Linear Function Quotes

As Alaska zipped through something obvious about linear equations, stoner/baller Hank Walsten said, "Wait, wait. I don't get it." "That's because you have eight functioning brain cells." "Studies show that Marijuana is better for your health than those cigarettes," Hank said. Alaska swallowed a mouthful of fries, took a drag on her cigarette, and blew a smoke at Hank. "I may die young," she said. "But at least I'll die smart. Now, back to tangents.

Like any good teacher, she tolerated little dissension. She smoked and talked and ate for an hour without stopping, and I scribbled in my notebook as the muddy waters of tangents and cosines began to clarify. But not everyone was so fortunate. As Alaska zipped through something obvious about linear equations, stoner/baller Hank Walsten said, "Wait, wait. I don't get it." "That's because you have eight functioning brain cells." "Studies show that marijuana is better for your health than those cigarettes," Hank said. Alaska swallowed a mouthful of french fries, took a drag on her cigarette, and blew smoke across the table at Hank. "I may die young," she said. "But at least I'll die smart. Now, back to tangents.

Ironically, Alfred Binet, one of the creators of the IQ test, intended the test to serve precisely the opposite function. In fact, he originally designed it (on commission from the French government) exclusively to identify children with special needs so they could get appropriate forms of schooling. He never intended it to identify degrees of intelligence or “mental worth.” In fact, Binet noted that the scale he created “does not permit the measure of intelligence, because intellectual qualities are not superposable, and therefore cannot be measured as linear surfaces are measured.” Nor did he ever intend it to suggest that a person could not become more intelligent over time. “Some recent thinkers,” he said, “[have affirmed] that an individual’s intelligence is a fixed quantity, a quantity that cannot be increased. We must protest and react against this brutal pessimism; we must try to demonstrate that it is founded on nothing.

But it must be seen that the term 'catastrophe' has this 'catastrophic' meaning of the end and annihilation only in a linear vision of accumulation and productive finality that the system imposes on us. Etymologically, the term only signifies the curvature, the winding down to the bottom of a cycle leading to what can be called the 'horizon of the event,' to the horizon of meaning, beyond which we cannot go. Beyond it, nothing takes place that has meaning for us - but it suffices to exceed this ultimatum of meaning in order that catastrophe itself no longer appear as the last, nihilistic day of reckoning, such as it functions in our current collective fantasy.

Time of course has showed the question up in all its young illogic. We can justify any apologia simply by calling life a successive rejection of personalities. No apologia I s any more than a romance—half a fiction—in which all the successive identities are taken on and rejected by the writer as a function of linear time are treated as separate characters. The writing itself even constitutes another rejection, another “character” added to the past. So we do sell our souls: paying them away to history in little installments. It isn’t so much to pay for eyes clear enough to see past the fiction of continuity, the fiction of cause and effect, the fiction of a humanized history endowed with “reason.

Work and life become inseparable. Capital follows you when you dream. Time ceases to be linear, becomes chaotic, broken down into punctiform divisions. As production and distribution are restructured, so are nervous systems. To function effectively as a component of just-in-time production you must develop a capacity to respond to unforeseen events, you must learn to live in conditions of total instability, or ‘precarity’, as the ugly neologism has it. Periods of work alternate with periods of unemployment. Typically, you find yourself employed in a series of short-term jobs, unable to plan for the future.

Major scientific insights are characteristically intuitive, and equally characteristically described in scientific papers by linear analytical arguments. There is no anomaly in this: it is, rather, just as it should be. The creative act has major right-hemisphere components. But arguments on the validity of the result are largely left-hemisphere functions.

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.

Just as functioning isn't uniform, it isn't linear either. There is a commonly seen phenomenon in autistic children where they'll make big gains in elementary school then regress when they hit adolescence. Or a child will be labeled a late bloomer, seeming practically "normal" in their teen years, then seem to backslide dramatically when they go off to college or enter the adult world of work and independent living

The psychology professor Richard Aslin once commented to me that he felt the idea of “consciousness” was a proxy for a whole host of variables correlated with our mental lives. We use “consciousness” as shorthand to easily describe the functions of a multitude of inborn, instinctual mechanisms such as language, perception, and emotion. It becomes evident that consciousness is best understood as a complex instinct as well. All of us come with a bucketful of instincts. Our incessant thought pattern jumps around. We have feelings about one idea, then its opposite, then our family, then an itch, then a favorite tune, then the upcoming meeting, then the grocery list, then the irritating colleague, then the Red Sox, then … It goes on and on until we learn, almost against our natural being, to have a linear thought.

