Nonlinear Quotes

People assume that time is a strict progression of cause to effect, but *actually* from a non-linear, non-subjective viewpoint - it's more like a big ball of wibbly wobbly... time-y wimey... stuff.

You are there and to their ears, being a Syrian sounds like you’re unclean, shameful, indecent; it’s like you owe the world an apology for your very existence.

I am not an atheist preacher. I am not an absolutist or chauvinist whose ways are immune to evolution. My core philosophy is that I might be wrong.

The old law of an eye for an eye didn’t make them blind to the fact that another man’s terrorist wasn’t their freedom fighter.

I was a linear thinker, and according to Zen linear thinking is nothing but a delusion, one of the many that keep us unhappy. Reality is nonlinear, Zen says. No future, no past. All is now.

Actually, from a non-linear, non-subjective viewpoint, its more like a big ball of wibbly wobbly timey wimey...stuff.

For some reason, notwithstanding the alienation and utter rejection, I consider myself a global citizen. They say misery calls for company and I’ve always been a man of funerals. The companion of the misfortunate, until they are not!

The blind faith in some half-assed conspiracy theories lines up with the logic of having to believe in something with no questions asked. It gives us peace and comfort. As simple as I was, I found that resorting to this absolute nonsense was the root of all our problems. It was a road of willingly-learned helplessness, for no action could make a difference, thereby no action was needed.

I have to stress that my duties towards victims of all sorts, be it helping, taking their side, or caring, ends the moment their status becomes a bargaining chip. The moment the victim becomes a righteous sufferer. For in my short time on this planet, history and on-going affairs are full of those competing in victimhood.

For I’m neither a submitter nor a hating retaliator, I acknowledge the boundaries of my existence; yet, I still care. I care regardless of the way they choose to reduce me to the brand that is the birthmark of the accident of my conception. I care less about what that brand signifies in terms of my character, potential, and intentions. For the harmed I care. For the real victims. It’s the most basic of my mandatory civil duties. Only in caring, am I a citizen of the world.

I’ve been told that I cannot change shit, so I might as well stop torturing myself. My emotions are ridiculed and branded as childish. I have been told that the world has given up on my people. I have been told, and realise that on many occasions, I myself am viewed as an outcast by some of those suffering. I’ve been confronted and my answer is always the same: I care even in my most fucked-up moments. I care even when gates of shit pour open to drown me; I care because I am a citizen of the world.

As a citizen of the world, it’s my instinct to keep the fallen and the suffering in my thoughts. The human brain fascinates me; its limitless bounds of empathy. You see, in my mind there is logic to it: do no harm, prevent harm, help, support, care for the harmed, face the harmer. My stupid idealist conscience considers sympathy, not pity, at its worst, the most basic and the least negotiable civil duty. Of course as a citizen of the world, I should strive to do more. That said, I am only a man and so I often do the least.

Today the network of relationships linking the human race to itself and to the rest of the biosphere is so complex that all aspects affect all others to an extraordinary degree. Someone should be studying the whole system, however crudely that has to be done, because no gluing together of partial studies of a complex nonlinear system can give a good idea of the behavior of the whole.

Nonlinear thinking means which way you should go depends on where you already are.

You get paid linearly for analyzing and solving problems. You get paid non-linearly for spotting and siezing opportunities.

Let's face it, the universe is messy. It is nonlinear, turbulent, and chaotic. It is dynamic. It spends its time in transient behavior on its way to somewhere else, not in mathematically neat equilibria. It self-organizes and evolves. It creates diversity, not uniformity. That's what makes the world interesting, that's what makes it beautiful, and that's what makes it work.

You've never heard of Chaos theory? Non-linear equations? Strange attractors? Ms. Sattler, I refuse to believe you're not familiar with the concept of attraction.

Complex systems are full of interdependencies—hard to detect—and nonlinear responses.

In the mantra of shared hatred and placing the blame on Israel, our cowardice to face the barbarity of our heads of states was replaced with a divine purpose. Contemplating the manifestation of the eradication of hatred I often concluded, the entirety of the Middle East’s theocracies and dictatorships would be replaced by total anarchy. We would be left with nothing, as our brotherhood of hatred was the only bond known to us. Enculturated in the malarkey of that demagoguery, forces beyond our control and comprehension seem to deceive us into a less harmful and satisfactory logic as opposed to placing some blame on ourselves and thus, having to act to reverse that state of affairs.

I am evolved as I freed myself from the expectations of others. These memories shape a nonlinear narrative, because queerness is intrinsically nonlinear, journeys that bend and wind. Two steps forward, one step back.

In light of my distanced telescopic exposure to the mayhem, I refused to plagiarise others’ personal tragedies as my own. There is an authorship in misery that costs more than empathy. Often I’d found myself dumbstruck in failed attempts to simulate that particular unfamiliar dolour. After all, no one takes pleasure in being possessed by a wailing father collecting the decapitated head of his innocent six year old. Even on the hinge of a willing attempt at full empathy with those cursed with such catastrophes, one had to have a superhuman emotional powers. I could not, in any way, claim the ability to relate to those who have been forced to swallow the never-ending bitter and poisonous pills of our inherited misfortune. Yet that excruciating pain in my chest seemed to elicit a state of agony in me, even from far behind the telescope. It could have been my tribal gene amplified by the ripple effect of the falling, moving in me what was left of my humanity.

The spot is a self-organizing system, created and regulated by the same nonlinear twists that create the unpredictable turmoil around it. It is stable chaos.

Domino effects give way to butterfly effects given nonlinearity. “Outsized” conflates with “unpredictable” as a small cause yields disproportionate effects.

People assume time is a strict progression of cause to effect, but actually, from a non-linear, non-subjective viewpoint, it's more like a big ball of wibbly wobbly timey wimey stuff

Primed to expect that our lives will follow a predictable path, we’re thrown when they don’t. We have linear expectations but nonlinear realities... We’re all comparing ourselves to an ideal that no longer exists and beating ourselves up for not achieving it.

Imperfect knowledge, incomplete assessment of feedback, limited memory and recall, as well as poor problem-solving skills result in a form of rationality that attains not optimal decisions but more or less satisfactory compromises between conflicting constraints.

You can’t navigate well in an interconnected, feedback-dominated world unless you take your eyes off short-term events and look for long term behavior and structure; unless you are aware of false boundaries and bounded rationality; unless you take into account limiting factors, nonlinearities and delays.

Creativity is a renewable resource. Challenge yourself every day. Be as creative as you like, as often as you want, because you can never run out. Experience and curiosity drive us to make unexpected, offbeat connections. It is these nonlinear steps that often lead to the greatest work.

to call the study of chaos “nonlinear science” was like calling zoology “the study of non elephant animals.

Humans operate on millennia-old hardware. We can comprehend linear relationships, but have trouble processing accelerating rates of change.

In a systemic world, there is no such thing as discrete or isolated events - impacts cascade and spill over. Drivers of disruption collide, intersect, and amplify.

So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician's trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand.[...]It is in those outliers and imperfections that the wildness lurks.

Things designed by people without skin in the game tend to grow in complication (before their final collapse). There is absolutely no benefit for someone in such a position to propose something simple: when you are rewarded for perception, not results, you need to show sophistication. Anyone who has submitted a “scholarly” paper to a journal knows that you usually raise the odds of acceptance by making it more complicated than necessary. Further, there are side effects for problems that grow nonlinearly with such branching-out complications. Worse: Non-skin-in-the-game people don’t get simplicity.

The world is not made up of separate parts operating in isolation. This reductionist view of an understandable, controlled, and predictable world is flawed. And so, the strings, wires, and controls used to manage this illusionary discrete world are obsolete.

Nonlinearity means that the act of playing the game has a way of changing the rules.

The very idea of massified advertising meant that large cirulation newpapers were not in the business of selling information to people but rather of selling the attention of their readers to commercial concerns... to tap into the resorvoir of resources constitutred by the growing urban populations

Chaos theory describes nonlinear systems. It’s now become a very broad theory that’s been used to study everything from the stock market to heart rhythms. A very fashionable theory. Very trendy to apply it to any complex system where there might be unpredictability.

This asymmetry means that the fragile suffers a disproportionate amount of downside from shocks.

Motivation is a fine example of social complexity. It is nonlinear and sometimes unpredictable. It cannot be defined or modeled with a single diagram.

Whenever the whole is different from the sum of the parts—whenever there’s cooperation or competition going on—the governing equations must be nonlinear.

Their incredible determination creates the need for nonlinear thinking, combined with boundless energy. Champions also earn money in nonlinear ways. While the masses essentially trade their time for money, the great ones realize this is probably the worst way to acquire wealth. Using

Linearity is a reductionist’s dream, and nonlinearity can sometimes be a reductionist’s nightmare. Understanding the distinction between linearity and nonlinearity is very important and worthwhile. To

Remember, the thought experiment is the starting point, not the end. The process is messy and nonlinear. And the answer, as we’ll see in the next section, will often come when you’re least expecting it.

The most important question for every client is "W X ho are you?" I'm not as interested in an answer as I am in teaching a process that the girl can use for the rest of her life. The process involves looking within to find a true core of self, acknowledging unique gifts, accepting all feelings, not just the socially acceptable ones, and making deep and firm decisions about values and meaning. The process includes knowing the difference between thinking and feeling, between immediate gratification and long-term goals, and between her own voice and the voices of others. The process includes discovering the personal impact of our cultural rules for women. It includes discussion about breaking those rules and formulating new, healthy guidelines for the self. The process teaches girls to chart a course based on the dictates of their true selves. The process is nonlinear, arduous, and discouraging. It is also joyful, creative and full of surprises.

