[PhilPhys] Chaos Workshop

[HAPSAT Society]

                                       Wednesday, March 10, 2010, 9:00-15:00

                  Institute for the History and Philosophy of Science and
Technology

                                                 University of Toronto



Workshop Venue:



Victoria College, Private Dining Room (PDR)

89 Charles St. West

Toronto, Ontario M5S 1K7





*Program*



*Morning Coffee*



9:00-9:30



*Introduction*

* *

9:30-9:35

* *

*Session 1: Chair *



9:35 – 10:50



Joseph Berkovitz



IHPST, University of Toronto



*The Ergodic Hierarchy, Randomness and Chaos*



*Abstract. *Various processes are often classified as both deterministic and
random or chaotic. The main difficulty in analyzing the randomness of such
processes is the apparent tension between the notions of randomness and
determinism: what type of randomness could exist in a deterministic process?
Ergodic theory seems to offer a particularly promising theoretical tool for
tackling this problem by positing a hierarchy, the so-called ‘ergodic
hierarchy’ (EH), which is commonly assumed to provide a hierarchy of
increasing degrees of randomness. However, that notion of randomness
requires clarification. The mathematical definition of EH does not make
explicit appeal to randomness; nor does the usual way of presenting EH
involve a specification of the notion of randomness that is supposed to
underlie the hierarchy. In this paper, we argue that EH is best understood
as a hierarchy of random behaviour if randomness is explicated in terms of
unpredictability. We then show that, contrary to common wisdom, EH is useful
in characterizing the behavior of dynamical systems, randomness and chaos.





*Coffee Break*



10:50 - 11:05

* *

* *

*Session 2*



11:05 – 12:20



*Chaos, Determinism, and Observational Equivalence: Alpha-Congruence and Its
Implications *



Christopher Belanger



IHPST, University of Toronto



*Abstract.* In 1991 the mathematicians Ornstein and Weiss published a paper
outlining a type of mathematical relationship called alpha-congruence, which
they claimed was a mathematically well-defined notion of observational
equivalence.  This is particularly interesting because many classes of
deterministic systems, including chaotic systems, can be proven to be
alpha-congruent to indeterministic systems.  This challenges not only the
commonly held intuition that there is a clear and strong distinction between
deterministic and indeterministic descriptions, but also suggests a new
source of problems for explanation and prediction in chaotic systems.  Some
authors have gone so far as to claim that this shows that it is empirically
undecidable whether chaotic systems are in fact deterministic or
indeterministic, and thus they may not be truly predictable even in
principle!  However, despite such potentially important and far-reaching
conclusions, when philosophers have discussed the matter they have tended to
make uncritical use of the aforementioned assumption made by Ornstein and
Weiss: that alpha-congruence can indeed function as a stand-in for
observational indistinguishability.  In this talk I will argue that for two
systems to be alpha congruent is not the same as for them to be
observationally indistinguishable, and thus that many of the more sweeping
philosophical claims made based on this assumption are flawed and in need of
further support.





*Lunch*



12:20 - 13:00



**

* *

*Session 3*



13:00 – 14:30



*Decision-Making with Chaotic Models*



Roman Frigg



Department of Philosophy, Logic and Scientific Method

London School of Economics



*Abstract*. Climate models are widely used to make forecasts, which provide
the basis for far-reaching policy decisions. However, upon closer
examination it turns out that climate models do not actually warrant the
probabilistic forecasts that are commonly derived from them. They are
chaotic and have intrinsic imperfections, which undermines their capacity to
provide decision-relevant probabilities. Although the IPPC has recognized
this fact, no research in to other methods of prediction has been carried
out. It is the aim of an ongoing project to address this issue by first
investigating how and why exactly probabilistic predictions break down in
chaotic models, and then gesture at alternative methods to get around the
problem. The proposal is that probabilistic reasoning should be given up
altogether. Chaotic models should be used to calculate non-probabilistic
odds for certain events, and these should be used to guide decision-making.
We introduce both the problem and the proposal and illustrate them with a
simple example.





*Session 4*



14:30-15:00



General Discussion
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