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Fractal Geometry

Fractal Geometry | collectibles from scoop.it | Scoop.it

"I find the ideas in the fractals, both as a body of knowledge and as a metaphor, an incredibly important way of looking at the world." Vice President and Nobel Laureate Al Gore, New York Times, Wednesday, June 21, 2000, discussing some of the "big think" questions that intrigue him.

This is a collection of pages meant to support a first course in fractal geometry for students without especially strong mathematical preparation, or any particular interest in science.
Each of the topics contains examples of fractals in the arts, humanities, or social sciences; these and other examples are collected in the panorama.
Fractal geometry is a new way of looking at the world; we have been surrounded by natural patterns, unsuspected but easily recognized after only an hour's training.

 

 


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Alfred North Whitehead: The Cosmology of Life

Alfred North Whitehead: The Cosmology of Life | collectibles from scoop.it | Scoop.it
Whitehead would conceive his work in Process and Reality as that of a cosmographer: it would make explicit the cosmology of our times as compared to the two main cosmologies that have dominated the...

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Classics for the people – why we should all learn from the ancient Greeks

Classics for the people – why we should all learn from the ancient Greeks | collectibles from scoop.it | Scoop.it
The dazzling thought-world of the Greeks gave us our ideas of democracy and happiness. Yet learning classics tends to be restricted to the privileged few. It’s time for ‘elitist dinosaurs’ to embrace a citizens’ classics for all

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Life’s Quantum Crystal Ball

Life’s Quantum Crystal Ball | collectibles from scoop.it | Scoop.it

Does the ability to predict the future—perhaps with quantum help—define the fundamental difference between living and inanimate matter?


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Emergence, self-organization and network efficiency in gigantic termite-nest-networks build using simple rules

Termites, like many social insects, build nests of complex architecture. These constructions have been proposed to optimize different structural features. Here we describe the nest network of the termite Nasutitermes ephratae, which is among the largest nest-network reported for termites and show that it optimizes diverse parameters defining the network architecture. The network structure avoids multiple crossing of galleries and minimizes the overlap of foraging territories. Thus, these termites are able to minimize the number of galleries they build, while maximizing the foraging area available at the nest mounds. We present a simple computer algorithm that reproduces the basics characteristics of this termite nest network, showing that simple rules can produce complex architectural designs efficiently.

 

Emergence, self-organization and network efficiency in gigantic termite-nest-networks build using simple rules
Diego Griffon, Carmen Andara, Klaus Jaffe

http://arxiv.org/abs/1506.01487 ;


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Eli Levine's curator insight, June 5, 1:53 PM

Confucius observed that when humans follow a particular, internalized code and logic, the need for the top-down command and control forms of social organization disappear, allowing for much more effective and efficient bottom-up systems of organization to arise.  In other words, laws from on high levels of government should be simple, basic, and in accordance with the present natural laws and conditions of bottom-up organization.  Imagine a border collie moving sheep in a particular direction.  It guides the system by moving them in the general direction that the farmer needs while simply correcting and focusing on those sheep who stray from the flock or begin to pull the flock in undesirable directions.  Each society probably uses different strategies depending upon their own internal logic and "state of propriety".

 

In the United States, it seems that we get extremely focused on the details and what was past rather than consider the general principles behind the laws, which are reflective of our actual values and stable desires as a nation.  We need to refer back to the principles and deeper meaning of the Constitution and not get so hung up about what is or isn't actually written in the Constitution.  It's this intuitive base level of understanding where the logic of our society is and how we are doing that is relative to that common direction we all share as Americans that is more likely to help us.  The details of which sheep are going where is insignificant relative to the big picture of what direction are the sheep as a flock headed and which ones are pulling us in those unhealthy directions.  Sadly, Americans prefer to look at the sheep rather than the flock at their own expense.  That's probably how we got so many highly detailed laws and rules that are contradictory or counter to our base principles and values.  Silly society.  Silly people.