People take the longest possible paths, digress to numerous dead ends, and make all kinds of mistakes. Then historians come along and write summaries of this messy, nonlinear process and make it appear like a simple, straight line.

The suppression dates back to the early Christians who tried to root out calendrical paganism, denounced classical cycles, and pushed underground entire branches of nonlinear learning, such as the hermetic fields of alchemy and astrology.

Chaos has become not just theory but also method, not just a canon of beliefs but also a way of doing science.

A chaotic system could be stable if its particular brand of irregularity persisted in the face of small disturbances.

That was acceptable, his father told him: you can always try to solve a problem by proving that no solution exists.

Revolutions do not come piecemeal. One account of nature replaces another.

physicist Paul Davies comments, nonlinear systems “possess the remarkable ability to leap spontaneously from relatively featureless states to those involving complex cooperative behavior.”5 And those behaviors? They can be as different as water to ice.

But [in bureaucracies], too, decision making takes place in a world full of unceratinties. Any actual system of information processing, planning and control will never be optimal but merely practical, applying rote responses to recurrent problems and employing a variety of contingency tactics to deal with unforeseen events.

If non-linear leaps in intelligence and ability are possible, why haven't these effects been observed in our schools? I believe the answer lies in the profound inertia of human thought: when an entire society believes something is impossible, it suppresses, by its very way of life, the evidence that would contradict that belief.

Nonlinearities are important not only because they confound our expectations about the relationship between action and response. They are even more important because they change the relative strengths of feedback loops. They can flip a system from one mode of behavior to another.

The solvable systems are the ones shown in textbooks. They behave. Confronted with a nonlinear system, scientists would have to substitute linear approximations or find some other uncertain backdoor approach. Textbooks showed students only the rare non-linear systems that would give way to such techniques. They did not display sensitive dependence on initial conditions. Nonlinear systems with real chaos were rarely taught and rarely learned. When people stumbled across such things-and people did-all their training argued for dismissing them as aberrations. Only a few were able to remember that the solvable, orderly, linear systems were the aberrations. Only a few, that is, understood how nonlinear nature is in its soul. Enrico Fermi once exclaimed, "It does not say in the Bible that all laws of nature are expressible linearly!" The mathematicians Stanislaw Ulam remarked that to call the study of chaos "nonlinear science" was like calling zoology "the study of nonelephant animals.

Complexity arises from the interaction of many parts, giving rise to difficulties in linear or reductionist analysis due to the nonlinearities generated by the interactions. Such nonlinear effects emerge from both positive (amplifying) and negative (damping) feedbacks, the key ingredients of complex systems.

This is how you discover your life’s meaning—by focusing on your daily actions rather than the content of your future eulogy. When generativity becomes your focus, the immediate impact of your actions is all the motivation you need. Every pact you make, every shift, every “What if?” becomes not just a step in your own journey, but a chance to inspire and elevate others. Your career is no longer a linear ladder you climb alone, but a nonlinear path of shared discovery.

In America's 'nonlinear war', with no frontline or clear political or territorial goals, the number of enemy killed apparently revealed who was 'winning'. 'The military kill' became 'the prime target, simply because the essential political target is too elusive for us, or worse, because we do not understand its importance'.

One of our greatest fears is to eat the wildness of the world. Our mothers intuitively understood something essential: the green is poisonous to civilization. If we eat the wild, it begins to work inside us, altering us, changing us. Soon, if we eat too much, we will no longer fit the suit that has been made for us. Our hair will begin to grow long and ragged. Our gait and how we hold our body will change. A wild light begins to gleam in our eyes. Our words start to sound strange, nonlinear, emotional. Unpractical. Poetic. Once we have tasted this wildness, we begin to hunger for a food long denied us, and the more we eat of it the more we will awaken.

Primed to expect that our lives will follow a predictable path, we’re thrown when they don’t. We have linear expectations but nonlinear realities. Even people who are linear in one area (a stable career, say, or long-running marriage) are nonlinear in others (recurrent health problems or frequent changes in their religious identity).

So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician's trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand.[...]Even though many economic and financial variables fall into distributions that approximate a bell curve, the picture is never perfect.[...]It is in those outliers and imperfections that the wildness lurks.

We have minds that are equipped for certainty, linearity and short-term decisions, that must instead make long-term decisions in a non-linear, probabilistic world.

The repetitions were never quite exact. There was pattern, with disturbances. An orderly disorder.

R6 explicitly acknowledges the non-linear, iterative nature of change.

Some carry out their work explicitly denying that it is a revolution; others deliberately use Kuhn’s language of paradigm shifts to describe the changes they witness.

In non-linear environments, assumptions amplify.

Spiderwebs are images of the nonlinear, of the many directions in which something might go, the many sources for it[.]

In the real, physical world or business world, most relationships are nonlinear.

It would be preferable if we were better at understanding cancer or the (highly nonlinear) weather than the origin of the universe. How

Utilizing a nonlinear approach and companion competencies makes it possible for people to move from good performance to great.

New Generation warfare was a multidimensional, nonlinear strategy that engineered and exploited social, moral, ethnic, and political tensions within a target country.

I would rather call evolution an "emergence myth" than an origin myth: it's an ongoing, nonlinear story in which past, present, and future all communicate with each other.

Kairos is sacred time, a nonlinear awareness that is an empath’s truer home.

The world is nonlinear. Trying to make it linear for our mathematical or administrative convenience is not usually a good idea even when feasible, and it is rarely feasible.

Man is the lowest-cost, 150-pound, nonlinear, all-purpose computer system which can be mass-produced by unskilled labor.

And, uh . . . to whom do you pray?' 'We worship the perfect cohesion of space and time and nonlinear probabilities represented by cabbage.' 'Wow, that's . . . yeah.

The solution lies in seeking out something that is neither good nor perfect. You want something remarkable, nonlinear, game changing, and artistic.

Though it was nonlinear and nonsensical, my path made perfect sense once I truly started walking it. I’d finally discovered an outlet for everything that had been trapped inside me.

Steve understood the value of science and law, but he also understood that complex systems respond in nonlinear, unpredictable ways. And that creativity, at its best, surprises us all.

In my early teens, I heard about Naked Lunch and its mutating typewriters and talking cockroaches. While I would hardly classify its dystopic vision as erotica now, at the time, Naked Lunch was my first foray into consuming smut. It was because of Burroughs that I knew about the particular musk that blooms when a rectum is penetrated, and that death-by-hanging produces spontaneous trouser tents. The first Burroughs I read was Naked Lunch, but I buried myself in a few of his stories, and thus the arc of my recollection is just as non-linear as his narrative.

Even more important is the way complex systems seem to strike a balance between the need for order and the imperative for change. Complex systems tend to locate themselves at a place we call “the edge of chaos.” We imagine the edge of chaos as a place where there is enough innovation to keep a living system vibrant, and enough stability to keep it from collapsing into anarchy. It is a zone of conflict and upheaval, where the old and new are constantly at war. Finding the balance point must be a delicate matter—if a living system drifts too close, it risks falling over into incoherence and dissolution; but if the system moves too far away from the edge, it becomes rigid, frozen, totalitarian. Both conditions lead to extinction. . . . Only at the edge of chaos can complex systems flourish.8 This threshold line, that edge between anarchy and frozen rigidity, is not a like a fence line, it is a fractal line; it possesses nonlinearity.

All right,” Malcolm said. “Let’s go back to the beginning.” He paused, staring at the ceiling. “Physics has had great success at describing certain kinds of behavior: planets in orbit, spacecraft going to the moon, pendulums and springs and rolling balls, that sort of thing. The regular movement of objects. These are described by what are called linear equations, and mathematicians can solve those equations easily. We’ve been doing it for hundreds of years.” “Okay,” Gennaro said. “But there is another kind of behavior, which physics handles badly. For example, anything to do with turbulence. Water coming out of a spout. Air moving over an airplane wing. Weather. Blood flowing through the heart. Turbulent events are described by nonlinear equations. They’re hard to solve—in fact, they’re usually impossible to solve. So physics has never understood this whole class of events. Until about ten years ago. The new theory that describes them is called chaos theory.

IN CHAOS THEORY, THE BUTTERFLY EFFECT IS THE SENSITIVE DEPENDENCY ON INITIAL CONDITIONS IN WHICH A SMALL CHANGE AT ONE PLACE IN A DETERMINISTIC NONLINEAR SYSTEM CAN RESULT IN LARGE DIFFERENCES IN A LATER STATE.

The real issues aren’t the quarks that hold together our physical bodies. The real issue is our own personal nonlinearity - the real us. We can’t see our real selves; we only see the containers we happen to be in right now. The real “us” is software, not hardware, which means it’s without mass, which means it has no time. We are eternal - saved or not. That’s the problem, because we each have an eternity ahead of us. Where will we spend it?

Algorithmic complexity theory and nonlinear dynamics together establish the fact that determinism reigns only over a quite finite domain; outside this small haven of order lies a largely uncharted, vast wasteland of chaos.

