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46-484: Present-day technologies are limited in various ways. Large atomically precise structures (that is, virtually defect-free) do not exist. Complex 3D nanoscale structures exist in the form of folded linear molecules such as DNA origami and proteins . As of 2018, it was also possible to build very small atomically precise structures using scanning probe microscopy to construct molecules such as FeCO and Triangulene , or to perform hydrogen depassivation lithography. But it

92-557: A Professor at the Universidad de Los Andes , Bogota . He was then Professor of Physics at the University of Oxford until 2007, having joined the faculty in 1992. After a period as Professor of Physics at the University of Miami in Florida , he was appointed Professor of Physics at George Washington University in 2018. While a student at school and university, Johnson was a sax player with

138-417: A collection of interacting objects". Definitions of complexity often depend on the concept of a " 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

184-415: A complex function. Some would argue that Zettl 's machines fit in this category; others argue that modern microprocessors and FPGAs also fit. 4. Systems of nanosystems/Productive nanosystems - these will be complex nanosystems that produce atomically precise parts for other nanosystems, not necessarily using novel nanoscale-emergent properties, but well-understood fundamentals of manufacturing. Because of

230-559: A defined system. Some definitions relate to the algorithmic basis for the expression of a complex phenomenon or model or mathematical expression, as later set out herein. One of the problems in addressing complexity issues has been formalizing the intuitive conceptual distinction between the large number of variances in relationships extant in random collections, and the sometimes large, but smaller, number of relationships between elements in systems where constraints (related to correlation of otherwise independent elements) simultaneously reduce

276-520: 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 in regards to other systems, rather 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

322-432: A function, language or set (Burgin 2005). This shows that tools of activity can be an important factor of complexity. In several scientific fields, "complexity" has a precise meaning: Other fields introduce less precisely defined notions of complexity: Complexity has always been a part of our environment, and therefore many scientific fields have dealt with complex systems and phenomena. From one perspective, that which

368-419: A number of approaches to characterizing complexity have been used in science ; Zayed et al. reflect many of these. Neil Johnson states that "even among scientists, there is no unique definition of complexity – and the scientific notion has traditionally been conveyed using particular examples..." Ultimately Johnson adopts the definition of "complexity science" as "the study of the phenomena which emerge from

414-404: A problem may be computationally solvable in principle, in actual practice it may not be that simple. These problems might require large amounts of time or an inordinate amount of space. Computational complexity may be approached from many different aspects. Computational complexity can be investigated on the basis of time, memory or other resources used to solve the problem. Time and space are two of

460-412: A sizable number of factors which are interrelated into an organic whole". Weaver's 1948 paper has influenced subsequent thinking about complexity. The approaches that embody concepts of systems, multiple elements, multiple relational regimes, and state spaces might be summarized as implying that complexity arises from the number of distinguishable relational regimes (and their associated state spaces) in

506-611: A view to resolving complex real-world problems. He is a Fellow of the American Physical Society (APS) and is the recipient of the 2018 Burton Award from the APS. He presented the Royal Institution Christmas Lectures "Arrows of time" on BBC TV in 1999. He has more than 300 published research papers across a wide variety of research topics and has supervised the doctoral theses of more than 25 students. He

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552-408: Is a relative property. For instance, for many functions (problems), such 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 1998: 226), while inductive Turing machines can decrease even the complexity class of

598-527: Is also notable for his books Financial Market Complexity published by Oxford University Press and Simply Complexity: A Clear Guide to Complexity Theory published by Oneworld Publications , and for his research on the many-body dynamics of insurgent conflict and online extremism. He attended Southend High School for Boys in Southend-on-Sea , Essex , UK . He received his BA/MA from St. John's College, Cambridge , University of Cambridge where he

644-479: Is also sometimes used in information theory as indicative of complexity, but entropy is also high for randomness. In the case of complex systems, information fluctuation complexity was designed so as not to measure randomness as complex and has been useful in many applications. More recently, a complexity metric was developed for images that can avoid measuring noise as complex by using the minimum description length principle. There has also been interest in measuring

690-519: Is an English physicist who is notable for his work in complexity theory and complex systems , spanning quantum information , econophysics , and condensed matter physics . He is currently Professor of Physics at George Washington University in Washington D.C. where he heads up a new initiative in Complexity and Data Science which combines cross-disciplinary fundamental research with data science, with

