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Chaos theory

Chaos theory
A double rod pendulum animation showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a completely different trajectory. The double rod pendulum is one of the simplest dynamical systems that has chaotic solutions. Chaos: When the present determines the future, but the approximate present does not approximately determine the future. Chaotic behavior can be observed in many natural systems, such as weather and climate.[6][7] This behavior can be studied through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps. Introduction[edit] Chaos theory concerns deterministic systems whose behavior can in principle be predicted. Chaotic dynamics[edit] The map defined by x → 4 x (1 – x) and y → x + y mod 1 displays sensitivity to initial conditions. In common usage, "chaos" means "a state of disorder".[9] However, in chaos theory, the term is defined more precisely. where , and , is: .

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A New Kind of Science A New Kind of Science is a best-selling,[1] controversial book by Stephen Wolfram, published in 2002. It contains an empirical and systematic study of computational systems such as cellular automata. Wolfram calls these systems simple programs and argues that the scientific philosophy and methods appropriate for the study of simple programs are relevant to other fields of science. Contents[edit] Computation and its implications[edit] The thesis of A New Kind of Science (NKS) is twofold: that the nature of computation must be explored experimentally, and that the results of these experiments have great relevance to understanding the natural world, which is assumed to be digital.

Moore's law Moore's law is the observation that, over the history of computing hardware, the number of transistors on integrated circuits doubles approximately every two years. The law is named after Intel co-founder Gordon E. Moore, who described the trend in his 1965 paper.[1][2][3] His prediction has proven to be accurate, in part because the law is now used in the semiconductor industry to guide long-term planning and to set targets for research and development.[4] The capabilities of many digital electronic devices are strongly linked to Moore's law: processing speed, memory capacity, sensors and even the number and size of pixels in digital cameras.[5] All of these are improving at roughly exponential rates as well. This exponential improvement has dramatically enhanced the impact of digital electronics in nearly every segment of the world economy.[6] Moore's law describes a driving force of technological and social change in the late 20th and early 21st centuries.[7][8] History[edit]

Scientists Uncover How Our Brains Recognize Faces GettyAlfred Pasieka/Science Photo Library When you see a face, what happens in your brain? How do your neurons process facial features to recognize a person you know? Thanks to a group of researchers at Caltech, we may finally have the answer. Game Theory First published Sat Jan 25, 1997; substantive revision Wed May 5, 2010 Game theory is the study of the ways in which strategic interactions among economic agents produce outcomes with respect to the preferences (or utilities) of those agents, where the outcomes in question might have been intended by none of the agents. The meaning of this statement will not be clear to the non-expert until each of the italicized words and phrases has been explained and featured in some examples. Doing this will be the main business of this article. First, however, we provide some historical and philosophical context in order to motivate the reader for the technical work ahead.

A Matter of Memories: :ARTICLE: Top 5 Time-saving Tips for Faster Scrapbooking Not too long ago, I hosted a giveaway that in order to enter readers had to leave a comment telling me your favorite time-saving tip when it comes to scrapbooking. While there were about a dozen different answers in total from the commenters, there were 5 that clearly stood out as the TOP choices to scrap faster and I wanted to discuss those five options in a little greater detail. #1 - SKETCHES This was the number one tip among respondents! Gödel's incompleteness theorems Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (i.e., any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. Background[edit]

Technological Singularity The technological singularity is the hypothesis that accelerating progress in technologies will cause a runaway effect wherein artificial intelligence will exceed human intellectual capacity and control, thus radically changing civilization in an event called the singularity.[1] Because the capabilities of such an intelligence may be impossible for a human to comprehend, the technological singularity is an occurrence beyond which events may become unpredictable, unfavorable, or even unfathomable.[2] The first use of the term "singularity" in this context was by mathematician John von Neumann. Proponents of the singularity typically postulate an "intelligence explosion",[5][6] where superintelligences design successive generations of increasingly powerful minds, that might occur very quickly and might not stop until the agent's cognitive abilities greatly surpass that of any human. Basic concepts

How Learning to Read Rewrites the Brain People who learn to read as adults show profound changes in deep structures of the brain, according to a new study. The findings may change researchers' perspectives on the extent of plasticity in the adult brain, the study said. In the study, researchers recruited a group of completely illiterate women from villages in northern India and taught them to read.

"It's Hard to Have Original Ideas When Everyone Around You Is the Same" This is absolutely true. I love starting up creating projects with a group of varied people. The input everyone gives and the environment that this kind of thing can create is pretty incredible. The hardest part is making sure you find the right people. Oddly enough, communication between different people is what causes this. Not just being around different people.

Human Portraits Hidden in the Topography of Maps Ink on original Michelin map of France Growing up, I've always thought the continent of Africa looked like a sideway face, but Ed Fairburn takes that imagination to a whole new level. The Cardiff-based illustrator finds portraits of human faces hidden amongst the topographical features in various maps of the world. Computational irreducibility Computational irreducibility is one of the main ideas proposed by Stephen Wolfram in his book A New Kind of Science. The idea[edit] Wolfram terms the inability to shortcut a program (e.g., a system), or otherwise describe its behavior in a simple way, "computational irreducibility". The empirical fact is that the world of simple programs contains a great diversity of behavior, but, because of undecidability, it is impossible to predict what they will do before essentially running them. The idea demonstrates that there are occurrences where theory's predictions are effectively not possible.

Emerging Memetic Singularity in the Global Knowledge Society 30 April 2009 | Draft IntroductionChecklist of constraintsVarieties of singularity -- Technological singularity | Cognitive singularity | Metasystem transition -- Communication singularity | Globality as singularity | Symmetry group singularity -- Subjective singularity | Spiritual singularity | Singularity of planetary consciousness -- Metaphorical singularityEnd times scenarios -- End of history | 2012 | Timewave theory | Eschatological scenarios | End of science -- End of culture | End of religion | End of civilization | End of security | End of privacy -- End of intelligence | End of ignorance | End of knowing | End of abundance | End of confidence -- End of hope | End of truth | End of faith | End of logic | End of rationality | End of modernism -- End of wisdom | End of tolerance | End of natureBlack holes and Event horizonsConclusion Introduction Historically these were a preoccupation of the Union of Intelligible Associations and are now a focus of Global Sensemaking.

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