How we think about probability

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Arjuna
 
Reply Sat 22 Aug, 2009 12:17 pm
@Aedes,
Aedes;84943 wrote:
Prothero -- how would you answer these questions?


I'm interested also. Here's some verbage from Wikipedia:

"In probability theory, a stochastic process, or sometimes random process, is the counterpart to a deterministic process (or deterministic system). Instead of dealing with only one possible "reality" of how the process might evolve under time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths are more probable and others less."

One take on this is that we use probability theory to look at a deterministic system as if the outcome is random... so that we can mark out a child distribution to extrapolate from.

Another take is this: anybody who uses the idea of a random process is imagining that a "starting point"...a known state.. deterministically gives rise to more than one possibility. Maybe some possibilities are more probable than others... this is the effect of determinism (the constant conditions of nature), but it doesn't matter. We can't rationally account for the emergence of one possibility over another. This is what it means for it to be a stochastic process.

This is roughly the system I was talking about... I just never noticed before that it's not contradicting determinism... it just limits determinism to the production of the possibilites... not the final outcome. Although there might be variations on the theme.
 
prothero
 
Reply Sat 22 Aug, 2009 04:10 pm
@Arjuna,
First a disclaimer, I do not pretend to have any particular expertise in any of these areas.

Second when one does read the summary analysis of experts there is no uniform consensus about the correct metaphysical or philosophical interpretation of current knowledge and experimental results.

Third, my particular viewpoint is strongly influenced (as we all are) by a broader worldview about the ultimate nature of reality. I believe strongly in free will, moral responsibility and mental agency. I have a very process view of reality so that reality consists of events (quanta, droplets or moments of experience) not of continuous uninterrupted being. The universe (reality) is becoming not being.

The question of determinism versus indeterminism has profound implications for the consideration of free will, moral responsibility, theological questions and ultimate questions of meaning (does the universe have a purpose?). Your answer to this question is among the most significant of any philosophical speculation or metaphysical assumption you might make about the ultimate nature of reality.

Having said this:
Laplace Determinism (Laplace's demon) From Wikipedia:"
We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

This intellect is often referred to as Laplace's demon. Note, however, that the description of the hypothetical intellect described above by Laplace as a demon does not come from Laplace, but from later biographers: Laplace saw himself as a scientist; and while hoping that humanity would progress to a better scientific understanding of the world, he recognized that, if and when such an understanding were eventually completed, a tremendous calculating power would still be needed to compute it all in a single instant. While Laplace saw foremost practical problems for mankind to reach this ultimate stage of knowledge and computation, later interpretations of quantum mechanics, which were adopted by philosophers defending the existence of free will, also leave the theoretical possibility of such an "intellect" contested." End of Wikipedia quote

I clearly think this is not only impossible in practical terms but also not possible in ontologic terms. The universe is not deterministic in this sense. Although nature has high degrees of order and predictability, Laplace type determinism is inherently not possible.

Scientific Determinism- I would define scientific determinism as that degree of order and predictability achievable by current levels of scientific knowledge and understanding. It is clear that we have great ability to control and predict certain kinds of events. There are many other events which remain unpredictable (human behavior, historical happenings, stock markets, quantum events, outcomes of specific events in games of chance etc.). There are those who assert that scientific determinism ultimately will be identical with Laplace type determinism but that is a strong metaphysical assumption or philosophical speculation.

Stochastic process- For a stochastic process a pattern of predictability occurs over many events (usually a probabilistic or statistical distribution) but the outcome of any single event while confined to a certain range of values or outcomes is not predictable. Thus, stochastic process is ordered and predictable but individual events remain unpredictable. Consideration of stochastic processes introduces problems respecting the definitions of chance, determinism, indeterminism, predictability and natural law. Nature and life are full of stochastic processes starting with quantum mechanics and ending with stellar evolution.

Mathematical randomnessGodel and the End of Physics".

Chaos theory, fractal systems and strange attractors imply that non linear dynamic complex systems even when operating under deterministic rules give unpredictable results. Determinism does not entail predictability in chaotic systems. All chaotic systems are unpredictable in the long run. Chaotic systems are not reversible due to information loss as the system evolves. It is not possible to trace a system backwards to its initial conditions. Chaotic systems can become autopoietic (self organizing), can evolve new features (emergence) and can adapt to their environment (evolve). All that is required is energy input into the system. One can consider the unpredictable nature of chaotic systems to be epistemological or ontological. Now chaotic systems and fractals are widespread in nature.

