... asymptotically deterministic.
Yet Hoefer's paper, linked to from Pigliucci's blog, explicitly claims we don't even know if the question of whether or not the universe is deterministic is decidable, yet Rosenberg is claiming that he knows it is asymtotically deterministic at the macro level. And, we are not just talking about quantum events with no large effects in the macro world, it may be impossible to determine whether chaotic system are deterministic or stochastic:
The usual idealizing assumptions are made: no friction, perfectly elastic collisions, no outside influences. The ball's trajectory is determined by its initial position and direction of motion. If we imagine a slightly different initial direction, the trajectory will at first be only slightly different. And collisions with the straight walls will not tend to increase very rapidly the difference between trajectories. But collisions with the convex object will have the effect of amplifying the differences. After several collisions with the convex body or bodies, trajectories that started out very close to one another will have become wildly differentSDIC (sensitive dependence on initial conditions - Jim).
In the example of the billiard table, we know that we are starting out with a Newtonian deterministic systemthat is how the idealized example is defined. But chaotic dynamical systems come in a great variety of types: discrete and continuous, 2-dimensional, 3-dimensional and higher, particle-based and fluid-flow-based, and so on. Mathematically, we may suppose all of these systems share SDIC. But generally they will also display properties such as unpredictability, non-computability, Kolmogorov-random behavior, and so onat least when looked at in the right way, or at the right level of detail. This leads to the following epistemic difficulty: if, in nature, we find a type of system that displays some or all of these latter properties, how can we decide which of the following two hypotheses is true?
1. The system is governed by genuinely stochastic, indeterministic laws (or by no laws at all), i.e., its apparent randomness is in fact real randomness.
2. The system is governed by underlying deterministic laws, but is chaotic.
In other words, once one appreciates the varieties of chaotic dynamical systems that exist, mathematically speaking, it starts to look difficultmaybe impossiblefor us to ever decide whether apparently random behavior in nature arises from genuine stochasticity, or rather from deterministic chaos. Patrick Suppes (1993, 1996) argues, on the basis of theorems proven by Ornstein (1974 and later) that There are processes which can equally well be analyzed as deterministic systems of classical mechanics or as indeterministic semi-Markov processes, no matter how many observations are made. And he concludes that Deterministic metaphysicians can comfortably hold to their view knowing they cannot be empirically refuted, but so can indeterministic ones as well. (Suppes (1993), p. 254)
I don't see how Rosenberg can be on board with this and then claim that nature is asymtotically deterministic.
And, research indicates that animal brains have built-in chaotic subsystems - i.e we can't know whether they are deterministic or not. For instance, this excerpt from Towards a scientific concept of free will as a biological trait: spontaneous actions and decision-making in invertebrates - ( http://rspb.royalsocietypublishing.org/content/early/2010/12/14/rspb.2010.2325.full| ):
A corresponding conclusion can be drawn from two earlier studies, which independently found that the temporal structure of the variability in spontaneous turning manoeuvres both in tethered and in free-flying fruitflies could not be explained by random system noise [63,64]. Instead, a nonlinear signature was found, suggesting that fly brains operate at criticality, meaning that they are mathematically unstable, which, in turn, implies an evolved mechanism rendering brains highly susceptible to the smallest differences in initial conditions (i.e. SDIC - Jim) and amplifying them exponentially . Put differently, fly brains have evolved to generate unpredictable turning manoeuvres. The default state also of flies is to behave variably. Ongoing studies are trying to localize the brain circuits giving rise to this nonlinear signature.
Results from studies in walking flies indicate that at least some component of variability in walking activity is under the control of a circuit in the so-called ellipsoid body, deep in the central brain . The authors tested the temporal structure in spontaneous bouts of activity in flies walking back and forth individually in small tubes and found that the power law in their data disappeared if a subset of neurons in the ellipsoid body was experimentally silenced. Analogous experiments have recently been taken up independently by another group and the results are currently being evaluated . The neurons of the ellipsoid body of the fly also exhibit spontaneous activity in live imaging experiments , suggesting a default-mode network also might exist in insects.
Even what is often presented to students as the simplest behaviour, the spinal stretch reflex in vertebrates, contains adaptive variability. Via the cortico-spinal tract, the motor cortex injects variability into this reflex arc, making it variable enough for operant self-learning . Jonathan Wolpaw and colleagues can train mice, rats, monkeys and humans to produce reflex magnitudes either larger or smaller than a previously determined baseline precisely because much of the deviations from this baseline are not noise but variability deliberately injected into the reflex. Thus, while invertebrates lead the way in the biological study of behavioural variability, the principles discovered there can be found in vertebrates as well.
One of the common observations of behavioural variability in all animals seems to be that it is not entirely random, yet unpredictable. The principle thought to underlie this observation is nonlinearity. Nonlinear systems are characterized by sensitive dependence on initial conditions. This means such systems can amplify tiny disturbances such that the states of two initially almost identical nonlinear systems can diverge exponentially from each other. Because of this nonlinearity, it does not matter (and it is currently unknown) whether the tiny disturbances are objectively random as in quantum randomness or whether they can be attributed to system, or thermal noise. What can be said is that principled, quantum randomness is always some part of the phenomenon, whether it is necessary or not, simply because quantum fluctuations do occur. Other than that it must be a non-zero contribution, there is currently insufficient data to quantify the contribution of such quantum randomness. In effect, such nonlinearity may be imagined as an amplification system in the brain that can either increase or decrease the variability in behaviour by exploiting small, random fluctuations as a source for generating large-scale variability. A general account of such amplification effects had already been formulated as early as in the 1930s . Interestingly, a neuronal amplification process was recently observed directly in the barrel cortex of rodents, opening up the intriguing perspective of a physiological mechanism dedicated to generating neural (and by consequence behavioural) variability .