We are currently experiencing a paradigm shift in scientific thinking and explanation, away from reductionist and constructivist approaches. This shift is the result of the introduction of computers and the internet. Scientific researchers are now capable of collecting and processing much more information than ever before, and advanced modeling techniques allow them to develop and test scientific theories in ways that were simply not possible 20 or even 10 years ago. Traditionally, physics operated with a reductionist approach: it breaks down complex phenomena into simpler parts that can be studied independently. Once the basic laws were understood, scientists thought they can explain complex phenomena with simple rules. This approach works to some degree, but it is equivalent to the idea that the whole is the sum of its parts. The paradigm begins to break down in very complex systems where the elements interact with each other. Subsequently, an idea was formulated and applied first in the fields of chemistry and biology, that the sum of the parts is more, or different, from the elements or forces that constitute it. Chemists and biologists were asking if their science can eventually be reformulated in terms of the underlying laws of physics, or if their disciplines really are proprietary domains with chemical or biological laws that are irreducible to the underlying physical processes. Eventually, the question became a major debate among physicists: Do complex systems develop properties that are genuinely new, and not reducible to the properties of the underlying elements? If this is the case, then those newly emerging qualities of the system would be unexplainable by the lower-level laws that determine the behavior of the elements only. This feature has been called “emergence.” In an influential paper entitled “More is different”, published in 1972 in the journal “Science”, the physicist and Nobel Laureate Philip Anderson writes:
“The main fallacy [of] the reductionist hypothesis [is that it] does not by any means imply a “constructionist” one: The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. In fact, the more the elementary particle physicists tell us about the nature of the fundamental laws, the less relevance they seem to have to the very real problems of the rest of science, much less to those of society.
The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity. The behavior of large and complex aggregates of elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles. Instead, at each level of complexity entirely new properties appear, and the understanding of the new behaviors requires research which I think is as fundamental in its nature as any other…[and will show] how the whole becomes not only more than the sum of but very different from the sum of the parts…” 
The concept of emergence entails that the sum is more than its parts, and that there can be a downward causation, because new qualities can emerge in more complex systems that are simply not there if you look at the elements themselves. We have many examples where complex systems arise from the interaction of components, and where these components alone cannot explain the emergence of the new qualities found in the system as a whole. Psychology cannot simply be explained as applied biology, and biology, or life itself, cannot be explained as a chemical process only. Chemistry is more than physics, Biology is more than chemistry, human psychology is more than biology, and sociology and politics is more than psychology. We get the view of a dynamic universe, structured by spontaneously emerging self-organization. It is layered according to levels of complexity; each layer has its own structural laws and is organized and shaped by causality from below as well as from above.
I want to illustrate the concept of emergence with some simple examples. The fact that a sphere is round gives it certain properties which are independent from the material out of which the sphere is constructed. The properties of a crystal cannot be found in the individual molecules that are the crystal’s building blocks. The subatomic particles that form individual atoms have no color. Once they are united in an atom, the new system, the atom, can absorb light and therefore takes on a particular color. Take a violin, a calculator, or a computer: their materiality supports the function of these devices, but they can only play music, perform calculations, or become as versatile and programmable as a computer when the unit as a whole, in its totality, has been created. A string by itself cannot play anything; in order to play music, the whole instrument is required. The emergence of the internet demonstrates how a decentralized system can organize itself. The stock market is another example: a self-organizing system that is more than the sum of its components (individual companies and their share price). The market regulates whole economies through the automatism of an exchange and trading mechanism. In all cases, the emergent properties, once they exist, have their own logic, which are independent from the underlying systems, or from the material in which they emerge.
We can speculate whether the relationship of the mind to the brain represents an emergent quality. Individual brain-cells have no emotion, or memory, or self-consciousness. Consciousness arises through the interactions of billions of brain cells, and once it exists, there is a downward causation: the new structural level of consciousness begins to determine the behavior of the components, as the recently discovered brain functions that are summarized under the term “neuroplasticity” demonstrate. We now know that brain functions can be re-located to new areas of the brain in case of injuries. (Stroke victims learn how to speak again, re-learn motor skills, etc.) Learning a skill will create new synaptic connections, or even trigger the growth of new nerve cells. Consciousness exists within matter, but once it exists it is no longer determined by it. The physical brain is a necessary, but not a sufficient condition for consciousness. The human mind, once created, acts according to a logic of motivations, emotions, and thought processes that is no longer determined by physical processes. Rather, it acts by ordering the causal chains of physical systems – The human mind begins to function as a cause in the physical world.
 Anderson, P.W., “More Is Different” in Science, 4 Aug. 1972 Vol. 177 No. 4047