Many organizations and militaries use VUCA as an acronym to describe the disruptive state of the world, given its Volatility, Uncertainty, Complexity, and Ambiguity. UN-VICE is an updated way of capturing the state and velocity of the world, with our acronym for UNknown, Volatile, Intersecting, Complex, and Exponential: - UNknown: Recognizing that you can’t know anything perfectly, and that many of our decisions are based on assumptions. Increased uncertainty lowers the value of ad-vice and requires increased self-reliance. - Volatile: Our world, and change itself, is evolving faster than ever before. Volatility is not inherently good or bad; it is simply impactful. In volatility we see shifting speed, texture, and magnitude of the changing environment. - Intersecting: The broader our filters, the more we realize that what we observe overlaps with other things. Boundaries are disappearing, connecting new areas through combinations. - Complex: These more-than-complicated systems have unreliable input-output relationships and cannot be summarized or modeled without losing their essence. Unpredictable situations with unknown unknowns. - Exponential: A nonlinear type of change that increases in its growth rate. To an observer, this change may happen gradually, then suddenly. Rapid acceleration of seemingly-small shifts.

In non linear systems-and the economy is most certainly nonlinear-chaos theory tells you that the slightest uncertainty in your knowledge of the initial conditions will often grow inexorably. After a while, your predictions are nonsense.

Our brain is not cut out for nonlinearities. People think that if, say, two variables are causally linked, then a steady input in one variable should always yield a result in the other one. Our emotional apparatus is designed for linear causality. For

Nonlinearity means that the act of playing the game has a way of changing the rules. [...] Analyzing the behavior of a nonlinear equation like the Navier-Stokes equation is like walking through a maze whose walls rearrange themselves with each step you take.

Glutamate signaling works in a fancier way that is essential to learning.2 To simplify considerably, while dendritic spines typically contain only one type of receptor, those responsive to glutamate contain two. The first (the “non-NMDA”) works in a conventional way—for every little smidgen of glutamate binding to these receptors, a smidgen of sodium flows in, causing a smidgen of excitation. The second (the “NMDA”) works in a nonlinear, threshold manner. It is usually unresponsive to glutamate. It’s not until the non-NMDA has been stimulated over and over by a long train of glutamate release, allowing enough sodium to flow in, that this activates the NMDA receptor. It suddenly responds to all that glutamate, opening its channels, allowing an explosion of excitation.

One of the ideas of this book is to give the reader a possibility to develop problem-solving skills using both systems, to solve various nonlinear PDEs in both systems. To achieve equal results in both systems, it is not sufficient simply “to translate” one code to another code. There are numerous examples, where there exists some predefined function in one system and does not exist in another. Therefore, to get equal results in both systems, it is necessary to define new functions knowing the method or algorithm of calculation.

By contrast, a twentieth-century fluid dynamicist could hardly expect to advance knowledge in his field without first adopting a body of terminology and mathematical technique. In return, unconsciously, he would give up much freedom to question the foundations of his science.

What is our UN-VICE in the context of Disruption 3.0? To sum up, UN-VICE is an updated way of capturing the state of the world. Framing the dynamics of systemic disruption as UNknown, Volatile, Intersecting, Complex, Exponential enables an empowering response. We are not helpless victims unable to make decisions. With UN-VICE, we have the power to shape our own futures. KEY POINTS: OUR UN-VICE ACRONYM - UNknown: Uncertainty becomes our comfort zone. Recognize you can’t know anything perfectly and many decisions are based on assumptions. Increased uncertainty lowers the value of advice and requires increased self-reliance. Learn how to respond regardless of the lack of precedents. - Volatile: Harness change for gain. Our world, and change itself, is evolving faster than ever before. Volatility is not new; we simply can’t ignore its impact. In volatility, we see the shifting speed and texture of the changing environment. - Intersecting: Everything connects to everything else. The broader our lens, the greater the insights gained from realizing how boundaries are disappearing. - Complex: Notice emergent properties and adapt. In complex environments, inputs do not map clearly to outputs. Practitioners must acknowledge emergent properties and reconcile the immediate with the indefinite. Such systems require critical thinking, experimentation, and judgment. Evaluate emerging issues, build resiliency, and learn to adapt to expanding complexity. - Exponential: Pay attention to nonlinear types of change that increase in growth rate. Notice rapid acceleration of seemingly small shifts. Monitoring early on will mean fewer surprises.

The two board games that best approximate the strategies of war are chess and the Asian game of go. In chess, the board is small. In comparison to go, the attack comes relatively quickly, forcing a decisive battle.... Go is much less formal. It is played on a large grid, with 361 intersections — nearly six times as many positions as in chess.... [A game of go] can last up to three hundred moves. The strategy is more subtle and fluid than chess, developing slowly; the more complex the pattern your stones initially create on the board, the harder it is for your opponent to understand your strategy. Fighting to control a particular area is not worth the trouble: You have to think in larger terms, to be prepared to sacrifice an area in order eventually to dominate the board. What you are after is not an entrenched position but mobility. With mobility you can isolate your opponent in small areas and then encircle them... Chess is linear, position oriented, and aggressive; go is nonlinear and fluid. Aggression is indirect until the end of the game, when the winner can surround the opponents' stones at an accelerated pace.

Warping begets warping in a nonlinear, self-bootstrapping manner. This is a fundamental feature of Einstein’s relativistic laws, and so different from everyday experience. It’s somewhat like a hypothetical science-fiction character who goes backward in time and gives birth to herself.

Indeed, except for the very simplest physical systems, virtually everything and everybody in the world is caught up in a vast, nonlinear web of incentives and constraints and connections. The slightest change in one place causes tremors everywhere else. We can't help but disturb the universe, as T.S. Eliot almost said. The whole is almost always equal to a good deal more than the sum of its parts. And the mathematical expression of that property-to the extent that such systems can be described by mathematics at all-is a nonlinear equation: one whose graph is curvy.

The value (“fitness”) of a given combination of building blocks often cannot be predicted by a summing up of values assigned to the component blocks. This nonlinearity (commonly called epistasis in genetics) leads to co-adapted sets of blocks (alleles) that serve to bias sampling and add additional layers to the hierarchy.

There are numerous brain rhythms, from approximately 0.02 to 600 cycles per second (Hz), covering more than four order of temporal magnitude. Many of these discrete brain rhythms have been known for decades, but it was only recently recognized that these oscillation bands form a geometric progression on a linear frequency scale or a linear progression on a natural logarithmic scale. leading to a natural separation of at least ten frequency bands. The neighbouring bands have a roughly constant ratio of e = 2,718 - the base for the natural logarithm. Because of this non-integer relationship among the various brain rhythms, the different frequencies can never perfectly entrain each other. Instead, the interference they produce gives rise to metastability, a perpetual fluctuation between unstable and transiently stable states, like waves in the ocean. The constantly interfering network rhythms can never settle to a stable attractor, using the parlance of nonlinear dynamics. This explains the ever-changing landscape of the EEG.

Time Warrior gives us a revolutionary, non-linear approach for dealing with time, as bold as it is fresh and new.

The Procrustean bed in life consists precisely in simplifying the non-linear and making it linear—the simplification that distorts.

The Butterfly Effect was no accident; it was necessary.

The repetitions were never quite exact. There was pattern, with disturbances. An orderly disorder.

That’s what procrastination does. It gives you enough time to consider divergent ideas, to think in non-linear ways, and to make unexpected moves.

So (and this would have happened earlier, but I am only remembering it now): I am visiting her one afternoon.

If you need to visualize the soul, think of it as a cross between a wolf howl, a photon, and a dribble of dark molasses. But what it really is, as near as I can tell, is a packet of information. It’s a program, a piece of hyperspatial software designed explicitly to interface with the Mystery. Not a mystery, mind you, the Mystery. The one that can never be solved. To one degree or another, everybody is connected to the Mystery, and everybody secretly yearns to expand the connection. That requires expanding the soul. These things can enlarge the soul: laughter, danger, imagination, meditation, wild nature, passion, compassion, psychedelics, beauty, iconoclasm, and driving around in the rain with the top down. These things can diminish it: fear, bitterness, blandness, trendiness, egotism, violence, corruption, ignorance, grasping, shining, and eating ketchup on cottage cheese. Data in our psychic program is often nonlinear, nonhierarchical, archaic, alive, and teeming with paradox. Simply booting up is a challenge, if not for no other reason than that most of us find acknowledging the unknowable and monitoring its intrusions upon the familiar and mundane more than a little embarrassing. But say you’ve inflated your soul to the size of a beach ball and it’s soaking into the Mystery like wine into a mattress. What have you accomplished? Well, long term, you may have prepared yourself for a successful metamorphosis, an almost inconceivable transformation to be precipitated by your death or by some great worldwide eschatological whoopjamboreehoo. You may have. No one can say for sure. More immediately, by waxing soulful you will have granted yourself the possibility of ecstatic participation in what the ancients considered a divinely animated universe. And on a day to day basis, folks, it doesn’t get any better than that.

Recognition for us is about presence, about profound listening, and about recognizing and affirming the light in each other as a mechanism for nurturing and strengthening internal relationships to our Nishnaabeg worlds. It is a core part of our political systems because they are rooted in our bodies and our bodies are not just informed by but created and maintained by relationships of deep reciprocity. Our bodies exist only in relation to Indigenous complex, nonlinear constructions of time, space, and place that are continually rebirthed through the practice and often coded recognition of obligations and responsibilities within a nest of diversity, freedom, consent, noninterference, and a generated, proportional, emergent reciprocity.

There is no linear additive process that, if all the parts are taken together, can be understood to create the total system that occurs at the moment of self-organization; it is not a quantity that comes into being. It is not predictable in its shape or subsequent behavior or its subsequent qualities. There is a nonlinear quality that comes into being at the moment of synchronicity.

