In Critical Thinking Lesson 2A, you learned
about the importance of making systematic observations--observations
that, because they control for the effects of various factors, allow
us to develop accurate answers to our questions. As you learned in
that lesson, what seems to be happening based on our unsystematic
and superficial observations of an event and what actually
is happening, which we discover after making more systematic and careful
observations, may turn out to be two different things. In other words,
appearances and reality do not always mesh in our everyday lives.
When thinking critically, we attempt to look below the surface characteristics
of events in order to see the reality that underlies them. The current
emphasis on teaching critical thinking is based fundamentally on the
idea that our everyday human judgement is not to be trusted completely:
our desires, imperfect perceptual processes, intellectual biases,
lapses of attention, and other similar limitations, can prevent us
from knowing reality accurately. In other words, our personal experiences
sometimes lead us astray.
Personal Experience
My personal experience tells me that the moon is largest just after
it has risen over the eastern horizon or just before it sets on the
western horizon. It is smallest when it is in the night sky over my
head. It is obvious to me that this is true: I have seen it
many times with my own eyes. But, as you learned in Chapter 4, what
my personal experience tells me must be true actually is false. The
apparent increase in the moon's size when it is near the horizon is
an optical illusion. The moon is neither closer to the Earth nor does
its actual size increase when it is nearer the horizon than when it
is directly overhead (see McCready,
2002 for a discussion of various explanations of the illusion).
For most of us, our personal experiences seem to be the most compelling
type of evidence on which to base our beliefs. But, as the example
of the moon illusion shows us, compelling personal experiences may
cause us to believe something that is not true.
In Chapter 4, you learned that perception "involves the interpretation
of sensory input" (p. 141). In other words, our perceptions of
the world are subjective: when we process sensory input, we
add information in order to create meaningful perceptions. This meaning
often closely reflects reality; but it may include inaccuracies that,
at times, cause us to misperceive reality (as in the case of optical
illusions). Because personal experiences include perceptions, they
also involve interpretations of sensory input. In addition, personal
experiences include conclusions that are drawn from these perceptions.
For example, if I take a pill that I believe is going to cure my headache,
and I perceive that the pain stops, I probably will conclude that
the pill cured my headache. The perceptions (pain followed by a reduction
of pain) and the conclusion (the pill cured my headache) together
make up my personal experience of the pill, which tells me that the
pill is an effective treatment for headaches. In other words, a personal
experience is an inference that is drawn from a set of subjective
observations (to infer means to derive a conclusion
from evidence assumed to be true).
The Critical Thinking Application at the end of Chapter 4 provided
an example of how personal experiences are inferences drawn from a
set of observations. You learned there about the contrast effect,
which refers to the effect of the comparisons one makes on one's
evaluation of an event. In other words, our personal experience
of an event is affected by what we compare that event to. For example,
as mentioned in the textbook, young males will experience a female
as being less attractive if they have just observed other females
who are extremely attractive (p. 173).In general, personal experiences
are strongly affected by contrast effects. If different people make
different comparisons, they will have different personal experiences.
In general, different people, all of whom observe the same event,
will have different personal experiences when they interpret the observed
event in different ways.
Coincidence
On September 11th, 2002, one year after the 9/11
terrorist attacks on the World Trade Center in New York City, the
winning lottery number in the evening drawing of the New York State
Lottery was "911." Many people concluded that this unusual
conjunction of events--the first anniversary of the attacks (Event
1) and the drawing of 911 in the lottery (Event 2)--must be meaningful
because it seemed to them highly unlikely to have occurred simply
by chance. (see
Paulos,
2002)
Personal experiences sometimes involve coincidences that we misinterpret
as being meaningful conjunctions of events. The term coincidence
refers to two (or more) events occurring together by chance.
Another way of saying this is that coincidence involves two (or more)
events occurring at random with respect to each other:
the occurrence of one event cannot be predicted from the other event.
For example, a "fair" coin is one in which a particular
coin toss cannot be predicted from the preceding toss, and each side
of the coin has a 50% chance of appearing on each toss. In other words,
if the coin comes up heads on the first toss, it has a 50% chance
of coming up heads (or tails) on the next toss (and the toss after
that, and so on). If the coin, when tossed two times in a row, comes
up heads both times, this is merely a coincidence: by chance
alone, we would expect this to happen 25% of the time (0.5 x 0.5 x
100).
