Re: query

[Victor Steinbok <Victor.Steinbok@verizon.net>]

At 10:57 AM -0400 10.05.03, gerald w. bracey wrote:
> This is not a set up for a gotcha.  I'd like people to tell me what 
> level they think the following text is pitched at.  Any other 
> commentary about it would be welcome as well.

The first thing that struck me, aside from the unusually frustrating 
language, is that the definition is wrong. A variable is not the 
symbol, but the object (in this case, the represented quantity) that 
is represented by the symbol. A variable is a conceptual entity, 
while a "symbol" is part of the notation and has no "concept" behind 
it.

To prove my point, just consider the last sentence. If the "variable" 
is only a symbol, how can we possibly say that "a variable y depends 
[on] another variable x"? Certainly, symbols do not depend on one 
another. The underlying quantities do. The other thing about the last 
sentence is that "function" does not depend on notation that is used. 
It represents a relationship not between symbols or variables, but 
two quantities, whether we use variables or not. "Variable", on the 
other hand, may just be interpreted to be short for "variable 
quantity" (not the alternative meaning of "quantity" here--the use 
here means "amount", everywhere else it means "measurable substance").

The whole piece reads as if it was intentionally written to sound 
pompous. The sentence structure is teetering on the brink of 
collapse--considering the denseness of the presentation, it would 
have benefited from shorter, to-the-point sentences.

As I reread the definition, another thing struck me--the "symbol" 
does not usually represent an "indefinite number of values". The 
number of values it represents is actually quite well defined. It may 
be infinite, but it is well defined. The important thing, that is 
missing, is that the symbol denotes only ONE quantity at a time--in a 
particular "discussion" the symbol can be used an as many times as 
you need it, but it must represent the same set of real or potential 
values. Also, the use of "indeterminate" is wrong--here it is used to 
me "arbitrary", when the mathematical meaning is "cannot be 
determined" (although it can be defined).

Another interesting obfuscation occurs in the first paragraph. Since 
the graphs are given, it is not clear (although it might have been 
explained earlier in the text) why the values cannot be found 
directly from graphs--instead, it says that they "can be found either 
by experiment or by computation". Maybe I am just nitpicking here.

Putting it all together, I would have guessed that this is from a 
textbook intended for algebra-poor MBA students. But if one considers 
the affective variables--the fact that Jerry is asking the 
question--I would have to guess that this is an Algebra I text. :-)

> "Each of the graphs in the preceding article shows a definite 
> relation between two  quantities such that when one is known the 
> other can be found either by experiment or by computation.  These 
> quantities are usually represented by certain symbols such as 
> p,v,x,y, etc, and are called variables.
>
> DEFINITION:  a variable is a symbol which may represent an 
> indefinite number of values throughout a particular discussion.
>
> For example, in the equation A =pi X R squared, A and R are 
> variables and represent the area and radius, respectively, of a 
> circle.  When A is expressed in terms of R, R is called the 
> independent variable and A the dependent variable or function of R. 
> In general, we may give the following definition:
>
> If a variable y depends another variable x, so that whe a value of x 
> is known, y is determined, then y is called a function of x.

--

	VS-)

"Rarely is the question asked: Is our children learning?"-G. W. Bush, 
Florence, S.C., Jan. 11, 2000