Most recently, the task of assembling the genetic story for specific phenotypic traits has begun. It is still in its early stages, but progress is accelerating nonlinearly. Hence the nervousness that has prevented open discussion of what’s going on in the geneticists’ parallel universe: the fear that we will discover scary population differences in what I have called cognitive repertoires.

In a non-linear and relative world, each person is empowered to change the course and meaning of their life completely. That change only takes an instant; it is a leap through a wormhole. Perceived

Implicitly, the mission of many twentieth-century scientists — biologists, neurologists, economists — has been to break their universes down into the simplest atoms that will obey scientific rules.

Implicitly, the mission of many twentieth-century scientists — biologists, neurologists, economists — has been to break their universes down into the simplest atoms that will obey scientific rules.

I am also realizing the nonlinear effect behind success in anything: It is better to have a handful of enthusiastic advocates than hordes of people who appreciate your work—better to be loved by a dozen than liked by the hundreds. This applies to the sales of books, the spread of ideas, and success in general and runs counter to conventional logic. The information age is worsening this effect.

When one combines the new insights gained from studying far-from-equilibrium states and nonlinear processes, along with these complicated feedback systems, a whole new approach is opened that makes it possible to relate the so-called hard sciences to the softer sciences of life—and perhaps even to social processes as well. (Such findings have at least analogical significance for social, economic or political realities. Words like “revolution,” “economic crash,” “technological upheaval,” and “paradigm shift” all take on new shades of meaning when we begin thinking of them in terms of fluctuations, feedback amplification, dissipative structures, bifurcations, and the rest of the Prigoginian conceptual vocabulary.) It is these panoramic vistas that are opened to us by Order Out of Chaos.

My sense of narrative structure was shaped by ROM (Spaceknight) comics. I'd find random issues at the flea market and read them out of order with no context. The entire series was based on a toy I never owned. None of this made any difference.

This synergistic character of nonlinear systems is precisely what makes them so difficult to analyze. They can’t be taken apart. The whole system has to be examined all at once, as a coherent entity. As we’ve seen earlier, this necessity for global thinking is the greatest challenge in understanding how large systems of oscillators can spontaneously synchronize themselves. More generally, all problems about self-organization are fundamentally nonlinear. So the study of sync has always been entwined with the study of nonlinearity.

One other thing—two men are about four times as effective as one man. There’s actually a study about it. ‘Non-Linear Tactical Factors In Small-Unit Engagements,’ I think the title is. It’s part of the syllabus at Recon School.” “Marines really do know how to read, eh?

New Generation warfare was a multidimensional, nonlinear strategy that engineered and exploited social, moral, ethnic, and political tensions within a target country. It included arming and training local civilians as paramilitary units, often seeded and even led by Russian Spetsnaz special operators posing as civilian fighters. New Gen warfare also appealed to ethnic unity, and against ethnic discrimination by the local government, and pushed those narratives out into the public arena through sophisticated mass media campaigns and “fake news.

I also employ the "scatter" technique of Sufi writers. Topics do not always appear in linear, "logical" order, but in a non-linear psycho-logical order calculated to produce new ways of thinking and perceiving. This technique also intends to assist the process of "internalization.

Meanwhile, people are busy using fractals to explain any system that has defied other, more reductionist approaches. Since they were successfully applied by IBM's Benoit Mandlebrot to the problem of seemingly random, intermittent interference on the phone lines, fractals have been used to identify underlying patterns in weather systems, computer files, and bacteria cultures. Sometimes fractal enthusiasts go a bit too far, however, using these nonlinear equations to mine for patterns in systems where none exist. Applied to the stock market to consumer behavior, fractals may tell less about those systems than about the people searching for patterns within them. There is a dual nature to fractals: They orient us while at the same time challenging our sense of scale and appropriateness. They offer us access to the underlying patterns of complex systems while at the same time tempting us to look for patterns where none exist. This makes them a terrific icon for the sort of pattern recognition associated with present shock—a syndrome we'll call factalnoia. Like the robots on Mystery Science Theater 3000, we engage by relating one thing to another, even when the relationship is forced or imagined. The tsunami makes sense once it is connected to chemtrails, which make sense when they are connected to HAARP. It's not just conspiracy theorists drawing fractalnoid connections between things. In a world without time, any and all sense making must occur on the fly. Simultaneity often seems like all we have. That's why anyone contending with present shock will have a propensity to make connections between things happening in the same moment—as if there had to be an underlying logic.

All this comes under the heading of what the journalist Thomas L. Friedman has called “the really scary stuff we already know.” Much worse is what he calls “the even scarier stuff we don’t know.” The problem, Friedman explains, is that what we face is not global warming but “global weirding.” Climate change is nonlinear: everything is connected to everything else, feeding back in ways too bewilderingly complex to model. There will be tipping points when the environment shifts abruptly and irreversibly, but we don’t know where they are or what will happen when we reach them.

The Newtonian model of biology is based on linear events in which chemical reactions occur in a sequence of steps. But that’s not actually how biology works; you can no longer explain something even as simple as how a cut heals without the understanding of the interconnected coherent information pathways you just read about. Cells share an intercommunication of information in a nonlinear way. The universe and all the biological systems within it share an integration of independent, entangled energy fields that, in turn, share information beyond space and time on a moment-to-moment basis.

There is a new science of complexity which says that the link between cause and effect is increasingly difficult to trace; that change (planned or otherwise) unfolds in non-linear ways; that paradoxes and contradictions abound; and that creative solutions arise out of diversity, uncertainty and chaos.

Had he stopped with the Butterfly Effect, an image of predictability giving way to pure randomness, then Lorenz would have produced no more than a piece of very bad news. But Lorenz saw more than randomness embedded in his weather model. He saw a fine geometrical structure, order masquerading as randomness.

Had he stopped with the Butterfly Effect, an image of predictability giving way to pure randomness, then Lorenz would have produced no more than a piece of very bad news. But Lorenz saw more than randomness embedded in his weather model. He saw a fine geometrical structure, order masquerading as randomness.

It uses the greatest random-access indexing system ever invented—one that computer scientists haven’t come even close to replicating. Whereas an index in the back of a book provides a single address—a page number—for each important subject, each subject in the brain has hundreds if not thousands of addresses. Our internal memories are associational, nonlinear. You don’t need to know where a particular memory is stored in order to find it. It simply turns up—or doesn’t—when you need it. Because of the dense network that interconnects our memories, we can skip around from memory to memory and idea to idea very rapidly.

Digital computers are themselves more complex than most things people build; they have very large numbers of states. This makes conceiving, describing, and testing them hard. Software systems have orders of magnitude more states than computers do. Likewise, a scaling-up of a software entity is not merely a repetition of the same elements in larger size; it is necessarily an increase in the number of different elements. In most cases, the elements interact with each other in some nonlinear fashion, and the complexity of the whole increases much more than linearly. The complexity of software is an essential property, not an accidental one.

Human history is a long saga of people learning to harness ever-increasing amounts of energy to maintain ever more complex, ordered systems, punctuated by periodic collapses—the Romans, the Maya—when civilizations became more complex than they could maintain, with the energy and technologies they had, in the face of changing conditions. At that point, small stresses sent overstretched social systems into a rapid downward spiral, which ended with major losses of people and social organization, as one stable complex system made a rapid nonlinear descent to a less complex one. But after a setback, humanity always innovated and rebuilt, a little bigger and more complex than before.

Basically, what I'm saying is not at all new to Eastern philosophy. It's never seen the world as anything else but a complex system. But it's a world view that, decade by decade, is becoming more important in the West-both in science and in the culture at large. Very, very slowly, there's been a gradual shift from an exploitative view of nature-man versus nature-to an approach that stresses the mutual accomodation of man and nature. What has happened is that we're beginning to lose our innocence, or naivete, about how the world works. As we begin to understand complex systems, we begin to understand that we're part of an ever-changing, interlocking, nonlinear, kaleidoscopic world.

In science as in life, it is well known that a chain of events can have a point of crisis that could magnify small changes. But chaos meant that such points were everywhere. They were pervasive. In systems like the weather, sensitive dependence on initial conditions was an inescapable consequence of the way small scales intertwined with large.

In science as in life, it is well known that a chain of events can have a point of crisis that could magnify small changes. But chaos meant that such points were everywhere. They were pervasive. In systems like the weather, sensitive dependence on initial conditions was an inescapable consequence of the way small scales intertwined with large.

Chaos should be taught, he argued. It was time to recognize that the standard education of a scientist gave the wrong impression. No matter how elaborate linear mathematics could get, with its Fourier transforms, its orthogonal functions, its regression techniques, May argued that it inevitably misled scientists about their overwhelmingly nonlinear world. “The mathematical intuition so developed ill equips the student to confront the bizarre behaviour exhibited by the simplest of discrete nonlinear systems,” he wrote. “Not only in research, but also in the everyday world of politics and economics, we would all be better off if more people realized that simple nonlinear systems do not necessarily possess simple dynamical properties.

Taking least squares is no longer optimal, and the very idea of ‘accuracy’ has to be rethought. This simple fact is as important as it is neglected. This problem is easily illustrated in the Logistic Map: given the correct mathematical formula and all the details of the noise model – random numbers with a bell-shaped distribution – using least squares to estimate α leads to systematic errors. This is not a question of too few data or insufficient computer power, it is the method that fails. We can compute the optimal least squares solution: its value for α is too small at all noise levels. This principled approach just does not apply to nonlinear models because the theorems behind the principle of least squares repeatedly assume bell-shaped distributions.