There are two thinking problems that lead people mistakenly to conclude
that two events have occurred together for some reason other than
by chance alone. First, we tend to pay attention to and, thus, to
remember striking conjunctions of events. Second, we tend to believe
that coincidences are highly improbable, even in cases when we should
expect them to occur. Let's look at these two problems in a little
more detail.
Paying Attention to Coincidences. In Critical
Thinking Lesson 1, you learned about the confirmation bias. Because
of the confirmation bias, we tend to pay close attention to information
that confirms our preconceptions, and to ignore information that disconfirms
them. Thus, when a coincidence seems to confirm a preconception, we
are very likely to remember it and to forget the many instances in
which the coincidental conjunction of events did not occur. For example,
many people believe that the full moon affects human behavior in various
unusual ways (Carroll,
2002; Roach,
2002). Because of this belief, when something unusual happens
during a full moon, people who have this preconception tend to pay
close attention to the conjunction of the two events (that is, to
the full moon and the unusual happening) and to remember it later,
even if it was only a coincidence. If the very same unusual thing
happens during any other phase of the moon, on the other hand, they
are unlikely to pay attention to the conjunction of the two events
(that is, to the non-full moon and the unusual happening). This causes
them to remember selectively those times when a full moon occurred
along with something unusual, and to forget selectively those times
when something unusual occurred along with another phase of the moon.
We typically pay very close attention to striking conjunctions of
events. For example, who wouldn't be struck by the following pairing
of events? One morning last week, George was thinking about a person
whom he once knew long ago (Event 1) and then, 60 seconds later,
he picked up a newspaper, opened it, and immediately saw that same
person's obituary (Event 2). Marks (2000) referred to such
unusual combinations of events as oddmatches. Such a pairing
of events seems too improbable to be due to chance. But Stanovich
(2001) argued that oddmatches such as George's will occur by chance
occasionally over the course of all of our lives:
Suppose on a given day you were involved in 100
distinct events.... You watch television, talk on the telephone,
meet people, negotiate the route to work or to the store, do household
chores, take in information while reading, complete complex tasks
at work, and so on. All these events contain several components
that are separately memorable. One hundred, then, is probably on
the low side, but we will stick with it.... How many possible different
pairs of events are there in the 100 events of your typical day?
Using a simple formula to obtain the number of combinations, we
calculate that there are 4,950 different pairings of events possible
in your typical day. This is true 365 days a year. (p. 182)
In a 10-year period of your life, there would be over 18 million
coincidental pairings of events possible. Given so many coincidences,
we would expect that at least a few of these would be oddmatches.
And because oddmatches are so striking to us, we tend to remember
them while forgetting most of the other millions of coincidences
that occur throughout our lives.
Estimating the Probability of Coincidences. We tend
to estimate probabilities poorly. To be specific, we often conclude
that probable events are improbable. Schick and Vaughn (2002) provided
a good example of this:
Let's say that you're at a party, and there are
twenty-three people present including yourself. What are the chances
that two of those twenty-three people have the same birthday? Is it
(a) 1 chance in 365, or 1/365; (b) 1/1,000; (c) 1/2; (d) 1/40; or
(e) 1/2,020? (pp. 53-54)
What do you think? Most people choose a low probability, such as
1/365. Few people choose the correct answer, which is 1/2. That is,
there is about a 50% chance that two out of 23 people will have the
same birthday (see Martin,
1998, for an explanation). Why do most people choose a very low
probability? Based on their personal experience, it probably seems
very unlikely to them that two people in a room will share the same
birthday. For example, you probably have met few people who have the
same birthday as you. But how many times have you asked a roomful
of people what there birthdays were in order to determine if two of
them shared a birthday? Perhaps you can try this in your psychology
class.
Given enough time, even highly improbable coincidences eventually
must occur. As Stephen Jay Gould stated, "give me a million
years [of flipping a coin] and I'll flip a hundred heads in a row
more than once" (quoted in Gilovich, 1991, p. 176). In other
words, coincidences happen all the time:
Drawing a royal flush in poker, getting heads
five times in a row, winning the lottery--all these events may seem
incredibly unlikely in any instance. But they're virtually certain
to happen sometime to someone. With enough chances for something
to happen, it will happen. (Schick & Vaughn, 2002, p. 55
CRITICAL THINKING QUESTIONS FOR LESSON 4
Question 4-1
Find a spot straight ahead of you and stare at it. Now, while keeping
your gaze fixed on this spot, use your peripheral vision to examine
objects to your right and left. Try to find objects that are at the
extremes of your peripheral vision. Do the objects appear colored to
you? What colors do you see? Now, look directly at these objects. Was
your personal experience of their color correct?
