or at any age).
For what it's worth, I can never ever remember *exactly* what the
correct formula for that is. It's roughly half the square, but I can
never remember the exact figure.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Warp wrote:
> Warp <war### [at] tagpovrayorg> wrote:
>> It probably is indeed a big problem that some people seem incapable of
>> seeing the big picture, the generic rules behind the specific examples,
>
> Then there's the other extreme of people, who are really good at it.
> Like that mathematician (I forget his name, but one of the famous ones)
> who was in grade school and the teacher told the students to sum all the
> numbers from 1 to 100, to keep them busy for at least half an hour, and
> practice summation. This guy gives the correct in far less than a minute,
> and the teacher is amazed.
That would be Gauss if I remember correctly. This sort of ability to
correctly generalize things seems to be to be at the core of
mathematical and scientific ability. It's unfortunate that it seems to
be so difficult to fully teach it, although there certainly is an aspect
of innate ability that complicates it (I mean, Gauss' ability certainly
wasn't due to that teacher's excellence).
> Unfortunately not many people have that kind of deduction power at
> that age (or at any age).
Well, he is called the "prince of mathematicians"
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>> Then there's the other extreme of people, who are really good at it.
>> Like that mathematician (I forget his name, but one of the famous ones)
>> who was in grade school and the teacher told the students to sum all the
>> numbers from 1 to 100, to keep them busy for at least half an hour, and
>> practice summation. This guy gives the correct in far less than a minute,
>> and the teacher is amazed.
>
> That would be Gauss if I remember correctly.
Wikipedia concurs:
http://en.wikipedia.org/wiki/Gauss
Oh well, I got a famous mathematician who's name starts with the right
letter! ;-)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Warp wrote:
> When I was in high-school I had a friend who didn't quite understand
> correctly the concept of forces, in particular the attracting force of
> gravity. (Simpler times were those, in high-school, where the world was
> purely Newtonian, but that's not important here...)
I miss those times too. I still haven't managed to find an
interpretation of QM that I'm philosophically satisfied with, and it
makes it tricky to think about other philosophical problems when I'm
still not solid on something that fundamental.
> No he was not a stupid person. In fact he was quite clever. It just
> seemed that he didn't quite fully grasp the concept of forces and what
> it actually means. (His reasoning would have been correct if the mountains
> were in vacuum, but he seemed to seriously think that since mountains
> attract each other because of gravity, they also move towards each other,
> even though they are sitting firmly on the surface of the Earth.)
>
> It's difficult to explain. It made much sense in the situation.
Your friend's mistake actually makes sense to me from how you explain
it. I suppose he knew that F=m*a, and thus any force implies some
acceleration no matter what the mass, so his reasoning was actually
largely correct. Really, it seems that his main misconception was not
directly about what forces do, but more about failing to account for all
the places they can come form (for instance, the resistive force due to
the cohesion of the rocks), and that it's only the net force that matters.
Still, I can see how an intelligent person could make that mistake,
since it's rather surprisingly close to correct. That said, without
hearing the reasoning I would have been absolutely baffled by the error.
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Orchid XP v8 <voi### [at] devnull> wrote:
> > Unfortunately not many people have that kind of deduction power at
> > that age (or at any age).
> For what it's worth, I can never ever remember *exactly* what the
> correct formula for that is. It's roughly half the square, but I can
> never remember the exact figure.
You shouldn't memorize the formula (like most people do). You should
understand where it comes from (as I wrote in my previous post).
Basically the general rule is: If you have to sum n numbers (whatever
those numbers might be), then summing the average of those numbers n times
with itself (or, in other words, multiplying the average by n) gives the
same result. If you think a bit about why this is so, it should be rather
simple.
(Answer: The average of the numbers is calculated by summing the numbers
and dividing the result by n (which is the total amount of numbers). If you
multiply this average by n, you are nullifying the division, which gives you
the original sum.)
With random numbers this rule doesn't help much (because calculating the
average of some random numbers would require you to sum those numbers
together, which was what you wanted to avoid doing in the first place), but
with consecutive numbers it does, because calculating the average of a
consecutive series of numbers can be done without having to all sum those
numbers.
For example, the average of all the numbers between 1 and 100 (inclusive)
is (1+100)/2. Now just multiply that by the total amount of numbers, and
you have the sum.
This same deduction works for any other ranges as well, even if the
numbers are not consecutive, as long as you can easily calculate their
average.
Example: Calculate the sum of all the even numbers between 2 and 100
(inclusive).