Quantum mechanics- particular events have a calculable probability of occurring, but the result of any particular event (or observation) is not predictable (or determined some might say). Many scientists feel quantum mechanics shows that the fundamental laws of nature are stochastic or statistical rather than deterministic.

Black body radiation did not follow the pattern predicted by Newtonian classical mechanics. The observed distributions of wavelengths and energies could be explained by Planks assumption that the energy could only be released in discrete packets or quanta.

The spectra of hydrogen and other elements does not follow the predicted pattern of classical mechanics. The actual spectra were predicted by Niels Bohrs assumption that only certain orbits or energy levels were permitted. Electrons can not occupy the space between orbits and electrons "change" orbits without passing through the "space" between them.

Matrix mechanics (Heisenberg and Born) and wave mechanics (DeBroglie and Schrodinger) are experimental equivalent (they predict the same observed results). The physical world can not be described in terms of variables that can change continuously in time only in discrete non continuous variables (despite our everyday notions and illusions to the contrary).

Schrodingers cat- was a thought experiment intended to make the point that indeterminacy at the quantum level can easily be transformed into indeterminancy at the level of everyday objects.

Quantum field theory (Dirac) an effort to develop a quantum theory of gravity and eventually a quantum theory of cosmology.

The observed phenomena of non locality and quantum entanglement and quantum pairing where two particles apparently interact or share information at speeds greater than light imply something profoundly wrong or incomplete about the general theory of relativity.

Thus there are profound problems with Newtonian classical mechanics and the mechanistic, deterministic and machine like views it inspired of nature and the world. There are likewise problems with general relativity and the continuously variable view of space and time which it inspires.

In my view, this brings into serious question the view that the world is deterministic (in the sense of Laplaces demon).

Since there is ultimately a choice of world views entailed here and neither view is contrary to reason, experience or science I choose the world view in which human freedom, moral responsibility, mental agency and certain conceptions of the divine remain.

The universe is highly ordered and highly predictable but not determined. In the words of Charles Hartshorne "The difference between a little freedom and no freedom: is all the difference in the world".

Much of this material is freely borrowed from the online Encyclopedia of Science and Religion which has several succinct and lucid explanations and articles.
 
Arjuna
 
Reply Sun 23 Aug, 2009 06:19 pm
@prothero,
prothero;85016 wrote:

Third, my particular viewpoint is strongly influenced (as we all are) by a broader worldview about the ultimate nature of reality. I believe strongly in free will, moral responsibility and mental agency. I have a very process view of reality so that reality consists of events (quanta, droplets or moments of experience) not of continuous uninterrupted being. The universe (reality) is becoming not being.


You say you strongly believe in free will... but is anyone really consistent in their view? Don't we all hop back and forth between free will and determinism in comprehending experience?

Or is it possible that people really do experience the world differently?

I was once shocked to discover there is such a thing as a sense of time. A met someone who routinely felt the passage of time in 30 minute increments by referring back to the length of an 'I Love Lucy' episode.

I wouldn't have believed it if I hadn't seen his accuracy first hand.

I'm dependent on clocks because most of the time I wouldn't be able to distinguish ten minutes from an hour. So I started trying to develop the skill of feeling time. I was surprised at the outcome. I discovered that I have a profound abhorrence of being able to feel the passage of time.

Someone could accuse me of being rigid by virtue of emotional bias. They might think I'm just stupid. Perhaps I just have a different way of being.

Are determinism and free will representative of different ways of being? Or is my assumption correct: we all use both modes of thinking whether we realize it or not? Is it possible that you can only be understood by someone who's just like you?
 
prothero
 
Reply Sun 23 Aug, 2009 07:50 pm
@Arjuna,
Arjuna;85213 wrote:
You say you strongly believe in free will... but is anyone really consistent in their view? Don't we all hop back and forth between free will and determinism in comprehending experience?

Or is it possible that people really do experience the world differently?

Is it possible that you can only be understood by someone who's just like you?


It depends on what you mean by "free will" and "determinism".

I postualted that the objective material world is highly ordered and highly predictable but not LaPlace type deterministic.

In a world without order and predictability free will would be a useless functionality and moral responsiblity would still be absent since the results of agency would be unpredictable and random (as they are in some respects and some cases).

Yes, people do view and in some respects experience the world quite differently. You can get some amusing and interesting examples from Olivers Sacks writings at least with respect to sensory experience.

In general your best discussions will be with people who differ from your views but not radically. Rationalists have a hard time with empiricists. Monists and idealists have a hard time with materialists. Theists have a hard time with atheists, etc. If your views are too radically different you wont be able to agree on such basic terms as "real", "exists" or "truth".
 
 

 
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