Calculating a Birthday Card
1. Introduction
My brother and his lovely wife gave me this birthday card.
In case the scans don't come across well, the card contains this (relevant)
text:
 78% of the people think you look like a monkey. 
 32% of the people think you smell like one, too. 
 You do the math. 
Since my brother and his lovely wife were kind enough to give me the card, I
decided to follow the card's instructions.
2. Defining Data
These statements come from a birthday card, and birthday cards (by definition)
only contain truths. Therefore, the definition of these sets may be assumed
to be true.
 Set L: 78% of the people think you look like a monkey.
L = 78%
 Set S: 32% of the people think you smell like one, too.
S = 32%
It is assumed that these data were gathered from a survey.
As a side note, I am curious as to the methodology used by Carlton Cards,
but who am I to dispute the facts presented by a birthday card?
3. Initial Analysis
The easy conclusion is that the values of Sets L and S should
be added together, thus:
L + S = 110%
A percentage of 110 is only numerically or logically valid in sports and
corporate motivational speaking. Since this is a birthday card and not
related to sports or corporate motivational speaking, clearly this summation
is incorrect.
The initial conclusion is rejected and we proceed to additional analysis.
4. Indepth Analysis
We will now look at the data in more detail. This analysis is hampered by
the lack of insight into Carlton Cards' methodology and research. However,
we can gain greater knowledge of Set S and define several
additional constants.
4.1 Expanding Set S
Further examination of Set S reveals an interesting subtlety. This
subtlety takes the form of the word "too." The definition of Set S,
in case you have forgotten, is:
 32% of the people think you smell like one, too. 
Restating the terms more completely, Set S is actually:
 32% of the people think you smell like a monkey
and think you look like a monkey.

This is a critical distinction. The set of people represented by Set
S is a subset of the set of people represented by Set L.
4.2 Defining Set N
Set N represents the set of people who think I look like a monkey
but do not think I smell like a monkey.
N = L  S = 46%
This value represents the set of people who think I look like a monkey, but
do not think I smell like a monkey. Set N is a subset of the set of
people represented by Set L.
4.3 Defining Set I
Set I represents the set of people who do not think I look like a
monkey.
I = 100%  L = 22%
(Alas, not knowing the methodology or details of Carlton Cards' research,
there is no way these to separate this set into subsets of those who do and
do not think I smell like a monkey.)
5. Final Table of Sets
The indepth analysis above leaves us with the following set of constants:
Set
 Value
 Definition 
L  78%
 The people who think I look like a monkey.

S  32%
 The people who think I look like a monkey and also think I smell
like a monkey.
(Subset of L.)

N  46%
 The people who think I look like a monkey but do not think I smell
like a monkey.
(Subset of L.)

I  22%
 The people who do not think I look like a monkey.

6. Conclusions
A rich set of conclusions may be drawn from the analysis of this coarse data.
Not only are the conclusions directly related to the mathematical analysis of
the statistics presented by this birthday card, but these data may be applied
to other, lesspure, sciences.
6.1 Mathematical/Statistical Analysis of Data
The sets presented in Section 5 provide me a somewhat depressing view of
myself and "the people".
 Set L shows the vast majority of people think I look like a monkey.
 Set S shows a significant number of people think I smell like a
monkey.
 Set N shows an alarmingly high number of people do not have
working olfactory organs.
 Set I shows that over onefifth of the people have never seen me,
yet were still willing to answer a survey about me.
6.2 CrossDiscipline Analysis of Data
Section 6.1 looks at the data from a mathematical point of view. However,
it is possible to extend the analysis even further by bringing it into other
disciplines. These are not so much refined conclusions as they are potential
avenues for future research. Only a few possible such avenues are discussed
here; others are left as an exercise for the reader.
6.2.1 Genetics
Given that physical traits are often shared by siblings, it is fairly likely
that my brother also looks and smells like a monkey. We have dissimilar hair
colors and body types, but that merely means that we must resemble different
types of monkeys.
6.2.2 Behavioral Psychology/Computer Science
By the conclusions, provided in Section 6.1, about me and their extension to
include my brother, alluded to in Section 6.2.1, an inference may be drawn
that women are attracted to men who look like a monkey and smell like one too.
My brother and I are both married to very intelligent, attractive, talented,
and sensitive women. If the two of us, pseudomonkeymen that we are, can
attract and form deep relationships with highly desirable women, then perhaps
other such pseudomonkeymen can as well.
6.2.3 Folklore/Developmental Musicology
These data show that applying statistics and mathematical analysis to cute
children's songs may render the songs impotent and void of the taunting power
they once held.
7. Ultimate Conclusion
In their card, my brother and his lovely wife suggested that I get some
chocolate.
I suggest you do the same.
Text copyright 2010 by Wayne Morrison, all rights reserved.
The birthday card is copyright by Carlton Cards, all rights reserved.
tewok
Storm Monkeys