The European and the African have an entirely different concept of time. In the European worldview, time exists outside man, exists objectively, and has measurable and linear characteristics. According to Newton, time is absolute: “Absolute, true, mathematical time of itself and from its own nature, it flows equitably and without relation to anything external.” The European feels himself to be time’s slave, dependent on it, subject to it. To exist and function, he must observe its ironclad, inviolate laws, its inflexible principles and rules. He must heed deadlines, dates, days, and hours. He moves within the rigors of time and cannot exist outside them. They impose upon him their requirements and quotas. An unresolvable conflict exists between man and time, one that always ends with man’s defeat—time annihilates him. Africans apprehend time differently. For them, it is a much looser concept, more open, elastic, subjective. It is man who influences time, its shape, course, and rhythm (man acting, of course, with the consent of gods and ancestors ). Time is even something that man can create outright, for time is made manifest through events, and whether an event takes place or not depends, after all, on man alone. If two armies do not engage in a battle, then that battle will not occur (in other words, time will not have revealed its presence, will not have come into being). Time appears as a result of our actions, and vanishes when we neglect or ignore it. It is something that springs to life under our influence, but falls into a state of hibernation, even nonexistence, if we do not direct our energy toward it. It is a subservient, passive essence, and, most importantly, one dependent on man.

The Coach’s head was oblong with tiny slits that served as eyes, which drifted in tides slowly inward, as though the face itself were the sea or, in fact, a soup of macromolecules through which objects might drift, leaving in their wake, ripples of nothingness. The eyes—they floated adrift like land masses before locking in symmetrically at seemingly prescribed positions off-center, while managing to be so closely drawn into the very middle of the face section that it might have seemed unnecessary for there to have been two eyes when, quite likely, one would easily have sufficed. These aimless, floating eyes were not the Coach’s only distinctive feature—for, in fact, connected to the interior of each eyelid by a web-like layer of rubbery pink tissue was a kind of snout which, unlike the eyes, remained fixed in its position among the tides of the face, arcing narrowly inward at the edges of its sharp extremities into a serrated beak-like projection that hooked downward at its tip, in a fashion similar to that of a falcon’s beak. This snout—or beak, rather—was, in fact, so long and came to such a fine point that as the eyes swirled through the soup of macromolecules that comprised the man’s face, it almost appeared—due to the seeming thinness of the pink tissue—that the eyes functioned as kinds of optical tether balls that moved synchronously across the face like mirror images of one another. 'I wore my lizard mask as I entered the tram, last evening, and people found me fearless,' the Coach remarked, enunciating each word carefully through the hollow clack-clacking sound of his beak, as its edges clapped together. 'I might have exchanged it for that of an ox and then thought better. A lizard goes best with scales, don’t you think?' Bunnu nodded as he quietly wondered how the Coach could manage to fit that phallic monstrosity of a beak into any kind of mask, unless, in fact, this disguise of which he spoke, had been specially designed for his face and divided into sections in such a way that they could be readily attached to different areas—as though one were assembling a new face—in overlapping layers, so as to veil, or perhaps even amplify certain distinguishable features. All the same, in doing so, one could only imagine this lizard mask to be enormous to the extent that it would be disproportionate with the rest of the Coach’s body. But then, there were ways to mask space, as well—to bend light, perhaps, to create the illusion that something was perceptibly larger or smaller, wider or narrower, rounder or more linear than it was in actuality. That is to say, any form of prosthesis designed for the purposes of affecting remedial space might, for example, have had the capability of creating the appearance of a gap of void in occupied space. An ornament hangs from the chin, let’s say, as an accessory meant to contour smoothly inward what might otherwise appear to be hanging jowls. This surely wouldn’t be the exact use that the Coach would have for such a device—as he had no jowls to speak of—though he could certainly see the benefit of the accessory’s ingenuity. This being said, the lizard mask might have appeared natural rather than disproportionate given the right set of circumstances. Whatever the case, there was no way of even knowing if the Coach wasn’t, in fact, already wearing a mask, at this very moment, rendering Bunnu’s initial appraisal of his character—as determined by a rudimentary physiognomic analysis of his features—a matter now subject to doubt. And thus, any conjecture that could be made with respect to the dimensions or components of a lizard mask—not to speak of the motives of its wearer—seemed not only impractical, but also irrelevant at this point in time.

