Complexity” Makes a Difference: Lessons from Critical Systems Thinking and the Covid-19 Pandemic in the UK
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Fractal Expressionism—Where Art Meets Science
Santa Fe Institute. February 14, 2002 9:04 a.m. Taylor page 1 Fractal Expressionism—Where Art Meets Science Richard Taylor 1 INTRODUCTION If the Jackson Pollock story (1912–1956) hadn’t happened, Hollywood would have invented it any way! In a drunken, suicidal state on a stormy night in March 1952, the notorious Abstract Expressionist painter laid down the foundations of his masterpiece Blue Poles: Number 11, 1952 by rolling a large canvas across the oor of his windswept barn and dripping household paint from an old can with a wooden stick. The event represented the climax of a remarkable decade for Pollock, during which he generated a vast body of distinct art work commonly referred to as the “drip and splash” technique. In contrast to the broken lines painted by conventional brush contact with the canvas surface, Pollock poured a constant stream of paint onto his horizontal canvases to produce uniquely contin- uous trajectories. These deceptively simple acts fuelled unprecedented controversy and polarized public opinion around the world. Was this primitive painting style driven by raw genius or was he simply a drunk who mocked artistic traditions? Twenty years later, the Australian government rekindled the controversy by pur- chasing the painting for a spectacular two million (U.S.) dollars. In the history of Western art, only works by Rembrandt, Velazquez, and da Vinci had com- manded more “respect” in the art market. Today, Pollock’s brash and energetic works continue to grab attention, as witnessed by the success of the recent retro- spectives during 1998–1999 (at New York’s Museum of Modern Art and London’s Tate Gallery) where prices of forty million dollars were discussed for Blue Poles: Number 11, 1952. -
Laplace's Deterministic Paradise Lost ?
“We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements Laplace’s deterministic paradise lost of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.” Miguel Angel Fuentes Santa Fe Institute, USA Pierre-Simon Laplace, ~1800 Instituto Balseiro and CONICET, Argentina Santa Fe Institute Santa Fe Institute Comments: Heisenberg uncertainty principle In the framework of quantum mechanics -one of the most successful created theories- is not possible to know -at the Einstein was very unhappy about this apparent randomness same time- the position and velocity of a given object. (~1927) in nature. His views were summed up in his famous phrase, 'God does not play dice.' ∆v ∆x m > h v v v (from Stephen Hawking’s lecture) ? Santa Fe Institute Santa Fe Institute In chaotic (deterministic) systems Same functionality (SAME ORGANISM) x(t) Not chaotic trajectory x(0) = c ∆x ± t ? Some expected initial condition + Mutations Santa Fe Institute Santa Fe Institute Same functionality (SAME ORGANISM) Many process can happen between regular-chaotic behavior Chaotic trajectory Some expected initial condition + Mutations Santa Fe Institute Santa Fe Institute 4.1 Parameter Dependence of the Iterates 35 4.1 Parameter Dependence of the Iterates 35 r values are densely interwr values oarevedenselyn andinterwoneovfindsen and onea sensitifinds a sensitive dependenceve dependence ononparameterparametervalues.values. -
Dissipative Structures, Complexity and Strange Attractors: Keynotes for a New Eco-Aesthetics
Dissipative structures, complexity and strange attractors: keynotes for a new eco-aesthetics 1 2 3 3 R. M. Pulselli , G. C. Magnoli , N. Marchettini & E. Tiezzi 1Department of Urban Studies and Planning, M.I.T, Cambridge, U.S.A. 2Faculty of Engineering, University of Bergamo, Italy and Research Affiliate, M.I.T, Cambridge, U.S.A. 3Department of Chemical and Biosystems Sciences, University of Siena, Italy Abstract There is a new branch of science strikingly at variance with the idea of knowledge just ended and deterministic. The complexity we observe in nature makes us aware of the limits of traditional reductive investigative tools and requires new comprehensive approaches to reality. Looking at the non-equilibrium thermodynamics reported by Ilya Prigogine as the key point to understanding the behaviour of living systems, the research on design practices takes into account the lot of