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
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.
"Rarely is the question asked: Is our children learning?"-G. W. Bush,
Florence, S.C., Jan. 11, 2000
- From: "gerald w. bracey" <email@example.com>
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