A. J. Alvarez-Socorro's curator insight, June 23, 2:07 AM

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Bacterial Ventures into Multicellularity: Collectivism through Individuality

Bacterial Ventures into Multicellularity: Collectivism through Individuality | collectibles from scoop.it | Scoop.it
Multicellular eukaryotes can perform functions that exceed the possibilities of an individual cell. These functions emerge through interactions between differentiated cells that are precisely arranged in space. Bacteria also form multicellular collectives that consist of differentiated but genetically identical cells. How does the functionality of these collectives depend on the spatial arrangement of the differentiated bacteria? In a previous issue of PLOS Biology, van Gestel and colleagues reported an elegant example of how the spatial arrangement of differentiated cells gives rise to collective behavior in Bacillus subtilus colonies, further demonstrating the similarity of bacterial collectives to higher multicellular organisms.

 

van Vliet S, Ackermann M (2015) Bacterial Ventures into Multicellularity: Collectivism through Individuality. PLoS Biol 13(6): e1002162. http://dx.doi.org/10.1371/journal.pbio.1002162 ;


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Five Things We Still Don’t Know About Water

Five Things We Still Don’t Know About Water | collectibles from scoop.it | Scoop.it

1. How Many Kinds of Ice Are There?

2. Are There Two Kinds of Liquid Water?

3. How Does Water Evaporate?

4. Is the Surface of Liquid Water Acidic or Basic?

5. Is Nanoconfined Water Different?

 

http://nautil.us/issue/25/water/five-things-we-still-dont-know-about-water ;


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Phase transitions in Pareto optimal complex networks

The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their topological structure can be diverse, resulting from different mechanisms including multiplicative processes and optimization. In spatial networks or in graphs where cost constraints are at work, as it occurs in a plethora of situations from power grids to the wiring of neurons in the brain, optimization plays an important part in shaping their organization. In this paper we study network designs resulting from a Pareto optimization process, where different simultaneous constraints are the targets of selection. We analyze three variations on a problem finding phase transitions of different kinds. Distinct phases are associated to different arrangements of the connections; but the need of drastic topological changes does not determine the presence, nor the nature of the phase transitions encountered. Instead, the functions under optimization do play a determinant role. This reinforces the view that phase transitions do not arise from intrinsic properties of a system alone, but from the interplay of that system with its external constraints.

 

Phase transitions in Pareto optimal complex networks
Luís F Seoane, Ricard Solé

http://arxiv.org/abs/1505.06937


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How random are complex networks

Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the dk-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks---the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain---and find that many important local and global structural properties of these networks are closely reproduced by dk-random graphs whose degree distributions, degree correlations, and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness.

 

How random are complex networks
Chiara Orsini, Marija Mitrović Dankulov, Almerima Jamakovic, Priya Mahadevan, Pol Colomer-de-Simón, Amin Vahdat, Kevin E. Bassler, Zoltán Toroczkai, Marián Boguñá, Guido Caldarelli, Santo Fortunato, Dmitri Krioukov

http://arxiv.org/abs/1505.07503


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The Mechanical and the Organic by David Abram

The Mechanical and the Organic by David Abram | collectibles from scoop.it | Scoop.it

Many scientists and theorists claim that the Gaia hypothesis is merely a fancy name for a set of interactions, between organisms and their presumably inorganic environment, that have long been known to science. Every high school student is familiar with the fact that the oxygen content of the atmosphere is dependent on the photosynthetic activity of plants. The Gaia hypothesis, according to such researchers, offers nothing substantive. It is simply a new—and unnecessarily obfuscating—way of speaking of old facts. In the dismissive words of biologist Stephen Jay Gould: "the Gaia Hypothesis says nothing new—it offers no new mechanisms. It just changes the metaphor. But metaphor is not mechanism!"


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Beyond Materialism and Idealism, a Philosophy of Organism?

Beyond Materialism and Idealism, a Philosophy of Organism? | collectibles from scoop.it | Scoop.it
Levi Bryant offered some ideas about materialism earlier this week over at Larval Subjects. I read and commented on his post while screeching through the BART transbay tube on my commute home from work.

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Bits from Brains for Biologically Inspired Computing

Inspiration for artificial biologically inspired computing is often drawn from neural systems. This article shows how to analyze neural systems using information theory with the aim of obtaining constraints that help to identify the algorithms run by neural systems and the information they represent. Algorithms and representations identified this way may then guide the design of biologically inspired computing systems. The material covered includes the necessary introduction to information theory and to the estimation of information-theoretic quantities from neural recordings. We then show how to analyze the information encoded in a system about its environment, and also discuss recent methodological developments on the question of how much information each agent carries about the environment either uniquely or redundantly or synergistically together with others. Last, we introduce the framework of local information dynamics, where information processing is partitioned into component processes of information storage, transfer, and modification – locally in space and time. We close by discussing example applications of these measures to neural data and other complex systems.

