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. In-depth 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 in-depth 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, less-pure, 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 one-fifth of the people have never seen me, yet were still willing to answer a survey about me.

6.2 Cross-Discipline 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, pseudo-monkeymen that we are, can attract and form deep relationships with highly desirable women, then perhaps other such pseudo-monkeymen 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.

	78% of the people think you look like a monkey.
	32% of the people think you smell like one, too.
	You do the math.