2 25 2000 Version
Ephemera
Ephemera
Things that do not endure are all around us. They are the work of man,
nature itself, even human culture and civilization(s).
Cinema, television, radio, advertisements are all ephemeral. What
wouldn't society give in a hundred years for an archive representing the
best ... and worst ... examples of items in those groups from this year
and decades past?
How could we preserve such material? What is changed by the
internet? How does this digitally-connected world work?
This presents material found from the world wide web, and email list
serves.
1 = 5 right?
Confusion Between a Number and an Operation
The following interesting example appeared in The International
Journal of Ephemera, Issue No.3 responding to this question:
"Now try to explain the following steps...
-5 = -5 (obviously)
25 - 30 = 1 - 6 (just the same)
25 - 30 + 9 = 1 - 6 + 9 (just added 9)
(5 - 3)2=(1 - 3)2 (using the binomial rules)
5 - 3 = 1 - 3 (square root of 4!)
5=1 !!!!"
The writer unfortunately confuses the value of a number with the result
from taking the square root operation. Taking the square root (an
operation) on both sides of (5 - 3)2 = (1 - 3)2 gives ± (5 - 3) =
± (1 - 3) or, more simply, (5 - 3) = ± (1 - 3). These give 2 =
± 2 Obviously only one is correct. For example, to find one side of a
square-shaped area with area of 4 measured in (length unit)2,
(equivalently expressed as x2 = 4), taking the square root of both sides
gives a result of x = ± 2. The length, in the context of the problem,
is only correctly expressed as x = 2 (length units).
Looking at this issue from a different perspective, if a = b, then a2 =
b2. The reverse, however, may not hold. For example from (-2)2 = (2)2
one cannot conclude -2 = 2
If a2 = b2, what can we say? We can say that |a| = |b|, or if you wish,
a = ± b. Whether either or both are correct is dependent on the
context of the problem. Similarly,
= |a|. Again, there is a clear distinction here and an important
difference which the careful reader will note.
In some statistical texts dealing with regression analysis one reads
assertions such as "R2 is the variance of the estimates divided by the
variance of Y. R is the square root of R2". We do not argue with the
first assertion, however the statement that "R is the square root of
R2" is not only misleading, it is also mathematically incorrect and may
indeed lead to the wrong answer where the correlation between variable
is negative! A correct statement would be that "R could be either ±
the square root of R2 depending on the sign of the slope."
From
http://ubmail.ubalt.edu/~harsham/zero/ZERO.HTM#roriginf