Numbers Are Us: Number Sense and Its Effects on Life
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Transcript of Numbers Are Us: Number Sense and Its Effects on Life
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Numbers Are Us:
Number Sense and Its Effects on Life
Keeok Park
La Verne, CA
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Numbers Are Us
Copyright © 2012 by Keeok Park
All Rights Reserved
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
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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
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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
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Conclusions …125
References …128
About the Author …140
This excerpt includes Introduction and Chapter 5: Interesting Numbers.
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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
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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
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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).
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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
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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.
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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
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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
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This is an excerpt from Numbers Are Us: Number Sense and Its
Effects on Life. The book is available on Amazon.com.
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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
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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
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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).
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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).
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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
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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).
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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
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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
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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
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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).
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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
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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?
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This is an excerpt from Numbers Are Us: Number Sense and Its
Effects on Life. The book is available on Amazon.com.
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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.