Numbers Are Us:

Number Sense and Its Effects on Life

Keeok Park

La Verne, CA

Numbers Are Us

Copyright © 2012 by Keeok Park

All Rights Reserved

kpark@laverne.edu

909 593 3511 ext. 4405

ISBN: 978-0-9843446-3-5

Available on Amazon.com

First Printing, 2012 Edition

Printed in the United States of America

Contents

Introduction …1

Why Should We Pay Attention to Number Sense?...1

Math Skills of U.S. Students ...3

Number-related Academic Disciplines …4

Organization of the Book …6

Reading Suggestions …7

Part I: Number Sense ...8

Chapter 1: Number Sense of Infants and Children ...9

Infants’ Number Sense …9

Estimating vs. Counting …11

Number Sense and Language Sense …13

Number Sense and Mathematics Performance ...14

Discalculia and Acalculia …16

Chapter 2: Number Sense of Animals, Fish, and Insects ...18

Crows ...19

Monkeys …20

Chicks ....22

Insects-Ants ...23

Insects-Honeybees …24

Fish ...25

Chapter 3: Measuring Number Sense ...27

Measuring Number Sense …27

Measuring Intuitive Number Sense …29

Part II: Role of Numbers in Life …32

Chapter 4: Importance of Numbers ...33

Two Cents and Cancellation of Health Insurance …33

One Cent and Health Insurance Problem …34

Numbers and Resume …36

One Vote and Filibuster …37

Fingernail Final and One Hundredth of a Second …8

One Extra Degree and Boiling Point of 212° F ...39

Blood Alcohol Content and Jail Time ...39

SAT, ACT, and College …40

Basic Skills Test and the Military …41

Credit Score …42

LTV ...43

Chapter 5: Interesting Numbers ...45

7 ... 45

666 …46

13 …47

4 ....48

Did the World End on May 21, 2011? ...49

Will the World End on December 21, 2012? ...51

Super Bowl Commercials …52

80/20 …53

6 Sigma ...54

Richter Scale …55

“2 + 2 = 5” ...56

Chapter 6: Misuse of Numbers …58

Numbers Used to Advance Policy Positions …59

Use of Estimated Numbers …62

Marketing “Enhancement” Tricks with Numbers …64

Vanity Sizing ...68

Distorted Graphic Representation of Numbers …71

Creative Accounting ...79

Part III: Effects of Number Sense on Life: Does It Matter? …84

Chapter 7: Effects of Number Sense on Life (Tendency to Organize

Life, Life Satisfaction, Life Skills, and World View) …85

Data Collection and Measurement ...87

Number Sense and Tendency to Organize Life …92

Number Sense and Life Satisfaction …100

Number Sense and Number Related Life Skills …107

Number Sense and World View …114

Relationships between Number Sense and Tendencies to Organize

Life, Life Satisfaction, Number Related Life Skills, and World View,

Controlling for Gender …116

Chapter 8: Effects of Number Sense on Life: Typology Development

and Model Building ...120

Number Sense Typology ...120

Number Sense Model ...122

Conclusions …125

References …128

About the Author …140

This excerpt includes Introduction and Chapter 5: Interesting Numbers.

1

Introduction

This book is about number sense. Number sense is an ability to

understand numbers and apply them to different aspects of life. It may

involve understanding of ideas, concepts, and problems concerning

numbers and applying them to real world situations. On a more formal

level, it may be defined as “an intuitive understanding of numbers, their

magnitude, relationships, and how they are affected by operations”

(University of North Carolina School of Education, n.d.). Those who

have a strong number sense can presumably estimate the number of

objects quickly, differentiate numbers with accuracy, estimate chances

involving life events easily, and make decisions based on numbers

without much difficulty.

Why Should We Pay Attention to Number Sense? We use number sense in a variety of situations in our daily life.

When we contemplate whether to go to the front or to the back of the

bus, we quickly estimate the number of people in each place because

we want to be in a less crowded area. When we decide to pick which

train car to board, we quickly estimate the number of people in line and

also the number of people in train cars. When we go to grocery stores,

we often compare prices of similar items in the process of finding the

item with the lowest price. When we are done with shopping, we want

to be in the shortest line possible for a speedy checkout. These are just

2

a few examples that show that we use our number sense to make

decisions that affect our daily lives.

