According to Ms. Anderson chaotic systems cannot be reliably predicted. These systems are harder to predict the further one attempts to model into the future. All these systems contain on if not three of properties:
Interaction Dominated Complexity - to Anderson this property reflects "...not the size of the system or its components but the high degree of interconnectedness between the components..." This property usually has a large number of components. Each part is determined by how it connects to other parts of the system. The connections may be identical. According to Anderson this property is fairly common in nature. Examples of this property are held by the human brain, a group of people irregularly interacting with one another or the words of a language and their sequencing into sentences. Obviously the emphasis is here is the interaction.
Component Dominated Complexity - here the complexity lies inside the components. In the first property it is the interaction that is complex as opposed to the component itself. How these components function is determined by specific properties within each component. There are distinct and different types of components in these systems. According to Anderson, humans deal with these kinds of systems all the time. She cites examples of complex architecture, or large pieces of software.
Systems containing components with non-linear responses. Anderson cites neurons in the brain as an example. This may not be enough information for our viewers to understand. We supply a more detailed explanation.
Nerve impulses have a domino effect. Each neuron receives an impulse and must pass it on to the next neuron and make sure the correct impulse continues on its path. Through a chain of chemical events, the dendrites (part of a neuron) pick up an impulse that's shuttled through the axon and transmitted to the next neuron.
Each neuron has a threshold level — the point at which there's no holding back. After the stimulus goes above the threshold level, more gated ion channels open and allow more Na+ inside the cell. This causes complete depolarization of the neuron and an action potential is created. In this state, the neuron continues to open Na+ channels all along the membrane. When this occurs, it's an all-or-none phenomenon. "All-or-none" means that if a stimulus doesn't exceed the threshold level and cause all the gates to open, no action potential results; however, after the threshold is crossed, there's no turning back: Complete depolarization occurs and the stimulus will be transmitted.Third Property
Systems with components that contain an internal state, in other words they contain a memory. For a somewhat fuller explanation we include this passage:
Biological neurons have a complex and dynamic internal state, which includes the con- centrations of proteins and other chemicals and the cell’s physical structure. This state is constantly changing in response to not only the external stimuli the cell receives but also the neuron’s internal processes driven by instructions from the genes. All the be- havior of a neuron is the result of this complex interaction between genome, internal state, and external stimuli.Holistic Analysis
Why do these systems resist reductional analysis? This was a question that puzzled Ms. Anderson. She realized that the very model used for investigation was the problem. This realization turned her to a holistic analysis, which she defines as "...viewing the phenomena as a unit..." and the need to take "...into account the system's environment." Anderson mentions three important reasons to focus on a holistic analysis - internal, external and temporal. The internal reason she labels the curse of dimensionality. She states,
The number of possible types of objects and the number of possible interactions between properties of multiple objects increases catastrophically through a combinatorial explosion when the number of dimensions (distinct properties) increases. This causes problems in fields like Machine Learning and is a reason real-world systems resist analysis using Logical methods.This first reason is related to the "frame problem" in philosophy and AI. Kammerman and Schmits give an excellent explanation of this problem. We will quote extensively from their 2004 paper.
Every researcher in the field of AI will eventually encounter the Frame Problem, often described as the problem of ‘knowing what stays the same as actions occur in a changing world’. This first encounter with the frame problem is often met with an underestimation of the problem, followed by many hours of trying to find different ways to get around it, only to find it is still quite present, and very hard to successfully get rid of.They go on to say,
This very problem, having to say which actions don’t change certain objects would result in a theoretically endless list, but at least as long as the number of actions you wanted to model times the number of different properties objects might have, was first noted by McCarthy and Hayes in 1969 when they discussed a form of logical reasoning about the world, later to be called situation calculus. In the paper that kicked it all off, “Some philosophical problems form the standpoint of artificial intelligence”, they first formulated this exact problem and opened up a discussion that would take 30 years before a conclusion could be reached.This problem remains essentially unsolved.
The second reason why Anderson was directed towards holistic analysis was external or environment of the phenomena being studied. To Anderson, the "...system cannot be separated from its environment."
If you take a squirrel from its natural habitat and attempt to study it in the laboratory you will likely get a different result than if you study it in the field. Ecologies of plants and animals are so intertwined that there is no way to isolate any component without affecting the analysis. Blood in a test tube behaves different than blood circulating in a body.Then there is a very important temporal factor that Anderson explains defeats reductional attempts to understand a system. This thesis is that "...systems never stop and have to keep adapting to a changing environment."
...most Scientists would be happiest if they could ask a specific question or do an experiment, and receive an answer that would not immediately be obsoleted by changing conditions. A system that is continuously changing is harder to understand analytically. Any static analysis will instantly become obsolete.As if all of this was so far not enough to discourage the modeled predictions of these systems, there is the issue of ambiguity in these systems, which we will discuss in our third part of this series.