Marketplace and Math Class?

[CCDN CCDN]

Does anyone have any ideas regarding todays current economic climate and an intriguing math lesson for High School students?

Thank You, CCDN
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[Alain Schremmer]

On Apr 25, 2008, at 4:52 PM, CCDN CCDN wrote:

> Does anyone have any ideas regarding todays current economic  
> climate and an intriguing math lesson for High School students?

Re This or that company's record profits:

The Fed prints only so many dollar bills. If one percent of the  
population takes a disproportionate amount of these dollars, then  
these are dollars that we don't have. Put more simply, the richer  
they get, the poorer we get. It's called the law of conservation of  
money, AKA Where did the money go?

Students seem fascinated.

Regards
--schremmer
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[Bret Taylor-2]

If we are going to give "real world problems" shouldn't they be factually
accurate?


----- Original Message -----
From: "Alain Schremmer" <schremmer.alain@...>
To: <mathedcc@...>
Sent: Friday, April 25, 2008 6:38 PM
Subject: Re: Marketplace and Math Class?

>
> On Apr 25, 2008, at 4:52 PM, CCDN CCDN wrote:
>
>> Does anyone have any ideas regarding todays current economic  climate and
>> an intriguing math lesson for High School students?
>
> Re This or that company's record profits:
>
> The Fed prints only so many dollar bills. If one percent of the
> population takes a disproportionate amount of these dollars, then  these
> are dollars that we don't have. Put more simply, the richer  they get, the
> poorer we get. It's called the law of conservation of  money, AKA Where
> did the money go?
>
> Students seem fascinated.
>
> Regards
> --schremmer
> ****************************************************************************
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> * To unsubscribe, email the message "unsubscribe mathedcc" to
> majordomo@... *
> * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 *
> ****************************************************************************

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[Alain Schremmer]

What's not factually accurate?
Regards
--schremmer
On Apr 25, 2008, at 7:37 PM, Bret Taylor wrote:

> If we are going to give "real world problems" shouldn't they be  
> factually accurate?
>
>
> ----- Original Message ----- From: "Alain Schremmer"  
> <schremmer.alain@...>
> To: <mathedcc@...>
> Sent: Friday, April 25, 2008 6:38 PM
> Subject: Re: Marketplace and Math Class?
>
>
>>
>> On Apr 25, 2008, at 4:52 PM, CCDN CCDN wrote:
>>
>>> Does anyone have any ideas regarding todays current economic  
>>> climate and an intriguing math lesson for High School students?
>>
>> Re This or that company's record profits:
>>
>> The Fed prints only so many dollar bills. If one percent of the  
>> population takes a disproportionate amount of these dollars, then  
>> these are dollars that we don't have. Put more simply, the richer  
>> they get, the poorer we get. It's called the law of conservation  
>> of  money, AKA Where did the money go?
>>
>> Students seem fascinated.
>>
>> Regards
>> --schremmer
>> *********************************************************************
>> *******
>> * To post to the list: email mathedcc@... *
>> * To unsubscribe, email the message "unsubscribe mathedcc" to  
>> majordomo@... *
>> * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 *
>> *********************************************************************
>> *******
>

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[Bret Taylor-2]

The feds don't print "only so many dollar bills."
The population doesn't "take" money from the government.

Because rich people get richer, that doesn't mean poor people get poorer.
It's not a zero sum game.
Bill Clinton getting richer since he left the White House did not make me
poorer.

"The Law of Conservation of Money" - I googled it and got zero hits.


----- Original Message -----
From: "Alain Schremmer" <schremmer.alain@...>
To: "Bret Taylor" <bret.taylor@...>
Cc: <mathedcc@...>
Sent: Friday, April 25, 2008 8:01 PM
Subject: Re: Marketplace and Math Class?

