prepareforchange--2019-07-27--The Answer to Earth Thriving Copy the Holofractal Universe

The Answer to Earth Thriving? Copy the Holofractal Universe!

Why is it that the Universe flows & manifests with infinite abundance & our Earth systems are not sustainable nor thriving?  The answers & detailed explanation are in Marshall Leffert’s new book, Cosmometry:  Exploring the HoloFractal Nature of the Cosmos, as he reveals a new understanding of the pure stillness of the unified energy field from which ‘everything’ emerges as Whole; & what’s most helpful he relates this geometry & energy information transfer on Earth, siting nature & music.  With over 400 images & Leffert’s concise language, the commons can fully comprehend this ‘intelligent world’ we live in to support a thriving New Earth, that I call Paradise!  “The fundamental patterning that is found throughout the cosmos is the master key to creating living systems that are healthy, sustainable & thriving” says Lefferts.  The wisdom of this…. “higher-order wholeness & design integrity of nature is vastly greater in its importance & relevance to human evolution……essential to establishing coherence & balance during this period of rapid & radical transition on Earth.”  Here the photo of the Vector Equilibrium, compliments of http://www.cosmometry.net, “the geometry of absolute equilibrium; all fluctuation ceases; we call zero-point or Unified Field… where lies pure infinite & creative potential!  “In order for anything to manifest in the universe, physically (energy) & metaphysically (consciousness), it requires a fluctuation in the Unified Field …resulting in… the Quantum & Spacetime Fields.”  In other words, mass & geometries form that we can observe & measure.  That’s the bare minimum beginning for you.  The TORUS photo featured at the top of this blog may be familiar.  It is “the ultimate, most balanced flow process found in sustainable systems at all scales”: atomic to galactic.  It “enables a seamless fractal embedding of energy flow wherein each entity has its unique identity while being connected to all else.”  How fascinating that the universal TORUS applies to humans, plants, trees, hurricanes, each of us surrounded by this field flowing in the top, out the bottom, & back up around to the top again.  These toroidal fields connect with each other:  our “Earth’s magnetic field is embedded inside the Sun’s field; & both are embedded inside our Galaxy Torus.  And it goes inward into the ecosystems & organs of our bodies, the cells they’re made of & the molecules, atoms & sub-atomic particles they’re made of……”  Now is it making some sense that we are all inter-connected unique entities, but part of a Whole Universe?!  This is why it is critical to understand the inter-connections on our Planet in order to rebuild every system, economic, social, financial, & reconnect with Nature to correct our imbalanced TORUS to return to a sustainable, thriving ecosystem.  “We can see that there is a seamlessly dynamic exchange of energy & information (consciousness) occurring throughout the entire cosmic experience.   And yet there is only one whole energy flow occurring throughout the entirety of it!” (what physicist David Bohm calls the Holomovement).  Lefferts, an accomplished Musician, is well aware of the physics, science & spirituality fields.  He is President, Bd. of Dir. @ Physicist Nassim Haramein’s The Resonance Project Foundation;  Assoc. Producer of Foster & Kimberly Gamble’s new THRIVE film, What on Earth will it Take? (due 2020); co-Founder of Gene Keys, & Superluminal Systems; Co-Director of Barbara Marx Hubbard’s Foundation for Conscious Evolution, & Consulting Producer of The Buckminster Fuller Institute.  There you have the bare minimum understanding of the Universe & our Planet reality.  It is crucial wisdom to apply this vibrant & sustainable system to repair Earth now; and, to build the Paradise we want for our near future.  “Cosmometry” is a fascinating read that will prepare & empower all of us to be a part of the balanced toroidal system of the Universe.  Blog 2 will address zero-point energy devices & the release of existing advanced technologies that will benefit the globe.  Blog 3 will reveal an example of a future regenerative (& moneyless)! city already brilliantly designed & engineered, The Venus Project.  Disclaimer: We at Prepare for Change (PFC) bring you information that is not offered by the mainstream news, and therefore may seem controversial. The opinions, views, statements, and/or information we present are not necessarily promoted, endorsed, espoused, or agreed to by Prepare for Change, its leadership Council, members, those who work with PFC, or those who read its content. However, they are hopefully provocative. Please use discernment! Use logical thinking, your own intuition and your own connection with Source, Spirit and Natural Laws to help you determine what is true and what is not. By sharing information and seeding dialogue, it is our goal to raise consciousness and awareness of higher truths to free us from enslavement of the matrix in this material realm.


sottnet--2019-05-14--SOTT FOCUS As Above So Below

SOTT FOCUS: As Above, So Below?

