Monday-Wednesday-Friday: 11:00-11:50, Lunt 101.
What is a coincidence? Is there a way to decide whether a coincidence is significant
or merely serendipitous?
To what extent can our prior experience be relied upon to predict the future?
Can we determine (or estimate) with any degree of certainty
when one phenomenon influences another?
Required Text:
The
Black Swan. (All other required reading will be provided in the form
of photocopies.)
Hume:
An Enquiry Concerning Human
Undestanding
Diaconis and Mosteller:
Methods for Studying Coincidences
Feynman:
The Character of Physical Law
Applying the scientific method correctly requires a nuanced view of these questions.
In this seminar, we shall explore some of the philosophical, legal,
linguistic, economic, mathematical, and
practical aspects of these questions.
Here is a sample of some of the problems we
will consider:
Coincidence:
In his book The Bible Code, Michael Drosnin discovers "hidden messages"
within the Bible by considering various letters spaces at equal
intervals (see the picture below).
The author finds phrases which appear to predict various historical events,
such as the assassination of Yitzhak Rabin (the phrase contains the assassin's name, university,
and his alleged motive). At first blush, it appears as though these messages
must be genuine, because for these phrases to occur otherwise would be too amazing a coincidence.
Is there a way to analyze this claim? If so,
does the same argument apply to Nostradamus? to
"Intelligent Design"? to Newton's theory of gravity?
How does our reaction to these ideas compare with our reaction to magic tricks?
The first time I visited London, I saw the Elgin Marbles at the British Museum.
While I was there, by coincidence, I ran into an Australian ex-prime minister.
What does the work "coincidence" mean in this previous sentence? Does it
mean anything more than an emotional reaction of surprise?
Is there any way to estimate how unlikely this meeting was?
Correlation:
Is the stock market a good long term investment?
Historical charts since 1872 show that
stocks have always outperformed bonds over thirty-year periods.
To what extent should we expect this trend to continue in the future?
Is this a mathematical question, an economics question, or a philosophy
question?
Many of the mathematical calculations involving probability assume
that that random events distribute themselves in a "bell curve."
However, in practice, this is not always the case.
In his book "The Black Swan," Nassim Taleb argues
that a bell curve assumption consistently underestimates the
probability of
of high impact events, which may actually occur much more frequently:
If this is true, how can we "predict" the unpredictable?
The question of correlation is closely related to the question of coincidence.
Suppose two infrequent events X and Y occur simultaneously.
A natural response is to suspect that the events
X and Y are correlated in some way. Is this a reasonable deduction?
Causation:
In Science, it is extremely important to
distinguish between causation and correlation.
For example, it is usually the case that when the Moon is the brightest object in the sky,
the temperature is colder than average.
Thus, the visual presence of the Moon is correlated with colder weather.
However, it does not appear likely that the Moon is causing the
cold weather, nor vice versa. (Compare: the correlation between the phases
of the Moon and the tides.) Given this is so, how may we distinguish between causation and
correlation? This is especially a problem when we are not able to control
the variables at hand.
It is also not clear whether this is a mathematical question or
a question or a philosophical
one.
On the other hand, this question
has important practical implications. Suppose that an epidemiological study shows
a correlation between eating a certain food item and cancer: is it a valid response
to recommend avoiding eating that particular food?
Although it seems possible to give a definition of causation, it is not without epistemological difficulties.
What are the philosophical underpinnings of the concepts of causation?
Prerequisites:
Although many of our discussions involve mathematics and statistics in
one way or another, no
prerequisites are required, except familiarity with the basic concepts of probability
studied at high school.
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