> What's not factually accurate?
> Regards
> --schremmer
> On Apr 25, 2008, at 7:37 PM, Bret Taylor wrote:
>
>> If we are going to give "real world problems" shouldn't they be
>> factually accurate?
>>
>>
>> ----- Original Message ----- From: "Alain Schremmer"
>> <schremmer.alain@...>
>> To: <mathedcc@...>
>> Sent: Friday, April 25, 2008 6:38 PM
>> Subject: Re: Marketplace and Math Class?
>>
>>
>>>
>>> On Apr 25, 2008, at 4:52 PM, CCDN CCDN wrote:
>>>
>>>> Does anyone have any ideas regarding todays current economic   climate
>>>> and an intriguing math lesson for High School students?
>>>
>>> Re This or that company's record profits:
>>>
>>> The Fed prints only so many dollar bills. If one percent of the
>>> population takes a disproportionate amount of these dollars, then
>>> these are dollars that we don't have. Put more simply, the richer   they
>>> get, the poorer we get. It's called the law of conservation  of  money,
>>> AKA Where did the money go?
>>>
>>> Students seem fascinated.
>>>
>>> Regards
>>> --schremmer
>>> *********************************************************************
>>> *******
>>> * To post to the list: email mathedcc@... *
>>> * To unsubscribe, email the message "unsubscribe mathedcc" to
>>> majordomo@... *
>>> * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 *
>>> *********************************************************************
>>> *******
>>
>

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[Alain Schremmer]

On Apr 25, 2008, at 8:22 PM, Bret Taylor wrote:


> The feds don't print "only so many dollar bills.

An infinite number?


> The population doesn't "take" money from the government.
>

Never said that. The above meant to say that, independently of the  
way the money percolates from whoever prints it, there is only so  
much money circulating.


> Because rich people get richer, that doesn't mean poor people get  
> poorer.
>

Inasmuch as  there is only so much money circulating … I don't see  
why not.


> It's not a zero sum game.
>

As a first approximation it is.


> Bill Clinton getting richer since he left the White House did not  
> make me poorer.
>

?

The statement I made was in the plural, in other words they were in  
the aggregate. Still in other words, they correspond to integrals.


> "The Law of Conservation of Money" - I googled it and got zero hits.
>

Just an instance of the fundamental theorem of the calculus (AKA  
Stokes theorem).

Other include the law of conservation of mass, the law of  
conservation of momentum, the law of conservation of energy and, last  
but not least, the fact that the Integral of Net Income over a time  
interval = Balance change over that time interval (Can't remember  
what accountants call it.)

Regards
--schremmer

> ----- Original Message ----- From: "Alain Schremmer"  
> <schremmer.alain@...>
> To: "Bret Taylor" <bret.taylor@...>
> Cc: <mathedcc@...>
> Sent: Friday, April 25, 2008 8:01 PM
> Subject: Re: Marketplace and Math Class?
>
>
>
>> What's not factually accurate?
>> Regards
>> --schremmer
>> On Apr 25, 2008, at 7:37 PM, Bret Taylor wrote:
>>
>>
>>> If we are going to give "real world problems" shouldn't they be  
>>> factually accurate?
>>>
>>>
>>> ----- Original Message ----- From: "Alain Schremmer"  
>>> <schremmer.alain@...>
>>> To: <mathedcc@...>
>>> Sent: Friday, April 25, 2008 6:38 PM
>>> Subject: Re: Marketplace and Math Class?
>>>
>>>
>>>
>>>>
>>>> On Apr 25, 2008, at 4:52 PM, CCDN CCDN wrote:
>>>>
>>>>
>>>>> Does anyone have any ideas regarding todays current economic    
>>>>> climate and an intriguing math lesson for High School students?
>>>>>
>>>>
>>>> Re This or that company's record profits:
>>>>
>>>> The Fed prints only so many dollar bills. If one percent of the  
>>>> population takes a disproportionate amount of these dollars,  
>>>> then these are dollars that we don't have. Put more simply, the  
>>>> richer   they get, the poorer we get. It's called the law of  
>>>> conservation  of  money, AKA Where did the money go?
>>>>
>>>> Students seem fascinated.
>>>>
>>>> Regards
>>>> --schremmer
>>>> *******************************************************************
>>>> ** *******
>>>> * To post to the list: email mathedcc@... *
>>>> * To unsubscribe, email the message "unsubscribe mathedcc" to  
>>>> majordomo@... *
>>>> * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 *
>>>> *******************************************************************
>>>> ** *******
>>>>
>>>
>>>
>
>

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[Bret Taylor-2]

My last reply on this thread.