dynamics occurring in nature and seeks to imagine living shapes suiting living contexts. When Edgar Morin speaks about the necessity of a method of complexity, considering the evolutive features of living systems, he probably means that a comprehensive method should be based on deep observations and flexible ordering laws. Actually designers and planners are engaged in a research field concerning fascinating theories coming from science and whose playground is made of cities, landscapes and human settlements. So, the concept of a dissipative structure and the theory of space organized by networks provide a new point of view to observe the dynamic behaviours of systems, finally bringing their flowing patterns into the practices of design and architecture. However, while science discovers the fashion of living systems, the question asked is how to develop methods to configure open shapes according to the theory of evolutionary physics. -
Self-Organized Complexity in the Physical, Biological, and Social Sciences
Introduction Self-organized complexity in the physical, biological, and social sciences Donald L. Turcotte*† and John B. Rundle‡ *Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, NY 14853; and ‡Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO 80309 he National Academy of Sciences convened an Arthur M. A complex phenomenon is said to exhibit self-organizing TSackler Colloquium on ‘‘Self-organized complexity in the phys- complexity only if it has some form of power-law (fractal) ical, biological, and social sciences’’ at the NAS Beckman Center, scaling. It should be emphasized, however, that the power-law Irvine, CA, on March 23–24, 2001. The organizers were D.L.T. scaling may be applicable only over a limited range of scales. (Cornell), J.B.R. (Colorado), and Hans Frauenfelder (Los Alamos National Laboratory, Los Alamos, NM). The organizers had no Networks difficulty in finding many examples of complexity in subjects Another classic example of self-organizing complexity is drain- ranging from fluid turbulence to social networks. However, an age networks. These networks are characterized by the concept acceptable definition for self-organizing complexity is much more of stream order. The smallest streams are first-order streams— elusive. Symptoms of systems that exhibit self-organizing complex- two first-order streams merge to form a second-order stream, ity include fractal statistics and chaotic behavior. Some examples of two second-order streams merge to form a third-order stream, such systems are completely deterministic (i.e., fluid turbulence), and so forth. Drainage networks satisfy the fractal relation Eq. -
Fractal Curves and Complexity
Perception & Psychophysics 1987, 42 (4), 365-370 Fractal curves and complexity JAMES E. CUTI'ING and JEFFREY J. GARVIN Cornell University, Ithaca, New York Fractal curves were generated on square initiators and rated in terms of complexity by eight viewers. The stimuli differed in fractional dimension, recursion, and number of segments in their generators. Across six stimulus sets, recursion accounted for most of the variance in complexity judgments, but among stimuli with the most recursive depth, fractal dimension was a respect able predictor. Six variables from previous psychophysical literature known to effect complexity judgments were compared with these fractal variables: symmetry, moments of spatial distribu tion, angular variance, number of sides, P2/A, and Leeuwenberg codes. The latter three provided reliable predictive value and were highly correlated with recursive depth, fractal dimension, and number of segments in the generator, respectively. Thus, the measures from the previous litera ture and those of fractal parameters provide equal predictive value in judgments of these stimuli. Fractals are mathematicalobjectsthat have recently cap determine the fractional dimension by dividing the loga tured the imaginations of artists, computer graphics en rithm of the number of unit lengths in the generator by gineers, and psychologists. Synthesized and popularized the logarithm of the number of unit lengths across the ini by Mandelbrot (1977, 1983), with ever-widening appeal tiator. Since there are five segments in this generator and (e.g., Peitgen & Richter, 1986), fractals have many curi three unit lengths across the initiator, the fractionaldimen ous and fascinating properties. Consider four. sion is log(5)/log(3), or about 1.47. -