 

Wibral M, Lizier JT and Priesemann V (2015) Bits from brains for biologically inspired computing. Front. Robot. AI 2:5. http://dx.doi.org/10.3389/frobt.2015.00005 


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Colbert Sesanker's curator insight, March 27, 5:55 PM

Consider this section from the Walter Pitts article above:

 

Interesting Section:

 

"There was a catch, though: This symbolic abstraction made the world transparent but the brain opaque. Once everything had been reduced to information governed by logic, the actual mechanics ceased to matter—the tradeoff for universal computation was ontology. Von Neumann was the first to see the problem. He expressed his concern to Wiener in a letter that anticipated the coming split between artificial intelligence on one side and neuroscience on the other. “After the great positive contribution of Turing-cum-Pitts-and-McCulloch is assimilated,” he wrote, “the situation is rather worse than better than before. Indeed these authors have demonstrated in absolute and hopeless generality that anything and everything … can be done by an appropriate mechanism, and specifically by a neural mechanism—and that even one, definite mechanism can be ‘universal.’ Inverting the argument: Nothing that we may know or learn about the functioning of the organism can give, without ‘microscopic,’ cytological work any clues regarding the further details of the neural mechanism."

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Anthropocene: The human age

Anthropocene: The human age | collectibles from scoop.it | Scoop.it
Momentum is building to establish a new geological epoch that recognizes humanity's impact on the planet. But there is fierce debate behind the scenes.

 

http://www.nature.com/news/anthropocene-the-human-age-1.17085


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ASundberg's curator insight, March 29, 9:30 AM

Brief historicization of the anthropocene discussion. 

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Soul Spelunker » Hermes, God of the Winged Caduceus

Soul Spelunker » Hermes, God of the Winged Caduceus | collectibles from scoop.it | Scoop.it
The story is told by Roman writer, Hyginus, that, one day, while Hermes was traveling through Arcadia, he witnessed two serpents engaged in a fierce battle. When Hermes placed his caduceus between them, they wrapped themselves around it and were at peace with one another. Thus, Hermes’ caduceus, to this day, has been associated with healing and a state of peace.

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Temple Medicine, Oracles and the Making of Modernity: The Ancient Greek Occult in Anthropology and Psychology

Temple Medicine, Oracles and the Making of Modernity: The Ancient Greek Occult in Anthropology and Psychology | collectibles from scoop.it | Scoop.it
Among the key figures in the hidden history of the human sciences are the Munich philosopher Carl du Prel (1839-1899) and the Cambridge classicist and psychologist Frederic W. H. Myers (1843-1901).

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Part I - Mind, Memory, and Archetype Morphic Resonance and the Collective Unconscious

Part I - Mind, Memory, and Archetype Morphic Resonance and the Collective Unconscious | collectibles from scoop.it | Scoop.it
http://t.co/lEXfPv7ZNY

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An Information-Theoretic Perspective on Coarse-Graining, Including the Transition from Micro to Macro

An information-theoretic perspective on coarse-graining is presented. It starts with an information characterization of configurations at the micro-level using a local information quantity that has a spatial average equal to a microscopic entropy. With a reversible micro dynamics, this entropy is conserved. In the micro-macro transition, it is shown how this local information quantity is transformed into a macroscopic entropy, as the local states are aggregated into macroscopic concentration variables. The information loss in this transition is identified, and the connection to the irreversibility of the macro dynamics and the second law of thermodynamics is discussed. This is then connected to a process of further coarse-graining towards higher characteristic length scales in the context of chemical reaction-diffusion dynamics capable of pattern formation. On these higher levels of coarse-graining, information flows across length scales and across space are defined. These flows obey a continuity equation for information, and they are connected to the thermodynamic constraints of the system, via an outflow of information from macroscopic to microscopic levels in the form of entropy production, as well as an inflow of information, from an external free energy source, if a spatial chemical pattern is to be maintained.