We've done an outstaninding job keeping politics out of this forum.  I'll
discuss politics on other forums, not here.

But, I would dare say that the total amount of money in circulation in 2008
is not closely approximated by the total amount of money in 1776, or even
1986.

Maybe a more realistic question might be this:

How could we determine the total wealth of the US in 1808, 1908, and 2008?
Using those numbers what is the average (mean and median) wealth of the US
population?


----- Original Message -----
From: "Alain Schremmer" <schremmer.alain@...>
To: "Bret Taylor" <bret.taylor@...>
Sent: Friday, April 25, 2008 8:54 PM
Subject: Re: Marketplace and Math Class?


On Apr 25, 2008, at 8:22 PM, Bret Taylor wrote:

> The feds don't print "only so many dollar bills."

An infinite number?

> The population doesn't "take" money from the government.

Never said that. The above meant to say that, independently of the
way the money percolates from whoever prints it, there is only so
much money circulating.

> Because rich people get richer, that doesn't mean poor people get  poorer.

Inasmuch as  there is only so much money circulating … I don't see
why not.

> It's not a zero sum game.

As a first approximation it is.

> Bill Clinton getting richer since he left the White House did not  make me
> poorer.

?

The statement I made was in the plural, in other words they were in
the aggregate. Still in other words, they correspond to integrals.

> "The Law of Conservation of Money" - I googled it and got zero hits.

Just an instance of the fundamental theorem of the calculus (AKA
Stokes theorem).

Other include the law of conservation of mass, the law of
conservation of momentum, the law of conservation of energy and, last
but not least, the fact that the Integral of Net Income over a time
interval = Balance change over that time interval (Can't remember
what accountants call it.)

Regards
--schremmer

> ----- Original Message ----- From: "Alain Schremmer"
> <schremmer.alain@...>
> To: "Bret Taylor" <bret.taylor@...>
> Cc: <mathedcc@...>
> Sent: Friday, April 25, 2008 8:01 PM
> Subject: Re: Marketplace and Math Class?
>
>
>> What's not factually accurate?
>> Regards
>> --schremmer
>> On Apr 25, 2008, at 7:37 PM, Bret Taylor wrote:
>>
>>> If we are going to give "real world problems" shouldn't they be
>>> factually accurate?
>>>
>>>
>>> ----- Original Message ----- From: "Alain Schremmer"
>>> <schremmer.alain@...>
>>> To: <mathedcc@...>
>>> Sent: Friday, April 25, 2008 6:38 PM
>>> Subject: Re: Marketplace and Math Class?
>>>
>>>
>>>>
>>>> On Apr 25, 2008, at 4:52 PM, CCDN CCDN wrote:
>>>>
>>>>> Does anyone have any ideas regarding todays current economic
>>>>> climate and an intriguing math lesson for High School students?
>>>>
>>>> Re This or that company's record profits:
>>>>
>>>> The Fed prints only so many dollar bills. If one percent of the
>>>> population takes a disproportionate amount of these dollars,  then
>>>> these are dollars that we don't have. Put more simply, the  richer
>>>> they get, the poorer we get. It's called the law of  conservation  of
>>>> money, AKA Where did the money go?
>>>>
>>>> Students seem fascinated.
>>>>
>>>> Regards
>>>> --schremmer
>>>> ******************************************************************* **
>>>> *******
>>>> * To post to the list: email mathedcc@... *
>>>> * To unsubscribe, email the message "unsubscribe mathedcc" to
>>>> majordomo@... *
>>>> * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 *
>>>> ******************************************************************* **
>>>> *******
>>>
>

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[Alain Schremmer]

On Apr 25, 2008, at 9:33 PM, Bret Taylor wrote:

> My last reply on this thread.

OK

> We've done an outstaninding job keeping politics out of this forum.

As I think I pointed out, what I wrote was merely an instance of the  
fundamental theorem of calculus. As such it is modeling, not politics.

> I'll discuss politics on other forums, not here.

This is a free country, you do what you want.