The extraordinary value of the I Ching is that it reveals the secrets of dynamic natural law. Working with its changes opens up access to the middle level of the Positive Paradigm Wheel, the “e” energy layer of Einstein's Unified Theory. This middle level serves as mediating, two-directional gate-keeper between the ever-changing surface rim and the universal, timeless center. You can't get from here to there, except through the middle layer which, in Western thinking, is effectively taboo, buried in the inaccessible "unconscious." To the extent that natural law is a blind spot in the prevailing, linear and exclusively empirical paradigm, we are left powerless to move beyond the surface level of experience. The realm of light and conscience which rests beyond, on the far side of the dynamic energy level, remains functionally inaccessible. Moral codes promoted by religionists or politicians are sometimes equated with conscience. But they're no substitute for direct experience. Only by becoming intelligently competent in managing the subtle energies of the middle level is it possible to travel further inwards for the immediate, personal experience of inner light. When the middle level becomes clogged with painful memories, negative emotions and socially taboo urges, it becomes a barrier to deeper knowing. The Book of Change is indispensable as a tool for restoring the unnecessarily "unconscious" to conscious awareness, so that the levels of human potential can be linked and unified. In Positive Paradigm context, survivors who prevail in dangerous times aren't those with the most material wealth, possessions or political power. They're the ones who've successfully navigated the middle realm, reached the far shore of enlightenment and returned to the surface with their new information intact. Those who succeed in linking the levels of experience are genius-leaders in whatever fields they choose to engage. They're the fortunate ones who've acquired the inner wealth necessary to both hear the inner voice of conscience and act on the guidance they receive.

Each group was required to propose its own “fitness function”—a linear equation that it could use to measure its own impact without ambiguity. For example, a two-pizza team in charge of sending advertising e-mails to customers might choose for its fitness function the rate at which these messages were opened multiplied by the average order size those e-mails generated. A group writing software code for the fulfillment centers might home in on decreasing the cost of shipping each type of product and reducing the time that elapsed between a customer’s making a purchase and the item leaving the FC in a truck. Bezos wanted to personally approve each equation and track the results over time. It would be his way of guiding a team’s evolution. Bezos was applying

For example, if we believed there was a linear relationship between the height values and the weight values of D, we might ask R to try to fit this model like so, using the lm() linear model function: model = lm(weight ~ height)

the second derivative conveys just the idea we want—a comparison between the value at x and the average value near x. It is worth noting that if f is linear, then the average of f(x - h) and f(x + h) will be equal to f(x), which fits with the familiar fact that the second derivative of a linear function f is zero.

The old ones exist outside the dimension we experience as linear time. Bound as most of us are by the flow of time, we aren’t able to experience their machine as a functioning whole. From any given point in our timeline, one part of the machine is viewed as having existed in the past. Another in the future. The only moment when it is possible for us to experience their device as a functioning whole is when it is flipped on. The image your subconscious carries is of the moment when our planet was about to be destroyed. That moment transcends history; it exists in the past, in the future—” “And in the now,

Rather than looking at business as a series of simple, linear activities, the systems view recognizes that it is a function of numerous processes interacting interdependently with one another resulting in both planned and unplanned consequences.

Public health historically has used a linear model focusing exclusively on the body functions or dysfunctions of the person and that assumes the person's body dysfunctions and activity limitations are totally responsible for the individual's lack of involvement in the society

The S curve is not just important as a model in its own right; it’s also the jack-of-all-trades of mathematics. If you zoom in on its midsection, it approximates a straight line. Many phenomena we think of as linear are in fact S curves, because nothing can grow without limit. Because of relativity, and contra Newton, acceleration does not increase linearly with force, but follows an S curve centered at zero. So does electric current as a function of voltage in the resistors found in electronic circuits, or in a light bulb (until the filament melts, which is itself another phase transition). If you zoom out from an S curve, it approximates a step function, with the output suddenly changing from zero to one at the threshold. So depending on the input voltages, the same curve represents the workings of a transistor in both digital computers and analog devices like amplifiers and radio tuners. The early part of an S curve is effectively an exponential, and near the saturation point it approximates exponential decay. When someone talks about exponential growth, ask yourself: How soon will it turn into an S curve? When will the population bomb peter out, Moore’s law lose steam, or the singularity fail to happen? Differentiate an S curve and you get a bell curve: slow, fast, slow becomes low, high, low. Add a succession of staggered upward and downward S curves, and you get something close to a sine wave. In fact, every function can be closely approximated by a sum of S curves: when the function goes up, you add an S curve; when it goes down, you subtract one. Children’s learning is not a steady improvement but an accumulation of S curves. So is technological change. Squint at the New York City skyline and you can see a sum of S curves unfolding across the horizon, each as sharp as a skyscraper’s corner. Most importantly for us, S curves lead to a new solution to the credit-assignment problem. If the universe is a symphony of phase transitions, let’s model it with one. That’s what the brain does: it tunes the system of phase transitions inside to the one outside. So let’s replace the perceptron’s step function with an S curve and see what happens.

