It might be helpful if you could clarify what you mean by natural and physical. Ex. some philosophers of mind argue that consciousness is not "reducible" to physical facts about the world, and is an emergent property of matter, in the same way wetness is an emergent property of atoms which in and of themselves are not individually wet. Not sure if that is the type of thing you're talking about...

Best,

Miles

Right magnetism is a natural system, that is based on a physical object called a magnet, but operates at a distance from that object despite the fact that there is no physical connection between the two magnets that inter-react. This is used for interesting things like radio to work. One doesn't worry about the physical antenna that was needed to create the radio waves, one just tunes ones radio to a specific station, and gets music. There are also those that will offer arguments that light is not, or at least not always a physical object. Most of the time when you have a natural system that is not Physical there is a wave force or field involved. But it depends on your definition of physical, doesn't it.

Everything that exist in nature is natural. We do not understand what is consciousness, they are debate about its nature but it is not supernatural. Reductionists beleives that everything in nature can be ultimately understood in terms of fundamental physics. Emergentists beleive that reality is stratified and that even chemistry which is one layer above fundamental physics cannot be reduced to fundamental physics. (see Polanyi)

The same with the economy, we do not understand it but it is a natural phenomenon. The debate is on the best approaches about understanding this natural phenomena.

The queries were interesting because they all arrive in a fundamental question: "What is our understanding of nature?" Empirical conclusions would attest that nature is found in physical things, while metaphysical arguments would go beyond what is physical. Even in "natural complexes" (as noted), one can have a metaphysical conclusion that is not necessarily "physical".

The word physical means to me something that exists, that is real. For example, the program in your computer is real but it is not made of atoms.

There are a lot of different emergentist positions see for example:

"Life’s Irreducible Structure,Live mechanisms and information in DNA are boundary conditions with a sequence of boundaries above them" by Michael Polanyi

"The principles of each level operate under the control of the next-higher level. The voice you produce is shaped into words by a vocabulary; a given vocabulary is shaped into sentences in accordance with a grammar; and the sentences are fitted into a style, which in turn is made to convey the ideas of the composition. Thus each level is subject to dual control: (i) control in accordance with the laws that apply to its elements in themselves, and (ii) control in accordance with the laws of the powers that control the comprehensive entity formed by these elements.

Such multiple control is made possible by the fact that the principles governing the isolated particulars of a lower level leave indeterminate conditions to be controlled by a higher principle. Voice production leaves largely open the combination of sounds into words, which is controlled by a vocabulary. Next, a vocabulary leaves largely open the combination of words to form sentences, which is controlled by grammar, and so on. Consequently, the operations of a higher level cannot be accounted for by the laws governing its particulars on the next-lower level. You cannot derive a vocabulary from phonetics; you cannot derive grammar from a vocabulary; a correct use of grammar does not account for good style; and a good style does not supply the content of a piece of prose.

Living beings comprise a whole sequence of levels forming such a hierarchy. Processes at the lowest level are caused by the forces of inanimate nature, and the higher levels control, throughout, the boundary conditions left open by the laws of inanimate nature. The lowest functions of life are those called vegetative. These vegetative functions, sustaining life at its lowest level, leave open - both in plants and in animals - the higher functions of growth and in animals also leave open the operations of muscular actions. Next, in turn, the principles governing muscular actions in animals leave open the integration of such actions to innate patterns of behavior; and, again, such patterns are open in their turn to be shaped by intelligence, while intelligence itself can be made to serve in man the still higher principles of a responsible choice."

Prigogine, Stuart Kauffman have more modern versions relative to life evolution.

All these scientists are trying to find new kind of physics.

All the fundamental principles onto which science is built are metaphysical principles. Einstein built general relativity on metaphysical principles that Ernst Mach and Leibniz had enunciated in opposition to Newton's metaphysics of absolute space. My first metaphysics principle is: the world=universe=nature is everything that exists.

Eisa is suggesting to God who is one, has no parents and no children and needs nothing as all is God's and is Singular i.e. unique, none is his partner or advisor is capable of taking all decision and Almighty. If a concept of God corresponds to this, it doe not matter with whatever beautiful name you call him or adore him.

By "Sciences of Creation" is meant the creation of the world that exists irrespective of our experience, perception or direct or instrumental observation. All sciences tend to understand this reality in their own ways, if there has not existed reality, surely there has been no science whatever it may be. Generally, science should lead to admiration of the Creator, but yhough scientists are not supposed to make ethical decisions except presenting thei findings, they now a days or again active to question the very existence of the Creator, In earlier stages of development of science in the Western world it was understable to some extent, but in the present day world it seems just misguiding people to go away from spirituality inbuilt in humans and urges to be expressed.