Why do we study or discuss numbers? We can think of at least

two reasons. One reason may be to satisfy our intellectual curiosity

about the world. We want to know about the social or natural world

better by observing it and by quantifying the outcome of our

observation. Another reason may be to use the knowledge about the

world to improve it. Satisfying intellectual curiosity and applying the

outcome of the intellectual curiosity to our lives are something that are

worth pursuing for.

We can appreciate our life better with numbers. We can talk

about how many verbal or non-verbal ways we can express our love,

appreciation, achievements, sorrow, anger, revenge, or other feelings.

Elizabeth Browning’s “How do I love thee? Let me count the ways” is

a poem that illustrates this (Academy of American Poets, 2012).

Appealing to our deep emotional feelings, that poem lists eight

different ways to adore a lover.

In addition, we can talk about the probability of getting

jackpots, probability of retrieving a precious lost item, or probability of

getting away with something that we should not have done. If we

decide to jaywalk, we use numbers to estimate the chances of getting

hit by vehicles, pedestrians, or bicycles. We also estimate the chances

of getting a ticket from a police officer. The language of numbers can

enrich our vocabulary tremendously and clarify our decisions if we

know how to incorporate it into our lives.

On the other hand, if we do not have number skills, we may

end up between a rock and a hard place. If we are not capable of

3

analyzing and interpreting numbers, we may have to either

unconditionally accept whatever ideas or arguments that are presented

to us with numbers, or reject them outright without considering their

merit at all. Obviously, we would be at a disadvantage in our workplace

and in our social circles if we keep doing either of these because others

may think we are naïve or incompetent.

One way to handle a lack of number skills is to hire another

person who has a strong number sense and to rely on that person to take

care of our number needs. That may work well up to a point. If we do

not know well the specialized language that the hired consultant uses,

who is going to watch our hired consultant? Managing the hired

consultant effectively requires us to be knowledgeable about the

number-laden language that he or she uses.

Math Skills of U.S. Students Given that most people acquire their math skills in school,

international comparisons of math test scores can be used to discuss

how well or to what extent students learn number skills in U.S. schools.

Every three years the OECD releases the math test results of the

students in its 34 member countries along with other partner countries

through the International Programme for International Student

Assessment (PISA). PISA has been assessing 15 year old students’

academic performances worldwide since 2000. The subject areas of

assessment are reading, mathematical literacy, and science literacy.

Students are tested on their ability to apply their knowledge to real-

world situations (Kerachsky, 2010; OECD 2010a).

4

In the United States, at least 5000 15 year-old students from

cross sections of the country are supposed to be included in each PISA

assessment. According to the 2009 test results, the average math test

score of the U.S. students was 487, ranking 30th among 65 countries.

The ranking in math was led by Shanghi, China (600), Singapore (562),

Hong Kong, China (555), South Korea (546), Taiwan (543), and

Finland (541). Because the average score of the students of all

countries is about 500 (493 in 2009), the U.S. score of 487 was below

the average (OECD 2010b).

We live in a global world. We are a country’s citizens and at

the same time the citizens of the world. With technological advances in

transportation and communication, we are connected with one another

economically, politically, and culturally. Beyond that, we strive to

improve human conditions and to raise the standard of living for

everyone. If an individual’s success may be hampered with low number

skills, a country’s success in the international arena may be hampered

with low number scores as well. From that perspective alone, the

secondary schools in the United States could do better in educating

their students about number sense.

Number-related Academic Disciplines There are several number related academic disciplines.

Statistics is probably the most closely related to numbers because it is

defined as the science of studying numbers. Mathematics is also very

closely related to numbers in that it uses them heavily and it has

specific number related sub disciplines like applied mathematics. Other

5

disciplines like engineering, accounting, and finance are also related to

numbers as these disciplines use them frequently.

Statistics is the science of studying numbers. There are two

types of statistics: descriptive and inferential. Descriptive statistics

concerns describing the nature of the data that we have, presenting their

summary in numbers or graphs. Presenting the mean salaries of all

employees of a company along with a standard deviation that can tell

us the spread of the salaries among the employees is an example.