Answer: The average of all those numbers is (2+100)/2. The total amount
of even numbers in that range is 50, so multiply that average by 50, and
you got your result.
Exercise: Calculate the sum of all the numbers between 100 and 1000
which are divisible by 7. (Obviously the range is non-inclusive because
neither 100 nor 1000 are divisible by 7.)
--
- Warp
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Orchid XP v8 wrote:
> Oh well, I got a famous mathematician who's name starts with the right
> letter! ;-)
And one who was also a child prodigy, too bad Galios had to go and kill
himself in a duel so early in his life.
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Warp wrote:
> http://www.youtube.com/watch?v=lCJ3Oz5JVKs
Full story if anyone wants it:
http://verizonmath.blogspot.com/
--
I think animal testing is a terrible idea. They get all nervous and give
the wrong answers.
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
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Kevin Wampler wrote:
> This reminds me of a story told by my high school physics teacher about
> a survey done to test people's understanding of basic science concepts
> which contained the question:
>
> "is there gravity on the moon"
>
> A large number of people got this wrong, which is odd but maybe not so
> surprising. What's more surprising is that the they were then asked:
>
> "You've seen the videos of people walking on the moon, if there's no
> gravity how do they do that?"
>
> Some people changed their answer at this point, but aparently a large
> number responded:
>
> "Because they have heavy boots!"
>
> I completely fail to understand the reasoning that would give rise to
> such a conclusion.
Trust me, I had this very discussion (with the same and similar
nonsensical answers) with a number of my high school friends in those days.
--
I think animal testing is a terrible idea. They get all nervous and give
the wrong answers.
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
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Kevin Wampler wrote:
> Orchid XP v8 wrote:
>> Oh well, I got a famous mathematician who's name starts with the right
>> letter! ;-)
>
> And one who was also a child prodigy, too bad Galios had to go and kill
> himself in a duel so early in his life.
Yes. Pity about his more famous brother, Galois, who died a similar death.
(I couldn't let *two* people make the same mistake and get away with it).
--
I think animal testing is a terrible idea. They get all nervous and give
the wrong answers.
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
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Mueen Nawaz wrote:
> Kevin Wampler wrote:
>> Orchid XP v8 wrote:
>>> Oh well, I got a famous mathematician who's name starts with the right
>>> letter! ;-)
>> And one who was also a child prodigy, too bad Galios had to go and kill
>> himself in a duel so early in his life.
>
> Yes. Pity about his more famous brother, Galois, who died a similar death.
>
> (I couldn't let *two* people make the same mistake and get away with it).
You know, I actually double-checked the spelling before I posted yet
somehow I *still* messed it up!
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Warp wrote:
> http://www.youtube.com/watch?v=lCJ3Oz5JVKs
As one of the comments said,
"Let me explain in simple terms why there stupid. There yanks!"
(I couldn't help noticing that whoever wrote this is actually using the
wrong word. Who's stupid, again?)
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Warp wrote:
> Orchid XP v8 <voi### [at] devnull> wrote:
>>> Unfortunately not many people have that kind of deduction power at
>>> that age (or at any age).
>
>> For what it's worth, I can never ever remember *exactly* what the
>> correct formula for that is. It's roughly half the square, but I can
>> never remember the exact figure.
>
> You shouldn't memorize the formula (like most people do). You should
> understand where it comes from (as I wrote in my previous post).
Indeed yes. It just takes a minute or two to puzzle it out each time,
which is mildly irritating...
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> I suppose the kid's reasoning was something like: "Hmm, actually if I
> take the *average* of all the numbers, and multiply it by the amount of
> numbers, I should get the correct result, because summing the average
> 100 times should be the same as summing all the original 100 numbers.
> Now, what is the average of all the numbers between 1 and 100? It must
> be (100+1)/2. Now multiply that by the amount of numbers, ie. 100, and
> we have the answer."
The version I heard was that he imagined the numbers written 1-100, and then
the same numbers written 100-1 underneath. Like this:
1 2 3 4 5 6 ...
100 99 98 97 96 95 ...
Now if you sum up both of those you should get twice the answer right? But
first he summed each column of two numbers to get:
101 101 101 101 101 ...
Then of course it's trivial.
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Kevin Wampler wrote:
> WE HAVE 300 MILLION CITIZENS. IF WE GAVE EVERYONE 1 MILLION DOLLARS
> WOULDN'T THAT BE 300 MILLION DOLLARS?
Oh dear god >_<
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