"A good poem has a unified structure, each word fits perfectly,
there is nothing arbitrary about it, metaphors hold together and interlock, the
sound of a word and its reflections of meaning complement each other. Likewise
postmodern physics asks: How well does everything fit together in a theory? How
inevitable are its arguments? Are the assumptions well founded or somewhat
arbitrary? Is its overall mathematical form particularly elegant?"
"A model is a simplified picture of physical reality; one in which, for example, certain contingencies such as friction, air resistance, and so on have been neglected. This model reproduces within itself some essential feature of the universe. While everyday events in nature are highly contingent and depend upon all sorts of external perturbations and contexts, the idealized model aims to produce the essence of phenomena." (F David Peat, "From Certainty to Uncertainty", 2002)
"A system at a bifurcation point, when pushed slightly, may
begin to oscillate. Or the system may flutter around for a time and then revert
to its normal, stable behavior. Or, alternatively it may move into chaos.
Knowing a system within one range of circumstances may offer no clue as to how
it will react in others. Nonlinear systems always hold surprises."
"A theory makes certain predictions and allows calculations
to be made that can be tested directly through experiments and observations.
But a theory such as superstrings talks about quantum objects that exist in a
multidimensional space and at incredibly short distances. Other grand unified
theories would require energies close to those experienced during the creation
of the universe to test their predictions."
"Although the detailed moment-to-moment behavior of a chaotic
system cannot be predicted, the overall pattern of its 'random' fluctuations
may be similar from scale to scale. Likewise, while the fine details of a
chaotic system cannot be predicted one can know a little bit about the range of
its 'random' fluctuation."
"An algorithm is a simple rule, or elementary task, that is repeated over and over again. In this way algorithms can produce structures of astounding complexity." (F David Peat, "From Certainty to Uncertainty", 2002)
"Chaos itself is one form of a wide range of behavior that
extends from simple regular order to systems of incredible complexity. And just
as a smoothly operating machine can become chaotic when pushed too hard (chaos
out of order), it also turns out that chaotic systems can give birth to
regular, ordered behavior (order out of chaos). […] Chaos and chance don’t mean
the absence of law and order, but rather the presence of order so complex that
it lies beyond our abilities to grasp and describe it."
"Chaos theory explains the ways in which natural and social
systems organize themselves into stable entities that have the ability to
resist small disturbances and perturbations. It also shows that when you push
such a system too far it becomes balanced on a metaphoric knife-edge. Step back
and it remains stable; give it the slightest nudge and it will move into a
radically new form of behavior such as chaos."
"Giving people new mental tools to represent aspects of the
world around them meant that they could now externalize and objectify that
world. Proceeding in this way they could treat the world as external to
themselves and as something to be contemplated within the imagination. The
world now became an object to be manipulated within the theater of the mind,
rather than an external tangible reality. This also meant that people could
gain increasing control over the world around them, yet always at the expense
of a loss of direct involvement. The more we objectify the world, the more we
are in danger of losing touch with that sense of immediacy felt by active participants
in nature."
"In a linear system a tiny push produces a small effect, so
that cause and effect are always proportional to each other. If one plotted on
a graph the cause against the effect, the result would be a straight line. In
nonlinear systems, however, a small push may produce a small effect, a slightly
larger push produces a proportionately larger effect, but increase that push by
a hair’s breadth and suddenly the system does something radically different."
"In chaos theory this 'butterfly effect' highlights the extreme
sensitivity of nonlinear systems at their bifurcation points. There the
slightest perturbation can push them into chaos, or into some quite different
form of ordered behavior. Because we can never have total information or work
to an infinite number of decimal places, there will always be a tiny level of
uncertainty that can magnify to the point where it begins to dominate the
system. It is for this reason that chaos theory reminds us that uncertainty can
always subvert our attempts to encompass the cosmos with our schemes and
mathematical reasoning."
"In essence, mathematicians wanted to prove two things: 1.Mathematics is consistent: Mathematics contains no internal contradictions. There are no slips of reason or ambiguities. No matter from what direction we approach the edifice of mathematics, it will always display the same rigor and truth. 2.Mathematics is complete: No mathematical truths are left hanging. Nothing needs adding to the system. Mathematicians can prove every theorem with total rigor so that nothing is excluded from the overall system." (F David Peat, "From Certainty to Uncertainty", 2002)
"It is not so much that particular languages evolve and then
cause us to see the world in a given way, but that language and worldview develop
side by side to the point where language becomes so ingrained that it
constantly supports a specific way of seeing and structuring the world. In the
end it becomes difficult to see the world in any other light."
"Lessons from chaos theory show that energy is always needed
for reorganization. And for a new order to appear an organization must be willing
to allow a measure of chaos to occur; chaos being that which no one can totally
control. It means entering a zone where no one can predict the final outcome or
be truly confident as to what will happen."