Inferential statistics concerns making inferences from observed samples

to their populations, usually testing hypotheses about differences or

relationships between two or more variables. For example, observing

the salaries of males and females from a sample to see if they are paid

differently and applying the outcome to the population from which the

sample is drawn is a form of inferential statistics.

What is the difference between mathematics and statistics?

Mathematics is the science of studying principles and relationships

among quantities expressed as magnitudes or numbers. As noted above,

statistics is the science of studying numbers. When analyzing numbers,

many theories, theorems, formulas, and operational processes from

many subfields of mathematics may be used in statistics. In that sense,

statistics has mathematics as its theoretical foundation. Statistics

focuses on the quantity, expressed as data, and its application.

Therefore, statistics is a much more applied science than mathematics.

Understanding each of these disciplines requires number sense.

6

Organization of the Book What is the extent of our understanding of number sense and

what difference does it make in our lives? In an effort to answer these

questions, this book is organized into three parts. The first part has

three chapters that answer questions such as when do we humans begin

to use number sense, is number sense unique to humans, and how do

we measure number sense? The second part has also three chapters and

they address questions like how important are numbers in our life, what

are some widely used numbers, and how can they be misused? The

third part has two chapters that try to answer the questions: What

difference does number sense make on different aspects of our life?

These questions are answered through cases, stories, research reports,

or empirical studies.

Perhaps there are other equally important or interesting

questions about numbers. For example, some may ask: Why do we

need to use numbers at all? Can we replace them with colors or names?

Can we limit our number use to our fingers and toes only? But the

technologically advanced world of the 21st century that we live in

requires more challenging questions. Hence, I stick to the questions

posed earlier and begin a journey of exploration.

The answers to these questions may not always be straight

forward and further inquiries may be needed to draw definitive

conclusions. In the process of answering some of these questions, this

book draws several tentative conclusions. All humans including infants

and all animals have an intuitive number sense, but only humans have

and use the formal number sense. Individuals’ respective number

senses can be measured using various indicators. Obviously, some

7

humans have better number senses than others perhaps due to brain

structure and training.

Also, number sense affects our lives greatly. It makes us

intelligent human beings who can think logically, analyze diverse

information, and take appropriate action to navigate our lives smoothly.

People with a better number sense are more likely to have more

organized lives and more satisfied lives than people with a worse

number sense. Those who have more of it are more likely to have a

more structured world view than those who have less of it if other

things are the same. Some people use their number sense to do good

things for others, while others use it to do bad things to others.

Reading Suggestions Readers who are interested in infants’ and animals’ number

sense may begin with Chapters 1 and 2 in Part I. Those who are

interested in a more practical issue of what roles numbers play in our

lives are advised to read Chapters 4, 5, and 6 in Part II first. Those who

are more academically oriented and are interested in the effects of

number sense on life may read Chapter 3 in Part I first and then move

on to Chapters 7 and 8 in Part III

8

This is an excerpt from Numbers Are Us: Number Sense and Its

Effects on Life. The book is available on Amazon.com.

45

Chapter 5: Interesting

Numbers

7 Some numbers are believed to be better than others. The

number 7 is one of them, as it is known as a symbol of luck and of

good future. Gamblers prefer that number over other numbers and

many casinos and some retail establishments are named after that

number. Although emphasizing the importance of the number 7 may

come from mostly commercial interests, the positive perception of the

number 7 is deeply ingrained in many people’s minds partly because it

is originated from our religious, cultural, or mythological history.

According to the Bible, God created the world in seven days.

The Greeks thought the number 7 is lucky because it is the perfect

number (Hembree, 2007). It is the sum of 3 and 4, and 3 symbolizes a

triangle and 4 symbolizes a square, both of which have perfect shapes.

In the early Jewish, Roman, and Islamic calendars, seven days of the

week were framed after seven planets (Sahibzada, 2005). Not everyone

may believe that the number seven is better than other numbers, but

virtually everyone is aware of the fact that many people think so.

