> "Smigrodzki, Rafal" :
> 1) Let's assume that the whole of reality is a mathematical construct - a
> self-evolving formal system, not constrained by the laws of physics (such as
> conservation laws), whose infinitesimally small subset is our observable
> physical world, with it's laws ultimately derived from a set of axioms and
> rules of production. No entity external to the totality of this system
> exists, hence it is not a simulation, but rather an explosion of pure
> mathematics, arising spontaneously and unavoidably from a true and absolute
> nothingness, in all the unimaginable ways pure math could develop, with new
> extensions of the axiom set adding themselves whenever undecidable
> theorems arise.
Good point. Let me do some ... bricolage.....
First. A self-evolving system seems to require a "loop" and
not a "tower of turtles, ad infinitum".
J.A. Wheeler, in example, wrote: "To endlessness no
alternative is evident but a loop, such as: physics
gives rise to observer-participancy; observer-participancy
gives rise to information; and information gives rise to
physics" ["Information, Physics, Quantum: The Search
for Links", in Complexity, Entropy and the Physics of
Information, ed. W.H. Zurek, Perseus Books, 1991].
Christof Schmidhuber also shares this kind of approach,
and pushes it to extremes.
Kauffman wonders if "Category Theory", or "Topos Theory",
with the elements recursively constructing themselves,
might be a suitable mathematical basis for these kinds of
systems. Self-evolving things are constantly generating new
kinds of members, with a generative, non-convergent, open-ended,
forever growing recursion. Recursions? And simulations?
Roger Penrose ["The Emperor's New Mind", 1989, paperback ed. pp
435-447] has calculated that, in order to produce a universe, like the
one in which we live, would require selection of a volume equal to
10^(-10^23) of the volume of the phase space of all possible universes.
Although that is a nonrigorous discussion of the probability that the
Weyl tensor = 0 (required for low-entropy recollapsing universes) this
number is a teeny tiny itsy bitsy little number. This calculation suggests
that it is virtually impossible that a universe that exhibits the entropy
and the order present in our universe could be created at random.
Created at random? "In the beginning was the Word" [John, I, 1, 3].
But Augustine - attention - replied "God made heaven and earth
in the beginning, not in the beginning of time, but in Christ. For he
was the Word with the Father, through whom and in whom all things
were made." [Augustine, "On Genesis", Catholic Univ. of America Press,
Washington, D.C., 1991]. Was St. Augustine saying that Christ was a
simulation? Who knows...
Hawking [A brief History of Time, pages 136-141] wrote "There would
be no singularities at which the laws of science broke down and no
edge of space-time at which one would have to appeal to God or some
new law to set the boundary conditions for space-time ..... The Universe
would be completely self-contained and not affected by anything outside
itself. It would neither be created nor destroyed. It would just be."
Too late! Aristotle already said "the world as a whole was not generated
and cannot be destroyed." [De Caelo, II, 1, 283b-27]. And much more
in "The Physics", VIII, 1, 250-252.
Gottfried Wilhelm Leibniz [The Monadology, 64-66] wrote:
But the machines of nature, namely, living bodies, are still machines
in their smallest parts ad infinitum. It is this that constitutes the
difference between nature and art, that is to say, between the divine
art and ours. And the Author of nature has been able to employ this divine
and infinitely wonderful power of art, because each portion of matter is not
only infinitely divisible, as the ancients observed, but is also actually subdivided
without end, each part into further parts, of which each has some motion of
its own; otherwise it would be impossible for each portion of matter to express
the whole universe. Whence it appears that in the smallest particle of matter
there is a world of creatures, living beings, animals, entelechies, souls.
Each portion of matter may be conceived as like a garden full of plants
and like a pond full of fishes. But each branch of every plant, each member
of every animal, each drop of its liquid parts is also some such garden or pond.
And though the earth and the air which are between the plants of the garden,
or the water which is between the fish of the pond, be neither plant nor fish;
yet they also contain plants and fishes, but mostly so minute as to be
imperceptible to us.
And Ockam (with Pier Damiani - De Divina Omnipotentia - and
Aristotle) states that not even God, who is in possession of
"potentia absoluta" - it means: miracles - not just of "potentia
ordinata" - usual physical laws, could erase the past, or re-write it.
Does it mean that, according to Ockam, simulations are forbidden?
But Ockam (as the Aquinas and also Wyclif) generously thinks
that God could create the multiverse, or many universes.
At last, Leibniz also wrote: "although the whole of this life were
said to be nothing but a dream and the physical world nothing but a
phantasm, I should call this dream or phantasm real enough if, using
reason well, we were never deceived by it.".
And that's all, for tonight.
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