 

An Information-Theoretic Perspective on Coarse-Graining, Including the Transition from Micro to Macro
Kristian Lindgren

Entropy 2015, 17(5), 3332-3351; http://dx.doi.org/10.3390/e17053332 ;


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Generalized communities in networks

A substantial volume of research has been devoted to studies of community structure in networks, but communities are not the only possible form of large-scale network structure. Here we describe a broad extension of community structure that encompasses traditional communities but includes a wide range of generalized structural patterns as well. We describe a principled method for detecting this generalized structure in empirical network data and demonstrate with real-world examples how it can be used to learn new things about the shape and meaning of networks.

 

Generalized communities in networks
M. E. J. Newman, Tiago P. Peixoto

http://arxiv.org/abs/1505.07478


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A. J. Alvarez-Socorro's curator insight, June 23, 2:08 AM

Generalized communities in networks

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Maintaining Homeostasis by Decision-Making

Common decision-making models arise from firm axiomatic foundations but do not account for a variety of empirically observed choice patterns such as risk attitudes in the face of high-impact events. Here, we argue that one reason for this mismatch between theory and data lies in the neglect of basic biological principles such as metabolic homeostasis. We use Bayesian model comparison to show that models based on homeostatic considerations explain human decisions better than classic economic models—both in a novel virtual foraging task and in standard economic gambles. Specifically, we show that in line with the principle of homeostasis human choice minimizes the probability of reaching a lower bound. Our results highlight that predictions from biological principles provide simple, testable, and ecologically rational explanations for apparent biases in decision-making.

 

Korn CW, Bach DR (2015) Maintaining Homeostasis by Decision-Making. PLoS Comput Biol 11(5): e1004301. http://dx.doi.org/10.1371/journal.pcbi.1004301


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Emergence, self-organization and network efficiency in gigantic termite-nest-networks build using simple rules

Termites, like many social insects, build nests of complex architecture. These constructions have been proposed to optimize different structural features. Here we describe the nest network of the termite Nasutitermes ephratae, which is among the largest nest-network reported for termites and show that it optimizes diverse parameters defining the network architecture. The network structure avoids multiple crossing of galleries and minimizes the overlap of foraging territories. Thus, these termites are able to minimize the number of galleries they build, while maximizing the foraging area available at the nest mounds. We present a simple computer algorithm that reproduces the basics characteristics of this termite nest network, showing that simple rules can produce complex architectural designs efficiently.


Emergence, self-organization and network efficiency in gigantic termite-nest-networks build using simple rules
Diego Griffon, Carmen Andara, Klaus Jaffe

http://arxiv.org/abs/1506.01487 ;


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Eli Levine's curator insight, June 5, 1:53 PM

Confucius observed that when humans follow a particular, internalized code and logic, the need for the top-down command and control forms of social organization disappear, allowing for much more effective and efficient bottom-up systems of organization to arise.  In other words, laws from on high levels of government should be simple, basic, and in accordance with the present natural laws and conditions of bottom-up organization.  Imagine a border collie moving sheep in a particular direction.  It guides the system by moving them in the general direction that the farmer needs while simply correcting and focusing on those sheep who stray from the flock or begin to pull the flock in undesirable directions.  Each society probably uses different strategies depending upon their own internal logic and "state of propriety".

 

In the United States, it seems that we get extremely focused on the details and what was past rather than consider the general principles behind the laws, which are reflective of our actual values and stable desires as a nation.  We need to refer back to the principles and deeper meaning of the Constitution and not get so hung up about what is or isn't actually written in the Constitution.  It's this intuitive base level of understanding where the logic of our society is and how we are doing that is relative to that common direction we all share as Americans that is more likely to help us.  The details of which sheep are going where is insignificant relative to the big picture of what direction are the sheep as a flock headed and which ones are pulling us in those unhealthy directions.  Sadly, Americans prefer to look at the sheep rather than the flock at their own expense.  That's probably how we got so many highly detailed laws and rules that are contradictory or counter to our base principles and values.  Silly society.  Silly people.

A. J. Alvarez-Socorro's curator insight, June 23, 2:07 AM

Interesting

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Bees

Bees | collectibles from scoop.it | Scoop.it

The world of bees is fascinating and varied. The common honeybee is the most well-known and well-studied species, but there are thousands of wild bee species that enliven our landscapes and help to pollinate crops and wildflowers. The widely reported threats to honeybees, which cause their colonies to collapse, also jeopardize the lives of these lesser-known and under-appreciated bee species.