"Mathematical fractals are generated by repeating the same
simple steps at ever decreasing scales. In this way an apparently complex
shape, containing endless detail, can be generated by the repeated application
of a simple algorithm. In turn these fractals mimic some of the complex forms
found in nature. After all, many organisms and colonies also grow though the
repetition of elementary processes such as, for example, branching and
division."
"Quantum chance is absolute. […] Quantum chance is not a
measure of ignorance but an inherent property. […] Chance in quantum theory is
absolute and irreducible."
"Science is like photographing a series of close-ups with
your back to the sun. No matter which way you move, your shadow always falls across
the scene you photograph. No matter what you do, you can never efface yourself
from the photographed scene."
"Science is that story our society tells itself about the
cosmos. Science supposedly provides an objective account of the material world
based upon measurement and quantification so that structure, process, movement,
and transformation can be described mathematically in terms of fundamental
laws."
"Science proceeds by abstracting what is essential from the accidental details of matter and process. […] Science begins with our relationship to nature. The facts it discovers about the universe are answers to human questions and involve human-designed experiments." (F David Peat, "From Certainty to Uncertainty", 2002)
"The danger arises when a culture takes its own story as the
absolute truth, and seeks to impose this truth on others as the yardstick of
all knowledge and belief."
"The quantum world is in a constant process of change and transformation. On the face of it, all possible processes and transformations could take place, but nature’s symmetry principles place limits on arbitrary transformation. Only those processes that do not violate certain very fundamental symmetry principles are allowed in the natural world."
"The theories of science are all about idealized models and, in turn, these models give pictures of reality. […] But when we speak of the quantum world we find we are employing concepts that simply do not fit. When we discuss our models of reality we are continually importing ideas that are inappropriate and have no real meaning in the quantum domain." (F David Peat, "From Certainty to Uncertainty", 2002)
"There are endless examples of elaborate structures and apparently complex processes being generated through simple repetitive rules, all of which can be easily simulated on a computer. It is therefore tempting to believe that, because many complex patterns can be generated out of a simple algorithmic rule, all complexity is created in this way." (F David Peat, "From Certainty to Uncertainty", 2002)
"To make a quantum observation or to register a measurement
in any way, at least one quantum of energy must be exchanged between apparatus
and quantum object. But because a quantum is indivisible, it cannot be split or
divided. At the moment of observation we cannot know if that quantum came from
the measuring apparatus or from the quantum object."
"Quantum theory forces us to see the limits of our abilities
to make images, to create metaphors, and push language to its ends. As we
struggle to gaze into the limits of nature we dimly begin to discern something
hidden in the dark shadows. That something consists of ourselves, our minds,
our language, our intellect, and our imagination, all of which have been stretched
to their limits."
"Quantum theory introduced uncertainty into physics; not an
uncertainty that arises out of mere ignorance but a fundamental uncertainty
about the very universe itself. Uncertainty is the price we pay for becoming
participators in the universe. Ultimate knowledge may only be possible for
ethereal beings who lie outside the universe and observe it from their ivory
towers."
"Where we find certainty and truth in mathematics we also
find beauty. Great mathematics is characterized by its aesthetics. Mathematicians
delight in the elegance, economy of means, and logical inevitability of proof.
It is as if the great mathematical truths can be no other way. This light of
logic is also reflected back to us in the underlying structures of the physical
world through the mathematics of theoretical physics."
"[…] while chaos theory deals in regions of randomness and chance,
its equations are entirely deterministic. Plug in the relevant numbers and out
comes the answer. In principle at least, dealing with a chaotic system is no
different from predicting the fall of an apple or sending a rocket to the moon.
In each case deterministic laws govern the system. This is where the chance of
chaos differs from the chance that is inherent in quantum theory."
"While chaos theory is, in the last analysis, no more than a
metaphor for human society, it can be a valuable metaphor. It makes us
sensitive to the types of organizations we create and the way we deal with the
situations that surround us."
"Quantum theory stresses the irreducible link between observer and observed and the basic holism of all phenomena. Indigenous science also holds that there is no separation between the individual and society, between matter and spirit, between each one of us and the whole of nature." (F David Peat, "The Blackfoot Physics", 2006)
"Art and music make manifest, by bringing into conscious awareness, that which has previously been felt only tentatively and internally. Art, in its widest sense, is a form of play that lies at the origin of all making, of language, and of the mind's awareness of its place within the world. Art, in all its forms, makes manifest the spiritual dimension of the cosmos, and expresses our relationship to the natural world. This may have been the cause of that natural light which first illuminated the preconscious minds of early hominids." (F David Peat, "Pathways of Chance", 2007)
No comments:
Post a Comment