Dear George,
I am referring to classical systems where the initial conditions can be
known exactly, in principle. The sensitivity to initial conditions means
what you are saying, viz., a positive Lyapunov exponent.
>> I use deterministic chaos as an example where to us things appear to be
>> governed by randomness whereas they are really not chance events at all.
>
>This is true for classical dynamics of few particles but as you agree,
untrue for
>quantum. Yet, even in complex classical systems, genuine randomness - and hence
>indeterminism - may occur due to the shear complexity of interactions, but the
>quantum argument is more robust.
>
>> I do realize that quantum mechanics does introduce probabilistic concepts as
>> an inherent feature of nature. But can't we understand the origin of
>> Planck's constant as resulting from God's hands partially shaking when
>> creating the universe. [The former is partly on a humorous context but not
>> quite so either.]
>
>How much of the former is serious? I am not being flippant, for by it you
seam to
>be saying that God HAS created the universe with some inherent randomness
(shaking
>of the hand = initial condition uncertainty?) which agrees with our present
>understanding of nature and the way I reconcile these notions.
Serious to the extent that what appears to us understandable in
probabilistic terms is known to God in a purely deterministic fashion. This
is a mystery which cannot be humanly fathomed.
>> Quantum theory is not the final theory and so the
>> underlying laws of Nature must somehow be consistent with the omniscience of
>> God.
>
>While quantum theory MAY not be the finial theory, it is practically so -
assuming
>one's definition of scientific knowledge is limited to what can be measured.
Even Dirac indicated that quantum mechanics was not final--his gut feeling,
I suppose.
>I do not view chance as being inconsistent with God's omniscience since even if
>there is an infinite dimension to nature's fluctuations and hence
possibilities,
>God's knowledge and control are not threatened since even our mathematics
implies
>different levels of infinity! Furthermore, God's sovereignty in not
impinged upon
>since to role a 7 on a six sided die numbered 1 - 6 is impossible; this is
one way
>of interpreting what the verse "...God determines the outcome" means.
>
>Sincerely
>George
I think there may be chance at our level, but certainly not at God's level.
Surely God is not burdened by the throw of dice.
Take care,
Moorad