 

http://www.nature.com/nature/outlook/bees/index.html 


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Machine intelligence

Machine intelligence | collectibles from scoop.it | Scoop.it

Research in the field of machine intelligence is seeing a resurgence. Big conceptual breakthroughs in artificial neural networks and access to powerful processors have led to applications that can process information in a human-like way. In addition, the creation of robots that can safely assist us with different tasks may soon become a reality. The Reviews in this Insight discuss the exciting developments in these fields and the opportunities for further research.

 

http://www.nature.com/nature/supplements/insights/machine-intelligence/index.html


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Bits from Brains for Biologically Inspired Computing

Inspiration for artificial biologically inspired computing is often drawn from neural systems. This article shows how to analyze neural systems using information theory with the aim of obtaining constraints that help to identify the algorithms run by neural systems and the information they represent. Algorithms and representations identified this way may then guide the design of biologically inspired computing systems. The material covered includes the necessary introduction to information theory and to the estimation of information-theoretic quantities from neural recordings. We then show how to analyze the information encoded in a system about its environment, and also discuss recent methodological developments on the question of how much information each agent carries about the environment either uniquely or redundantly or synergistically together with others. Last, we introduce the framework of local information dynamics, where information processing is partitioned into component processes of information storage, transfer, and modification – locally in space and time. We close by discussing example applications of these measures to neural data and other complex systems.

 

Wibral M, Lizier JT and Priesemann V (2015) Bits from brains for biologically inspired computing. Front. Robot. AI 2:5. http://dx.doi.org/10.3389/frobt.2015.00005 


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Colbert Sesanker's curator insight, March 27, 5:55 PM

Consider this section from the Walter Pitts article above:

 

Interesting Section:

 

"There was a catch, though: This symbolic abstraction made the world transparent but the brain opaque. Once everything had been reduced to information governed by logic, the actual mechanics ceased to matter—the tradeoff for universal computation was ontology. Von Neumann was the first to see the problem. He expressed his concern to Wiener in a letter that anticipated the coming split between artificial intelligence on one side and neuroscience on the other. “After the great positive contribution of Turing-cum-Pitts-and-McCulloch is assimilated,” he wrote, “the situation is rather worse than better than before. Indeed these authors have demonstrated in absolute and hopeless generality that anything and everything … can be done by an appropriate mechanism, and specifically by a neural mechanism—and that even one, definite mechanism can be ‘universal.’ Inverting the argument: Nothing that we may know or learn about the functioning of the organism can give, without ‘microscopic,’ cytological work any clues regarding the further details of the neural mechanism."

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►Greek Mythology: “The Nereids, Fifty Sea Nymphs”.-

►Greek Mythology: “The Nereids, Fifty Sea Nymphs”.- | collectibles from scoop.it | Scoop.it
►Greek Mythology: “The Nereids, Fifty Sea Nymphs”:
“A Mermaid” by John William Waterhouse (1900).

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Human Computation and Convergence

Humans are the most effective integrators and producers of information, directly and through the use of information-processing inventions. As these inventions become increasingly sophisticated, the substantive role of humans in processing information will tend toward capabilities that derive from our most complex cognitive processes, e.g., abstraction, creativity, and applied world knowledge. Through the advancement of human computation - methods that leverage the respective strengths of humans and machines in distributed information-processing systems - formerly discrete processes will combine synergistically into increasingly integrated and complex information processing systems. These new, collective systems will exhibit an unprecedented degree of predictive accuracy in modeling physical and techno-social processes, and may ultimately coalesce into a single unified predictive organism, with the capacity to address societies most wicked problems and achieve planetary homeostasis.

 

Human Computation and Convergence
Pietro Michelucci

http://arxiv.org/abs/1503.05959


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►Greek Mythology: “Poseidon, The God of Sea”.-

►Greek Mythology: “Poseidon, The God of Sea”.- | collectibles from scoop.it | Scoop.it
►Greek Mythology: “Poseidon, The God of Sea”:
“Neptune and Triton” by Gian Lorenzo Bernini (1620-1622). Victoria and Albert Museum of London.

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