According to Robert Krulwich of NPR, the number 7 is leading

to be the World’s Favorite Number, although 3, 11, and 13 are not far

behind it. His statement is from Alex Bellos’ experiment about favorite

numbers at www.favoritenumber.net. Bellos has been asking people to

46

tell him their favorite number and explain why they favor that number

(see Bellos 2011).

After about 13,000 submissions, he has noticed some patterns:

“odd numbers are more popular than even numbers, prime numbers

more popular than non-primes, birthdays are often favorites” (Krulwich

2011). Through his website, many intellectual and passionate

explanations of why they favor a number have come out. For example,

one person explained why 37 is chosen as a favorite number: “It looks

mysterious, like a cloaked villain from a silent movie” (Krulwich

2011). Apparently people are passionate about numbers and our brains

have a deep desire to connect with numbers and make memorable

stories out of them.

666 One “bad” number we all remember is 666. It is the “number of

the beast” used in the Book of revelation in the Bible. The actual verse

is the following: “And that no man might buy or sell, save he that had

the mark, or the name of the beast, or the number of his name. Here is

wisdom. Let him that hath understanding count the number of the

beast: for it is the number of a man; and his number is Six hundred

threescore and six.” (Revelation 13:17, 18). Various scholars and

commentators associate 666 with Nero (Cory, 2006), anti-Christ, the

social security number, the Uniform Commercial Code, or other

individual or code (see, for example, Allen 2010).

The number 666 generates fear and apprehension among some

people not only because it may indicate the seal of anti-Christ, but also

because it may foretell the end of the world, which may come after the

47

epic battle of Armageddon between the good forces and the evil forces.

Based on this prophecy of the Bible, some people try to associate the

number 666 with a specific person or a code and try to predict the end

of the world, even though the Bible itself states that no one, even the

angels, knows when the end of the world will come. Perhaps, they

possess some special, unauthentic prophetic powers that even the Bible

does not recognize?

13

Another “bad” number that is associated with misfortune is 13,

which forms Friday, the 13th. Superstitious people think that Friday, the

13th is a day of bad luck. There is even a word for fearing Friday, the

13th. It is called friggatriskaidekaphobia (Freeman, 2010). It is

connected to many unfortunate biblical events like the crucifixion and

the beginning of Noah’s flood. The number 13 is considered to be odd

or irregular as opposed to the number 12, which is considered to be

more complete. This probably stems from the “completeness” of the

twelve hours of the clock, twelve months of the year, twelve signs of

the zodiac, twelve gods of Olympus, twelve apostles of Jesus, and

others (Loach, 2004).

There is a word for fearing the number 13 and it is called

Triskaidekaphobia (Freeman, 2010). It is a combination of Greek word

thirteen and phobia. In some Western countries including the United

States, some high-rise buildings lack a 13th floor, many airports skip the

13th gate, and hospitals and hotels regularly have no room number 13

(Roach, 2004).

48

The combination of the 13th and Friday makes some people

think that bad luck is coupled with an “unnatural” number, making that

day surely unlucky. Based on this superstition, some people try to

avoid doing some things on the Friday, the 13th. For example, they may

try to avoid opening a new business, starting a new journey, betting on

sports, or initiating other significant endeavors. Unless one really

believes in this superstition literally, Friday the 13th is probably a very

good day to start any and all things. Life is short and time is limited.

We should use each and every day of the year fully if we want to have

fulfilling life on this earth.

4 Just as the number 13 is associated with bad luck in some

Western countries, the number 4 is associated with bad luck in East

Asian countries and some Southeast Asian countries. The fear of the

number 4 is known as Tetraphobia. It stems from the coincidence that

the pronunciation of the word for “four” is the same as that for the

word “death” in Chinese. Although the Japanese and Korean languages

are very different from Chinese and from one another, they both often

use some Chinese characters including these two words.

In China, Japan, Korea, and Taiwan, hospitals and hotels avoid

the number 4 just like those in some Western countries avoid the

number 13. In the United States, some studies report that, on the fourth

of every month, there's a spike in coronary-related fatalities among

Americans of Japanese and Chinese ancestry. The spike amounts to 13

to 27 percent (Sherwood, 2009).