Measures of Complexity a Non--Exhaustive List
Measures of Complexity a non--exhaustive list Seth Lloyd d'Arbeloff Laboratory for Information Systems and Technology Department of Mechanical Engineering Massachusetts Institute of Technology [email protected] The world has grown more complex recently, and the number of ways of measuring complexity has grown even faster. This multiplication of measures has been taken by some to indicate confusion in the field of complex systems. In fact, the many measures of complexity represent variations on a few underlying themes. Here is an (incomplete) list of measures of complexity grouped into the corresponding themes. An historical analog to the problem of measuring complexity is the problem of describing electromagnetism before Maxwell's equations. In the case of electromagnetism, quantities such as electric and magnetic forces that arose in different experimental contexts were originally regarded as fundamentally different. Eventually it became clear that electricity and magnetism were in fact closely related aspects of the same fundamental quantity, the electromagnetic field. Similarly, contemporary researchers in architecture, biology, computer science, dynamical systems, engineering, finance, game theory, etc., have defined different measures of complexity for each field. Because these researchers were asking the same questions about the complexity of their different subjects of research, however, the answers that they came up with for how to measure complexity bear a considerable similarity to eachother. Three questions that researchers frequently ask to quantify the complexity of the thing (house, bacterium, problem, process, investment scheme) under study are 1. How hard is it to describe? 2. How hard is it to create? 3. What is its degree of organization? Here is a list of some measures of complexity grouped according to the question that they try to answer. -
Role of Nonlinear Dynamics and Chaos in Applied Sciences
v.;.;.:.:.:.;.;.^ ROLE OF NONLINEAR DYNAMICS AND CHAOS IN APPLIED SCIENCES by Quissan V. Lawande and Nirupam Maiti Theoretical Physics Oivisipn 2000 Please be aware that all of the Missing Pages in this document were originally blank pages BARC/2OOO/E/OO3 GOVERNMENT OF INDIA ATOMIC ENERGY COMMISSION ROLE OF NONLINEAR DYNAMICS AND CHAOS IN APPLIED SCIENCES by Quissan V. Lawande and Nirupam Maiti Theoretical Physics Division BHABHA ATOMIC RESEARCH CENTRE MUMBAI, INDIA 2000 BARC/2000/E/003 BIBLIOGRAPHIC DESCRIPTION SHEET FOR TECHNICAL REPORT (as per IS : 9400 - 1980) 01 Security classification: Unclassified • 02 Distribution: External 03 Report status: New 04 Series: BARC External • 05 Report type: Technical Report 06 Report No. : BARC/2000/E/003 07 Part No. or Volume No. : 08 Contract No.: 10 Title and subtitle: Role of nonlinear dynamics and chaos in applied sciences 11 Collation: 111 p., figs., ills. 13 Project No. : 20 Personal authors): Quissan V. Lawande; Nirupam Maiti 21 Affiliation ofauthor(s): Theoretical Physics Division, Bhabha Atomic Research Centre, Mumbai 22 Corporate authoifs): Bhabha Atomic Research Centre, Mumbai - 400 085 23 Originating unit : Theoretical Physics Division, BARC, Mumbai 24 Sponsors) Name: Department of Atomic Energy Type: Government Contd...(ii) -l- 30 Date of submission: January 2000 31 Publication/Issue date: February 2000 40 Publisher/Distributor: Head, Library and Information Services Division, Bhabha Atomic Research Centre, Mumbai 42 Form of distribution: Hard copy 50 Language of text: English 51 Language of summary: English 52 No. of references: 40 refs. 53 Gives data on: Abstract: Nonlinear dynamics manifests itself in a number of phenomena in both laboratory and day to day dealings. -
Santa Fe Institute 2014 Complex Systems Summer School