Here is an old idea: our world is part of a living universe, with a mind of its own, a place that is not only a playground for indulging desires, but also a school for learning from the suffering generated by the struggle of existence. This idea lay at the heart of the ancient philosophy of Stoicism, established in Athens in the early 3rd century BC. In Comets And The Horns Of Moses, Laura Knight-Jadczyk summarized the Stoics' basic philosophy thus:When I read this, I was reminded of fractal patterns, a very common mathematical structure. Here is a selection of those patterns as they occur in nature:Modern science's sober view of the universe pooh-poohs the notion of a 'divine element'. It's just an object of study - vast and mysterious, certainly, but ultimately just like any other object. If you expect to be taken seriously in 'the scientific community', you keep your amazement low key when you discover how brilliantly the Universe's machinery is engineered. We are expected to believe that the highest forms of order - of which our civilization with all its technological marvels is just one small part - simply originate out of nothing: there is neither a plan involved, nor purpose, nor intelligence, they say. Just... BOOM!How can that be?From solar systems to animals, in Nature everything is functional and perfectly organized, allowing for some adaptability in response to dynamic changes, but otherwise following strict sets of rules. That it takes inherently structured form is alone a clear indicator of intelligence. But for the 'serious' scientist (who is invariably a neo-Darwinist, whether or not he is aware of it), that's a 'no-go' area. Intelligence can only be ascribed to creatures like us, they say. Nature's biological marvels only give the appearance of design but are simply the result of random mutation, "a happy chemical accident," as the legendary atheist and evolutionary theorist Richard Dawkins put it.Orderly structures created by Nature, no matter how sophisticated, are 'only' natural. If that is the case, what is so special about human beings? At what point does intelligence and consciousness enter the fray?Despite the sophisticated heights science has reached, we remain incapable of reproducing life - certainly, not by any technological means. Mother Nature's technology is far superior to our capabilities and comprehension. We didn't invent life on Earth, she did. We just apply the little we learn from her in rather small, and generally not so brilliant, ways. Yet modern man tends to consider himself the only intelligent, and certainly the most sophisticated, life form. In our arrogance, we say, "mankind knows better," while in reality every observation, every theory, every invention is Nature's intellectual property.In Evolution 2.0 - Breaking the Deadlock Between Darwin and Design, electrical engineer and information theorist Perry Marshall describes the struggle between two opposing camps: the Neo-Darwinists/Atheists on one side, who claim, Random Mutation + Natural Selection + Time = Evolution, and the advocates of Intelligent Design (along with the Creationists) on the other side, who claim 'god' created the universe and everything in it. Marshall concludes that Darwinists underestimate Nature, while Creationists underestimate God, and reminds us that it has already been established, in numerous ways, that DNA is literally code - a highly sophisticated one that exceeds every programming language we can conceive of.The question is: where did this code come from? Random chance, the atheists claim. If so, where is the evidence for that?Also taking aim at the case for random mutation is geneticist Theodosius Dobzhansky , who conducted extensive experiments that bombarded fruit flies with radiation for 30 years, inducing DNA mutations, which he - in line with the prevailing theory - expected would accelerate 'evolution' in the flies. But his experiments turned out to be highly detrimental to the fruit flies' health. There is in fact no documented case, or application in any field of science, where noise/randomness adds information content -. In cases of evolutionary processes the evidence points to adaptive mutation. Imagine a damaged text on a page, where letters are missing: you rec_nstruct and fill in t_e g_ps.From the Wikipedia entry on Rare Earth Hypothesis If that were true, the occurrence of life on Earth must have been a bodacious coincidence, let alone the formation of the universe! Was life on earth and the creation of the universe really just randomly occurring, happy accidents? Some scientists find the 'leap of faith' this requires too difficult to take. Biologist Dr. Rupert Sheldrake has said of the Big Bang theory: "As my friend Terrence McKenna used to say, 'Modern science is based on the principle: give me one free miracle and we'll explain the rest!'" Many scientists literally believe that order miraculously emerges from nothingness.So,It sounds like they're really saying: "We don't know the cause, unless... but let's not go there."The word 'matter' derives from the Latin mater meaning 'origin', 'source', 'mother'. The universe, in all its manifestations, is a well-designed, highly functional, holistic structure, and everything it gives birth to follows its rules - rules which scientists attempt to understand in order to gain knowledge. Like a child learns from its mother, scientists learn from matter. But is there only matter?In philosophy, panpsychism is the view that consciousness, mind, or soul (psyche) is a universal and primordial feature of all things. Panpsychists like the ancient Stoics, Plato, Leibniz, William James or Alfred North Whitehead saw themselves as minds in a world of mind. The psychologist C.G. Jung, with his concept of the collective unconscious, was also of this mindset.The young and curious human mind extrapolates intelligent explanations, scientific models, blueprints and mathematical rule sets, from nature's super-old mind. This informs us about how things work, which makes us intelligent and enables us to further refine our pattern recognition abilities. The application of mathematical rules and concepts, which we as 'intelligent beings' supposedly developed on our own, have physical results in the material world, so it would seem that they existed long before mankind existed. But where exactly is the world of information - of mathematics and ideas - located, if not in our mind? Nature's mind Our mind is strictly a material product of some as-yet-undiscovered brain function, goes the prevailing view. But scientists have been unable to pinpoint a biological location where memories are stored, while studies on rats have shown that, after teaching them a trick, no matter how much of their brain is subsequently cut away (until, of course, the rat dies), they still remember it.Norbert Wiener, MIT's legendary 'father of cybernetics' said:According to Tom Stonier , 'father of information theory', information is a fundamental constituent of the universe:There seems to be a 'pool' or field of non-material information which informs matter, and guides it along established pathways, or 'habits' as Dr. Rupert Sheldrake puts it. Sheldrake proposed the theory of morphic resonance and morphic fields , which could explain many other strange phenomena - from precognition and swarm behavior to remote-viewing, to name a few. What if the mind or mental 'center' of creatures are essentially receivers of information from a vast, non-local and highly intelligent information field?In this framework, there is no 'dead matter', but rather different levels of organisation, including life as one form. Although much more simply organized in comparison to living matter, what we call 'inanimate matter' also adapts and behaves in different ways under certain circumstances, undergoing chemical reactions and complex processes, and proceeding over unimaginably long periods of time.Think of the formation of our planet, which took place long before it could sustain life. There was an evolution of 'dead' matter before that, forming the 'metabolism' of a star system. Consider how well-organized a planet must be to make life possible, and how fine-tuned weather and climate systems must be to regulate the subsequent existence of life. Where do we draw the line between 'life' and 'death'?Are galaxies alive? Do they communicate with each other? Cosmic phenomena have striking similarities to neuronal networks. As Stephen Smith from the Thunderbolts Project writes in 'Electric Universe: Power Lines':Everything seems to be connected: systems feeding systems, cycles within cycles, rules built upon rules. It's as if all is part of one larger organism. Imagine an astronomer living on a planet that is actually an electron orbiting an atom, located within a molecule that is part of a cell cluster inside the guts of a fruit fly, who asks the same question...Proponents of man-made global warming believe the planet - specifically the biosphere - is undergoing radical change due to excessive human activity causing resource depletion and runaway levels of greenhouse gases. This, they posit, meddles catastrophically with the delicate climate controls that sustain life on Earth. If we would just (drastically) reduce our 'carbon footprint', eco-systems would survive, and humanity with them.However, on the one hand they overestimate the physical impact human civilization has on systems that derive most of their energy and 'informational content' from the Sun, cosmic rays and other cosmic phenomena. On the other hand, they ignore the historical accounts of past (non-industrial, though highly organized) civilizations collapsing at times of great environmental upheaval.Returning to the Stoic idea, Knight-Jadczyk wrote of one of the most important Stoics, Posidonius:In the book Earth Changes and the Human-Cosmic Connection, engineer Pierre Lescaudron explored the 'signs and seasons' of our times - erroneously framed as 'man-made climate change' in modern science - in the context of historical episodes of civilizational collapse:Where do you think we are today on the 'dynastic cycle'?Although not consciously formulated, it strikes me as prescient that the 'Yellow Vest' revolt in France kicked off last November because of popular resistance to a planned increase in fuel tax, the ostensible reason for which was to reduce reliance on cars for transport while raising revenues for 'fighting climate change' and 'saving the planet'. The increase in extreme and unseasonal weather in recent years has by now surely been noticed by most people, although visceral realization of what it portends is, for the most part, still missing. In the meantime, social unrest grows, and governments become increasingly totalitarian, which suggests we can expect even greater 'cosmic reaction' to come...If the Universe itself is an organism with a mind of its own, then the same might apply to macro-systems like galaxies, solar systems, and so on down the scale, with the world 'below' manifesting much of the same patterns as the world 'above'. All are subject to the principles of evolution and devolution: order and chaos, growth and decay, health and sickness. As with each living thing, on a long enough timescale, every macro-system is subject to entropy and eventually collapses, and until then it functions as a corrupted form of order.Today's elites pursue their drive for domination and control of other people and of all life. The emergent 'postmodern' manifestation of civilization they have birthed is civilization in a highly advanced state of corrupted order, a pathological (in)competence hierarchy. Predatory and warlike, yet effeminate and juvenile, it somehow continues to sustain large numbers of people, yet starves them of meaning and fundamental well-being thanks to an endless stream of infotainment masquerading as factual information.The spiraling social unrest and extreme weather phenomena - among which I include the increase in comets and asteroids in near-Earth orbit - seem then to constitute an immune reaction to this macrosocial devolution, in part from the planet-as-organism, and in part from us, as one connected 'super-organism'.That our civilization could be wiped out in the blink of an eye is a very real threat . Consider the Younger Dryas Impact hypothesis and the growing body of evidence supporting it: large comet fragments hit the North American Ice Cap at the end of the last ice age and caused cataclysmic flooding . If an advanced civilization existed back then, as some researchers suspect, there wouldn't have been much of it left afterwards, which probably accounts for the ancient myths about a terrible deluge that brought civilization to its knees. Does history repeat? Or at least rhyme? Have we become so inured in our secular techno-specialness that we have forgotten just how unimportant we are from a cosmic perspective? And does human civilization need a little (or large) reminder of that from time to time?