At the same time, Kaufmann discovered that in developing his genetic networks, he had reinvented some of the most avant-garde work in physics and applied mathematics-albeit in a totally new context. The dynamics of his genetic regulatory networks turned out to be a special case of what the physicists were calling "nonlinear dynamics." From the nonlinear point of view, in fact, it was easy to see why his sparsely connected networks could organize themselves into stable cycles so easily: mathematically, their behavior was equivalent to the way all the rain falling on the hillsides around a valley will flow into a lake at the bottom of the valley. In the space of all possible network behaviors, the stable cycles were like basins-or as the physicists put it, "attractors.

The quantum attention function can reduce a wave instantaneously to a tiny local region. The wave function evolves naturally, without an observer, from a mix of states into a single, well-defined state. To measure we introduced a matrix of extra non-linear mathematical components known as attention function, which rapidly promotes one state at the expense of others, in a stochastic way.

The previous two chapters can basically be distilled to the following: —“Break it down to its component parts” reductionism doesn’t work for understanding some vastly interesting things about us. Instead, in such chaotic systems, minuscule differences in starting states amplify enormously in their consequences. —This nonlinearity makes for fundamental unpredictability, suggesting to many that there is an essentialism that defies reductive determinism, meaning that the “there can’t be free will because the world is deterministic” stance goes down the drain. —Nope. Unpredictable is not the same thing as undetermined; reductive determinism is not the only kind of determinism; chaotic systems are purely deterministic, shutting down that particular angle of proclaiming the existence of free will.

The computer will still be unable to predict whether Princeton, New Jersey, will have sun or rain on a day one month away. At noon the spaces between the sensors will hide fluctuations that the computer will not know about, tiny deviations from the average. By 12:01, those fluctuations will already have created small errors one foot away. Soon the errors will have multiplied to the ten-foot scale, and so on up to the size of the globe.

When I first started dual enrollment at Lake City Community College you could print in the library for free. I printed whole books. Like James Legge's 1891 "Tao Te Ching" translation. He was to parentheses what Emily Dickinson was to the Em Dash. "To know and yet (think) we do not know is the highest (at­tain­ment); not to know (and yet think) we do know is a dis­ease." I'd sit around listening to records as their dot matrix printer whirred. Slowly printing a book from the 6th century BCE. They had those hard blue plastic headphones. Your ears would ache. But Rimsky-Korsakov was pretty metal. Herbert Benson's "The Relaxation Response" had me picking "ZOOM" as my meditation mantra. Reading Vonnegut with his nonlinear narrative. Books will often have Acknowledgments. A page or two. Things that helped you. What matters. Everything I write is an Acknowledgment. What matters. And I've printed whole books.

Blurring the line between possible and impossible, linear and non-linear time, fiction and reality, fate and free will, 1Q84 is both a metaphysical mind-teaser and a fast-paced thriller where the stakes for Tengo and Aomame couldn’t be any higher. Murakami’s most ambitious novel to date, 1Q84 is also an extraordinary love story, a story about the power of a single moment of deep connection to transcend time and space—and justify even the greatest of risks.

The books written by Paul Valéry, Walter Benjamin, Ludwig Wittgenstein, Marshall McLuhan, Gilles Deleuze, Douglas Hofstadter, and Niklas Luhmann can be understood as attempts to do justice to the New Media world at a level of technical depiction. And what is more: these books are no longer books in the strict sense of the word, but mosaics consisting of quotations and fragments of thought. They perform an art of writing which might be called cinematic - composing books as if they were movies. These books try to burst through the limits of the book form. Of course, most of these attempts have failed. But even this failure is instructive. The information processing system ‘book’ is clearly no longer up to the complexity of our social systems. For this reason, authors who are aware of this and yet want to remain authors, organise their books according to structures and patterns taken from nonlinear information processing systems (BoIz, 1994, p. 2).

Hunting in my experience—and by hunting I simply mean being out on the land—is a state of mind. All of one’s faculties are brought to bear in an effort to become fully incorporated into the landscape. It is more than listening for animals or watching for hoofprints or a shift in the weather. It is more than an analysis of what one senses. To hunt means to have the land around you like clothing. To engage in a wordless dialogue with it, one so absorbing that you cease to talk with your human companions. It means to release yourself from rational images of what something “means” and to be concerned only that it “is.” And then to recognize that things exist only insofar as they can be related to other things. These relationships—fresh drops of moisture on top of rocks at a river crossing and a raven’s distant voice—become patterns. The patterns are always in motion. Suddenly the pattern—which includes physical hunger, a memory of your family, and memories of the valley you are walking through, these particular plants and smells—takes in the caribou. There is a caribou standing in front of you. The release of the arrow or bullet is like a word spoken out loud. It occurs at the periphery of your concentration. The mind we know in dreaming, a nonrational, nonlinear comprehension of events in which slips in time and space are normal, is, I believe, the conscious working mind of an aboriginal hunter. It is a frame of mind that redefines patience, endurance, and expectation. The focus of a hunter in a hunting society was not killing animals but attending to the myriad relationships he understood bound him into the world he occupied with them. He tended to those duties carefully because he perceived in them everything he understood about survival. This does not mean, certainly, that every man did this, or that good men did not starve. Or that shamans whose duty it was to intercede with the forces that empowered these relationships weren’t occasionally thinking of personal gain or subterfuge. It only means that most men understood how to behave.

Vibration always worried Libchaber. Experiments, like real nonlinear systems, existed against a constant background of noise. Noise hampered measurement and corrupted data. In sensitive flows—and Libchaber’s would be as sensitive as he could make it—noise might sharply perturb a nonlinear flow, knocking it from one kind of behavior into another. But nonlinearity can stabilize a system as well as destabilize it. Nonlinear feedback regulates motion, making it more robust. In a linear system, a perturbation has a constant effect. In the presence of nonlinearity, a perturbation can feed on itself until it dies away and the system returns automatically to a stable state. Libchaber believed that biological systems used their nonlinearity as a defense against noise. The transfer of energy by proteins, the wave motion of the heart’s electricity, the nervous system—all these kept their versatility in a noisy world. Libchaber hoped that whatever structure underlay fluid flow would prove robust enough for his experiment to detect.

analogue tape is notoriously forgiving on transient peaks, applying small amounts of tape saturation (or distortion) on the occasional stray hit, and thereby keeping the transient levels in some degree of order. Of course, in an entirely digital production chain, it’s highly likely that these transient peaks have passed through the majority of recording and mixing without any of these pleasant ‘non-linearities’ slipping in, and therefore the average level is several decibels quieter than a comparable analogue recording.

Paint in several colors was squeezed out of tubes and mixed and applied to woven fabric stretched on a wooden frame so artfully we say we see a woman hanging out a sheet rather than oil on canvas. Ana Teresa Fernandez’s image on that canvas is six feet tall, five feet wide, the figure almost life-size. Though it is untitled, the series it’s in has a title: Telaraña. Spiderweb. The spiderweb of gender and history in which the painted woman is caught; the spiderweb of her own power that she is weaving in this painting dominated by a sheet that was woven. Woven now by a machine, but before the industrial revolution by women whose spinning and weaving linked them to spiders and made spiders feminine in the old stories. In this part of the world, in the creation stories of the Hopi, Pueblo, Navajo, Choctaw, and Cherokee peoples, Spider Grandmother is the principal creator of the universe. Ancient Greek stories included an unfortunate spinning woman who was famously turned into a spider as well as the more powerful Greek fates, who spun, wove, and cut each person’s lifeline, who ensured that those lives would be linear narratives that end. Spiderwebs are images of the nonlinear, of the many directions in which something might go, the many sources for it; of the grandmothers as well as the strings of begats. There’s a German painting from the nineteenth century of women processing the flax from which linen is made. They wear wooden shoes, dark dresses, demure white caps, and stand at various distances from a wall, where the hanks of raw material are being wound up as thread. From each of them, a single thread extends across the room, as though they were spiders, as though it came right out of their bellies. Or as though they were tethered to the wall by the fine, slim threads that are invisible in other kinds of light. They are spinning, they are caught in the web. To spin the web and not be caught in it, to create the world, to create your own life, to rule your fate, to name the grandmothers as well as the fathers, to draw nets and not just straight lines, to be a maker as well as a cleaner, to be able to sing and not be silenced, to take down the veil and appear: all these are the banners on the laundry line I hang out.

According to chaos theory, although it is impossible to predict the individual behavior of each element in a complex dynamic system (for instance, the individual neurons or neuronal groups in the primary visual cortex), patterns can be discerned at a higher level by using mathematical models and computer analyses. There are “universal behaviors” which represent the ways such dynamic, nonlinear systems self-organize. These tend to take the form of complex reiterative patterns in space and time—indeed the very sorts of networks, whorls, spirals, and webs that one sees in the geometrical hallucinations of migraine. Such chaotic, self-organizing behaviors have now been recognized in a vast range of natural systems, from the eccentric motions of Pluto to the striking patterns that appear in the course of certain chemical reactions to the multiplication of slime molds or the vagaries of weather. With this, a hitherto insignificant or unregarded phenomenon like the geometrical patterns of migraine aura suddenly assumes a new importance. It shows us, in the form of a hallucinatory display, not only an elemental activity of the cerebral cortex but an entire self-organizing system, a universal behavior, at work.*3

In daily life, the Lorenzian quality of sensitive dependence on initial conditions lurks everywhere. A man leaves the house in the morning thirty seconds late, a flowerpot misses his head by a few millimeters, and then he is run over by a truck. Or, less dramatically, he misses a bus that runs every ten minutes—his connection to a train that runs every hour. Small perturbations in one’s daily trajectory can have large consequences. A batter facing a pitched ball knows that approximately the same swing will not give approximately the same result, baseball being a game of inches. Science, though—science was different.