Santa Fe Institute 2014 Complex Systems Summer School Introduction to Nonlinear Dynamics Instructor: Liz Bradley Department of Computer Science University of Colorado Boulder CO 80309-0430 USA [email protected] www.cs.colorado.edu/∼lizb Syllabus: 1. Introduction; Dynamics of Maps chs 1 & 10 of [52] • a brief tour of nonlinear dynamics [34] (in [18]) • an extended example: the logistic map – how to plot its behavior – initial conditions, transients, and fixed points – bifurcations and attractors – chaos: sensitive dependence on initial conditions, λ, and all that – pitchforks, Feigenbaum, and universality [23] (in [18]) – the connection between chaos and fractals [24], ch 11 of [52] – period-3, chaos, and the u-sequence [33, 36] (latter is in [18]) – maybe: unstable periodic orbits [3, 26, 51] 2. Dynamics of Flows [52], sections 2.0-2.3, 2.8, 5, and 6 (except 6.6 and 6.8) • maps vs. flows – time: discrete vs. continuous – axes: state/phase space [10] • an example: the simple harmonic oscillator – some math & physics review [9] – portraying & visualizing the dynamics [10] • trajectories, attractors, basins, and boundaries [10] • dissipation and attractors [44] • bifurcations 1 • how sensitive dependence and the Lyapunov exponent manifest in flows • anatomyofaprototypicalchaoticattractor: [24] – stretching/folding and the un/stable manifolds – fractal structure and the fractal dimension ch 11 of [52] – unstable periodic orbits [3, 26, 51] – shadowing – maybe: symbol dynamics [27] (in [14]); [29] • Lab: (Joshua Garland) the logistic map and the driven pendulum 3. Tools [2, 10, 39, 42] • ODE solvers and their dynamics [9, 35, 37, 46] • Poincar´esections [28] • stability, eigenstuff, un/stable manifolds and a bit of control theory • embedology [30, 31, 32, 41, 48, 49, 47, 54] ([41] is in [39] and [47] is in [55];) • Lab: (Joshua Garland) nonlinear time series analysis with the tisean package[1, 32]. -
Annotated List of References Tobias Keip, I7801986 Presentation Method: Poster
Personal Inquiry – Annotated list of references Tobias Keip, i7801986 Presentation Method: Poster Poster Section 1: What is Chaos? In this section I am introducing the topic. I am describing different types of chaos and how individual perception affects our sense for chaos or chaotic systems. I am also going to define the terminology. I support my ideas with a lot of examples, like chaos in our daily life, then I am going to do a transition to simple mathematical chaotic systems. Larry Bradley. (2010). Chaos and Fractals. Available: www.stsci.edu/~lbradley/seminar/. Last accessed 13 May 2010. This website delivered me with a very good introduction into the topic as there are a lot of books and interesting web-pages in the “References”-Sektion. Gleick, James. Chaos: Making a New Science. Penguin Books, 1987. The book gave me a very general introduction into the topic. Harald Lesch. (2003-2007). alpha-Centauri . Available: www.br-online.de/br- alpha/alpha-centauri/alpha-centauri-harald-lesch-videothek-ID1207836664586.xml. Last accessed 13. May 2010. A web-page with German video-documentations delivered a lot of vivid examples about chaos for my poster. Poster Section 2: Laplace's Demon and the Butterfly Effect In this part I describe the idea of the so called Laplace's Demon and the theory of cause-and-effect chains. I work with a lot of examples, especially the famous weather forecast example. Also too I introduce the mathematical concept of a dynamic system. Jeremy S. Heyl (August 11, 2008). The Double Pendulum Fractal. British Columbia, Canada. -
Chaos Theory and Its Application to Education: Mehmet Akif Ersoy University Case*
Educational Sciences: Theory & Practice • 14(2) • 510-518 ©2014 Educational Consultancy and Research Center www.edam.com.tr/estp DOI: 10.12738/estp.2014.2.1928 Chaos Theory and its Application to Education: Mehmet Akif Ersoy University Case* Vesile AKMANSOYa Sadık KARTALb Burdur Provincial Education Department Mehmet Akif Ersoy University Abstract Discussions have arisen regarding the application of the new paradigms of chaos theory to social sciences as compared to physical sciences. This study examines what role chaos theory has within the education process and what effect it has by describing the views of university faculty regarding chaos and education. The partici- pants in this study consisted of 30 faculty members with teaching experience in the Faculty of Education, the Faculty of Science and Literature, and the School of Veterinary Sciences at Mehmet Akif Ersoy University in Burdur, Turkey. The sample for this study included voluntary participants. As part of the study, the acquired qualitative data has been tested using both the descriptive analysis method and content analysis. Themes have been organized under each discourse question after checking and defining the processes. To test the data, fre- quency and percentage, statistical techniques were used. The views of the attendees were stated verbatim in the Turkish version, then translated into English by the researchers. The findings of this study indicate the presence of a “butterfly effect” within educational organizations, whereby a small failure in the education process causes a bigger failure later on. Key Words Chaos, Chaos and Education, Chaos in Social Sciences, Chaos Theory. The term chaos continues to become more and that can be called “united science,” characterized by more prominent within the various fields of its interdisciplinary approach (Yeşilorman, 2006). -