theirishtimes--2019-06-20--Where simple curves become more complex than you think

Where ‘simple curves’ become more complex than you think

The preoccupations of mathematicians can seem curious and strange to normal people. They sometimes expend great energy proving results that appear glaringly obvious. One such result is called the Jordan curve theorem. We all know that a circle has an inside and an outside, and that this property also holds for a much larger collection of closed curves.  A “simple closed curve” is a closed continuous loop in a plane that does not intersect itself. Such a distorted version of a circle is also called a Jordan curve, after the French mathematician Camille Jordan, who first proved some of its key properties.  The Jordan curve theorem states that every simple closed curve, no matter how complicated or convoluted, divides the plane into two regions, an inside and an outside. The theorem appears so trivial that it does not require a proof. But results such as this can be much more profound than a first glance might suggest and, on occasions, things that appear obvious can turn out to be false.  Bernard Bolzano, a Bohemian mathematician, philosopher and priest, was the first person to pose the curve problem in explicit form. He was convinced of the need to introduce rigour into mathematical analysis. He claimed that, for a closed loop in a plane, a line connecting a point enclosed by the loop (inside) to a point distant from it (outside) must intersect the loop. This seems obvious enough, but Bolzano realised that it was a non-trivial problem.  The first proof of the curve theorem appeared in Jordan’s influential book Cours d’analyse, first published in 1882. The theorem is easily stated and easy to prove for curves that are polygons, consisting of straight line segments.  However, for general curves it is quite difficult to prove since “simple” curves can have some bizarre properties, such as being jagged everywhere with no definite direction, or as being fractal in nature like the boundary of a snowflake. This makes it difficult to distinguish which points are inside and which are outside. The proof uses advanced ideas from the branch of mathematics known as topology.  The “travelling salesman problem”, or TSP, seeks the shortest route a salesman can choose to visit a number of cities and return to his starting point. The solution of this optimisation problem is a Jordan curve. Such curves have served as inspiration for artists.  Prof Robert Bosch of Oberlin College in Ohio uses results from optimisation theory to produce artistic images using these simple loops. The illustration shows a sculpture – Embrace – by Bosch, where a simple closed curve separates two regions, represented by metals of different colours. Bosch solved a TSP problem with 726 cities to form the boundary in this sculpture.  Intuition serves as an invaluable means of discovering new mathematics, but it can also lead us astray. There is always a need for rigour in proving seemingly-obvious results.  For Jordan curves, the great German mathematician Felix Klein expressed the problems thus: “Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.”  Peter Lynch is emeritus professor at UCD school of mathematics and statistics – he blogs at thatsmaths.com