736-481: Is being increasingly used in the study of cosmology , big history , and cultural evolution with increasing granularity, as well as increasing quantification. Eric Chaisson has advanced a cosmoglogical complexity metric which he terms Energy Rate Density. This approach has been expanded in various works, most recently applied to measuring evolving complexity of nation-states and their growing cities. Neil F. Johnson Neil Fraser Johnson (born 1961)

782-462: Is concerned with the complexity of strings of data . Complex strings are harder to compress. While intuition tells us that this may depend on the codec used to compress a string (a codec could be theoretically created in any arbitrary language, including one in which the very small command "X" could cause the computer to output a very complicated string like "18995316"), any two Turing-complete languages can be implemented in each other, meaning that

828-499: Is generally used to characterize something with many parts where those parts interact with each other in multiple ways, culminating in a higher order of emergence greater than the sum of its parts. The study of these complex linkages at various scales is the main goal of complex systems theory . The intuitive criterion of complexity can be formulated as follows: a system would be more complex if more parts could be distinguished, and if more connections between them existed. As of 2010 ,

874-439: Is not yet possible to combine components in a systematic way to build larger, more complex systems. Principles of physics and examples from nature both suggest that it will be possible to extend atomically precise fabrication to more complex products of larger size, involving a wider range of materials. An example of progress in this direction would be Christian Schafmeister's work on bis-peptides . In 2005, Mihail Roco , one of

920-437: Is often said to be due to emergence and self-organization. Chaos theory has investigated the sensitivity of systems to variations in initial conditions as one cause of complex behaviour. Recent developments in artificial life , evolutionary computation and genetic algorithms have led to an increasing emphasis on complexity and complex adaptive systems. In social science , the study on the emergence of macro-properties from

966-424: Is some debate about whether or not state-of-the art integrated circuits qualify here, since they operate despite emergent nanoscale properties, not because of them. Therefore, the argument goes, they don't qualify as "novel" nanoscale properties, even though the devices themselves are between one and a hundred nanometers. 3. Complex nanomachines - the assembly of different nanodevices into a nanosystem to accomplish

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1012-415: Is somehow complex – displaying variation without being random – is most worthy of interest given the rewards found in the depths of exploration. The use of the term complex is often confused with the term complicated. In today's systems, this is the difference between myriad connecting "stovepipes" and effective "integrated" solutions. This means that complex is the opposite of independent, while complicated

1058-403: Is the opposite of simple. While this has led some fields to come up with specific definitions of complexity, there is a more recent movement to regroup observations from different fields to study complexity in itself, whether it appears in anthills , human brains or social systems . One such interdisciplinary group of fields is relational order theories . The behavior of a complex system

1104-493: Is the property of a project which makes it difficult to understand, foresee, and keep under control its overall behavior, even when given reasonably complete information about the project system. Maik Maurer considers complexity as a reality in engineering. He proposed a methodology for managing complexity in systems engineering :                              1.           Define

1150-483: The law of requisite variety , Boisot and McKelvey formulated the ‘Law of Requisite Complexity’, that holds that, in order to be efficaciously adaptive, the internal complexity of a system must match the external complexity it confronts. The application in project management of the Law of Requisite Complexity, as proposed by Stefan Morcov, is the analysis of positive, appropriate and negative complexity . Project complexity

1196-499: The travelling salesman problem , for example. It can be solved, as denoted in Big O notation , in time O ( n 2 2 n ) {\displaystyle O(n^{2}2^{n})} (where n is the size of the network to visit – the number of cities the travelling salesman must visit exactly once). As the size of the network of cities grows, the time needed to find the route grows (more than) exponentially. Even though

1242-711: The architects of the USA's National Nanotechnology Initiative, proposed four states of nanotechnology that seem to parallel the technical progress of the Industrial Revolution, of which productive nanosystems is the most advanced. 1. Passive nanostructures - nanoparticles and nanotubes that provide added strength, electrical and thermal conductivity, toughness, hydrophilic/phobic and/or other properties that emerge from their nanoscale structure. 2. Active nanodevices - nanostructures that change states in order to transform energy, information, and/or to perform useful functions. There

1288-403: The classes, and measures of geometry, topology, and density of manifolds . For non-binary classification problems, instance hardness is a bottom-up approach that first seeks to identify instances that are likely to be misclassified (assumed to be the most complex). The characteristics of such instances are then measured using supervised measures such as the number of disagreeing neighbors or

