Discover the most popular and inspiring quotes and sayings on the topic of Nonlinear. Share them with your friends on social media platforms like Facebook, Twitter, or your personal blogs, and let the world be inspired by their powerful messages. Here are the Top 100 Nonlinear Quotes And Sayings by 92 Authors including Nicola Yoon,Cecelia Ahern,Steven Strogatz,Michael Nesmith,Abha Maryada Banerjee for you to enjoy and share.
ahh, calculus. the mathematics of change
predictably unpredictable
Change is most sluggish at the extremes precisely because the derivative is zero there.
Chaos theory says that even a small change in initial conditions can lead to wildly unpredictable results. A butterfly flaps her wings now and a hurricane forms in the future.
Linear thinking typifies a highly developed industry. It starts to get these patterns built into it somehow. I'm not sure how that happens, but certainly you take a look at dinosaurs.
Nothing in this World is Static...Everything is Kinetic..
If there is no 'progression'...there is bound to be 'regression'...
I am a great fan of science, but I cannot do a quadratic equation.
Considering the inconceivable complexity of processes even in a simple cell, it is little short of a miracle that the simplest possible model - namely, a linear equation between two variables - actually applies in quite a general number of cases.
Nothing about my life or my career has been linear.
...Gradation; gradation; and then a sudden leap...
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.
The pattern appears so ethereally, that it is hard to remember that the shape is an attractor. It is not just any trajectory of a dynamical system. It is the trajectory toward which all other trajectories converge.
Given an approximate knowledge of a system's initial conditions and an understanding of natural law, one can calculate the approximate behavior of the system.
Deep in the chaotic regime, slight changes in structure almost always cause vast changes in behavior. Complex controllable behavior seems precluded.
Time is a series of fluctuating variables.
When, and only when, you clearly see the inner roots to an outer condition, can you change them and thus it.
The only thing constant is change
strange attractor - do
I don't believe that life is linear. I think of it as circles - concentric circles that connect.
That's calculus in a nutshell. It takes a problem that can't be done with regular math because things are constantly changing - the changing quantities show up on a graph as curves - it zooms in on the curve till it becomes straight, and then it finishes off the problem with regular math.
This circuit is interesting because it has inclines and declines. Not just up, but down as well.
It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.
Curve: The loveliest distance between two points.
Equilibrations
If you walk back
and forth
through a puddle pretty
soon
you wet the whole
driveway but of
course dry
the puddle up.
The form follows the function.
Sensitive dependence on initial conditions; one word, one act, can change the world. Well they named it chaos theory.
I pull my T-shirt over my face and am about to plunge in when it occurs to me that I'm approaching this, as Kiernan would say, far too linearly.
The wave function of this situation is going to collapse quite soon.
Is your learning curve a horizontal line?
When you have a large space to conquer, the curve is the natural solution.
The global climate is a complex interactive system, with all kinds of nonlinear feedback loops.
Aspiring to these wide generalizations, the analysis of quadratic functions soars to a pitch from whence it may look proudly down on the feeble and vain attempts of geometry proper to rise to its level or to emulate it in its flights.
Don't worry about where you are. Watch the first derivative.
I'm no mathematics whizz, but even I know that when the variables start piling up, it's time to ditch the equation and see if you can find a cheat sheet.
By definition, revolutions are not linear, one step at a time, event A leading to event B, and so on. Many causes operate on each other at once. Revolutions shift into place suddenly, like the pattern in a kaleidoscope. They do not so much proceed as crystallize.
It is interesting thus to follow the intellectual truths of analysis in the phenomena of nature. This correspondence, of which the system of the world will offer us numerous examples, makes one of the greatest charms attached to mathematical speculations.
The orthogonal features, when combined, can explode into complexity.
Laws which are consistent in theory often prove chaotic in practice.
for any non-biological system, the distribution of output follows a power law curve.
You cannot run a linear system on a finite planet indefinitely.
The Only Thing That Is Constant Is Change -
The only constant is change.
The resulting, stable singularities now carry the name BKL in honor of Belinsky, Khalatnikov, and Lifshitz. A BKL singularity is chaotic. Highly chaotic. And lethal. Highly lethal.
Complex question can only be solved by patience.
A non-analogue image has an extremely compressed life. It starts as this and, in increasingly short time spans, becomes that.
Hey, chaotic trajectories are just as deterministic as any other kind.
It's an improvisation on a theme. You know where you want to go, but you don't know how to get there. It's not linear.
Time is only linear for engineers and referees.
Giving never moves in a straight line - it always moves in circles.