theirishtimes--2019-10-02--Emergence Complex behaviour arising from simple roots

Emergence: Complex behaviour arising from simple roots

It is exhilarating to watch a large flock of birds swarming in ever-changing patterns. Swarming is an emergent behaviour, resulting from a set of simple rules followed by each individual animal, bird or fish, without any centralised control or leadership.  A murmuration of starlings is a breathtaking sight, with thousands of birds moving in harmony, almost filling the skies. They may be seen just before dusk, as they gather over their roosting site, performing their acrobatics before settling for the night. Starling murmurations can be seen in many parts of Ireland but, despite the tens of thousands of birds in a flock, starling numbers have fallen drastically in recent decades.  When Aristotle observed that the whole may be greater than the sum of its parts, he must have been thinking of the phenomenon of emergence. Emergence is large-scale behaviour resulting from multitudinous interactions at smaller scales. Life itself is the primary example, resulting from chemical processes at the atomic scale.  The natural world abounds in emergence: ripples in the sand, cyclones in the atmosphere, the growth of crystals, patterns in plants and zebra stripes are all examples. The laws of classical mechanics emerge from the rules of quantum mechanics applied on macroscopic scales. They can predict many things, but it would be difficult to predict a rainbow if one had never been observed.  Randomness at small scales can result in orderly patterns at large scales. The patterns may be geometrically simple, like the rainbow, or highly intricate like ice-crystals on a window. The latter are fractals, beautiful and intricate patterns arising from very simple rules. The most complex of these, the Mandelbrot set, is generated by repeated application of a simple quadratic expression.  Swarming is a behaviour pattern exploited by many animal species. There is flocking of birds, shoaling of fish, herding of wildebeests and so on. Why do birds and animals evolve swarming behaviour? The primary reasons are defence against predators, keeping warm at night and sharing information on good feeding areas. Swarm behaviour can be simulated using mathematical models implemented as algorithms or computer programs.  One of the earliest computer simulations of swarming was done with an algorithm called Boids. The program represented each bird as a point moving in accordance with three simple rules, called alignment, cohesion and separation. Each bird moves in the same direction as its neighbours, stays comfortably close to them and takes evasive action to prevent collisions. To evade predators, additional strategies are required. The Boids algorithm produced realistic simulations of bird flocks.  A collection of people may also engage in swarm behaviour, in sporting events, demonstrations, riots, strikes, and religious assemblies. The stock market exhibits herd behaviour, with frenzied buying and selling. This is often driven by emotion rather than reason, with greed not far from sight.  Modellers struggle to simulate this and to predict the markets. The mathematical modelling of swarming behaviour is also useful in computer animation. Computer simulations have been used in many films, creating crowd scenes that appear realistic.  Originally for modelling birds, the Boids algorithm was later applied to shoaling fish and other swarming animals. Subsequent models have used more elaborate rules, with several concentric zones surrounding each bird, resulting in more faithful simulation of observed behaviour. However, recent research with starling flocks indicates that each bird is influenced primarily by the six or so birds closest to it.  Peter Lynch is emeritus professor at UCD school of mathematics & statistics – He blogs at thatsmaths.com


sottnet--2019-12-25--New way to solve quadratic equations

New way to solve quadratic equations

If you studied algebra in high school (or you're learning it right now), there's a good chance you're familiar with the quadratic formula. If not, it's possible you repressed it.By this point, billions of us have had to learn, memorise, and implement this unwieldy algorithm in order to solve quadratic equations, but according to mathematician Po-Shen Loh from Carnegie Mellon University,In a new research paper , Loh celebrates the quadratic formula as a "remarkable triumph of early mathematicians" dating back to the beginnings of the Old Babylonian Period around 2000 BCE, but also freely acknowledges some of its ancient shortcomings."It is unfortunate that for billions of people worldwide, the quadratic formula is also their first (and perhaps only) experience of a rather complicated formula which they must memorise," Loh writes That arduous task - performed by approximately four millennia worth of maths students, no less - may not have been entirely necessary, as it happens. Of course, there have always been alternatives to the quadratic formula , such as factoring, completing the square, or even breaking out the graph paper.But the quadratic formula is generally regarded as the most comprehensive and reliable method for solving quadratic problems, even if it is a bit inscrutable. This is what it looks like:That formula can be used to solve standard form quadratic equations, where ax+ bx + c = 0.In September, Loh was brainstorming the mathematics behind quadratic equations when he struck upon a new, simplified way of deriving the same formula - an alternative method which he describes in his paper as a "computationally-efficient, natural, and easy-to-remember algorithm for solving general quadratic equations"."I was dumbfounded," Loh says of the discovery. "How can it be that I've never seen this before, and I've never seen this in any textbook?"In Loh's new method, he uses an averaging technique that concentrates on the sum of the two numbers making up b in ax+ bx + c = 0, as opposed to the more commonly taught way of focusing on the product of two numbers that make up c, which often requires guesswork to solve problems."If the sum of two numbers is 2, then their average is 1," Loh explains on his website "So, whatever the numbers are, they are 1 plus some amount, and 1 minus the same amount. All we need to do is to find a z such that 1 + z and 1 - z work as the two numbers, and z is allowed to be 0."When that z value can be determined per Loh's alternative quadratic method, it's possible to solve the roots of any quadratic equation, provided a number of other conditions are satisfied In Loh's paper, he admits he would "be very surprised if this approach has entirely eluded human discovery until the present day, given the 4,000 years of history on this topic", but says the alternative technique - which combines steps pioneered by Babylonian, Greek, and French mathematicians - is "certainly not widely taught or known (the author could find no evidence of it in English sources)".However, since first sharing his pre-print paper describing the simple proof online in October, Loh says his attention has been drawn to a 1989 research article that is effectively identical to his own method - going some way to justify his disbelief that this alternative method had not been identified before now.All that remains to be solved then, is the mystery of why this technique hasn't become more widely known previous to this, since it gives us, in Loh's words , "a delightful alternative approach for solving quadratic equations, which is practical for integration into all mainstream curricula".(Not to mention, of course, that it might just mean that nobody need ever again memorise the quadratic formula.)We still don't know how this escaped wider notice for millennia, but if Loh's instincts are right, maths textbooks could be on the verge of a historic rewriting - and we don't take textbook-changing discoveries lightly."I wanted to share it as widely as possible with the world," Loh says , "because it can demystify a complicated part of maths that makes many people feel that maybe maths is not for them."The research paper is available at pre-print website arXiv.org , and you can read Po-Shen Loh's generalised explanation of the simple proof here


theverge--2019-03-22--The Windows 10 calculator will soon be able to graph math equations

Microsoft is adding a graphing mode to the Windows 10 calculator. The company made the calculator open-sourced on GitHub earlier this month and has received over thirty suggestions from contributors so far, as spotted by ZDNet.  The graphing mode is the first open-sourced suggestion to be chosen. It was Microsoft engineer Dave Grochocki’s idea, who suggested that students could use the graphing feature to study algebra. He pointed out that algebra is the stepping stone to more advanced mathematics and other science and engineering courses, but it’s also a class that students in the US commonly fail.  A lot of basic calculator apps don’t have a graphing feature, so the Windows 10 calculator might also be getting a leg up on rival apps. As of now, the feature’s still under development but GitHub notes indicate users would be able to graph linear, quadratic, and exponential equations.


