From: jimruttshow8596
A complex system is a broad class of phenomena rather than something that can be precisely defined by a single measure [04:53:00]. Measuring complexity is challenging because there are many ways to do it, and a universal answer does not exist [01:25:00]. Different fields often have their own sets of measures that work well for specific applications [02:25:00].
Characteristics of Complex Systems
Complex systems exhibit several distinguishing properties:
- Non-Simplicity Complex systems are rarely truly simple [02:58:00]. Even seemingly simple components can lead to complexity when they interact; for instance, while a single electron might be considered simple, three electrons can become complex [03:02:00]. This is analogous to the famous three-body problem in gravity, where interactions between three celestial bodies make predictions incredibly difficult [03:13:00].
- Interacting Parts and Feedback Loops They involve thousands of chemical reactions, feedback loops, and interacting components, as seen in the metabolism of a bacterium [03:53:00].
- Balance of Order and Disorder Many complex systems exist at what some call the “edge of chaos,” balancing between complete disorder and strict order [06:10:00]. This means they are not purely random, which would have high algorithmic complexity but lack intuitive complexity, nor are they perfectly ordered, like a salt crystal or a number consisting of a billion repeated ones, which can be described very simply [06:44:00]. Complex systems require significant information to describe but are not random [09:25:00].
- Computational Depth Generating or understanding the state of a complex system can require many computational steps, even if the initial description is short. For example, the first billion digits of pi, while derived from a simple formula, require a significant amount of computation to produce [13:51:00]. This property is known as logical depth [12:17:00].
- Thermodynamic Depth Related to logical depth, thermodynamic depth measures the physical resources, such as free energy, consumed to assemble a system from its actual initial state [19:06:00]. For instance, the metabolism of a bacterium has “humongous” thermodynamic depth due to the billions of years of evolution and countless sacrifices required for natural selection to produce it [19:36:00].
- Mutual Information Complex systems often possess a vast amount of mutual information, meaning different parts of the system share information and are highly interdependent [48:32:00]. This interdependence is a symptom of complexity but not a sufficient condition, as a system of a billion identical bits also has high mutual information but is not complex [49:50:00]. Integrated information, a more intricate form of mutual information, measures the degree to which one can infer the operation of different parts from each other [51:31:00].
- Multiscale Entropy Complex systems typically exhibit a lot of information at each scale [01:01:24]. When observed at different levels of coarse-graining (how much detail is included), complex systems, like living organisms, maintain a high degree of complexity. For example, a human cell is complex at its cellular level, and even tiny mechanisms within it, like mitochondria, are “extremely complicated” [01:01:53].
- Dynamic and Unforeseen Behaviors Complex networks, such as the power grid, can exhibit dynamic and often unforeseen behaviors [58:43:00]. They may even operate in regimes where they tend to be chaotic, leading to unpredictable outcomes [58:50:00].
Examples of Complex Systems
Examples of complex systems discussed include:
- The metabolism of a bacterium [03:40:00]
- Weather systems, particularly in places like New England [31:09:00]
- Networks such as the power grid or the neural connections in the human brain [57:29:00]
- Living systems, from individual cells to entire organisms like humans [01:01:27]
- Engineered systems, such as a car, where effective complexity can be measured by the length of the blueprints and descriptions needed to achieve its functional requirements [00:47:35]
Measuring Complex Systems
The measurement of complexity is often purpose-driven. To define a measure like effective complexity, which differentiates between random and non-random information, one must first define what aspects of the system are “important” [26:01:00]. For a bacterium, this might involve defining its purpose (e.g., taking in food and reproducing) within its environment [26:50:00].
Coarse-graining, a concept popularized by Murray Gell-Mann, is crucial in measuring complexity [29:12:00]. It involves looking at a system at a particular scale and intentionally omitting information below that scale [29:34:00]. This approach helps in defining the level of detail necessary to describe a system’s “effective” or “important” information.
Ultimately, there isn’t a single, universally applicable measure of complexity [01:03:18]. Different measures serve different purposes, whether describing how hard something is to characterize (like Shannon entropy) [00:10:07], how hard it is to produce (like computational or thermodynamic depth) [00:46:20], or combining these aspects [00:47:01]. The choice of measure depends on the specific context and the utility it provides for understanding the system in question [02:58:00].