If you are sitting in a room that contains objects that are familiar
to you, it is very likely that they appeared colored to you. If, on
the other hand, you are sitting in a room that contains objects that
are not familiar to you, they probably appeared to be black and white.
In fact, the light coming from objects in your peripheral vision falls
on a part of the eye that contains no color receptors, so you should
be unable to see the colors of these objects (Schick & Vaughn, 2002;
also see page 132 in the textbook). Yet, we often do experience their
colors.
Based on your observations, you probably concluded that we can see
the colors of objects in our peripheral vision, but your personal experience
in this case would be mistaken. In fact, you probably still believe
that you can see the colors of objects in your peripheral vision. But
put this belief aside for a minute so that you can consider possible
alternative explanations of your experience. That is, provide a possible
reason why we see the colors of objects in our peripheral vision even
though the light coming from them falls on a part of the eye that is
incapable of detecting color.
Suggested Answer
Question 4-2
Last night, Andrea dreamed that her aunt had died in an automobile
accident. She awoke very upset by the dream and wanted to call her aunt
in order to warn her to be careful. But she stopped herself when she
thought that she was just being silly about what was only a dream. Later
that day, however, Andrea's mother phoned to tell her that her aunt
had been struck and killed by a car that morning as she was crossing
a busy street. Andrea was devastated and felt terribly guilty that she
hadn't warned her aunt. She believed that her dream had been a psychic
premonition of her aunt's death. Think of an alternative explanation
of Andrea's dream.
Suggested Answer
Question 4-3
It was mentioned above that, on September 11, 2002, the winning lottery
number in the evening drawing of the New York State Lottery was 911.
This was taken by many as some sort of highly unusual occurrence that
must have an important meaning. But others argued that it was just a
coincidence that we should have expected to occur somewhere at some
time. Estimate how likely it is that, on any particular day, the numbers
911 (in that order) will be drawn in the New York State lottery if three
numbers (from 0 to 9) are selected in the drawing. (If you don't know
how to perform probability calculations, click
here.)
Suggested Answer
Question 4-4
A fair coin will come up heads 50% of the time when it is tossed and
tails the other 50% of the time. Which of the following sequences of
10 tosses of a fair coin is most likely to occur (where H stands for
heads and T stands for tails)?
- HHHHHHHHHH
- HTHTHTHTHT
- HHTHTTHTTH
Suggested
Answer
Bibliography and References
Carroll, R. T. (2002). Full moon and lunar effects. Skeptic's Dictionary.
Retrieved May 3, 2003, from http://skepdic.com/fullmoon.html
Gilovich, T. (1991). How we know what isn't so: The fallibility
of human reason in everyday life. New York: Free Press.
Marks, D. (2000). The psychology of the psychic (2nd ed.). Amherst,
NY: Prometheus.
Martin, B. (1998, September/October). Coincidences: Remarkable or Random?
Skeptical Inquirer, 22(5). Retrieved April 27, 2003, from http://www.csicop.org/si/9809/coincidence.html
McCready, D. (2002). The moon illusion explained. Retrieved
April 8, 2003, from http://facstaff.uww.edu/mccreadd/
Paulos, J. A. (2002, Oct. 6). The 9-11 lottery coincidence. Who's
Counting? Retrieved April 27, 2003, from http://abcnews.go.com/sections/scitech/WhosCounting/whoscounting021006.html
Roach, J. (2002, December 18). Full moon effect on behavior minimal,
studies say. National Geographic News. Retrieved May 3, 2003,
from http://news.nationalgeographic.com/news/2002/12/1218_021218_moon.html
Schick, T., & Vaughn, L. (2002). How to think about weird things:
Critical thinking for a new age (3rd ed.). Boston: McGraw Hill.
Stanovich, K. E. (2001). How to think straight about psychology
(6th ed.). New York: Longman.