newyorker--2019-03-28--A Groundbreaking Mathematician on the Gender Politics of Her Field

This month, the mathematician Karen Uhlenbeck became the first woman to win one of the field’s most prestigious awards, the Abel Prize, which is awarded by the Norwegian Academy of Science and Letters. Uhlenbeck, who is seventy-six and an emeritus professor at the University of Texas at Austin, has done revolutionary work across several disciplines; indeed, the academy lauded “her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” The specifics of some of her discoveries are hard to understand—let alone summarize (see below)—but her career has awed her peers and upended any lingering stereotypes about women and math.  I recently spoke by phone with Uhlenbeck, who is currently a visiting scholar at the School of Mathematics at the Institute for Advanced Study, in Princeton. During our conversation, which has been edited for length and clarity, we discussed how she got into math, the struggles of women in a male-dominated field, and whether mathematicians really have “aha!” moments of discovery.  I read that when you found out you had won the Abel Prize, you were coming out of church. Is that correct?  That’s right. We go to the Unitarian Universalist Church, and I glanced at my phone and I had an e-mail from a colleague at Princeton saying I should accept the call from Norway. So I did. I was surprised that I could press a button and return the call.  You’re the mathematician, so I don’t know what the odds are that if you’re getting a call from Norway, it’s to accept some sort of prize, but it seems like they should be fairly high, right?  I don’t know. I hadn’t noticed I had a call from Norway at that point, but I went and looked, and I did.  When did you first realize that mathematics fascinated you? How old were you, and what was that discovery?  Well, I was really a freshman in college. I had always been interested in physics, mostly physics and astronomy, and I read everything I could find on physics and astronomy when I was in grade school and high school. I didn’t think too much of mathematics, but I started college in 1960, and in the wake of Sputnik they had put in honors-calculus classes, and I managed to get into the honors-calculus class, and I just took to it.  I still remember when I first saw the rigorous definition of a derivative, which involves taking the limit of difference quotients to give meaning to an expression that looks at first glance to be zero divided by zero. I was so excited I turned to a friend next to me and said, “Are you allowed to do that?” I really loved that course and I did very well in it, and I switched my major from physics to math.  And what was your first mathematics job out of college?  I graduated from college and then I went to graduate school, and I spent a year at N.Y.U, New York Courant Institute, in New York, and then I married my college boyfriend and he was a student at Harvard, so I transferred to Brandeis University. And, actually, my first job after I finished Brandeis was a very exciting one. I was a postdoc at the University of California, Berkeley, during the Vietnam War, and that was a momentous event in my life.  The Vietnam War and demonstrations—the tear gas, the speeches, classes were cancelled one semester in the wake of Kent State, and it was . . . oh, and there was a lot of fuss about women, too, at that time.  What specifically do you mean by “fuss about women”?  I can’t really give a synopsis of the history of the doors in academia being open to women, but this was right at the time when women were being accepted into graduate school and given jobs, and a lot of people didn’t think that women were suitable and lots of things were said and lots of improper things done. And the University of California, Berkeley, was a very political place.  You said you were moved by the various political goings on at the time, which is interesting because you’re in a profession that I think most people think of as one of the least political things you could be doing. Did you see it that way? Or did you see mathematics as something different?  Well, the fact is I saw mathematics as something different, and I was kind of startled to find it juxtaposed with the political unrest next to it. I was startled to see the politics appear in the math department. It was eye-opening to me, what the world was like. I think up until that time I had seen mathematics as a very bookish thing and that what went on in the mathematical community had nothing to do with the life out there on the streets, and this is not true.  So how does it connect?  It’s done by humans, and all of what goes on between humans appears in the mathematics community, perhaps toned down quite a bit, but it’s not a world of pure brains, people behaving rationally and unemotionally. There are . . . I don’t know, I haven’t thought this question through. I’m sorry.  This is a new question for me.  How did you feel like men were reacting to you, as this intellectually serious person? What was that like for you?  It’s really hard to describe to people who are not somewhere near me in age what it was like for women then. The women who had jobs during World War Two were fired. Men came home from the war, and women sat home. And it was only because of the women’s movement and books like Betty Friedan’s “The Feminine Mystique” that the consciousness came up that women could actually do other things. I figured if I’d been five years older, I could not have become a mathematician, because the disapproval would be so strong.  And I do have to say that, in being a mathematician, I’m lucky. I was a very good student, and I was a good mathematician. It took me a long time to realize it. And when I went one-on-one with people and talked to them, they recognized this and they accepted it and they accepted me. The broader world was not so accepting. That is, I sort of had the feeling that a lot of faculty wives in the early days were really very disapproving of women students, and the world out there was not so encouraging, but I felt that, as a very good student, I was accepted by my mathematical colleagues fairly easily.  Reading about your career, it seems like bringing more women into the field of mathematics and supporting them while they’re there are things that have mattered to you. How do earlier eras compare to this one?  There is no comparison. I don’t want to say the playing field is level. I don’t want to say all the problems are gone. I don’t want to say that there are not difficulties for women. But the landscape is completely different. And I actually was not involved in the beginning. When I started out as a student, it was clear that the way to become a mathematician was not to hang around with other women. So I made my way through my career and, at some point, I achieved a certain amount of fame and I looked around and talked with my other women colleagues and we said, “Where are the women coming behind us?”  And, at that point, when I had some success, I was offered some support and money by the Institute for Advanced Study at Princeton to run a women’s program. I became very involved in encouraging younger women. And I have been doing this ever since. I should say most of my protégées are in their forties and fifties. I’m less of a good mentor to twenty-year-olds than I am to forty-year-olds, at this age.  Let me ask about your work as a mathematician. Are you in a lab? Are you at your desk? Are you sitting with a pen and paper? Are you on the computer? How does that process of discovering something work, for people who don’t know? Because I don’t know!  Well, I think it’s different for everybody. I don’t know if he minds telling this story, but my colleague at Chicago many years ago, Bob Zimmer, is now president of the University of Chicago. I distinctly remember him telling me he got his best ideas doing mathematics when he was doing things like taking out the garbage. [Zimmer noted that, in the midst of research, “ideas can, and sometimes do, emerge at all times—including doing household tasks like taking out the garbage or cleaning up the kitchen, trying to get kids to sleep, supposedly watching a movie, or taking a walk.”] I usually sit in my chair and work on my knees, writing on a pad of paper with a pen that writes upside down if I want to lean back.  But when I’m thinking about a problem I worry about it all the time. I go do something else, but then my mind will drift back to it and I’ll think about it. Some people will say they take notes. I don’t take notes; I scribble and then I give it a rest for a while, and then I go back and I pick it up and I often go through the same thought processes over again, but sometimes something new comes into it. And sometimes I go and I explain something to somebody. I have a colleague and I go in and I explain and, in the process of explaining where I’m stuck, I’ll see how to get further.  So for me it’s not sitting at a desk; it’s going back and forth between focussing on it, standing back, reading something else, picking up a book of things you might find useful. But it’s very disordered, in my case.  You said you worry about it. I imagine that when most people have trouble at work—when I have trouble at work—we can complain to someone about something. But I imagine that, for someone with a job that ninety-nine per cent of people don’t actually understand, that might be additionally stressful. Or did you marry a math genius?  My husband is also a mathematician. Lots of women mathematicians are married to male mathematicians, and maybe more male mathematicians would be married to more women mathematicians if there were more women mathematicians. But the answer is: other mathematicians understand completely. They know that you’re abstract and your mind is off somewhere and you’re really not paying attention. And then when you focus, you come back and you say, “Oh, I’m sorry! We should pay attention to this!” So it helps a lot to have somebody who understands it, and there certainly are . . . you have to talk to the spouse of a mathematician who wasn’t a mathematician to get a real insight into that.  What is it that you are most proud of in your career, and can you put it in layman’s terms for me and our readers, who might not understand why what you’re going to tell us is interesting or important or both?  Well, O.K., I’ll do the best I can. I won’t pick the thing that I actually am proudest of, but I’ll explain the thing that I did that I’m well-known for, which I think I might be able to explain a little bit. The physicists have a model that they use in string theory and in particle physics, which is called the theory of gauge fields. And they had some equations that they wrote about these very abstract objects that they use all the time in physics. These equations are called the Yang-Mills equations, or the Yang-Mills-Higgs equations.There’s a large variety of them and there are lots of new ones now that they have string theory.  Well, when I started in the field, these equations were not very well-defined mathematically. They have a large invariance, and looking at them is a little wobbly, meaning you can move the answers around a lot, and you have the same physical thing but your mathematical description of this physical thing has a lot of indeterminacy in it. And I realized that, to treat these equations as standard mathematical equations, you had to destroy this indeterminacy and make the equation more rigid. And I’m well-known for that result. I think it’s such a clear step that if I hadn’t done it, somebody else would have done it.  I don’t know about that. Did you have an “aha!” moment with this or with any other things, the way you’d see in a movie?  Oh, sure, sure. I did have an “aha!” moment. I really did. I had to solve a second equation. And I looked at that second equation and I tried so hard to do it, and I could do it with a gap of a couple dimensions. It doesn’t matter too much what that means. I just couldn’t do it, and I worried at this problem for a long time, and then suddenly I realized that you could do it by something very simple called the continuity method, which is technical in mathematics. That is, you solve the problem in a region and the solution persists to the end and then, when you get at the end, you have a technique of finding a solution in a little neighborhood of the end, so by doing that you can solve the whole equation, and it’s called the continuity method and it’s a very simple method. And I remember that was a real “aha!” moment.  Oh, it seems simple. I’m sure I could have figured it out if I’d just been given a little bit of time! Do you worry or think about the practical impact or uses of the very advanced mathematics you’re doing? Is that something mathematicians think about, or is the idea that more knowledge is better, and knowledge will be put to good or bad use, but this is what progress is and how civilization works?  No, I don’t think about it too much. I recognize that mathematics is a language and that, when you have the language, you generally find uses for it. So I’ve stopped worrying about the fact that it doesn’t look useful. I do worry about the long-term effects of it. In particular, right now it seems to me that what’s going on in artificial intelligence, with deep learning and so forth, has very frightening prospects, so I worry about it only philosophically.  Doctor, thank you so much for talking. I was hoping you were going to be an absent-minded, crazy mathematician, but instead you’re a normal, lovely human being. So unfortunately this won’t be as exciting.  Sorry about that! I want to add something. Some of the young women are absent-minded, crazy mathematicians. But in my day you couldn’t afford to be!  I’m sure some of the young men are, too.  Oh, yes, young men are always crazy.  This post has been updated to correct an error in transcription.