As a result I early asked the question, "Why should I do all the analysis in terms of Fourier integrals? Why are they the natural tools for the problem?" I soon found out, as many of you already know, that the eigenfunctions of translation are the complex exponentials. If you want time invariance, and certainly physicists and engineers do (so that an experiment done today or tomorrow will give the same results), then you are led to these functions. Similarly, if you believe in linearity then they are again the eigenfunctions. In quantum mechanics the quantum states are absolutely additive; they are not just a convenient linear approximation. Thus the trigonometric functions are the eigenfunctions one needs in both digital filter theory and quantum mechanics, to name but two places. Now when you use these eigenfunctions you are naturally led to representing various functions, first as a countable number and then as a non-countable number of them-namely, the Fourier series and the Fourier integral. Well, it is a theorem in the theory of Fourier integrals that the variability of the function multiplied by the variability of its transform exceeds a fixed constant, in one notation l/2pi. This says to me that in any linear, time invariant system you must find an uncertainty principle.

If machinery is conceived transcendently as instrumental technology it is essentially determined in opposition to social relations, but if it is integrated immanently as cybernetic technics it redesigns all oppositionality as non-linear flow. There is no dialectic between social and technical relations, but only a machinism that dissolves society into the machines whilst deterritorializing the machines across the ruins of society, whose ‘general theory … is a generalized theory of flux’, which is to say: cybernetics. Beyond the assumption that guidance proceeds from the side of the subject lies desiring production: the impersonal pilot of history. Distinctions between theory and practice, culture and economy, science and technics, are useless after this point. There is no real option between a cybernetics of theory or a theory of cybernetics, because cybernetics is neither a theory nor its object, but an operation within anobjective partial circuits that reiterates ‘itself’ in the real and machines theory through the unknown. ‘Production as a process overflows all ideal categories and forms a cycle that relates itself to desire as an immanent principle.’ Cybernetics develops functionally, and not representationally: a ‘desiring machine, a partial object, does not represent anything’. Its semi-closed assemblages are not descriptions but programs, ‘auto’-replicated by way of an operation passing across irreducible exteriority. This is why cybernetics is inextricable from exploration, having no integrity transcending that of an uncomprehended circuit within which it is embedded, an outside in which it must swim. Reflection is always very late, derivative, and even then really something else. (294-5)

In the theory of nerve functioning everything happens as if we were obliged to submit to the alternative of anthropomorphism or the anatomical conception of the reflex, when perhaps it is necessary to go beyond it. Before any systematic interpretation, the description of the known facts shows that the fate of an excitation is determined by its relation to the whole of the organic state and to the simultaneous or preceding excitations, and that the relations between the organism and its milieu are not relations of linear causality but of circular causality,

Many of today’s software companies also fit in this group, including most software-as-a-service (SaaS) companies. Even though their products are digital, these companies still function linearly, with value flowing from the companies to their customers. The only difference is that software companies benefit from the low marginal cost of digital distribution.

All forms of complex causation, and especially nonlinear transformations, admittedly stack the deck against prediction. Linear describes an outcome produced by one or more variables where the effect is additive. Any other interaction is nonlinear. This would include outcomes that involve step functions or phase transitions. The hard sciences routinely describe nonlinear phenomena. Making predictions about them becomes increasingly problematic when multiple variables are involved that have complex interactions. Some simple nonlinear systems can quickly become unpredictable when small variations in their inputs are introduced.23 As so much of the social world is nonlinear, fifty plus years of behavioral research and theory building have not led to any noticeable improvement in our ability to predict events. This is most evident in the case of transformative events like the social-political revolution of the 1960s, the end of the Cold War, and the rise and growing political influence of fundamentalist religious groups. Radical skepticism about prediction of any but the most short-term outcomes is fully warranted. This does not mean that we can throw our hands up in the face of uncertainty, contingency, and unpredictability. In a complex society, individuals, organizations, and states require a high degree of confidence—even if it is misplaced—in the short-term future and a reasonable degree of confidence about the longer term. In its absence they could not commit themselves to decisions, investments, and policies. Like nudging the frame of a pinball machine to influence the path of the ball, we cope with the dilemma of uncertainty by doing what we can to make our expectations of the future self-fulfilling. We seek to control the social and physical worlds not only to make them more predictable but to reduce the likelihood of disruptive and damaging shocks (e.g., floods, epidemics, stock market crashes, foreign attacks). Our fallback strategy is denial.