> But, I would dare say that the total amount of money in circulation  
> in 2008 is not closely approximated by the total amount of money in  
> 1776, or even 1986.

That is why what I said was only a first approximation. But I would  
dare say that the total amount of money in circulation in 2008 is  
rather closely approximated by the total amount of money in 2007.

As you know, continuous functions can be seen as locally constant  
functions and a characteristic of the fundamental theorem of calculus  
is that it involves integrals (of order 1 and 0) over intervals. If  
those intervals are centuries, then the first approximation obviously  
fails. And, over, say, 40 years, inflation needs indeed to be taken  
into account. But, in constant dollars, I think that the first  
approximation still holds true over the last 40 years.

So, I don't see what in all I wrote was not "factually accurate".

> Maybe a more realistic question might be this:
>
> How could we determine the total wealth of the US in 1808, 1908,  
> and 2008? Using those numbers what is the average (mean and median)  
> wealth of the US population?

I don't understand this: Over what period of time? In what sense is  
it more realistic?

Regards
--schremmer

> ----- Original Message ----- From: "Alain Schremmer"  
> <schremmer.alain@...>
> To: "Bret Taylor" <bret.taylor@...>
> Sent: Friday, April 25, 2008 8:54 PM
> Subject: Re: Marketplace and Math Class?
>
>
> On Apr 25, 2008, at 8:22 PM, Bret Taylor wrote:
>
>> The feds don't print "only so many dollar bills."
>
> An infinite number?
>
>> The population doesn't "take" money from the government.
>
> Never said that. The above meant to say that, independently of the
> way the money percolates from whoever prints it, there is only so
> much money circulating.
>
>> Because rich people get richer, that doesn't mean poor people get  
>> poorer.
>
> Inasmuch as  there is only so much money circulating … I don't see
> why not.
>
>> It's not a zero sum game.
>
> As a first approximation it is.
>
>> Bill Clinton getting richer since he left the White House did not  
>> make me poorer.
>
> ?
>
> The statement I made was in the plural, in other words they were in
> the aggregate. Still in other words, they correspond to integrals.
>
>> "The Law of Conservation of Money" - I googled it and got zero hits.
>
> Just an instance of the fundamental theorem of the calculus (AKA
> Stokes theorem).
>
> Other include the law of conservation of mass, the law of
> conservation of momentum, the law of conservation of energy and, last
> but not least, the fact that the Integral of Net Income over a time
> interval = Balance change over that time interval (Can't remember
> what accountants call it.)
>
> Regards
> --schremmer
>
>> ----- Original Message ----- From: "Alain Schremmer"  
>> <schremmer.alain@...>
>> To: "Bret Taylor" <bret.taylor@...>
>> Cc: <mathedcc@...>
>> Sent: Friday, April 25, 2008 8:01 PM
>> Subject: Re: Marketplace and Math Class?
>>
>>
>>> What's not factually accurate?
>>> Regards
>>> --schremmer
>>> On Apr 25, 2008, at 7:37 PM, Bret Taylor wrote:
>>>
>>>> If we are going to give "real world problems" shouldn't they be  
>>>> factually accurate?
>>>>
>>>>
>>>> ----- Original Message ----- From: "Alain Schremmer"  
>>>> <schremmer.alain@...>
>>>> To: <mathedcc@...>
>>>> Sent: Friday, April 25, 2008 6:38 PM
>>>> Subject: Re: Marketplace and Math Class?
>>>>
>>>>
>>>>>
>>>>> On Apr 25, 2008, at 4:52 PM, CCDN CCDN wrote:
>>>>>
>>>>>> Does anyone have any ideas regarding todays current economic  
>>>>>> climate and an intriguing math lesson for High School students?
>>>>>
>>>>> Re This or that company's record profits:
>>>>>
>>>>> The Fed prints only so many dollar bills. If one percent of the  
>>>>> population takes a disproportionate amount of these dollars,  
>>>>> then these are dollars that we don't have. Put more simply,  
>>>>> the  richer they get, the poorer we get. It's called the law  
>>>>> of  conservation  of money, AKA Where did the money go?
>>>>>
>>>>> Students seem fascinated.
>>>>>
>>>>> Regards
>>>>> --schremmer
>>>>> ******************************************************************
>>>>> * ** *******
>>>>> * To post to the list: email mathedcc@... *
>>>>> * To unsubscribe, email the message "unsubscribe mathedcc" to  
>>>>> majordomo@... *
>>>>> * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 *
>>>>> ******************************************************************
>>>>> * ** *******
>>>>
>>
>