sottnet--2019-04-08--Scientists discover exotic new patterns of synchronization

networks break up into "clusters" of oscillators that synchronize.  Not you; not anyone. Crickets sing in synchrony; metronomes placed side by side sway into lockstep; some fireflies blink together in the dark. All across the United States, the power grid operates at 60 hertz, its innumerable tributaries of alternating current synchronizing of their own accord. Indeed, we live because of synchronization. Neurons in our brains fire in synchronous patterns to operate our bodies and minds, and pacemaker cells in our hearts sync up to generate the beat.Yet the phenomenon went entirely undocumented until 1665, when the Dutch physicist and inventor Christiaan Huygens spent a few days sick in bed. A pair of new pendulum clocks - a kind of timekeeping device that Huygens invented - hung side by side on the wall. Huygens noticed that the pendulums swung exactly in unison, always lurching toward each other and then away. Perhaps pressure from the air was synchronizing their swings? He conducted various experiments. Standing a table upright between the clocks had no effect on their synchronization, for instance. But when he rehung the clocks far apart or at right angles to each other, they soon fell out of phase. Huygens eventually inferred that the clocks' "sympathy," as he called it, resulted from the kicks that their swings gave each other through the wall.When the left pendulum swings left, it kicks the wall and the other pendulum rightward, and vice versa. The clocks kick each other around until they and the wall attain their most stable, relaxed state. For the pendulums, the most stable behavior is to move in opposite directions, so that each pushes the other in the direction it's already going, the way you push a child on a swing. And this is also easiest for the wall; it no longer moves at all, because the pendulums are giving it equal and opposite kicks. Once in this self-reinforcing, synchronous state, there's no reason for the system to deviate. Many systems synchronize for similar reasons, with kicks replaced by other forms of influence.Another Dutchman, Engelbert Kaempfer, traveled to Thailand in 1690 and observed the localTwo centuries later, the English physicist John William Strutt (better known as Lord Rayleigh) noticed that standing two organ pipes side by side can "cause the pipes to speak in absolute unison, in spite of inevitable small differences."It wasn't until 1967 that the pulsating chirps of crickets inspired the American theoretical biologist Art Winfree to propose a mathematical model of synchronization. Winfree's equation was too difficult to solve, but in 1974, a Japanese physicist named Yoshiki Kuramoto saw how to simplify the math. Kuramoto's model described a population of oscillators (things with rhythms, like metronomes and heartbeats) and showed why coupled oscillators spontaneously synchronize.Kuramoto, then 34, had little prior experience in. When he showed his model to experts in the discipline, they failed to grasp its significance. Discouraged, he set the work aside.Five years later, Winfree came across a précis of a talk Kuramoto had given about his model and realized that it offered a revolutionary new understanding of a subtle phenomenon that pervades the world."I didn't imagine at all that my model would have a wide applicability," said Kuramoto, now 78, by email.But, as ubiquitous as Kuramoto's model became, any illusions physicists had of understanding synchronization shattered in 2001. Once again, Kuramoto was at the center of the action.(If it's a firefly, it might flash every time the arrow points up.) When a pair of arrows are coupled, the strength of their mutual influence depends on the sine of the angle between their pointing directions. The bigger this angle, the bigger the sine, and therefore the stronger their mutual influence.Thus, the arrows will drift until they find this state of synchrony. Even oscillators that have different natural frequencies, when coupled, reach a compromise and oscillate in tandem.But that basic picture only explains the onset of global synchronization, where a population of oscillators all do the same thing. As well as being the simplest kind of sync, "there are plenty of examples of global synchronization; that's why people paid so much attention to that," said Adilson Motter , a physicist at Northwestern University in Chicago, and a leading sync scientist. "But in 2001, Kuramoto discovered something very different. And that's where the story of different states starts."It was Kuramoto's Mongolian post-doc, Dorjsuren Battogtokh, who first noticed a new kind of synchronous behavior in a computer-simulated population of coupled oscillators. The identical oscillators, which were all identically coupled to their neighbors, had somehow split into two factions: Some oscillated in sync, while the rest drifted incoherently.Kuramoto presented his and Battogtokh's discovery at a 2001 meeting in Bristol, but the result didn't register in the community until Steven Strogatz , a mathematician at Cornell University, came across it in the conference proceedings two years later. "When I came to understand what I was seeing in the graphics, I didn't really believe it," Strogatz said."What was so weird," he explained, "was thatStrogatz and his graduate student Daniel Abrams , who now studies synchronization as a professor at Northwestern, reproduced the peculiar mix of synchrony and asynchrony in computer simulations of their own and explored the conditions under which it arises. Strogatz dubbed it the "chimera" state after a mythological fire-breathing monster made of incongruous parts. (Months earlier, Strogatz had written a popular book called Sync , about the pervasiveness of global synchronization.)Two independent teams realized this chimera state in the lab in 2012, working in different physical systems, and more experiments have seen it since. Many researchers suspect chimeras arise naturally."We believe that further detailed studies may open new therapeutic methods for promoting seizure prediction and termination," said co-author Iryna Omelchenko of the University of Berlin.But the chimera state is still not fully understood. Kuramoto worked out the math verifying that the state is self-consistent, and therefore possible, but that doesn't explain why it arises. Strogatz and Abrams further developed the math, but other researchers want "a more seat-of-the-pants, physical explanation," Strogatz said, adding, "I think it's fair to say that we haven't really hit the nail on the head yet" about why the chimera state occurs.The discovery of chimeras ushered in a new era in sync science, revealing the conceivably