Posted on November 30, by Scott Alexander [epistemic status:
Overview[ edit ] Definitions of complexity often depend on the concept of a confidential " system " — a set of parts or elements that have relationships among them differentiated from relationships with other elements outside the relational regime.
Many definitions tend to postulate or assume that complexity expresses a condition of numerous elements in a system and numerous forms of relationships among the elements. However, what one sees as complex and what one sees as simple is relative and changes with time.
Warren Weaver posited in two forms of complexity: Some definitions relate to the algorithmic basis for the expression of a complex phenomenon or model or mathematical expression, as later set out herein. Weaver perceived and addressed this problem, in at least a preliminary way, in drawing a distinction between "disorganized complexity" and "organized complexity".
In Weaver's view, disorganized complexity results from the particular system having a very large number of parts, say millions of parts, or many more. Though the interactions of the parts in a "disorganized complexity" situation can be seen as largely random, the properties of the system as a whole can be understood by using probability and statistical methods.
A prime example of disorganized complexity is a gas in a container, with the gas molecules as the parts.
Some would suggest that a system of disorganized complexity may be compared with the relative simplicity of planetary orbits — the latter can be predicted by applying Newton's laws of motion. Of course, The relationship between critical thinking and real-world systems, including planetary orbits, eventually become theoretically unpredictable even using Newtonian dynamics; as discovered by modern chaos theory.
These correlated relationships create a differentiated structure that can, as a system, interact with other systems. The coordinated system manifests properties not carried or dictated by individual parts. The organized aspect of this form of complexity vis-a-vis to other systems than the subject system can be said to "emerge," without any "guiding hand".
The number of parts does not have to be very large for a particular system to have emergent properties. A system of organized complexity may be understood in its properties behavior among the properties through modeling and simulationparticularly modeling and simulation with computers.
An example of organized complexity is a city neighborhood as a living mechanism, with the neighborhood people among the system's parts.
The source of disorganized complexity is the large number of parts in the system of interest, and the lack of correlation between elements in the system. In the case of self-organizing living systems, usefully organized complexity comes from beneficially mutated organisms being selected to survive by their environment for their differential reproductive ability or at least success over inanimate matter or less organized complex organisms.
Robert Ulanowicz 's treatment of ecosystems. For instance, for many functions problemssuch a computational complexity as time of computation is smaller when multitape Turing machines are used than when Turing machines with one tape are used.
Random Access Machines allow one to even more decrease time complexity Greenlaw and Hoover This shows that tools of activity can be an important factor of complexity.
Varied meanings[ edit ] In several scientific fields, "complexity" has a precise meaning: In computational complexity theorythe amounts of resources required for the execution of algorithms is studied.
The most popular types of computational complexity are the time complexity of a problem equal to the number of steps that it takes to solve an instance of the problem as a function of the size of the input usually measured in bitsusing the most efficient algorithm, and the space complexity of a problem equal to the volume of the memory used by the algorithm e.
This allows classification of computational problems by complexity class such as PNP, etc. An axiomatic approach to computational complexity was developed by Manuel Blum. It allows one to deduce many properties of concrete computational complexity measures, such as time complexity or space complexity, from properties of axiomatically defined measures.
In algorithmic information theorythe Kolmogorov complexity also called descriptive complexity, algorithmic complexity or algorithmic entropy of a string is the length of the shortest binary program that outputs that string.
Minimum message length is a practical application of this approach. Different kinds of Kolmogorov complexity are studied: An axiomatic approach to Kolmogorov complexity based on Blum axioms Blum was introduced by Mark Burgin in the paper presented for publication by Andrey Kolmogorov.
It is possible to treat different kinds of Kolmogorov complexity as particular cases of axiomatically defined generalized Kolmogorov complexity. Instead of proving similar theorems, such as the basic invariance theorem, for each particular measure, it is possible to easily deduce all such results from one corresponding theorem proved in the axiomatic setting.
This is a general advantage of the axiomatic approach in mathematics. The axiomatic approach to Kolmogorov complexity was further developed in the book Burgin and applied to software metrics Burgin and Debnath, ; Debnath and Burgin, In information processingcomplexity is a measure of the total number of properties transmitted by an object and detected by an observer.
Such a collection of properties is often referred to as a state. In physical systemscomplexity is a measure of the probability of the state vector of the system. This should not be confused with entropy ; it is a distinct mathematical measure, one in which two distinct states are never conflated and considered equal, as is done for the notion of entropy in statistical mechanics.
In mathematicsKrohn—Rhodes complexity is an important topic in the study of finite semigroups and automata.
In Network theory complexity is the product of richness in the connections between components of a system,  and defined by a very unequal distribution of certain measures some elements being highly connected and some very few, see complex network.
In software engineeringprogramming complexity is a measure of the interactions of the various elements of the software. This differs from the computational complexity described above in that it is a measure of the design of the software.Relationship between critical thinking and ethics.
Critical thinking plays a huge role in ethics. Critical thinking is a clear and rational, open minded and informed. Ethics is moral principles that govern a person or group behavior and rule of conduct. Critical thinking forces employees and managers to look at a situation and weigh all possible solutions before coming up with a final answer.
It can be a long process that requires input from. The Link Between Writing and Critical Thinking. Given this view of critical thinking, what is the connection with writing?
Quite simply, writing is both a process of doing critical thinking and a product communicating the results of critical thinking. Critical thinking can lead to clearer thinking and clearer writing. During writing, especially when writing for a given audience, it is necessary to engage in critical thinking when planning out an argument and providing the premises and conclusions.
Dartmouth Writing Program support materials - including development of argument. Fundamentals of Critical Reading and Effective Writing.
Mind Mirror Projects: A Tool for Integrating Critical Thinking into the English Language Classroom (), by Tully, in English Teaching Forum, State Department, Number 1 Critical Thinking Across the Curriculum Project, Metropolitan Community College.
The relationship between critical thinking skills and critical thinking dispositions is an empirical question. Some people have both in abundance, some have skills but not the disposition to use them, some are disposed but lack strong skills, and some have neither.