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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