Conscious mind-brain, as an emergent functionality is a systemic emergence – phase transition – in the dynamic state space of the evolving non-linear matter-energy-information complex system that has a diachronic and synchronic account. The conscious mind as an emergent functionality is the self-organising, self-referential, self-learning, dynamically closed, self-realizing potential of a goal-oriented causal dynamics (teleodynamics) of hierarchically nested evolving matter-energy-information complex system (brain) instantiated in a self-propagating recursive constraining of the structure (neuronal) and function (virtual)." Neither Mind nor Brain. An Interdisciplinary Inquiry.

believe there are infinite ways of telling stories – linear and non-linear, multiple viewpoints and single viewpoints, first and third person, and so forth. An infinity of choice faces you whenever embarking upon a new work. However, I no longer believe, as Johnson believed, for instance, that the novel must be radically reinvented as it progresses or otherwise it will die. If you look at the tradition that he felt himself a part of, it’s odd in a way, because Tristram Shandy in particular so explodes all the notions of traditional fictional writing and all the possibilities of experimental writing right at the infancy of the British novel that Johnson’s view that you can build upon that seems wrong.

Key to the success of many with ADHD is finding the “right life” in which to live. This means a job in which their particular talents for nonlinear thinking and quick emergency response are prized, and a spouse who can appreciate, or at least learn to live with, an often uneven distribution of work within the relationship. Without these things, many with ADHD feel that they don’t really fit into the world, or that the face that they put forward in order to fit in is false. The other critical factor for the success of an ADHD spouse in a relationship is for both partners to continue to respect differences and act on that respect. Here’s what one woman with ADHD says about living a life in which others assume that “different” is not worthy of respect: I think [my husband] uses the ADD as an excuse to be bossy and stuff sometimes but I find it very upsetting and hard on my self esteem to have my disorder and learning disabilities used that way. We do have very different perspectives but reality is perspective. Just because I see things differently from someone else doesn’t make one wrong or right…how I experience life is colored by my perception, it is what it is. I hate how people try to invalidate my thoughts feelings and perceptions because they are different from theirs. Like telling me [since] they feel…different[ly] from me [that their feelings] should make me magically change! It doesn’t work that way. Even if my ADD makes me see or remember something “not right” it’s still MY reality. It is like those movies where the hero has something crazy going on where they experience reality differently from everyone else.

Almost all official statistics and policy documents on wages, income, gross domestic product (GDP), crime, unemployment rates, innovation rates, cost of living indices, morbidity and mortality rates, and poverty rates are compiled by governmental agencies and international bodies worldwide in terms of both total aggregate and per capita metrics. Furthermore, well-known composite indices of urban performance and the quality of life, such as those assembled by the World Economic Forum and magazines like Fortune, Forbes, and The Economist, primarily rely on naive linear combinations of such measures.6 Because we have quantitative scaling curves for many of these urban characteristics and a theoretical framework for their underlying dynamics we can do much better in devising a scientific basis for assessing performance and ranking cities. The ubiquitous use of per capita indicators for ranking and comparing cities is particularly egregious because it implicitly assumes that the baseline, or null hypothesis, for any urban characteristic is that it scales linearly with population size. In other words, it presumes that an idealized city is just the linear sum of the activities of all of its citizens, thereby ignoring its most essential feature and the very point of its existence, namely, that it is a collective emergent agglomeration resulting from nonlinear social and organizational interactions. Cities are quintessentially complex adaptive systems and, as such, are significantly more than just the simple linear sum of their individual components and constituents, whether buildings, roads, people, or money. This is expressed by the superlinear scaling laws whose exponents are 1.15 rather than 1.00. This approximately 15 percent increase in all socioeconomic activity with every doubling of the population size happens almost independently of administrators, politicians, planners, history, geographical location, and culture.

Time may be looked at culturally as well, in terms of human historical development, as Jean Baudrillard does, and when it is viewed in this way, something interesting occurs: we see that time is not necessarily linear nor even unidirectional but may well move the way the wind does, now in this direction, now in that. Near the end of his admittedly esoteric work The Illusion of the End, in which he confronts the massive wave of revisionist history that accompanied the closing years of the twentieth century, Baudrillard has this to say: We have to accord a privileged status to all that has to do with non-linearity, reversibility, all that is of the order not of an unfolding or an evolution, but of a winding back, a reversion in time. Anastrophe versus catastrophe. Perhaps, deep down, history has never unfolded in a linear fashion; perhaps language has never unfolded in a linear fashion. Everything moves in loops, tropes, inversions of meaning, except in numerical and artificial languages which, for that very reason, no longer are languages.20

An alive society is a society that is active with arguments of different opinions at different level; noisy; edgy; aggressive; non-linear and colored with wide range of expressions; a society that permits the progression of thoughts by allowing questions, not only for them to arise but also to be discussed; a society that sees questions as a sign of prosperous health, not a virus that should be treated or a threat that should be corrected or an enemy to be eliminated; a society that is not scared of the word 'subversive' for subversiveness was and still the only catalyst that leads to experiments in discovering new findings of any sort; be it scientific, philosophical, artistic, economic, political and so on; a society that celebrates the capability if its inhabitants being alive; a society that is not only curios but also anxious enough to embark on the journey out of their boxes; a society that sees a resistance as an important message that there is something wrong with its system that needs to be tended to immediately, cleverly; a society that believes that cleverness is a skill that can only be achieved by practicing a lot of 'trial and error'.

Interestingly enough, creative geniuses seem to think a lot more like horses do. These people also spend a rather large amount of time engaging in that favorite equine pastime: doing nothing. In his book Fire in the Crucible: The Alchemy of Creative Genius, John Briggs gathers numerous studies illustrating how artists and inventors keep their thoughts pulsating in a field of nuance associated with the limbic system. In order to accomplish this feat against the influence of cultural conditioning, they tend to be outsiders who have trouble fitting into polite society. Many creative geniuses don’t do well in school and don’t speak until they’re older, thus increasing their awareness of nonverbal feelings, sensations, and body language cues. Einstein is a classic example. Like Kathleen Barry Ingram, he also failed his college entrance exams. As expected, these sensitive, often highly empathic people feel extremely uncomfortable around incongruent members of their own species, and tend to distance themselves from the cultural mainstream. Through their refusal to fit into a system focusing on outside authority, suppressed emotion, and secondhand thought, creative geniuses retain and enhance their ability to activate the entire brain. Information flows freely, strengthening pathways between the various brain functions. The tendency to separate thought from emotion, memory, and sensation is lessened. This gives birth to a powerful nonlinear process, a flood of sensations and images interacting with high-level thought functions and aspects of memory too complex and multifaceted to distill into words. These elements continue to influence and build on each other with increasing ferocity. Researchers emphasize that the entire process is so rapid the conscious mind barely registers that it is happening, let alone what is happening. Now a person — or a horse for that matter — can theoretically operate at this level his entire life and never receive recognition for the rich and innovative insights resulting from this process. Those called creative geniuses continuously struggle with the task of communicating their revelations to the world through the most amenable form of expression — music, visual art, poetry, mathematics. Their talent for innovation, however, stems from an ability to continually engage and process a complex, interconnected, nonlinear series of insights. Briggs also found that creative geniuses spend a large of amount of time “doing nothing,” alternating episodes of intense concentration on a project with periods of what he calls “creative indolence.” Albert Einstein once remarked that some of his greatest ideas came to him so suddenly while shaving that he was prone to cut himself with surprise.

He ran long at the White House, and arrived late to his next meeting with Hillary Clinton, Jake Sullivan and Frank Ruggiero—their first major strategy session on Taliban talks after the secret meeting with A-Rod. She was waiting in her outer office, a spacious room paneled in white and gilt wood, with tasseled blue and pink curtains and an array of colorfully upholstered chairs and couches. In my time reporting to her later, I only ever saw Clinton take the couch, with guests of honor in the large chair kitty-corner to her. She’d left it open for him that day. “He came rushing in. . . . ” Clinton later said. “And, you know, he was saying ‘oh I’m so sorry, I’m so sorry.’ ” He sat down heavily and shrugged off his coat, rattling off a litany of his latest meetings, including his stop-in at the White House. “That was typical Richard. It was, like, ‘I’m doing a million things and I’m trying to keep all the balls in the air,’ ” she remembered. As he was talking, a “scarlet red” flush went up his face, according to Clinton. He pressed his hands over his eyes, his chest heaving. “Richard, what’s the matter?” Clinton asked. “Something horrible is happening,” he said. A few minutes later, Holbrooke was in an ambulance, strapped to a gurney, headed to nearby George Washington University Hospital, where Clinton had told her own internist to prepare the emergency room. In his typically brash style, he’d demanded that the ambulance take him to the more distant Sibley Memorial Hospital. Clinton overruled him. One of our deputies on the SRAP team, Dan Feldman, rode with him and held his hand. Feldman didn’t have his BlackBerry, so he scrawled notes on a State Department expense form for a dinner at Meiwah Restaurant as Holbrooke dictated messages and a doctor assessed him. The notes are a nonlinear stream of Holbrooke’s indomitable personality, slashed through with medical realities. “Call Eric in Axelrod’s office,” the first read. Nearby: “aortic dissection—type A . . . operation risk @ > 50 percent”—that would be chance of death. A series of messages for people in his life, again interrupted by his deteriorating condition: “S”—Secretary Clinton—“why always together for medical crises?” (The year before, he’d been with Clinton when she fell to the concrete floor of the State Department garage, fracturing her elbow.) “Kids—how much love them + stepkids” . . . “best staff ever” . . . “don’t let him die here” . . . “vascular surgery” . . . “no flow, no feeling legs” . . . “clot” . . . and then, again: “don’t let him die here want to die at home w/ his fam.” The seriousness of the situation fully dawning on him, Holbrooke turned to job succession: “Tell Frank”—Ruggiero—“he’s acting.” And finally: “I love so many people . . . I have a lot left to do . . . my career in public service is over.” Holbrooke cracked wise until they put him under for surgery. “Get me anything you need,” he demanded. “A pig’s heart. Dan’s heart.