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[Alain Schremmer]

On Apr 25, 2008, at 9:33 PM, Bret Taylor wrote:

> How could we determine the total wealth of the US in 1808, 1908,  
> and 2008? Using those numbers what is the average (mean and median)  
> wealth of the US population?

There is this bar with a bunch of people having a quiet drink on a  
Friday evening before going back home from work. Bill Gates walks in.  
The average wealth of the people in the bar has suddenly shot up sky  
high.

Regards
--schremmer
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Bret Posted:
>My last reply on this thread.
>
>We've done an outstaninding job keeping politics out of this forum.  
>I'll discuss politics on other forums, not here.

   At issue in this thread is not a question of politics, but of economics.  And what this thread illustrates is something else altogether.

   There is a fashion gaining popularity in colleges to teach "quantitative reasoning" ("QR") courses.  As I understand it, these are supposed to be terminal courses in which a variety of real world problems are presented, with the hope of impressing non-science students of the ubiquity and importance of mathematics.

   It is a lovely idea, but it requires math teachers to be familiar with diverse subjects from geology to taxation.  In this case, economics (specifically, money and banking).  I am sorry to say it, but I do not know of another group of people more innocent of the real world than mathematicians.  This particular thread reveals the hopeless naivety of the theory that underpins QR.

Haim
_____________________________________________________________
Click to learn about options trading and get the latest information.
http://thirdpartyoffers.netzero.net/TGL2211/fc/Ioyw6ijmQXyFozwJMdUGLfPqpLUxbbZcPfqg0Hz4FcvrzaHE7yR5J9/


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[Bret Taylor-2]

I understand and agree with the cdoncept of teaching real world problems in
math.  I am not opposed to it.

But, the example given was filled with "political agenda."

I don't think a math class is the place to present a problem that starts
with, "Since we all know the Laffer Curve is an accurate representation of
tax revenue generation" and if someone suggested a problem with that premise
I would be just as opposed to it as I was a problem that has as its premise
"The governemtn prints only so much money, so what happens when a few people
take a disproportionate share?"

Sorry, but that is just so innacurate a representation of how the economy
works that it has no place in an economics class, much less a math class.
It is a statement more suited for a George Orwell novel.


----- Original Message -----
From: <hpipik@...>
To: <mathedcc@...>
Sent: Monday, April 28, 2008 12:26 AM
Subject: Re: Marketplace and Math Class?

> Bret Posted:
>>My last reply on this thread.
>>
>>We've done an outstaninding job keeping politics out of this forum.
>>I'll discuss politics on other forums, not here.
>
>   At issue in this thread is not a question of politics, but of economics.
> And what this thread illustrates is something else altogether.
>
>   There is a fashion gaining popularity in colleges to teach "quantitative
> reasoning" ("QR") courses.  As I understand it, these are supposed to be
> terminal courses in which a variety of real world problems are presented,
> with the hope of impressing non-science students of the ubiquity and
> importance of mathematics.
>
>   It is a lovely idea, but it requires math teachers to be familiar with
> diverse subjects from geology to taxation.  In this case, economics
> (specifically, money and banking).  I am sorry to say it, but I do not
> know of another group of people more innocent of the real world than
> mathematicians.  This particular thread reveals the hopeless naivety of
> the theory that underpins QR.
>
> Haim
> _____________________________________________________________
> Click to learn about options trading and get the latest information.
> http://thirdpartyoffers.netzero.net/TGL2211/fc/Ioyw6ijmQXyFozwJMdUGLfPqpLUxbbZcPfqg0Hz4FcvrzaHE7yR5J9/
>
>
> ****************************************************************************
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> * To unsubscribe, email the message "unsubscribe mathedcc" to
> majordomo@... *
> * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 *
> ****************************************************************************

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[Alain Schremmer]

On Apr 28, 2008, at 6:08 AM, Bret Taylor wrote:

> I understand and agree with the cdoncept of teaching real world  
> problems in math.  I am not opposed to it.
>
> But, the example given was filled with "political agenda."