The entire company, he said, would restructure itself around what he called “two-pizza teams.” Employees would be organized into autonomous groups of fewer than ten people—small enough that, when working late, the team members could be fed with two pizza pies. These teams would be independently set loose on Amazon’s biggest problems. They would likely compete with one another for resources and sometimes duplicate their efforts, replicating the Darwinian realities of surviving in nature. Freed from the constraints of intracompany communication, Bezos hoped, these loosely coupled teams could move faster and get features to customers quicker. There were some head-scratching aspects to Bezos’s two-pizza-team concept. Each group was required to propose its own “fitness function”—a linear equation that it could use to measure its own impact without ambiguity. For example, a two-pizza team in charge of sending advertising e-mails to customers might choose for its fitness function the rate at which these messages were opened multiplied by the average order size those e-mails generated. A group writing software code for the fulfillment centers might home in on decreasing the cost of shipping each type of product and reducing the time that elapsed between a customer’s making a purchase and the item leaving the FC in a truck. Bezos wanted to personally approve each equation and track the results over time. It would be his way of guiding a team’s evolution.

1930s Functionalism/Modernism Exterior •Facade: Cube shapes and light-color plaster facades, or thin, standing wood panels. •Roof: Flat roof, sometimes clad in copper or sheet metal. •Windows: Long horizontal window bands often with narrow—or no—architraves; large panes of glass without mullions or transoms. Emphasis on the horizontal rather than on the vertical. Windows run around corners to allow more light and to demonstrate the new possibilities of construction and materials. •Outside door: Wooden door with circular glass window. •Typical period details: Houses positioned on plots to allow maximum access to daylight. Curving balconies, often running around the corner; corrugated-iron balcony frontage. Balcony flooring and fixings left visible. The lines of the building are emphasized. Interior •Floors: Parquet flooring in various patterns, tongue-and-groove floorboards, or linoleum. •Interior doors: Sliding doors and flush doors of lamella construction (vaulted, with a crisscross pattern). Masonite had a breakthrough. •Door handles: Black Bakelite, wood, or chrome. •Fireplaces: Slightly curved, brick/stone built. Light-color cement. •Wallpaper/walls: Smooth internal walls and light wallpapers, or mural wallpaper that from a distance resembled a rough, plastered wall. Internal wall and woodwork were light in color but rarely completely white—often muted pastel shades. •Furniture: Functionalism, Bauhaus, and International style influences. Tubular metal furniture, linear forms. Bakelite, chrome, stainless steel, colored glass. •Bathroom: Bathrooms were simple and had most of today’s features. External pipework. Usually smooth white tiles on the walls or painted plywood. Black-and-white chessboard floor. Lavatories with low cisterns were introduced. •Kitchen: Flush cupboard doors with a slightly rounded profile. The doors were partial insets so that only about a third of the thickness was visible on the outside—this gave them a light look and feel. Metal-sprung door latches, simple knobs, metal cup handles on drawers. Wall cabinets went to ceiling height but had a bottom section with smaller or sliding doors. Storage racks with glass containers for dry goods such as salt and flour became popular. Air vents were provided to deal with cooking smells.

In Die Welt von Gestern, Stefan Zweig attributed the decline of civil order in Europe to the myth of progress.7 In all the ideologies of his day – communism, socialism, Nazism, fascism – Zweig saw the same pernicious attempt to rewrite the principles of social order in terms of a linear progression from past to future. The cult of the leader, of the ‘vanguard party’, of the ‘avant-garde’ – all supposed that society has a direction, in the way that businesses have a purpose and armies have a goal. And all licensed the increasing conscription of the citizen, and the steady absorption of the functions of society into the machinery of the state.