49

The fear of “four” makes some Asian Americans avoid residing

in houses with that number. As a result, they are reluctant to buy

houses with a street number 4, 44, or 444. In Arcadia, California, where

almost 60% of the residents are Asian Americans, the city council

decided to let residents change their address just as many other cities do

in the San Gabriel Valley. This was in response to the reality that many

properties with more than one four in their address will not sell at all or

at least valued 25 to 30% less than other properties (Ni, 2011). If

allowed to change their “problem” address, some Asian Americans

may change it to a number that includes 7, a number that is believed to

be associated with “luck,” or 8, a number that is believed to be

associated with “blessings.”

This avoidance of number 4 is not much different from some

Westerners’ avoidance of number 13 or number 666. Many high-rises

in the United States do not have a 13th floor and even former President

Reagan and his wife Nancy changed their address from 666 St. Cloud

Road to 668 St. Cloud Road in Bel Air when they took up their

residence in Bel Air after retirement (Ni, 2011). If these “avoidance”

decisions are made for business reasons to make customers or residents

more comfortable with addresses, there should be no qualms there. On

the other hand, too much obsession with a number that is just like any

other number can create unnecessary stress and anxiety that no one

needs.

Did the World End on May 21, 2011? We have heard many “end of the world” predictions in the past.

Some ardent Christian or pseudo Christian believers predicted the

50

coming of Jesus and the end of the world throughout modern history.

Others made end of the world predictions based on scientific reasons

including Y2K (Year 2000) and Halley’s Comet. For example, Harold

Camping and his religious group predicted the end of the world on May

21, 2011.

This was based on his calculations of years in the Bible. May

21, 2011 was 7000 years from the Noah’s flood and 13,023 years from

creation (ebiblefellowship, 2011). Based on his reading of the Bible,

Camping and his group predicted that a great earthquake will shake

New Zealand and trigger an apocalypse at 6:00PM on May 21, 2011

(Berton, 2011). His group spent millions of dollars to advertise their

“rapture” predictions and urged people to prepare for them.

This prediction of rapture created a dilemma for those who

believed that they would be “literally” taken to heaven. What happens

to those “left behind” after believers are taken to heaven? What would

happen to their beloved pets after they themselves are taken to heaven?

Many businesses were sprung up to address these issues. A company

promised to deliver pre-written letters to those who are left behind

urging them to convert to Christianity or otherwise to encourage them

to stay on when mail, email, and phone systems would not work after

the rapture. Another company made contracts with many believers to

look after their pets after they are taken to heaven after the rapture.

There are just two catches. One is that the owners and employees of the

businesses must be atheists; otherwise, they themselves may be taken to

heaven as well. Another one is that there are no refunds to those who

signed contacts if the predicted apocalypse does not happen (Kim and

Forer, 2011).

51

Will the World End on December 21, 2012? Some doomsday pundits who track the Mayan Long Count

calendar predict that the world as we know it may end on December 21,

2012. The Mayan Long Count calendar begins at 0.0.0.0.0. “Each zero

goes from 0-19 and each represent a tally of Mayan days. So, for

example, the first day in the Long Count is denoted as 0.0.0.0.1. On the

19th day we’ll have 0.0.0.0.19, on the 20th day it goes up one level and

we’ll have 0.0.0.1.0.” This process goes on to the next level and so on

(O’Neill, 2008).

The basic unit, known as kin, is a day. The right most (first)

digit, second digit, and fourth digit range from 0 to 19, the third digit

ranges from 0 to 17, and the last (left most) digit ranges from 1 to 13.

Because of these legends, 0.0.0.0.0 was actually written as 13.0.0.0.0.

The Mayan Long Count calendar started 13.0.0.0.0 on August 11th

3114 BCE and it will reach 13.0.0.0.0 again on December 21, 2012,

5126 years after the first 13.0.0.0.0 (the Institute for Dynamic

Educational Advancement, 2008).

Some point out that the end of Mayan calendar coincides with

the winter solstice in 2012 and, on that day, the sun will be aligned with

the center of the Milky Way (see, for example, Joseph, 2007), implying

that some significant events may happen. If these predictions make

people live their life fully as if today is the last day, they may have

some positive impacts, renewing their resolve to succeed and do good

things to others before it’s too late. On the other hand, if they make

people afraid of making long-term plans and prevent them from

visualizing their positive future, they will have negative effects.