All of audio as we know it is an attempt to be more and more perfectly linear. Linearity means higher quality sound. Hypersonic sound is exactly the opposite: it's 100 percent based on non-linearity.
The alternation of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
The path behind is twisted, the path ahead unknown.
Nature, when left to universal laws, tends to produce regularity out of chaos.
The idea that memory is linear is nonsense. What we have in our heads is a collection of frames. As to time itself-can it be linear when all these snatches of other presents exist at once in your mind? A very elusive and tricky concept, time.
We are dealing with a multidimensional paraphysical phenomenon which is largely indigenous to planet earth.
I regard it in fact as the great advantage of the mathematical technique that it allows us to describe, by means of algebraic equations, the general character of a pattern even where we are ignorant of the numerical values which will determine its particular manifestation.
But there was in the air that kind of distortion that bent you a little; it caused your usual self to grow slippery, to wander off and shop, to get blurry, bleed, bevel with possibility.
Algebraic to the limit!
By adapting and adjusting to randomness, you shape but do not control your endpoint.
You know that the formula is askew when even if the formula is working, it's not; when even if everything's going right, something is wrong.
Analysis does not owe its really significant successes of the last century to any mysterious use of sqrt(-1), but to the quite natural circumstances that one has infinitely more freedom of mathematical movement if he lets quantities vary in a plane instead of only on a line.
Fuck that: take shagging n peeve oot ay the equation n yir left wi the sqare root ay swee fuck all!
The great problem of today is, how to subject all physical phenomena to dynamical laws. With all the experimental devices, and all the mathematical appliances of this generation, the human mind has been baffled in its attempts to construct a universal science of physics.
The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.
It is possible to build a system that could assure you of increase on constant basis
People interpret things in a linear form but science proves otherwise.
Between the two. Harmony emerges from integration. Chaos and rigidity arise when integration is blocked.
Small islands of coherence in a sea of chaos can shift the whole system to a higher order.
Whatsoever has exceeded its proper limit is in an unstable position.
Arc, amplitude, and curvature sustain a similar relation to each other as time, motion, and velocity, or as volume, mass, and density.
But we must not underestimate the potency of the mathematical process of abstraction. A surprising variety of things happen to have both magnitude and direction and to combine according to the parallelogram law; and many of them are not at all reminiscent of journeys.
Chaos is a friend of mine.
The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing.
[Statement of the second law of thermodynamics, 1862]
The way I think about things and experience things is not particularly linear, and it's not orderly, and it's not pyramidical, and there are a lot of loops.
Change occurs on a continuum and does not move in a straight line.
Let no one ignorant of Mathematics enter here.
the path of change is unpredictable.
Shrink, shrink variation, to reduce the loss.
One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden.
We may train ourselves to be adaptable as possible, to respond appropriately in each situation, but the ideal of controlling the outcome or steering events as they occur must be relinquished. Chaos rules it all.
Only change, not loss
hard on a curve and lost control of the
This was the tricky bit. The really tricky bit, trickiness cubed.
The most complex object in mathematics, the Mandelbrot Set ... is so complex as to be uncontrollable by mankind and describable as 'chaos'.
In economics, when you put together a highly elastic thing and a highly inelastic thing, you create extraordinary potential for turbulence, volatility, and for unstable prices.
Form follows function straight to hell.
If a self-organizing system becomes too static, it runs down; if it becomes too chaotic, it breaks apart.
Change moves incrementally from breath to breath and moment to moment, allowing for course-correction along the way.
Elliptical, adj.
The kiss I like the most is one of the slow ones. It's as much breath as touch, as much no as yes. You lean in from the side, and I have to turn a little to make it happen.
If a system is chaotic (most are), then it implies that however good the resolving power may be, the time over which the system is predictable is limited. Perfect predictability is not achievable, simply because we are limited in our resolving power.
Baseball players or cricketers do not need to be able to solve explicitly the non-linear differential equations which govern the flight of the ball. They just catch it.
In the abstract world of American economists, equations run both ways; they believe that by changing the sign of a variable from plus to minus or from minus to plus or the price and quantity of x or y, the direction of historical movement can be reversed.
I thin many people's deviant behavior starts with dreams because dreams are so non-linear ... as if there's an assumption that everything has to be linear or has to be plotted.
untrammelled flow
As you deal with more and more complex systems, it becomes harder and harder to find deep and interesting properties.
subjective disturbance
From one perspective, we're in the early stage in artificial intelligence, but exponentials start out slowly, and then they take off.
Function influence but does not dictate form
The world appears rectilinear, but is in fact curvilinear - a literal truth in physics, and a metaphorical one in metaphysics.
You seek too much information and not enough transformation.