Proof:
Assume GOOD + BAD + VERY BAD >= GOOD + BAD + BAD
=> BAD + VERY BAD >= BAD + BAD
=> VERY BAD >= BAD
OTOH BAD > VERY BAD
So BAD >= VERY BAD and VERY BAD > BAD
=><= So the original assumption must be false
Thus GOOD + BAD + VERY BAD < GOOD + BAD + BAD
Therefore leaving the font size alone is a better option than messing
about with it. Q.E.D.
Hehe, no, you have a tangent; you're assuming all internet users are
distributed equally among all values of "Default". When you weight each
of those original three "Default" rows by how many internet users the
world over fall into them, *then* you have a proof.
For example, let's say:
x is the number of people where the default is too small
y is the number of people where the default is too large
z is the number of people where the default is just right
For convenience sake, let's make it relative and have x + y + z = 1
This makes: z = 1 - (x + y)
So, this gives us the table:
+-------------+-------------+-------------+
| VBx | Gx | Bx |
+-------------+-------------+-------------+
| Gy | VBy | By |
+-------------+-------------+-------------+
| B - Bx - By | B - Bx - By | G - Gx - Gy |
+-------------+-------------+-------------+
This means we get the three summations:
VBx + Gy + B - Bx - By -> (VB - B)x + (G - B)y + B
Gx + VBy + B - Bx - By -> (G - B)x + (VB - B)y + B
Bx + By + G - Gx - Gy -> (B - G)x + (B - G)y + G
Now what say we assign GOOD BAD and VERY BAD arbitrary values of 1, 0 and
-1:
(-1 - 0)x + (1 - 0)y + 0 -> -x + y
(1 - 0)x + (-1 - 0)y + 0 -> x - y
(0 - 1)x + (0 - 1)y + 1 -> -x - y + 1
Okay, so what is greater than what here?
1) y - x (decreasing font size is better)
2) x - y (increasing font size is better)
3) 1 - x - y (leaving font size alone is better)
You know that both x and y are values from 0 to 1, so all you need is
either x or y to find out. Also notice how #3 exactly equals z from above!
Without performing a global census, we can still infer something for these
results though; let's say x = 0.5 (half of all browser uses have the
default set too small):
1) y - 0.5
2) 0.5 - y
3) 1 - 0.5 - y
Because x + y + z = 1 we know that if there are *any* people which fall
into category z, y must be less than 0.5 and so:
1) y - 0.5 = negative
2) 0.5 - y = positive
3) 1 - 0.5 - y = positive
You'll notice that while 2 and 3 are both positive, they are also the same
summation and are equal. Therefore if half of all internet users have a
default font size which is too small, increasing the font size and leaving
the font size alone are both equally good alternatives.
Likewise, if half of all users have the default font size too large:
1) 0.5 - x = positive
2) x - 0.5 = negative
3) 1 - x - 0.5 = positive (same as 1)
This means that both decreasing the font size and leaving it alone are
equally good alternatives.
Half and half... think about it. If the percentage of people with a
default text either too large or too small is greater than 50, then it
makes sense to decrease or increase the font size respectively for
everyone. If both of these user groups make up less than 50% of the
whole, then it makes sense to leave the font size alone.
The only trouble is, what does the current user spectrum look like? And
just how many of them have the know-how to change the font size
themselves? And we're not even getting into the subjectiveness of what is
too large and/or too small!!!!
Time to leave well enough alone I
think!
Grey