Time behaves differently in super-fluids and black holes, this is related to light propagation. Particles lose their identity in both super-fluids and black holes. Waves only exist inside of time. The energy of a photon is stored as a rate of change in frequency and the number of times there is a change in direction instead of speed. Speed is the linear dimension and wave amplitude is one of the perpendicular dimensions and the digital horizon may not exist as a function of the way in which time is related to the other perpendicular dimension.

On one side of the argument is the perspective of the design school of strategy, which was discussed in Chapter 1 and which was heavily influenced by the technical rational period of thought prevalent in the early nineteenth century, which continues through to today. This perspective is anchored in principles of industrialism and reflects one of modernity’s key tenets—objective representationalism, the idea that the purpose of knowledge is to represent, without logical contradiction, the “way things really are,” or the linear, functional causes of actions.

Use your brain to knock out your opponent. Now that we have a basic understanding of diffuse axonal injury, the obvious next question is, “How can I use this knowledge to become a better fighter?” Sometimes the right visualization of the process is all it takes so give your training a significant edge. When you throw a punch, think about how your punch will rotate your opponent’s head. If you give your opponent a linear palm strike to the face, you will probably do a lot of damage to your opponent, but if you can strike and then move your hand up and over, forcing your opponent to look up at the ceiling, you will probably have a better chance of knockout from that strike. Another way to adjust your training is to practice hitting something that can rotate. Some heavy bags or double-end bags can rotate when you hit them, or you can try out the Quest Training AllStrike, which functions much like a focus mitt in the shape of a human head for fine-tuning your targeting, but it also provides realistic rotational feedback. If you can start understanding when you are spinning a head versus when you are pushing it back, you are on your way to being a better knockout artist.

Experts have been revered—and well paid—for years for their “It is my opinion that ... ” judgments. As James March has stated, however, such reverence may serve a purely social function. People and organizations have to make decisions, often between alternatives that are almost equally good or bad. What better way to justify such decisions than to consult an expert, and the more money he or she charges, the better. “We paid for the best possible medical advice,” can be a palliative for a fatal operation (or a losing legal defense), just as throwing the I Ching can relieve someone from regretting a bad marriage or a bad career choice. An expert who constructs a linear model is not as impressive as one who gives advice in a “burst” of intuition derived from “years of experience.” (One highly paid business expert we know constructs linear models in secret.) So we value the global judgment of experts independently of its validity. But there is also a situational reason for doubting the inferiority of global, intuitive judgment. It has to do with the biased availability of feedback. When we construct a linear model in a prediction situation, we know exactly how poorly it predicts. In contrast, our feedback about our own intuitive judgments is flawed. Not only do we selectively remember our successes, we often have no knowledge of our failures—and any knowledge we do have may serve to “explain” them (away). Who knows what happens to rejected graduate school applicants? Professors have access only to accepted ones, and if the professors are doing a good job, the accepted ones will likewise do well—reinforcing the impression of the professors’ good judgment. What happens to people misdiagnosed as “psychotic”? If they are lucky, they will disappear from the sight of the authorities diagnosing them; if not, they are likely to be placed in an environment where they may soon become psychotic. Finally, therapy patients who commit suicide were too sick to begin with—as is easily supported by an ex post perusal of their files.

What the Net seems to be doing is chipping away my capacity for concentration and contemplation. New thought came more readily to a brain that had already learned how to rearrange itself to read. By allowing us to filter out distractions, to quiet the problem-solving functions of the frontal lobes, deep reading becomes a form of deep thinking. People who read linear text comprehend more, remember more and learn more than those who read text peppered with links. Frequent interruptions scatter our thoughts, weaken our memory and make us tense and anxious. Improving our ability to multitask actually hampers our ability to think deeply and creatively. What we are doing when we multitask is learning to be skillful at a superficial level. The Roman philosopher Seneca may have put it best two thousand years ago: "To be everywhere is to be nowhere." After spending time in a quiet rural setting, close to nature, people exhibit greater attentiveness, stronger memory and generally improved cognition.

My many years of advising companies and making value-driven equity bets has made it crystal clear to me that the ascent of great companies is not linear but more a step function. There are critical moments when decisions are made that inexorably shape the company’s future trajectory. To get these crux moves right, you must flexibly adapt your strategy to emerging circumstances.