In 1958, Fortune singled Nash out for his achievements in game theory, algebraic geometry, and nonlinear theory,

Reinvention of language was required. Thus after a decade of thinking I have created a new fractal (2,5D) nonlinear scalable, mental-model compatible language, supported by a novel GUI.

Our brain is not cut out for nonlinearities. Our emotional apparatus is designed for linear causality. This is why there are routes to success that are nonrandom, but very few people have the mental stamina to follow them.

was a linear thinker, and according to Zen linear thinking is nothing but a delusion, one of the many that keep us unhappy. Reality is nonlinear, Zen says. No future, no past. All is now.

What is science? Science is asking series of questions and finding the right answer through hard work resulted into laws of nature or technological advancements. So children, who are attending the science congress, one of the suggestion I can give you Don’t get afraid of asking questions. Go on asking till you get satisfied answer. Only questioning minds have made the world to live livable in spite of world’s non-linear dynamics.

consider what’s happening in this book when I describe sandbox play as the beginning of the age of the individual, dinner as the ritualized celebration of industrialization, television as a new hearth, clockwork mechanics as the foundation of twentieth-century developmental health, penmanship as up-skilling for a burgeoning capitalist economy, and card catalogs as a representation of an obsolete epistemological attitude. I’m situating the familiar technologies of the past in a hopeful story about a digital future—a future that requires folks to understand information in a drastically new way. If the old education cultivated habits of mind for a card-catalog world, then the new education needs to build habits of mind for a world of nonlinear hyperlinks. Luckily, situation theory can help.

The good news is that you don’t need a Jeff to make this type of decision. You only need to ruthlessly stick to the simple-to-understand (but sometimes hard-to-follow) principles and process that insist on customer obsession, encourage thinking long term, value innovation, and stay connected to the details. None of us, including Jeff, knew exactly what we would end up building; it’s more like we stuck with the process and surrendered to where it was taking us. Prime was a perfect example of the multicausal, nonlinear way in which business initiatives both major and minor got decided on and executed at Amazon. Correspondingly, we can’t tell a linear story of how we came up with Prime because there isn’t one. Instead, this chapter will reflect that there were a lot of little tributaries that emptied into the river of Prime.

None of this is to say that experts are inflexible automatons. Experts act with demonstrably more flexibility than novices in a particular domain. Psychologists specify two types of expert flexibility. In the first type, the expert internalizes many of the domain’s salient features and hence sees and reacts to most of the domain’s contexts and their effects. This flexibility operates effectively in relatively stable domains. The second type of flexibility is more difficult to exercise. This flexibility requires experts to recognize when their cognitively accessible models are unlikely to work, forcing the experts to go outside their routines and their familiar frameworks to solve problems. This flexibility is crucial to success in nonlinear, complex systems. So how do experts ensure they incorporate both types of flexibility? Advocates of cognitive flexibility theory suggest the major determinant in whether or not an expert will have more expansive flexibility is the amount of reductive bias during deliberate practice.4 More reductive bias may improve efficiency but will reduce flexibility. To mitigate reductive bias, the theory prescribes exploring abstractions across diverse cases to capture the significance of context dependence.

The minority stress model is also, conveniently, the go-to explanation for the phenomenon of detransition. A speaker at the AACAP 2022 annual meeting41 explained that when, after social transition and medical treatments, people decide to turn back and live in congruence with their sex, it does not necessarily mean they regret transitioning. “For a small minority, gender trajectories are non-linear and dynamic.” These individuals have “evolving paths.” It is simply “a shift in expression,” and “internal and external factors” must be considered, including family and society stigma. Conservative homes and the military were mentioned.

Nonlinearity suggests that instead of resisting upheavals and uncertainties like these, we should accept them. Yours is not the only life that seems to be following its own inscrutable path. Everyone else’s is, too.

Comfort vision. The principle: The animation should have a non-linear speed change to make it more comfortable. The animation should change from gradual strength to gradual weakness smoothly. The smoother the curve change, the more comfortable the feel.

Examples of common algorithms used in supervised learning include regression analysis (i.e. linear regression, logistic regression, non-linear regression), decision trees, k-nearest neighbors, neural networks, and support vector machines, each of which are examined in later chapters.

None of this is to say that experts are inflexible automatons. Experts act with demonstrably more flexibility than novices in a particular domain. Psychologists specify two types of expert flexibility. In the first type, the expert internalizes many of the domain’s salient features and hence sees and reacts to most of the domain’s contexts and their effects. This flexibility operates effectively in relatively stable domains. The second type of flexibility is more difficult to exercise. This flexibility requires experts to recognize when their cognitively accessible models are unlikely to work, forcing the experts to go outside their routines and their familiar frameworks to solve problems. This flexibility is crucial to success in nonlinear, complex systems.

The vogue for geometrical architecture and painting came and went. Architects no longer care to build blockish skyscrapers like the Seagram Building in New York, once much hailed and copied. To Mandelbrot and his followers the reason is clear. Simple shapes are inhuman. They fail to resonate with the way nature organizes itself or with the way human perception sees the world. In the words of Gert Eilenberger, a German physicist who took up nonlinear science after specializing in superconductivity: “Why is it that the silhouette of a storm-bent leafless tree against an evening sky in winter is perceived as beautiful, but the corresponding silhouette of any multi-purpose university building is not, in spite of all efforts of the architect? The answer seems to me, even if somewhat speculative, to follow from the new insights into dynamical systems. Our feeling for beauty is inspired by the harmonious arrangement of order and disorder as it occurs in natural objects—in clouds, trees, mountain ranges, or snow crystals. The shapes of all these are dynamical processes jelled into physical forms, and particular combinations of order and disorder are typical for them.

Reality is nonlinear, Zen says. No future, no past. All is now.

They had talked about turbulence, but time passed, and even Carruthers was no longer sure where Feigenbaum was headed. “I thought he had quit and found a different problem. Little did I know that this other problem was the same problem. It seems to have been the issue on which many different fields of science were stuck—they were stuck on this aspect of the nonlinear behavior of systems.

Feigenbaum brought to Los Alamos a conviction that his science had failed to understand hard problems—nonlinear problems. Although he had produced almost nothing as a physicist, he had accumulated an unusual intellectual background. He had a sharp working knowledge of the most challenging mathematical analysis, new kinds of computational technique that pushed most scientists to their limits. He had managed not to purge himself of some seemingly unscientific ideas from eighteenth-century Romanticism. He wanted to do science that would be new. He began by putting aside any thought of understanding real complexity and instead turned to the simplest nonlinear equations he could find.

They were studying the behavior of matter near the point where it changes from one state to another—from liquid to gas, or from unmagnetized to magnetized. As singular boundaries between two realms of existence, phase transitions tend to be highly nonlinear in their mathematics. The smooth and predictable behavior of matter in any one phase tends to be little help in understanding the transitions. A pot of water on the stove heats up in a regular way until it reaches the boiling point. But then the change in temperature pauses while something quite interesting happens at the molecular interface between liquid and

Wilson’s renormalization group theory provided a different route into infinitely dense problems. Until then the only way to approach highly nonlinear problems was with a device called perturbation theory. For purposes of calculation, you assume that the nonlinear problem is reasonably close to some solvable, linear problem—just a small perturbation away. You solve the linear problem and perform a complicated bit of trickery with the leftover part, expanding it into what are called Feynman diagrams. The more accuracy you need, the more of these agonizing diagrams you must produce. With luck, your calculations converge toward a solution. Luck has a way of vanishing,

Although the connection between numerics and physics was faint, Feigenbaum had found evidence that he needed to work out a new way of calculating complex nonlinear problems. So far, all available techniques had depended on the details of the functions. If the function was a sine function, Feigenbaum’s carefully worked-out calculations were sine calculations. His discovery of universality meant that all those techniques would have to be thrown out. The regularity had nothing to do with sines. It had nothing to do with parabolas. It had nothing to do with any particular function. But why? It was frustrating. Nature had pulled back a curtain for an instant and offered a glimpse of unexpected order. What else was behind that curtain?

