Fist, let me explain why it is important to think clearly about
cause-and-effect relationships.
It turns out that judgements about cause-and-effect often lead to
real-world actions. For example, you might find that certain locations are
associated with a high number of weird diseases. If you think there is
something about the location (e.g. Love Canal) that is _causing_ weird
diseases, you might well decide to take drastic action, such as moving
everybody out. On the other hand, it may turn out that the location (e.g.
the Mayo Clinic) is _not_ causing the diseases, and it would be a really
bad idea to move everybody out.
These are not made-up examples: The people who lived near Love Canal would
have been better off almost anywhere else, while the people in the Mayo
Clinic would be worse off almost anywhere else.
There are innumerable other examples where one must determine whether there
is a causal relationship between two things. Large numbers of lives and
dollars depend on such determinations every day.
There is a lot more to this than "bickering about the semantics of the
words".
=========
The notion of cause-and-effect is more subtle than the notions of ordinary
logic, as we now discuss:
The following three ideas are equivalent:
Plain English: If A then B.
Formal logic: A ==> B ... "A implies B"
Boolean algebra: B + ~A ... "B or not A"
And they are closely related to (i.e. a limiting case of):
Probability: P(B|A) ... "probability of B given A"
But as we shall see, those four ideas are _not_ anywhere close to
"A causes B".
To see this, consider the following example:
"A" means: person developed rabies symptoms
"B" means: person was bitten by wild animal
and I have a dataset with many rows (one for each person) and two columns
(A and B). Within this dataset it turns out that A ==> B. You can check
that in every row, we either have B or ~A; that is, either the person was
bitten, or the person did not show rabies symptoms.
OTOH it would be absurd to suppose that A causes B. The person's rabies
symptoms are not the _cause_ of the bite. The cause cannot happen after
the effect.
We conclude that in general, it is _not_ safe to infer a cause-and-effect
relationship from an ordinary collection of data. You can infer that A
implies B, but not that A causes B.
Even if you have timing information as well as statistical information
t(dawn) > t(cock-crowing) and
P(dawn | cock-crowing) > 0.9999
you cannot safely infer that the rooster caused the dawn.
======
Now that we have seen some of the pitfalls, let us move into positive
territory and see under what conditions one _can_ infer causation.
The best modern work on this topic has its roots in epidemiology, and
borrows some colorful terminology from that field. For instance, the term
"intervention" corresponds essentially to what a physicist would call a
"perturbation". Meanwhile the term "counterfactual" corresponds
essentially to what a physicist would call a "hypothetical".
To return to the rabies example:
a) Suppose we intervene by vaccinating a bunch of people, and then take
some more data. We find a reduction in the number of people with rabies
symptoms, but _no_ reduction the number of people bitten by wild animals.
b) Conversely, suppose we intervene to reduce the number of people
bitten by wild animals. That _will_ reduce the incidence of human rabies
symptoms, OTBE (Other Things Being Equal).
... Those two interventions strongly support the conclusion: "wild-animal
bites contribute to causing human rabies cases and not vice versa".
Note 1: Of course this is a simplification -- but it is not wrong and
it could be used as the basis of non-ridiculous policy decisions.
Note 2: We can reach this conclusion without knowing anything about the
temporal ordering of the bites and the rabies symptoms. OTOH if we do have
timing information we can use it to bolster the conclusion.
This example illustrates the general rule that to infer a cause-and-effect
relationship, you need to study how the system responds to interventions
(i.e. perturbations).
You need to be careful to specify the details of the intervention.
You also need to be careful to specify what OTBE means. As an illustration
of this pitfall, consider a lever with four labelled points:
================
A B C D
and we want to know whether point C rises when I raise point A. Well, that
rather depends on whether the fulcrum is at point B or point D! To repeat:
it does not suffice to say that the intervention is raising A. Raising A
at constant B is very different from raising A at constant D.
BTW, for those of you who can't deal with online papers in PostScript format:
a) At my suggestion David kindly put up a .pdf version of the paper I
recommended yesterday; it's at ftp://ftp.research.microsoft.com/pub/tr/tr-94-11.pdf
b) Ghostscript and Ghostview are very nice and very useful. They're
available for free from: http://www.cs.wisc.edu/~ghost/
3) The pitfalls of noticing that A and B are associated without
understanding whether or not A causes B make up a big part of Feynman's
sermon about cargo-cult science. The most widely-available source for this
is _The Pleasure of Finding Things Out_: http://www.amazon.com/exec/obidos/ASIN/0738203491/
4) Feynman also made the point that a chain of deductions need not be
ordered the way a chain of causation is; see _The Character of Physical
Law_ starting on page 46. http://www.amazon.com/exec/obidos/ASIN/0262560038/
=============
In some circles it is fashionable to think that physics teachers are much
much more logical than politicians. Yet every day we expect elected
officials to make determinations such as
* will XYZ vaccine cause a large reduction in disease?
* will putting bomb-detectors in airports cause a reduction
in the number of bombings?
... and in each case will the reductions be worth the cost?
It would be nice if physics teachers would set a good example, and teach
others how to think clearly about cause-and-effect. Saying "F causes ma
and not vice versa" is not exactly starting off on the right foot.