The main theme of Goddess symbolism is the mystery of birth and death and the renewal of life, not only human but all life on earth and indeed in the whole cosmos. Symbols and images cluster around the parthenogenetic (self-generating) Goddess and her basic functions as Giver of Life, Wielder of Death, and, not less importantly, as Regeneratrix, and around the Earth Mother, the Fertility Goddess young and old, rising and dying with plant life. She was the single source of all life who took her energy from the springs and wells, from the sun, moon and moist earth. This symbolic system represents cyclical, not linear, mythical time. In art this is manifested by the signs of dynamic motion: whirling and twisting spirals, winding and coiling snakes, circles, crescents, horns, sprouting seeds and shoots.

My many years of advising companies and making value-driven equity bets has made it crystal clear to me that the ascent of great companies is not linear but more a step function.

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.

We need a revolution in mental health awareness to help us grasp the wonder and complexity of human behavior, health and functioning, and the nuances and intersections of brilliance and madness. This starts with dismantling myopic myths that prevent us from seeing the simultaneous wonder and complexity of our fullest selves. It involves providing access to the tools that mitigate being overtaken by the ravages of burnout and mental decompensation: the very risks of living in the modern world. Our sense-making approaches need to be comprehensive- grounded both scientifically and medically, steeped in love, and in ways that account for the multidimensionality of emotional and spiritual essence. Those that go beyond what the mind can first conceive of. This new mental health imperative relies upon universal precautions and a vehement resistance to linear checklists and binary labels that frame our gorgeous spirits solely as either complex and fraught or indomitable and wondrous. It also relies not on good will and best practices but the moral courage of policy makers to treat human beings like human beings. Dogs are often treated better than people. This is our new imperative: to radically change the way we care for ourselves and one another. We cannot extricate ourselves from the fact that the lines we walk are incredibly thin and blurry, and our only hope is to rewrite and navigate them together in solidarity, with every measure of creative reason and conscious community that can be mustered...

Yes, even disabled people secretly yearn to be "normal" on days when it feels like our bodies let us down. We have so internalized the expectation that our bodies should function in a linear way that we can feel frustrated when they don't play along.

The function of history is to provide not a linear record, but a blueprint for living, specific to a particular people in a particular place.

There are some things that don’t function as one would assume. For example, the impulse and linear thinking associated with the search for happiness most often produce questions like, “What’s in it for me?” or “How do I get what I want?” Paradoxically, if you will, that very question pushes authentic happiness away. Now, to try to explain that to someone in such a way that they hear and are interested by the idea is going to probably involve some paradox and non-linearity.

Each group was required to propose its own “fitness function”—a linear equation that it could use to measure its own impact without ambiguity. For example, a two-pizza team in charge of sending advertising e-mails to customers might choose for its fitness function the rate at which these messages were opened multiplied by the average order size those e-mails generated.

Someone with a linear payoff needs to be right more than 50 percent of the time. Someone with a convex payoff, much less. The hidden benefit of antifragility is that you can guess worse than random and still end up outperforming. Here lies the power of optionality—your function of something is very convex, so you can be wrong and still do fine—the more uncertainty, the better.

(a) The more nonlinear, the more the function of something divorces itself from the something. If traffic were linear, then there would be no difference in traffic time between the two following situations: 90,000, then 110,000 cars on the one hand, or 100,000 cars on the other.

The vestibular system tells us about up and down and whether we are upright or not. It tells us where our heads and bodies are in relation to the earth’s surface. It sends sensory messages about balance and movement from the neck, eyes, and body to the CNS for processing and then helps generate muscle tone so we can move smoothly and efficiently. This sense tells us whether we are moving or standing still, and whether objects are moving or motionless in relation to our body. It also informs us what direction we are going in, and how fast we are going. This is extremely useful information should we need to make a fast getaway! Indeed, the fundamental functions of fight, flight, and foraging for food depend on accurate information from the vestibular system. Dr. Ayres writes that the “system has basic survival value at one of the most primitive levels, and such significance is reflected in its role in sensory integration.” The receptors for vestibular sensations are hair cells in the inner ear, which is like a “vestibule” for sensory messages to pass through. The inner-ear receptors work something like a carpenter’s level. They register every movement we make and every change in head position—even the most subtle. Some inner-ear structures receive information about where our head and body are in space when we are motionless, or move slowly, or tilt our head in any linear direction—forward, backward, or to the side. As an example of how this works, stand up in an ordinary biped, or two-footed, position. Now, close your eyes and tip your head way to the right. With your eyes closed, resume your upright posture. Open your eyes. Are you upright again, where you want to be? Your vestibular system did its job. Other structures in the inner ear receive information about the direction and speed of our head and body when we move rapidly in space, on the diagonal or in circles. Stand up and turn around in a circle or two. Do you feel a little dizzy? You should. Your vestibular system tells you instantly when you have had enough of this rotary stimulation. You will probably regain your balance in a moment. What stimulates these inner ear receptors? Gravity! According to Dr. Ayres, gravity is “the most constant and universal force in our lives.” It rules every move we make. Throughout evolution, we have been refining our responses to gravitational pull. Our ancient ancestors, the first fish, developed gravity receptors, on either side of their heads, for three purposes: 1) to keep upright, 2) to provide a sense of their own motions so they could move efficiently, and 3) to detect potentially threatening movements of other creatures through the vibrations of ripples in the water. Millions of years later, we still have gravity receptors to serve the same purposes—except now vibrations come through air rather than water.