Lecture Notes on Descriptional Complexity and Randomness
Lecture notes on descriptional complexity and randomness Peter Gács Boston University [email protected] A didactical survey of the foundations of Algorithmic Information The- ory. These notes introduce some of the main techniques and concepts of the field. They have evolved over many years and have been used and ref- erenced widely. “Version history” below gives some information on what has changed when. Contents Contents iii 1 Complexity1 1.1 Introduction ........................... 1 1.1.1 Formal results ...................... 3 1.1.2 Applications ....................... 6 1.1.3 History of the problem.................. 8 1.2 Notation ............................. 10 1.3 Kolmogorov complexity ..................... 11 1.3.1 Invariance ........................ 11 1.3.2 Simple quantitative estimates .............. 14 1.4 Simple properties of information ................ 16 1.5 Algorithmic properties of complexity .............. 19 1.6 The coding theorem....................... 24 1.6.1 Self-delimiting complexity................ 24 1.6.2 Universal semimeasure.................. 27 1.6.3 Prefix codes ....................... 28 1.6.4 The coding theorem for ¹Fº . 30 1.6.5 Algorithmic probability.................. 31 1.7 The statistics of description length ............... 32 2 Randomness 37 2.1 Uniform distribution....................... 37 2.2 Computable distributions..................... 40 2.2.1 Two kinds of test..................... 40 2.2.2 Randomness via complexity............... 41 2.2.3 Conservation of randomness............... 43 2.3 Infinite sequences ........................ 46 iii Contents 2.3.1 Null sets ......................... 47 2.3.2 Probability space..................... 52 2.3.3 Computability ...................... 54 2.3.4 Integral.......................... 54 2.3.5 Randomness tests .................... 55 2.3.6 Randomness and complexity............... 56 2.3.7 Universal semimeasure, algorithmic probability . 58 2.3.8 Randomness via algorithmic probability........ -
The Edge of Chaos – an Alternative to the Random Walk Hypothesis
THE EDGE OF CHAOS – AN ALTERNATIVE TO THE RANDOM WALK HYPOTHESIS CIARÁN DORNAN O‟FATHAIGH Junior Sophister The Random Walk Hypothesis claims that stock price movements are random and cannot be predicted from past events. A random system may be unpredictable but an unpredictable system need not be random. The alternative is that it could be described by chaos theory and although seem random, not actually be so. Chaos theory can describe the overall order of a non-linear system; it is not about the absence of order but the search for it. In this essay Ciarán Doran O’Fathaigh explains these ideas in greater detail and also looks at empirical work that has concluded in a rejection of the Random Walk Hypothesis. Introduction This essay intends to put forward an alternative to the Random Walk Hypothesis. This alternative will be that systems that appear to be random are in fact chaotic. Firstly, both the Random Walk Hypothesis and Chaos Theory will be outlined. Following that, some empirical cases will be examined where Chaos Theory is applicable, including real exchange rates with the US Dollar, a chaotic attractor for the S&P 500 and the returns on T-bills. The Random Walk Hypothesis The Random Walk Hypothesis states that stock market prices evolve according to a random walk and that endeavours to predict future movements will be fruitless. There is both a narrow version and a broad version of the Random Walk Hypothesis. Narrow Version: The narrow version of the Random Walk Hypothesis asserts that the movements of a stock or the market as a whole cannot be predicted from past behaviour (Wallich, 1968).