To some extent, these topics are fascinating and they make us

curious to find out more about them. But they are not so important that

52

we abandon our responsibilities and hopes for the future, let alone to

sell all the possessions and prepare for them. If one calendar ends,

another will begin. We have winter solstice every year. It simply marks

the shortest day and the longest night of the year.

Super Bowl Commercials Many of us remember at least one memorable Super Bowl

commercial. How much do you think a 30 second Super Bowl

commercial costs? The answer is more than $3 million. In 2009, NBC

charged an average of 3 million dollars for a 30 second Super Bowl

commercial (Smith, 2009). In 2010, CBS charged an average of 2.8

million dollars for a 30 second commercial (Kennedy, 2010). In 2011

the price went back up to $3 million per 30 second commercial (Smith

2011). In 2012, it was about 3.5 million dollars (Associated Press

2012). It appears that it is going up every year. More than three million

dollars are charged for a 30 second commercial? If we divide 3.5

million dollars by 30 seconds, it is much more than $100,000 per

second.

So many people watch the Super Bowl that advertisers are

willing to pay that much money to reach new and current customers.

Usually more than 100 million people watch the Super Bowl. In 2010,

Nielsen reported that about 106.5 million people watched the 2010

Super Bowl, becoming the most watched program in U.S. television

history. That number surpassed 10.97 million for the 1983 finale of

“M-A-S-H.”(Bauder, 2010). In 2011, the number of people who

watched the Super Bowl swelled to 111 million, surpassing its previous

53

record (Associated Press, 2011). The number was 111.3 million in

2012. Every year, the number seems to go up (Associated Press, 2012).

Whether spending that much money is effective in making

people buy things that they advertise is questionable. At the same time,

if they spend that much money for name or brand recognition, perhaps

the money is well spent.

80/20 In the management field, there is a concept called the Pareto

Principle, also known as the 80/20 rule. It refers to the phenomenon

that in many organizations, 80 percent of the work is done by 20

percent of workers. This principle is named after Vilfredo Pareto, who

observed that 80% of the wealth in Italy was owned by 20% of the

country’s people. This principle may be extended to other areas of

management in that 20% of the input may generate 80% of the output,

20% of the customers may generate 80% of the sales revenue, and so

on. In a broader sense, it can be interpreted as recognizing that things in

life are not distributed evenly (Azad, 2009).

The principle emphasizes that in many organizations, only a

few employees are vital and many others may not be. If managers

follow this emphasis, they should focus on the vital few rather than the

trivial many. A more democratic perspective would call for inspiring

and training the 80% of the employees who are not that productive so

that they can become more like the select few high performers.

If we extend this analogy further, we may say that a few

outliers often make or break an organization. There are always some

outliers who do not want to go by the rules of their organization, test

the limits of the rules, and get on the nerves of their managers. When

54

inventing new excuses for not complying with rules, humans are very

creative.

A few months ago, I encountered a newspaper article about an

employee who urinated on the office door of his coworker with whom

he had some disagreements. He did it twice and was captured on a

video camera, which led to a misdemeanor charge. Obviously, most

employees know how to resolve conflicts with other employees in a

civil manner. Those few who do not are outliers and they do not

represent the vast majority of civil employees. Because of the existence

of the outliers, some organizational rules are encompassing, going

beyond what most people do or do not do.

6 Sigma Another number-phrase that is often used in the management

field is 6 sigma. It is a quality improvement program that is used to

reduce the number of defects in manufacturing or business processes.

Six sigma stems from a 6 standard deviation from the mean, indicating

that it is far away from the mean, or that it is a rare phenomenon.

One sigma would be one standard deviation from the mean and

6 sigma would be 6 standard deviations from the mean. The goal of the

program is to make business processes virtually defect-free. A

manufacturing process with six sigma indicates that its products are

virtually defect-free, only about 3 defects per million processes. “If the

process mean varies at most 1.5 sigma from the target value, then on

average at most 3.4 defectives per million opportunities (DPMO) will

occur if the output is normally distributed” (Klefsjo, Bergquist, and

Edgeman 2006, 7).

