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Throughout history, mankind has sought order for all aspects of life.
People are often afraid, though, of how the "gods" - usually the belief
system, the normative moral order, or the rulers of a particular society -
will react to attempts at solving the mysteries of the natural world. The
perennial belief that "Science does not remove the terror of the gods" (Dobbs
7) has often led to an avoidance of scientific research altogether. One by
one, though, many mysteries have been solved through the application of
scientific principles including why objects fall to the earth, why lightning
moves from the clouds to the earth (not vice versa), and why each living thing
is unique. Scientific principles have also been applied in cases
traditionally thought to be governed by luck, such as games of chance. In
systems such as games of chance and the stock market, the scientific
principles of probability and statistics are used to manage risk and remove
uncertainty. Peter L. Bernstein's _Against the Gods: The Remarkable Story of
Risk_ traces the development of probability and statistics from their origins
(beginning even before the introduction of Arabic numerals to Europe) to the
present-day.
Risk and uncertainty have been the subject of numerous studies throughout
history, primarily due to their association with fiscal matters, as discussed
in Bernstein's work. The terms are commonly used but they often lack clear
definitions. Merriam-Webster defines "risk" as "possibility of loss or
injury" (1011) and "uncertainty" as "[a] lack of...knowledge...about an
outcome or result" (1285). These definitions are correct, to a certain
extent. Why has mankind often sought to avoid risk and uncertainty? We
surely wish to avoid loss or injury, but there are always two sides to a risk:
loss and gain. One should not so easily dismiss risk as there is a chance to
gain. A person must accept the possibility that s/he might lose in order to
accept the possibility that s/he might win. This is often hard to do, though,
as the chance of losing often overshadows the chance of winning in the
prospective risk-taker's mind.
A relationship exists between the risk and uncertainty. Uncertainty
reflects the degree of willingness to accept risk. Weighing the uncertainty
of outcomes and acceptances of risks are everyday activities for many people:
questions such as "If I drink eight shots of tequila, will I get sick?",
"Which job should I take?" (or conversely, "Who should we hire for this
position?"), and "Which stocks should I buy/sell?" are commonplace in our
society. With the willingness to accept risk comes the weighing of
uncertainties. When most people are aware of the presence of uncertainty,
they are almost always (to use Bernstein's term) risk-averse. They seem to
accept the biblical adage that "My people are destroyed for a lack of
knowledge..." (Hosea. 4.6) as the literal truth. Leaving out the destruction,
the biblical adage is the dictionary definition of uncertainty. People know
to be wary of uncertainty, for if it is ignored and risk is taken lightly,
destruction can follow. Risk and uncertainty are thus inextricable from one
another. The relationship of risk and uncertainty has been studied to one
degree or another by researchers of many disciplines, including psychologists
and mathematicians. In fact, the study of their relationship with the goal of
reducing uncertainty and managing risk has engendered the growth of its own
branch of mathematics: probability.
Probability is the branch of mathematics most concerned with uncertainty
and the quantification of risk. It is "the chance that a given event will
occur" (Merriam-Webster 928). Probability is a measure of the likelihood of an
event. It also gives a measure of the likelihood that all other possible
events will not occur. When a situation with several possible outcomes is
encountered, one most often determines (or attempts to determine) the relative
probability of each outcome, as well as the risk involved with each. Ideally,
use of the principles of probability leads to reduced uncertainty and
effectively manages of risk. Whether or not to accept the risk can then be
determined based on the likelihood of the desired outcome. But how does one
determine relative probabilities of situational outcomes that lead to specific
events? Statistical methods are employed in the search for uncertainty
reduction.
Statistics deals with the analysis of past experiences in the hope of
predicting future outcomes. It is the branch of mathematics that deals with
large quantities of data: collecting the data, analyzing the data, and
interpreting the data. Statistics and probability often go hand in hand.
When attempting to determine the relative probabilities of outcomes, numerical
data about previous occurrences of the same (or similar) situation(s) are
compiled and examined in detail. The data are analyzed to provide an educated
guess as to the relative probabilities of outcomes. Statistical data -
information about the past - is widely accepted as an accurate representation
of the future. In many cases, statistics can be used to predict probabilities
of future outcomes quite accurately. For instance, in Galton's pea plant
research, the diameters of the plants' stems regressed to the mean over
several generations (Bernstein 166-167). This example shows that statistical
data is used to determine the probability of an outcome (stem diameter, in
this case) when the sample size is large enough. But this is not always the
case.
Statistics is not an exact science, at least not in respect to predicting
the future. A past occurrence of an event does not necessarily prove that the
event will occur again, even under the same circumstances. One could, for
example, determine the average price per gallon of gasoline over the last year
(or any suitable amount of time). While it is possible that the price will
continue at about this level, there are many unseen factors affecting the gas
price: tension in the Middle East, U.S. trade relations with petroleum-
producing nations, the value of the U.S. dollar in the world market, etc.
While each of these will possibly remain at the current status quo, there is
no way to tell with any degree of certainty whether they will continue to do
so. There is also no way to tell with certainty if they will affect gas
prices at all. As Bernstein notes: "the past seldom obliges by revealing to
us when wildness will break out in the future" (334). Predictions of future
outcomes based on statistical data are not necessarily accurate.
Probability and statistics are tools used to reduce uncertainty and
effectively manage risk. They are used for the prediction of future outcomes
in which there is a degree of uncertainty. Probability uses statistical data
to provide as much information as possible about a situation based on similar
situations that have already occurred. Based on past experience, we assume
that the sun will come up tomorrow. There is no way to prove this with 100%
certainty, but the sun's rise every day for as long as we care to remember is
proof enough for the majority of us. But the principles of probability and
statistics are not a guarantee of future outcomes by their nature.
Probability and statistics are merely guides for risk management and
uncertainty reduction based on past experience.
Bernstein's Against the Gods is very interesting. The aspect of the work
that is perhaps the most interesting is Bernstein's own definition of risk.
He declares that the "heroes" he has discussed "have transformed the
perception of risk from chance of loss to opportunity for gain, from FATE and
ORIGINAL DESIGN to sophisticated, probability-based forecasts of the future,
and from helplessness to choice." (337). These men who have questioned and
fought the established order of their respective times - who have truly gone
against the gods - have given us the modern definition of risk. A chance for
gain is included, and the future no longer looks so bleak. Perhaps we are not
truly condemned to repeat history.
Bernstein's definition of risk provides hope that careful calculations of
probabilities of future outcome based on past experience and risk management
can pay off. Using Bernstein's definition of risk and one's own knowledge of
probability and statistics, one can often make the right choices (or at least
the best choices given the situation) regarding risk. [Is this an over-
generalization? Yes.] Bernstein's definition of risk admonishes us to be
risk-aware rather than risk-averse. There is still much to learn about
mankind's reactions to risk and uncertainty, but perhaps science does remove
the terror of the gods after all.
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-= References =-
Bernstein, Peter L. _Against the Gods: The Remarkable Story of Risk_. New
York: John Wiley & Sons, 1998.
Dobbs, J.R. _The Book of the SubGenius_. New York: Simon & Schuster, 1983.
The Holy Bible. Revised Standard Version. Second Edition. Park Ridge:
Cokesbury, 1963.
"Probability." _Merriam-Webster's Collegiate Dictionary_. 10th ed. 1993.
"Risk."
"Statistics."
"Uncertainty."
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Issue#105 of "GwD: The American Dream with a Twist -- of Lime" ISSN 1523-1585
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