Waterhouse seeks happiness. He achieves it by breaking Nip code systems and playing the pipe organ. But since pipe organs are in short supply, his happiness level ends up being totally dependent on breaking codes. He cannot break codes (hence, cannot be happy) unless his mind is clear. Now suppose that mental clarity is designated by Cm, which is normalized, or calibrated, in such a way that it is always the case that where Cm = 0 indicates a totally clouded mind and Cm = 1 is Godlike clarity—an unattainable divine state of infinite intelligence. If the number of messages Waterhouse decrypts, in a given day, is designated by Ndecrypts, then it will be governed by Cm in roughly the following way: Clarity of mind (Cm) is affected by any number of factors, but by far the most important is horniness, which might be designated by σ, for obvious anatomical reasons that Waterhouse finds amusing at this stage of his emotional development. Horniness begins at zero at time t = t0 (immediately following ejaculation) and increases from there as a linear function of time: The only way to drop it back to zero is to arrange another ejaculation. There is a critical threshold σc such that when σ > σc it becomes impossible for Waterhouse to concentrate on anything, or, approximately, which amounts to saying that the moment σ rises above the threshold σc it becomes totally impossible for Waterhouse to break Nipponese cryptographic systems. This makes it impossible for him to achieve happiness (unless there is a pipe organ handy, which there isn’t). Typically, it takes two to three days for σ to climb above σc after an ejaculation: Critical, then, to the maintenance of Waterhouse’s sanity is the ability to ejaculate every two to three days. As long as he can arrange this, σ exhibits a classic sawtooth-wave pattern, optimally with the peaks at or near σc [see below] wherein the grey zones represent periods during which he is completely useless to the war effort. So much for the basic theory.

Research in resonance and sound shows that if living beings operate or resonate on similar vibrations, one can affect the other. Yet another set of studies hints that there is sharing of energy and intention through the upper range of the electromagnetic spectrum. Replicated studies indicate a significant decrease in gamma rays from patients during alternative healing practices. This suggests that the body’s gamma emitter, a form of potassium, regulates the surrounding electromagnetic field.93 Gamma rays materialize when matter (such as an electron) and its antimatter counterpart (a positron) annihilate on impact. As we have seen, antimatter has the opposite charge and spin of matter. When electrons and positrons collide, they release specific types of gamma rays. Years ago, Nikola Tesla suggested that the gamma rays found on earth emanate from the zero-point field.94 Though it appears as a vacuum, this field is actually quite full, serving as a crossroads for virtual and subatomic particles and fields. When we perform healing, it is possible that we are actually tapping into this zero-point or universal field, shifting its power through intention. Still another theory is that we are accessing torsion fields, fields that travel at 109 times the speed of light. These fields are hypothesized as conveying information without transmitting energy and with no time lapse.95 Part of this suggested effect is based on the definition of time as a vector of the magnetic field. When torsion and gravitational fields function in opposing directions, the torsion field can conceivably alter the magnetic functions, and therefore the vector of time. When superimposed on a specific area in a gravitational field, it might also reduce the effect of gravity in that spot.96 These torsion fields have been researched by Peter Gariaev and Vladimir Poponin, Russian scientists who discovered that photons travel along the DNA molecule in spirals rather than along a linear pathway, which shows that DNA has the ability to bend light around itself. Some physicists believe that this twisting or “torsion-shaped” energy is an intelligent light, emanating from higher dimensions and different from electromagnetic radiation, giving rise to DNA. Many researchers now believe that these torsion waves are consciousness, composing the soul and serving as the precursor to DNA.97