55

Richter Scale “A moderate magnitude 5.0 earthquake strikes Southern

California” is a news headline that we often encounter in California.

Seismologists use the Richter scale, developed by Charles Richter of

the California Institute of Technology, to quantify the magnitude of

earthquakes. It begins with 0 but does not have any upper bound. A

Richter scale score of 0 indicates virtually no shaking. As the score

increases by a whole number on the scale, the magnitude of shaking

amplitude increases by ten times and the amount of energy released

increases by about 31 times (U.S. Geological Survey, 2012).

As a result, the intervals between the scale scores are not equal

as they increase exponentially. Therefore, the Richter scale has

categories, ranking, and exponential intervals.

According to Muskal (2011), the strongest earthquake recorded

occurred in Chile in 1960 and measured magnitude 9.5. The strongest

earth quake recorded in the United States was the 1964 quake in Prince

William Sound, Alaska, at 9.2. The deadliest quake in history is

believed to have been an 8.0 temblor in Shaanxi, China, in 1556, in

which 830,000 are believed to have died. In March 2011, a 9.0 quake

shook off the coast of Japan, becoming one of the strongest earthquakes

in history.

“2 + 2 = 5” The phrase “two plus two equals five” is a slogan used in

George Orwell’s novel, Nineteen Eighty-Four (see Orwell, 1961, 290).

It is a false dogma that is forced upon individuals by the state (the

Party) in the process of controlling their beliefs. In a complete

56

totalitarian state, individuals may be brainwashed by the state to believe

whatever it wants them to believe, losing their free will and

independent thought. Although “two and two make four” is an

unchallengeable logical truth, those who are brainwashed by the state

may believe or try to believe that it is false because it is incompatible

with the dogma that is preached by the state, which, in this example, is

“two and two make five.”

Although this is unlikely to happen, some individuals may

worry about the possibility of seeing totalitarian states even more

oppressive than the former Soviet Union and the former Nazi Germany

in the future. Although “two plus two equals five“ is logically

impossible under normal circumstances, it may possibly be used in

limited conditions. For example, it can be a title for a song, art work,

play, movie, and others.

According to Lyons (1991, 415-416), it was widely used in the

former Soviet Union under Stalin to indicate that the five year

economic plan should be completed in four years. If we go beyond

integers, some computational procedures may make “two plus two

equals five “ appear to be true with the help of rounding. For example,

2.3 + 2.3 = 4.6. If we round them off, the first 2.3 becomes 2 and the

second 2.3 becomes 2, and the outcome becomes 5. In formal

calculations, these would not be proper, but in the creative human

mind, they may possibly hold some water, perhaps?

57

This is an excerpt from Numbers Are Us: Number Sense and Its

Effects on Life. The book is available on Amazon.com.

128

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About the Author

Keeok Park is Professor and Chair of the Department of

Management and Leadership at the University of La Verne. He has a

Ph.D. in political science from the State University of New York

(SUNY) at Stony Brook. He has taught leadership in organizations,

urban policy and administration, public policy, conflict management,

research methods, statistics, and other courses at the State University of

New York at Stony Brook, the University of Virginia in Charlottesville,

and the University of La Verne. He has provided consulting services to

a number of public and private organizations regarding needs

assessment, budget forecasting, research sampling, academic

performance risk assessment strategies, policy analysis, and other areas.

His research articles on urban policy, local government

structure, fiscal administration, judicial decision-making, and other

topics have appeared in the American Political Science Review, the

Public Administration Review, the Political Research Quarterly, the

Urban Affairs Review, the State and Local Government Review, the

International Studies Quarterly, the Washington Post, the Legal Times,

and numerous other journals and edited volumes. His two textbooks,

Making Sense of Statistics and Essentials of Research Methods, were

published by the University of La Verne Press. He is in the process of

writing a series of fact-based short stories about challenges in life. The

series includes Challenges in College Teaching, Challenges at Work,

Challenges at Home, Challenges to Physical Health, Challenges on the

Road, and Challenges for the Future.