On Wednesday, July 17, 2002, at 10:27 AM, Hal Finney wrote:
> ...
> Yes, in this case probably the better statement would be "heavy rains
> with insufficient drainage cause flooding". Things can have more than
> one cause. In practice the difficulty seems to be to distinguish the
> irrelevant from the relevant aspects.
Pearl favors carefully constructing diagrams, specifically directed
acyclic graphs, DAGs, to explicate the exceptions and causal connections
more clearly. Ordinary natural language is of such coarse granularity
that all sorts of mischief arises.
He gives a funny example, attributed to Suppes, of a situation where a
golfer was hitting a drive. The ball went wide, but struck a tree branch
and bounced into the hole. Almost everyone when asked what the "cause"
of the hole-in-one was says the tree branch "caused" it. (Not in an
agency sense, but in terms of it being the important causal link.)
Now of course in nearly all possible worlds, a golf ball hitting a tree
branch is a _scattering_ event, essentially an entropy-increasing,
dissipative event. No golfer tries to hit into some trees in the hope
that a tree branch will _cause_ a hole in one.
Pearl's book has many such examples illustrating his points.
However, nothing in it has profoundly changed my world view. Most of
this stuff is just common sense to anyone trained even a little bit in
the sciences. The main usefulness is in formalizing certain models for
use in cognitive systems, diagnosis, and even some legal areas (where
weird causality inversions are all too common, as with the jury award
for the woman who claimed a CAT scan caused her to lose her psychic
powers).
>
> I think what is necessary is to go from the specific and concrete
> events to an abstraction which represents an entire category of events.
> In any given instance of flooding, everything contributes in a sense.
> If a particular stone were located somewhere else, the details of
> the flooding would be different. But if we look at flooding as an
> abstraction, then we can identify other aspects which are associated
> with the set of events that the abstraction covers.
>
> You still have the problem of distinguishing correlation from causation,
> but at least this allows you to identify possible causative factors.
> And in general there will be more than one.
This is the main thrust of Pearl's book. Lots of discusson of Bayesian
networks, DAGs, and "d-separation criteria." ("A path p is said to be
d-separated (or blocked) by a set of nodes Z if and only if 1. p
contains a chain i --> m --> j or a fork i <-- m --> j such that the
middle node m is in Z or 2. p contains an inverted fork (or collider)
i --> m <-- j such that the middle node m is not in Z and such that no
desecendant of m is in Z."
If this stuff appeals to you, take a look at Pearl.
(The notation is not as dense as it looks here, as this is a definition
to be used many times. And the formal notation is vastly more useful
than "word problem" language, IMO.)
>
> I believe the Huw Price book I mentioned argued that this arrow of
> time is not really fundamental, but rather is due to the low entropy
> of the initial conditions. Particularly if you look at it from the
> MWI perspective, in equilibrium there will be as many merges of worlds
> (or "branches") as splits.
There have been some computer simulations of reversed-billiard ball or
gas expansion experiments. One I looked at recently is "Does
Indeterminism Give Rise to an Intrinsic Time Arrow?," Dolev, Elitzur,
Hemmo. quant-ph/0101088
The results are what I would have expected: if the positions and
velocities of the balls are known exactly, then a time-reversed "break"
certainly reverses the motions back to an initial configuration. If,
however, the positions and velocities are altered by even a small
epsilon, the reversal doesn't restore the initial configuration.
(Several related names for this: Feigenbaum's weather model results
which partly led to chaos theory, sensitive dependence on initial
conditions, and the important difference between numbers with finite
base expansions and the "reals." On this last point, even in the balls
were round to one part in 10^25, and their positions and velocities
known to the same precision, the "differences" that are 26 or 35 or 50
decimal places out will eventually "come marching in" and give big
changes in the first few decimal places, which will utterly "change" the
table configuration. Time reversal may not work with the "reals.")
((Ultra-speculative, hand-waving intuition: Strong links between this
notion and two other areas: Smale's observation that many things would
be computable instead of incomputable if computers used real numbers
(somehow!). And the issue that if points are replaced by open sets (or
neighborhoods), mathematics changes in interesting ways. I surmise these
are duals to each other,))
Needless to add, but I should anyway: given the Uncertainty Principle,
if in fact it really is part of the Universe and is not an artifact of a
determistic "absolute precision" model, then h throws a monkeywrench
into any kind of "run the billiard table backwards" model.
In large systems with objects whose positions and velocities are only
determined to finite precision, reversibility is impossible even in
principle. Running the reversal many times would lead to many past
configurations.
Price's "block universe" is not compelling to me, except in very simple
universes/systems looked at for periods where the differences don't show
up. (I see some role for "epsilon-delta" proofs here, which ties in with
the posets and latttices of the Markopoulou/Smolin/Isham views.)
This makes me intensely skeptical of the idea that if the universe were
to start contracting back to a Big Crunch that organisms would begin to
age backwards at some point, that billiard tables would return to the
initial triangle, and so on.
--Tim May
(.sig for Everything list background)
Corralitos, CA. Born in 1951. Retired from Intel in 1986.
Current main interest: category and topos theory, math, quantum reality,
cosmology.
Background: physics, Intel, crypto, Cypherpunks
Received on Fri Jul 19 2002 - 11:21:43 PDT
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