Quantifying the complexity of a system

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Discussion Overview

The discussion centers on methods for quantifying the complexity of various systems, with a focus on comparing different levels of complexity in systems such as a double pendulum, the global climate, and an animal brain. The scope includes theoretical approaches and computational complexity.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions the existence of generally accepted methods for quantifying system complexity and suggests a comparative approach based on examples like a double pendulum versus the global climate and an animal brain.
  • Another participant references specific methods, including the phase rule, virial theorem, and Cramer's rule, as potential frameworks for understanding complexity.
  • A different viewpoint emphasizes computational complexity, proposing that the length of the algorithm required to model a system could serve as a measure of its complexity.
  • One participant introduces Kolmogorov complexity as a relevant concept for measuring complexity in computational terms.
  • A later reply inquires about the application of these measures to biological systems, specifically questioning how complexity might be quantified for bacteria.

Areas of Agreement / Disagreement

Participants express varying perspectives on the methods for quantifying complexity, with no consensus on a single approach or framework. Multiple competing views remain regarding the definitions and applications of complexity measures.

Contextual Notes

Participants have not fully explored the assumptions underlying the proposed methods, and the discussion lacks clarity on the specific definitions of complexity being used.

BWV
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Are there generally accepted methods for quantifying the complexity of a system, enabling comparison and the requirements for quantitatively modeling it? Think everyone would agree that in complexity, for example a double pendulum is less complex than the global climate which is in turn less complex than an animal brain, but is there a useful way to quantify this?
 
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More along the lines of computational complexity. one measure would be perhaps the length of the algorithm needed to model it?
 
Yes thanks, does this get used at all on biological systems? Wonder how a bacteria would come out
 

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