I understand that you are exercising your first amendment rights. But  
as, presumably, a mathematician, you might have made an attempt at  
making your case. You haven't.

> I don't think a math class is the place to present a problem that  
> starts with, "Since we all know the Laffer Curve is an accurate  
> representation of tax revenue generation" and if someone suggested  
> a problem with that premise I would be just as opposed to it as I  
> was a problem that has as its premise

> "The governemtn prints only so much money,

It is a bit disingenuous to ignore the fact that I already agreed  
that I should have said something like "During any time interval of,  
say, 10 to 30 years, the monetary mass can, as a first approximation,  
be considered as constant."

> so what happens when a few people take a disproportionate share?"

That is indeed the question?

I understand that you have no wish to give your own conjecture but  
you haven't explained where my use of the fundamental theorem of the  
calculus was incorrect.

> Sorry, but that is just so innacurate a representation of how the  
> economy works that it has no place in an economics class, much less  
> a math class.


That is just an assertion without any visible means of support.

> It is a statement more suited for a George Orwell novel.

Ditto.

Regards
--schremmer


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[Alain Schremmer]

OOPS. I missed something:

> On Apr 28, 2008, at 6:08 AM, Bret Taylor wrote:
>
> I don't think a math class is the place to present a problem that  
> starts with, "Since we all know the Laffer Curve is an accurate  
> representation of tax revenue generation" and if someone suggested  
> a problem with that premise I would be just as opposed to it as I  
> was a problem that has as its premise

This is of course where we differ. Slogans ought not to be ignored  
but taken apart if only to find a counter slogan.

At the time when the Laffer curve became all the rage, and even  
though I was well aware of the context in which the Laffer curve was  
being touted, I was intrigued by its "stopping effect". So, I did  
spend a bit of time on finding counter-examples simple enough that  
they could be used in a conversation to counter said "stopping  
effect". To my great delight, it was an exercise in almost pure logic.

And as such, I wouldn't shy away from using such a "controversial  
issue" in class. Unfortunately, as evidenced by the stuff on  
freemathtexts.org, I barely have the class time necessary to convince  
students that mathematics is not a matter of "just do what I say" but  
one of "what does the situation call for?"—in other words, a matter  
of logic rather than unquestioning belief.

Regards
--schremmer
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[Alain Schremmer]

On Apr 28, 2008, at 4:26 AM, hpipik@... wrote:

>    There is a fashion gaining popularity in colleges to teach  
> "quantitative reasoning" ("QR") courses.  As I understand it, these  
> are supposed to be terminal courses in which a variety of real  
> world problems are presented, with the hope of impressing non-
> science students of the ubiquity and importance of mathematics.

Truth to tell, I wasn't aware of this new danger—presentation of my  
case upon request :-))

I thought that the "mathematics by applications" idea was dead. I  
guess this was wishful thinking on my part. In any case, I once got  
flamed on this list (Re: Types of Knowledge Posted: Mar 2, 2004 8:51  
PM) for saying that not until one is past differential calculus, does  
mathematics have (non-contrived) application to speak of.

So, it seems I was wrong and that this QR thing is a resurgence of  
this Hydra like "idea".

> It is a lovely idea,

 From the NYT:

http://www.nytimes.com/2008/04/25/science/25math.html?
_r=1&ref=education&oref=slogin

But perhaps more to the point (the above research is full of holes),  
couldn't it be because those applications being so trite, they have  
two related advantages: each is a world unto itself, and they free  
the teacher from having to develop an overarching grasp of a course  
in mathematics. In less grand words, recipes are easier for the  
teacher to show and tell than to instill the art of being logical.

> but it requires math teachers to be familiar with diverse subjects  
> from geology to taxation.  In this case, economics (specifically,  
> money and banking).  I am sorry to say it, but I do not know of  
> another group of people more innocent of the real world than  
> mathematicians.

Or afraid thereof.

Regards
--schremmer
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