"A complex system is a system formed out of many components
whose behavior is emergent, that is, the behavior of the system cannot be
simply inferred from the behavior of its components. The amount of information
necessary to describe the behavior of such a system is a measure of its
complexity."
"A dictionary definition of the word ‘complex’ is: ‘consisting of interconnected or interwoven parts’ […] Loosely speaking, the complexity of a system is the amount of information needed in order to describe it. The complexity depends on the level of detail required in the description. A more formal definition can be understood in a simple way. If we have a system that could have many possible states, but we would like to specify which state it is actually in, then the number of binary digits (bits) we need to specify this particular state is related to the number of states that are possible." (Yaneer Bar-Yamm, "Dynamics of Complexity", 1997)
"Many of the systems that surround us are complex. The goal of understanding their properties motivates much if not all of scientific inquiry. […] all scientific endeavor is based, to a greater or lesser degree, on the existence of universality, which manifests itself in diverse ways. In this context, the study of complex systems as a new endeavor strives to increase our ability to understand the universality that arises when systems are highly complex." (Yaneer Bar-Yamm, "Dynamics of Complexity", 1997)
"There are two approaches to organizing the properties of complex systems that will serve as the foundation of our discussions. The first of these is the relationship between elements, parts and the whole. Since there is only one property of the complex system that we know for sure - that it is complex - the primary question we can ask about this relationship is how the complexity of the whole is related to the complexity of the parts. […] The second approach to the study of complex systems begins from an understanding of the relationship of systems to their descriptions. The central issue is defining quantitatively what we mean by complexity." (Yaneer Bar-Yamm, "Dynamics of Complexity", 1997)
"Traditional geometry is the study of the properties of
spaces or objects that have integral dimensions. This can be generalized to
allow effective fractional dimensions of objects, called fractals, that are embedded
in an integral dimension space. […] Fractals are often defined as geometric objects
whose spatial structure is self-similar. This means that by magnifying one part
of the object, we find the same structure as of the original object. The object
is characteristically formed out of a collection of elements: points, line segments,
planar sections or volume elements. These elements exist in a space of the same
or higher dimension to the elements themselves."
"When we think about methodology, we must keep purpose in mind.
Our purpose in studying complex systems is to extract general principles.
General principles can take many forms. Most principles are articulated as
relationships between properties - when a system has the property x, then it
has the property y. When possible, relationships should be quantitative and
expressed as equations. In order to explore such relationships, we must
construct and study mathematical models. Asking why the property x is related
to the property y requires an understanding of alternatives. What else is
possible? As a bonus, when we are able
to generate systems with various properties, we may also be able to use them
for practical applications."
"Although complexity is very important for survival, scale also matters. In general, larger scale challenges should be met with larger scale responses. The rule of thumb is that the complexity of the organism has to match the complexity of the environment at all scales in order to increase the likelihood of survival." (Yaneer Bar-Yam, "Making Things Work: Solving Complex Problems in a Complex World", 2004)
"Complex problems are the problems that persist - the problems that bounce back and continue to haunt us. People often go through a series of stages in dealing with such problems - from believing they are beyond hope, to galvanizing collective efforts of many people and dollars to address the problem, to despair, retreat, and rationalization." (Yaneer Bar-Yam, "Making Things Work: Solving Complex Problems in a Complex World", 2004)
"Descriptions underlie everything from science to art. Science explores the descriptions we share (or should share) when we look at the world. Art explores the differences between the descriptions that exist in each of our minds. Thinking is always about descriptions even when we don’t realize it because what we have in our minds is a kind of description, not the system itself." (Yaneer Bar-Yam, "Making Things Work: Solving Complex Problems in a Complex World", 2004)
"If the degree of complexity is relative, our job is to describe how different observers measure complexity. Each observer considers the complexity of a system to be the length of a description that he needs to describe the system. Because of differences in the observers the length of their descriptions differ. The trick is to understand the systematic way the lengths differ so that this variation can be part of our understanding. In this section we focus on what happens when observers use different languages." (Yaneer Bar-Yam, "Making Things Work: Solving Complex Problems in a Complex World", 2004)
"The notion that complexity is measured by the length of the description. […] The idea that complexity is not an absolute, but is relative to who is giving the description and who is receiving the description should not discourage us from thinking about complexity. Descriptions are always relative to the observer and this is already recognized in basic physics." (Yaneer Bar-Yam, "Making Things Work: Solving Complex Problems in a Complex World", 2004)
"There is no doubt that science has made great progress by taking things apart, but it has become increasingly clear that many important questions can only be addressed by thinking more carefully about relationships between and amongst the parts. Indeed, one of the main difficulties in answering questions or solving problems - any kind of problem - is that we think the problem is in the parts, when it is really in the relationships between them."
"What do people do today when they don’t understand 'the
system'? They try to assign responsibility to someone to fix the problem, to
oversee 'the system', to coordinate and control what is happening. It is time
we recognized that 'the system' is how we work together. When we don’t work
together effectively putting someone in charge by its very nature often makes
things worse, rather than better, because no one person can understand 'the
system' well enough to be responsible. We need to learn how to improve the way
we work together, to improve 'the system' without putting someone in charge, in
order to make things work." (Yaneer Bar-Yam, "Making Things Work: Solving Complex
Problems in a Complex World", 2004)
"When parts are acting independently, the fine scale behavior is more complex. When they are working together, the fine scale complexity is much smaller, but the behavior is on a larger scale. This means that complexity is always a trade-off, more complex at a large scale means simpler at a fine scale. This trade-off is a basic conceptual tool that we need in order to understand complex systems." (Yaneer Bar-Yam, "Making Things Work: Solving Complex Problems in a Complex World", 2004)
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