Textbooks showed students only the rare nonlinear systems that would give way to such techniques. They did not display sensitive dependence on initial conditions. Nonlinear systems with real chaos were rarely taught and rarely learned. When people stumbled across such things—and people did—all their training argued for dismissing them as aberrations. Only a few were able to remember that the solvable, orderly, linear systems were the aberrations. Only a few, that is, understood how nonlinear nature is in its soul. Enrico Fermi once exclaimed, “It does not say in the Bible that all laws of nature are expressible linearly!” The mathematician Stanislaw Ulam remarked that to call the study of chaos “nonlinear science” was like calling zoology “the study of non elephant animals.

In epidemiology, for example, it was well known that epidemics tend to come in cycles, regular or irregular. Measles, polio, rubella—all rise and fall in frequency. May realized that the oscillations could be reproduced by a nonlinear model and he wondered what would happen if such a system received a sudden kick—a perturbation of the kind that might correspond to a program of inoculation. Naïve intuition suggests that the system will change smoothly in the desired direction. But actually, May found, huge oscillations are likely to begin. Even if the long-term trend was turned solidly downward, the path to a new equilibrium would be interrupted by surprising peaks. In fact, in data from real programs, such as a campaign to wipe out rubella in Britain, doctors had seen oscillations just like those predicted by May’s model. Yet any health official, seeing a sharp short-term rise in rubella or gonorrhea, would assume that the inoculation program had failed.

with a shift of natural sciences into systems thinking and complexity, and social sciences and humanities doing the same, it seems that they once again seem to come closer to each other. Not because the social sciences and humanities are becoming “harder” and more quantifiable, but because natural sciences are becoming “softer” with an emphasis on unpredictability, irreducibility, non-linearity, time-irreversibility, adaptivity, self-organization, emergence – the sort of things that may always have been better suited to capture the social order.

We know that everything that is anything is made from matter and energy being interrelated aspects of the same thing. The First Law of Thermodynamics tells us that energy can neither be created nor destroyed. However, if this is true, the obvious question is: what created it in the first place? It appears that either something had to have come from nothing, or something has always been. In the case that something has always been, if time can be in fact nonlinear and can infinitely regress in a loop, going backward on itself at the end of itself, it would be possible that there is no beginning or end of the universe at all, but a continuation of the same thing, as if the universe were breathing in and out, filling up its lungs with everything, and then emptying them back out, over and over. Or similarly, everything is, was, and will always be across space-time for all eternity. Every moment in time and location in space has a coordinate on the map of space-time and the map exists at all times at the same time, forever. However in both cases, if something has always been something where did that something come from. Who or what made it? How can anything be anything without having been made by something else? If the universe is entirely based on cause and effect, which appears to be, how could there be no first cause for there to be an effect. Alternatively, in what is known as quantum field theory, physicists have also found that particles known as virtual particles can come into existence from apparent nothingness. Which is to say, it is perhaps possible that a feature of nothing is to create something. However, if a feature of nothing is to create something, how can it be nothing? And if nothing isn’t nothing, what is it, and what made it? Even if one subscribes to the notion of a god, that’s fine, but that doesn’t resolve the question of where a god would have come from. Everything ultimately brings us back to the same question: How can anything come from nothing? Or something be infinite? And neither concept seem to concur with any human sensibilities, meaning there is some mystery of everything that our brains can’t seem to comprehend, as if the rules of the game were made of logic, but the reason for the game was made of something else. The only truth is, of course, no matter what anyone says or how they say it, nobody has any idea what’s going on beneath their feet, inside their brain, or above their head. Maybe at some point in the future, we, or some iteration of us, will know precisely how everything works and why with one little equation. Maybe Newton will be wrong and Einstein will be wrong and thousands of other Einsteins of the future will be wrong until someone somehow isn’t.

Our technologies have got ahead of our theories. Our theories are still fundamentally reductionist, componential and linear. Our technologies, however, are increasingly complex, emergent and non-linear.

The equations of fluid flow are nonlinear partial differential equations, unsolvable except in special cases. Yet Ruelle worked out an abstract alternative to Landau’s picture, couched in the language of Smale, with images of space as a pliable material to be squeezed, stretched, and folded into shapes like horseshoes.

We project a straight line only because we have a linear model in our head—the fact that a number has risen for 1,000 days straight should make you more confident that it will rise in the future. But if you have a nonlinear model in your head, it might confirm that the number should decline on day 1,001.

nonlinear force—like, say, the terminal velocity of rectitude or the angular acceleration of dumb luck.

Therefore all the things that appear in CLS—network analysis, digital mapping, linear and nonlinear regressions, topic modeling, topology, entropy—are just fancier ways of talking about word frequency changes.

As we let go of perfection, we are more open to accepting a nonlinear path to our goals.

Comfort vision The principle: The animation should have a non-linear speed change to make it more comfortable. The animation should change from gradual strength to gradual weakness smoothly. The smoother the curve change, the more comfortable the feel.

The butterfly effect is the idea that small things can have non-linear impacts on a complex system. The concept is imagined with a butterfly flapping its wings in the Amazon Forest and causing a typhoon in the Pacific. Imagine the butterfly effect applied to your actions. A small act of kindness in your neighborhood or city gaining strength and spreading to benefit the many. Perhaps, that thought will make you think twice in moments of weakness.

Without ownership, your inputs are very closely tied to your outputs. In almost any salaried job, even one paying a lot per hour like a lawyer or a doctor, you’re still putting in the hours, and every hour you get paid. Without ownership, when you’re sleeping, you’re not earning. When you’re retired, you’re not earning. When you’re on vacation, you’re not earning. And you can’t earn nonlinearly.

Instead, there were a number of different stressors, each of which forced the people to react in different ways to accommodate the changing situation(s). Complexity theory, especially in terms of visualizing a nonlinear progression and a series of stressors rather than a single driver, is therefore advantageous both in explaining the Collapse at the end of the Late Bronze Age and in providing a way forward for continuing to study this catastrophe.

Writers wanting him to confirm their theories about discrimination in the publishing world—Anti-Semitism! Sexism! Racism! Ageism!—as the sole and true reason their 800-page experimental non-linear punctuation-free neo-novel had been turned down by every publisher in the country.

Whereas the goal of the ego/mind is primarily to do, act, acquire, or perform, the intention of contemplation is to “become.” While the intellect wants to know “about,” contemplation seeks Knowingness itself and autonomous wisdom. Rational thinking is time related, sequential, and linear, whereas contemplation occurs outside of sequential time. It is nonlinear and related to comprehension of essence. Devotional contemplation is a way or style of being in the world whereby one’s life becomes a prayer.

If you feel you’ve lost the thread on your life or anything resembling motivation, what can help is to actually get lost—and by that I mean immerse yourself in the nonlinear, explore the full dimension of who you are, what you’ve experienced, and all the things you have right in front of you that you might have overlooked.

They experience moments in time as separate, nonlinear blips, like little lights randomly going on and off, with few linkages in time between one interaction and another. They act inconsistently, as their consciousness hops from one experience to another. This is one reason why they’re often indignant when you remind them of their past behavior. For them, the past is gone and has nothing to do with the present.

It’s not cheating; it’s expedited nonlinear puzzle completion.

THE LINEAR LIFE IS DEAD ↓ THE NONLINEAR LIFE INVOLVES MORE LIFE TRANSITIONS ↓ LIFE TRANSITIONS ARE A SKILL WE CAN, AND MUST, MASTER

Instead, life is filled with chaos and complexity, periods of order and disorder, linearity and nonlinearity. In place of steady lines, observers now see loops, spirals, wobbles, fractals, twists, tangles, and turnabouts.

More to the point, nonlinearity helps explain why we all feel so overwhelmed all the time. Trained to expect that our lives will unfold in a predictable series of stately life chapters, we’re confused when those chapters come faster and faster, frequently out of order, often one on top of the other. But the reality is: We’re all the clouds floating over the horizon, the swirl of cream in the coffee, the jagged dash of lightning. And we’re not aberrations because of this; we’re just like everything else.

The word “synergy” Fuller got from metallurgy. It’s been used in metallurgy for several centuries and it refers to alloying. When you smelt two metals together, you get a new metal that has properties that neither of the first two had. And Fuller began to notice that there were synergies in every science, not just metallurgy. And so, he coined the word synergy to describe non-linear, non-elementalistic relationships. He is always looking for non-additive relationships where you can put two and two together and get five instead of four. You get more because of the new structure created when you put the parts together. That’s why his domes are up to a thousand time stronger than any other structure containing the same space built by traditional geometry. His domes are all synergetic.

In opposition to this old-fashioned way of thinking, they advocate a postmodern ‘nonlinear thought’. The precise content of the latter is not clearly explained either, but it is, apparently, a methodology that goes beyond reason by insisting on intuition and subjective perception.183 And it is frequently claimed that so-called postmodern science – and particularly chaos theory – justifies and supports this new ‘nonlinear thought’. But this assertion rests simply on a confusion between the three meanings of the word ‘linear’.184

Dr. Alistair Cockburn made this same observation in the study of software engineering; the most often overlooked, but most important, active components of complex software systems are…the people working within the system. The wonderful title of his paper describes people as the opposite of automatons: “Characterizing People as Non-Linear 1st Order Components in Software Development.

But first I’d need to change my whole approach. I was a linear thinker, and according to Zen linear thinking is nothing but a delusion, one of the many that keep us unhappy. Reality is nonlinear, Zen

People assume that time is a strict progression of cause to effect, but actually, from a nonlinear, non-subjective viewpoint, it's more like a big ball of wibbly-wobbly, timey-wimey... stuff. ~The Tenth Doctor as played by David Tennent, Season 3 Episode 10 'Blink'.