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

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.

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.

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.

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.

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.

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.

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.

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...

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.

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.

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.

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.

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.

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

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.

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.