countless exotic forms that synchronization can take. Now, theorists are working to pin down the rules for when and why the different patterns occur. These researchers have bold hopes of learning how to predict and control synchronization in many real-world contexts.Motter and his team are finding rules about how to stabilize the synchronization of power grids and more stably integrate the U.S. grid with intermittent energy sources like solar and wind. Other researchers are looking for ways of nudging systems between different synchronous states, which could be useful for correcting irregular heartbeats. Novel forms of sync could have applications in encryption."There's a lot of new vibrancy to thinking about sync," said Raissa D'Souza , a professor of computer science and mechanical engineering at University of California, Davis. "We're gaining the tools to look at these exotic, intricate patterns beyond just simple, full synchronization or regions of synchronization and regions of randomness.", as assumed in the original Kuramoto model.In a seminal paper in 2014, Louis Pecora of the United States Naval Research Laboratory and his co-authors put the pieces together about how to understand synchronization in networks. Building on previous work, they showed thatRemote synchronization jibes with findings about real-world networks, such as social networks. "Anecdotally it's not your friend who influences your behavior so much as your friend's friend," D'Souza said.In 2017, Motter's group discovered that oscillators can remotely synchronize even when the oscillators between them are drifting incoherently. This scenario "breeds remote synchronization with chimera states," he said. He and his colleagues hypothesize that this stateThe state might also suggest new forms of secure communication and encryption.As theorists explore the math underpinning these exotic states, experimentalists have been devising new and better platforms for studying them. "Everyone prefers their own system," said Matthew Matheny of the California Institute of Technology. In a paper in Science last month, Matheny, D'Souza, Michael Roukes and 12 co-authors reported a menagerie of new synchronous states in a network of "nanoelectromechanical oscillators," or NEMs - essentially miniature electric drumheads, in this case. The researchers studied a ring of eight NEMs, where each one's vibrations send electrical impulses to its nearest neighbors in the ring. Despite the simplicity of this eight-oscillator system, "we started seeing a lot of crazy things," Matheny said.In many cases, NEMs decoupled from their nearest neighbors and remotely synchronized, vibrating in phase with tiny drumheads elsewhere in the ring. For example, in one pattern, two nearest neighbors oscillated together, but the next pair adopted a different phase; the third pair synced up with the first and the fourth pair with the second. They also found chimeralike states (though it's hard to prove that such a small system is a true chimera).NEMs are more complicated than simple Kuramoto oscillators in that the frequency at which they oscillate affects their amplitude (roughly, their loudness). This inherent, self-referential "nonlinearity" of each NEM gives rise to complex mathematical relationships between them. For instance, the phase of one can affect the amplitude of its neighbor, which affects the phase of its next-nearest neighbor. The ring of NEMs serves as "a proxy for other things that are out in the wild," said Strogatz. When you include a second variable, like amplitude variations, "that opens up a new zoo of phenomena."Roukes, who is a professor of physics, applied physics and biological engineering at Caltech, is most interested in what the ring of NEMs suggests about huge networks like the brain. "This is very, very primordial compared to the complexity of the brain," he said. "If we already see this explosion in complexity, then it seems feasible to me that a network of 200 billion nodes and 2,000 trillion [connections] would have enough complexity to sustain consciousness."In the quest to understand and control the way things sync up, scientists are searching for the mathematical rules dictating when different synchronization patterns occur. That major research effort is unfinished, but it's already clear thatThe link between synchronization and symmetry was first solidified by Pecora and co-authors in their 2014 paper on cluster synchronization. The scientists mapped the different synchronized clusters that can form in a network of oscillators to that network's symmetries. In this context, symmetries refer to the ways a network's oscillators can be swapped without changing the network, just as a square can be rotated 90 degrees or reflected horizontally, vertically or diagonally without changing its appearance.D'Souza, Matheny and their colleagues applied the same potent formalism in their recent studies with NEMs. Roughly speaking, the ring of eight NEMs has the symmetries of an octagon. Butof the "symmetry group" called D8, which specifies all the ways you can rotate and reflect an octagon that leave it unchanged. When the NEMs sync up with their next-nearest neighbors, for example, alternating their pattern around the ring, D8 reduces to the subgroup D4. This means the network of NEMs can be rotated by two positions or reflected across two axes without changing the pattern.Even chimeras can be described in the language of clusters and symmetry subgroups. "The synchronized part is one big synchronized cluster, and the desynchronized part is a bunch of single clusters," said Joe Hart, an experimentalist at the Naval Research Lab who collaborates with Pecora and Motter.Hart admitted. In February, Motter, Hart, Raj Roy of the University of Maryland and Yuanzhao Zhang of Northwestern reported in Physical Review Letters that introducing an asymmetry into a cluster actually strengthens its synchrony. For example, making the coupling between two oscillators in the cluster unidirectional instead of mutual not only doesn't disturb the cluster's synchrony, it actually makes its state more robust to noise and perturbations from elsewhere in the network.These findings about asymmetry hold in experiments with artificial power grids. At the American Physical Society meeting in Boston last month, Motter presented unpublished results suggesting that "generators can more easily oscillate at the exact same frequency, as desired, if their parameters are suitably different," as he put it. He thinks nature's penchant for asymmetry will make it easier to stably sync up diverse energy supplies."A variety of tasks can be achieved by a suitable combination of synchrony and asynchrony," Kuramoto observed in an email.


