Instead what is needed is an entirely different approach so far used by only a few researchers that does not attempt to build models of coupled, non-linear
chaotic systems such as climate.
Cutting a hole in the pool table won't win favour at your local bar, but it can teach us more about
chaotic systems such as the climate or planetary motion
Not exact matches
Sources who have seen parts of it said the report chronicles an aggressive and fast - growing startup, resulting in a frequently
chaotic and «hostile work environment» without adequate
systems in place to ensure that violations
such as sexual harassment and retaliatory behavior were dealt with professionally.
For example, the idea that the brain is a complex non-linear dynamic
system is mentioned only fleetingly - leaving me with the feeling that we had missed an opportunity for a useful discussion (
such as perhaps making a connection with the ideas advocated by Polkinghorne regarding the possibility of
chaotic systems «amplifying» quantum level uncertainties up to the macro-level).
However, Moeness Amin, an electrical engineer at Villanova University, Pennsylvania, says
such applications would be difficult because the environment outside prisons is more
chaotic and could trip up the
system.
The weather conditions may appear highly consistent from day to day, but
such systems are still highly
chaotic.
Most theorists hold that
such ejections should be quite common during the
chaotic tumult of a planetary
system's early days, when closely - packed worlds whirling around a star can scatter off each other like billiard balls in a break shot.
A quick visit to dictionary.com explains it as
such: «a
chaotic effect caused by something seemingly insignificant, the phenomenon whereby a small change in a complex
system can have a large effect somewhere else».
As
such, my 5.1 speaker
system received a nice workout, especially during sequences involving the
chaotic streets of New York.
Also, I note that by common usage the term «abrupt» (w.r.t. SLR) implies that «mainstream» experts would be surprised to observe
such a response to AGW; nevertheless, the Earth's circulatory steams are inherently
chaotic, and chaos theory clearly demonstrates that
such systems can be subject to «strange attractors» that can increase the probability of occurrence of phenomenon towards the tail of a «fat - tailed» probability density function (PDF),
such as that shown in Figure 3.
When observing
such systems in general (social, economical, ecological...
systems), the usual behavior when perturbed is to react less than might be expected due to internal dampening until a compensatory capacity is breached, then flip into a pronounced
chaotic state and sooner or later attach to a different attractor, that means, stabilize again.
And
such a feat is likely to remain impossible for the foreseeable future, because a) the mathematics are
chaotic (in the technical sense, which I presume I don't need to explain), and b) the data we have, though already voluminous, is not even close quantitatively and qualitatively to the fantastic precision needed to specify the state of the planetary
system as definitively as that.
But since the climate is dependent on chaos - driven events,
such as: sunspots, solar flares, vulcanism, and the actions of humanity, it can also (I believe) be considered a
chaotic system.
Objection: Climate is an inherently
chaotic system, and as
such its behavior can not be predicted.
Such chaotic behaviour may limit the predictability of nonlinear dynamical
systems.»
«A dynamical
system such as the climate
system, governed by nonlinear deterministic equations (see Nonlinearity), may exhibit erratic or
chaotic behaviour in the sense that very small changes in the initial state of the
system in time lead to large and apparently unpredictable changes in its temporal evolution.
Whilst an attempt to apply chaos theory to climate may not yield anything useful in the short term, it seems to me to be by far the most likely course of inquiry to eventually make sense of the vast array of interactive elements within
such an apparently
chaotic system.
In principle small changes —
such as in trace atmospheric gases — can accumulate in
chaotic systems and precipitate wildly out of proportion to the initial impetus.
--
such a model would quickly depart from the unfolding climate found on Earth because
chaotic systems defy prediction.
In that sense it is improper to talk about «
chaotic systems» because there exists no
such thing.
Because it isn't given and anyone with even a passing understanding of
chaotic systems knows that
such a valiant claim is completely baseless unless backed up by thorough treatment of the
system as complex as it is.
Spence — my point about long - distance correlation
such as ENSO was not regarding
chaotic systems per se — obviously temporal chaos often involves spatially extended attractors, which is very likely a good description of ENSO.
By mathematical and physical necessity (Newton's «three - body problem»)
such systems are
chaotic / fractal, non-random but indeterminate, self - similar on every scale — subject to Edward Lorenz's celebrated «butterfly effect,» a «sensitive dependence on initial conditions» that renders all non-linear projections futile.
How and why would this planet's
chaotic climate
system have
such couplings.
In a
system as complex and
chaotic as climate,
such an action may even trigger unexpected consequences.
It's
such a
chaotic, uncertain
system and those models are all unreliable.
A deterministically
chaotic system subject to control variables —
such as CO2 — multiple positive and negative feedbacks and multiple equilibria.
I do not «believe» in cycles or other
such efforts to make sense of a
chaotic system.
You can easily find
such cycles in a variety of
chaotic systems, like say the stock market.
The idea is that in a
chaotic system, a small change like a butterfly flapping its wings in some distant part of the globe can influence a large - scale effect,
such as the formation and trajectory of a storm like the recent Hurricane Sandy.
Chaotic processes in the climate
system may allow the cause of
such an abrupt climate change to be undetectably small.»
(Part of the How to Talk to a Global Warming Skeptic guide) Objection: Climate is an inherently
chaotic system, and as
such its behavior can not be predicted.
The individual path of a realization in a
chaotic system can't be predicted, but one still can apply means of statistics to
such a
system.
The resulting situation is in most cases stable as long as external factors do not force a change, but attractors of a
chaotic system may give the impression of
such stability.
The non-linear fluctuation of climate in the vicinity of a
chaotic bifurcation is a Dragon King —
such as occurred in Earth
systems around 1910, the mid 1940's, the late 1970 ′ and 1998/2001 — and not a black swan.
My interests, more specifically, are related to: * The consequence of scaling behaviour in non-linear coupled
systems (both
chaotic and non-
chaotic) * The consequence of external forcings on
such systems * The limitations of numerical methods used to analyse these
systems, particularly with regard to initial conditions
phil said: «It is beyond any doubt that a large dissipative open
system with obvious
chaotic dynamics
such as the climate, is subject to internally driven nonlinear oscillations over a wide range of time scales.»
Indeed, in a
chaotic system (
such as weather / our atmosphere) one would expect there to be changes in clouds and their patterns.