There is so much work to do here~
Miracles! Let's take a closer look at the religious
concepts of miracles and see if they make scientific
sense. I will attempt to place the concept of miracles
in purely mathematical form beyond dispute.
Quoted text are all the Catholic Encyclopedia, circa 1908...
"The wonder of the miracle is due to the fact that
its cause is hidden, and an effect is expected other
than what actually takes place. Hence, by comparison
with the ordinary course of things, the miracle is
called extraordinary. In analyzing the difference
between the extraordinary character of the miracle
and the ordinary course of nature, the Fathers of
the Church and theologians employ the terms
....above, contrary to, and outside nature."
"These terms express the manner in which the miracle
is extraordinary."
Miracles:
Above, outside and contrary to nature.
1) Above nature
"A miracle is said to be above nature when the effect
produced is above the native powers and forces in
creatures of which the known laws of nature are
the expression, as raising a dead man to life."
a) Resurrection:
Characteristics of the risen body
"All shall rise from the dead in their own, in their
entire, and in immortal bodies; but the good shall rise
to the resurrection of life, the wicked to the resurrection
of Judgment.
"But there is a difference between the earthly and the
risen body; for the risen bodies of both saints and
sinners shall be invested with immortality.
In conclusion resurrection is the essence of the soul
living on for eternity such as how Newton, Plato or
Christ 'live on' and have tangible effects in
perpetuity.
Or, a disturbance to a system that never settles down
such as spring that continues bouncing an extraordinary
amount of time. Or an idea so interesting that once
created continues to effect humanity throughout history.
The mathematical representation of this effect takes
the form of...a transient of nearly infinite length.
Self-Organized Pattern Formation in a
Swarm System as a Transient Phenomenon
of Nonlinear Dynamics
6 Summary and Outlook
In this paper, a self-organized system was reported
that generates a variety of complex patterns.
At least for small system sizes these patterns
are transient. A lower bound of the transient time
was shown that suggests an exponential increase
in the average transient time with increasing
system size.
http://heikohamann.de/pub/hamannMCMDS11a.pdf
2) Outside nature
"A miracle is said to be outside, or beside, nature
when natural forces may have the power to produce
the effect, at least in part, but could not of
themselves alone have produced it in the way it
was actually brought about. Thus the effect in
abundance far exceeds the power of natural forces,
or it takes place instantaneously without the
means or processes which nature employs."
Butterfly effect
From Wikipedia,
The butterfly effect is the concept that small causes can
have large effects.
In chaos theory, the butterfly effect is the sensitive
dependence on initial conditions in which a small change
in one state of a deterministic nonlinear system can result
in large differences in a later state. The name, coined
by Edward Lorenz for the effect which had been known
long before, is derived from the metaphorical example
of the details of a hurricane (exact time of formation,
exact path taken) being influenced by minor perturbations
such as the flapping of the wings of a distant butterfly
several weeks earlier.
https://en.wikipedia.org/wiki/Butterfly_effect
3) Contrary to nature
"Again, the term contrary to nature does not mean "unnatural"
in the sense of producing discord and confusion. The forces
of nature differ in power and are in constant interaction.
This produces interferences and counteractions of forces.
This is true of mechanical, chemical, and biological forces.
So, also, at every moment of the day I interfere with and
counteract natural forces about me. I study the properties
of natural forces with a view to obtain conscious control
by intelligent counteractions of one force against another.
Intelligent counteraction marks progress in chemistry,
in physics — e.g., steam locomotion, aviation — and in
the prescriptions of the physician. Man controls nature,
nay, can live only by the counteraction of natural forces.
Though all this goes on around us, we never speak of
natural forces violated. These forces are still working
after their kind, and no force is destroyed, nor is any
law broken, nor does confusion result."
"The introduction of human will may bring about a
displacement of the physical forces, but no
infraction of physical processes."
Emergence
Strong emergence describes the direct causal action of a
high-level system upon its components; qualities produced
this way are irreducible to the system's constituent parts
(Laughlin 2005). The whole is other than the sum
of its parts. An example from physics of such emergence
is water, being seemingly unpredictable even after an
exhaustive study of the properties of its constituent
atoms of hydrogen and oxygen.[9] It follows then
that no simulation of the system can exist, for such
a simulation would itself constitute a reduction
of the system to its constituent parts (Bedau 1997).
Non-living, physical systems
In physics, emergence is used to describe a property,
law, or phenomenon which occurs at macroscopic scales
(in space or time) but not at microscopic scales,
despite the fact that a macroscopic system can be
viewed as a very large ensemble of microscopic
systems.
https://en.wikipedia.org/wiki/Emergence
Jonathan
God made no act without a cause,
Nor heart without an aim,
Our inference is premature,
Our premises to blame.
Catholic Encyclopedia
Miracle
http://www.newadvent.org/cathen/10338a.htm
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