Wikipedia: In philosophy, naturalism is the "idea or belief that only natural (as opposed to supernatural or spiritual) laws and forces operate in the world.

Implicit in this definition of naturalism is the belief that nature can be conceptually penetrate or told, that the conceptual exaust what exist.  I hold that everything is natural but I do not assume that all that is natural can be modeled, understood conceptually.  In other words I hold that the natural do not reduced to what could in principle be understood.  There is no proof for this belief nor there is a proof for the opposite conceptual reduction belief.  I think that the reduction belief is the most ambitious and thus the one that has the burden of the proof.  

Is there a single example of a natural system, a natural entity for which we could consider that we totally scientifically (conceptually) understand it?  I do not think so.   Science or scientific knowledge is constantly advancing and this progress is most probably without end but the limit of such knowledge is the limit of the conformity of nature with order and law. All the order that exist in nature and which all of our science is only a tiny part have been created and stabilized at some point in the past of the universe and did not exist before.   There is no reason to believe that this process of creation of order is itself conceptually reducible.  All that we know, all of science is not intrinsic to nature but human creation and under constant revision and only valid up to a certain approximation.  So in absolute sense we know absolutely nothing certain or absolutly true but only know approximatly some aspect of nature.  And the more we know about nature and the more we realize that we know almost nothing about nature but more importantly is that conceptual knowning is only one mode of access which even at its limit is limited and do not penetrate the whole of what exist.  Before science, before philosophy itself or this idea of that the world is constructed in such a way that it can be totally told or conceptually expressed, before the totalitarian conceptual constuction project of the cosmos was formulated, the world was told in myths, in stories and was anthropomophically told.  Human being have a very special mammalian nervous system which anthropomorphize everything, that access other humans, other animals and plants and natural process and objects anthropomorphically.  Basically we have this in-built capacity to use perceptual information and from there created a controled hallucination of anthropomorphic narratives.  Any anthropomorphic narrative is constructed from the re-enactment of sensory-motor schemata of the mammalian nervous system.  This a a simulation mode of access to reality whose simulation primitive are the sensory-motor schemata of the mammalian nervous system, the mammalian reality engine.  Human language are rooted in the mammalian reality engine. Although a lot of the mammalian reality engine will eventually be conceptually understood and penetrate, what will not be conceptually reduced in it is the human creative nexus, the core growth nexus of the human interaction with the world. It is natural but not conceptual.  It is lived but not thinkable. 

Normally we define physical systems as things that impinge on our mental events or in other words things we can observe. Thus if there is purely mental or spiritual thing like a person called God who lives in a realm outside our spacetime or other spiritual beings by definition ( if they have any influence on our observed physical universe) such beings would be classed as physical. Even if we assume our world is a dream or illusion then the physics of the simulated world would be classed as physical as it would be the world we experience. The world we experience by definition is our physical world.

As to "natural" systems things that ae designed by a person are usually defined as not natural while things that evolve ("naturally") ae seen as natural.

Such natural systems can include "undirected" emergent observable relationships of agents involved in design processes.

E.g. many believe that super human systems such as cities and universes have their own nature or personality; and can be though of as if they were a person. Whether such systems have their own mental events is something that is perhaps impossible to verify, but we can say whether such systems act as if they did. I.e. act as if they have agency or personality.  

Sam,

I suggest that mathematics is 'natural'. And has no component that is physical.

Russell and Whitehead reformulated Einstein's dual-parameter space-time as a single-parameter web of causally primitive events. Conflating causal order with time order, they were reducing space-time to time alone. That forgotten "event ontology" was the only reduction in the fundamental parameters of physics since Newton's original reduction to space, time and mass. They leveraged the reduction to treat the mind-body problem in the remainder of their careers. Descartes' instantaneous extension-in-space is eliminated from physics in favor of the causal web, which accommodates human sentient events and their phenomenology among the other causally primitive events required by the scheme. Whitehead's discrete version, based on discrete time, is re-invented for physics today as causal set theory, without awareness of Whitehead's ontology. Not long ago I noticed that temporal succession makes frequency ratios, useful for defining energy ratios in accord with Planck's E=hf. (A directed graph of 3 arrows forming a triangle is the simplest to show frequency ratios.) The simple discovery, which continues to elude the physicists, allows for the construction of the common particles using directed graphs as quantum schematics, each arrow depicting a quantum. The mass-ratios of the particles to one another are derivable from their graphs. The immaterial events at the basis of physics are natural, even though both Russell and Whitehead based the epistemology of physics on human sentient events, which assume a natural place in the causal web of events. Whitehead generalized sentience to all the causally primitive events (his "occasions of experience") while Russell remained agnostic about the events that are not human moments of experience.