thepoliticalinsider--2019-01-30--Boy Calls 911 with a Numbers Crisis He Couldnt Crack

Boy Calls 911 with a Numbers Crisis He Couldn’t Crack

Prepared to deal with almost any emergency, 911 dispatchers rarely know what sort of assistance they might need to provide on a given day.  So when an Indiana dispatcher, Antonia Bundy, received a distress call recently from an unidentified boy who “had a really bad day,” she didn’t hesitate to jump in.  “What happened at school that made you have a bad day?” Bundy asked the caller, as Fox News and other outlets reported.  Then the Lafayette dispatcher found out it was math — and more specifically, fractions — that were the cause of the boy’s anguish.  “Is there a problem you want me to help you with?” she asked the boy.  Fortunately, the call center was far from busy at that moment — so Bundy could concentrate on solving this different type of “problem.”  “I was very thankful I was able to take the time to assist him,” she said later in an interview with WLFI-TV.  In the recording of the phone call, Bundy can be heard working through the problem with the boy: What is three-fourths plus one-fourth?  After instructing him to write out the numbers on a piece of paper, the two worked together to ultimately find the answer: Three-fourths plus one-fourth equals 1.  “I’m sorry for calling you, but I really needed help,” the boy said after they had solved the pesky equation.  “You’re fine. We’re always here to help,” she answered.  Related: Arizona Boy, Home Alone, Fights Off Intruder, Punches Him in the Face  Though officials made it clear that calling 911 for homework help isn’t exactly endorsed, they embraced the endearing moment between Bundy and the boy.  “They [dispatchers] train for many emergency situations — homework help is not one they plan for,” read the eventual tweet from the Lafayette Police Department.. “We don’t recommend 911 for homework help, but this dispatcher helped a young boy out and brightened his day,”  Lafayette Police Sgt. Matt Gard also commented on the unusual encounter: “We want to make sure everything is good, and make sure he knows [that] we appreciate him calling.”  Gard praised Bundy’s efforts and her rock-solid character in an interview with ABC 7: “She’s very much a dedicated employee. It doesn’t surprise us that she goes above and beyond on a regular basis,” he said.  People on Twitter, too, commended her actions.  One user illustrated the subjectivity of emergencies. “911 is the center of all emergencies,” said this person’s tweet.  “This dispatcher clearly understands that it may not be an emergency to us, but it is to somebody. Great job helping this very stressed young man in his time of need.”  Read more at LifeZette.com:   John McCain’s Daughter: ‘I Hate This Country Without Him in It’   ‘The View’ Derails After Co-Hosts Bring Up the Kasich-in-2020 Idea: ‘That’s Crazy!’   Border Patrol Wives Invite Pelosi to See the Reality of the Security Problems in Texas