1334-411: The complexity of classification problems in supervised machine learning . This can be useful in meta-learning to determine for which data sets filtering (or removing suspected noisy instances from the training set) is the most beneficial and could be expanded to other areas. For binary classification , such measures can consider the overlaps in feature values from differing classes, the separability of

1380-413: The difficulty of solving them. Problems can be classified by complexity class according to the time it takes for an algorithm – usually a computer program – to solve them as a function of the problem size. Some problems are difficult to solve, while others are easy. For example, some difficult problems need algorithms that take an exponential amount of time in terms of the size of the problem to solve. Take

1426-468: The discrete (i.e. atomic) nature of matter and the possibility of exponential growth, this stage is seen as the basis of another industrial revolution. There are currently many different approaches to building productive nanosystems: including top-down approaches like Patterned atomic layer epitaxy and Diamondoid Mechanosynthesis . There are also bottom-up approaches like DNA Origami and Bis-peptide Synthesis. A fifth step, info/bio/nano convergence,

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1472-450: The elements. However, what one sees as complex and what one sees as simple is relative and changes with time. Warren Weaver posited in 1948 two forms of complexity: disorganized complexity, and organized complexity. Phenomena of 'disorganized complexity' are treated using probability theory and statistical mechanics , while 'organized complexity' deals with phenomena that escape such approaches and confront "dealing simultaneously with

1518-492: The field). These systems are present in the research of a variety disciplines, including biology , economics , social studies and technology . Recently, complexity has become a natural domain of interest of real world socio-cognitive systems and emerging systemics research. Complex systems tend to be high- dimensional , non-linear, and difficult to model. In specific circumstances, they may exhibit low-dimensional behaviour. In information theory , algorithmic information theory

1564-445: 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 –

1610-468: The latter can be predicted by applying Newton's laws of motion . Of course, most real-world systems, including planetary orbits, eventually become theoretically unpredictable even using Newtonian dynamics; as discovered by modern chaos theory . Organized complexity, in Weaver's view, resides in nothing else than the non-random, or correlated, interaction between the parts. These correlated relationships create

1656-440: The length of two encodings in different languages will vary by at most the length of the "translation" language – which will end up being negligible for sufficiently large data strings. These algorithmic measures of complexity tend to assign high values to random noise . However, under a certain understanding of complexity, arguably the most intuitive one, random noise is meaningless and so not complex at all. Information entropy

1702-410: The likelihood of the assigned class label given the input features. A recent study based on molecular simulations and compliance constants describes molecular recognition as a phenomenon of organisation. Even for small molecules like carbohydrates , the recognition process can not be predicted or designed even assuming that each individual hydrogen bond 's strength is exactly known. Driving from

1748-427: The method.                              5.           Model the system.                              6.           Implement the method. Computational complexity theory is the study of the complexity of problems – that is,

1794-400: The micro-properties, also known as macro-micro view in sociology . The topic is commonly recognized as social complexity that is often related to the use of computer simulation in social science, i.e. computational sociology . Systems theory has long been concerned with the study of complex systems (in recent times, complexity theory and complex systems have also been used as names of

1840-503: The most important and popular considerations when problems of complexity are analyzed. There exist a certain class of problems that although they are solvable in principle they require so much time or space that it is not practical to attempt to solve them. These problems are called intractable . There is another form of complexity called hierarchical complexity . It is orthogonal to the forms of complexity discussed so far, which are called horizontal complexity. The concept of complexity

1886-420: The properties) through modeling and simulation , particularly 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. There are generally rules which can be invoked to explain the origin of complexity in a given system. The source of disorganized complexity is the large number of parts in

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1932-476: 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. See e.g. Robert Ulanowicz 's treatment of ecosystems . Complexity of an object or system

1978-510: The system.                              2.           Identify the type of complexity.                              3.           Determine the strategy.                              4.           Determine

2024-464: The variations from element independence and create distinguishable regimes of more-uniform, or correlated, relationships, or interactions. 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

2070-479: Was added later by Roco. This is the convergence of the three most revolutionary technologies, since every living thing is made up of atoms and information. Clanking replicator Ribosome Synthetic biology Complexity Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity , randomness , collective dynamics , hierarchy , and emergence . The term

2116-464: Was elected as a Scholar throughout his undergraduate career. He obtained a First each year, and obtained top First in the final examinations. He was awarded the Hartree and Maxwell prizes. He was awarded a scholarship to attend Harvard University as a Kennedy Scholar where he received his PhD in 1989. Following his PhD, he was first appointed as a Research Fellow at the University of Cambridge , then as

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