TODAY IN SCIENCE HISTORY ®  •  TODAYINSCI ®
Celebrating 24 Years on the Web
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “The Superfund legislation... may prove to be as far-reaching and important as any accomplishment of my administration. The reduction of the threat to America's health and safety from thousands of toxic-waste sites will continue to be an urgent�issue �”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index N > Category: Nonlinear

Nonlinear Quotes (4 quotes)

Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space. For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.
A simple system representing cellular convection is solved numerically. All of the solutions are found to be unstable, and almost all of them are nonperiodic.
The feasibility of very-long-range weather prediction is examined in the light of these results
Abstract from his landmark paper introducing Chaos Theory in relation to weather prediction, 'Deterministic Nonperiodic Flow', Journal of the Atmospheric Science (Mar 1963), 20, 130.
Science quotes on:  |  Bound (120)  |  Chaos Theory (4)  |  Convection (3)  |  Design (203)  |  Different (595)  |  Differential Equation (18)  |  Equation (138)  |  Feasibility (4)  |  Finite (60)  |  Flow (89)  |  Hydrodynamics (5)  |  Light (635)  |  Long (778)  |  Mathematics (1395)  |  Modification (57)  |  Numerical (39)  |  Ordinary (167)  |  Phase (37)  |  Phase Space (2)  |  Possess (157)  |  Prediction (89)  |  Range (104)  |  Represent (157)  |  Respect (212)  |  Result (700)  |  Simple (426)  |  Small (489)  |  Solution (282)  |  Solution. (53)  |  Space (523)  |  State (505)  |  System (545)  |  Unstable (9)  |  Weather (49)  |  Weather Prediction (2)

For a smart material to be able to send out a more complex signal it needs to be nonlinear. If you hit a tuning fork twice as hard it will ring twice as loud but still at the same frequency. That’s a linear response. If you hit a person twice as hard they’re unlikely just to shout twice as loud. That property lets you learn more about the person than the tuning fork. - When Things Start to Think, 1999.
…...
Science quotes on:  |  Complex (202)  |  Frequency (25)  |  Hard (246)  |  Hit (20)  |  Learn (672)  |  Let (64)  |  Linear (13)  |  Loud (9)  |  Material (366)  |  More (2558)  |  Need (320)  |  Person (366)  |  Property (177)  |  Response (56)  |  Ring (18)  |  Same (166)  |  Send (23)  |  Shout (25)  |  Signal (29)  |  Smart (33)  |  Start (237)  |  Still (614)  |  Thing (1914)  |  Think (1122)  |  Tuning Fork (2)  |  Twice (20)  |  Unlikely (15)  |  Will (2350)

Man continues to be the only 150 pound nonlinear servomechanism that can be wholly mass-produced by unskilled labor.
In 'Mechanisms in Anxiety', Journal of Neuropsychiatry (Sep-Oct 1963), 5, 416. Also appears as “Man is the only…reproduced…” for the opening sentence by Ashley Montagu in 'Forward: Origin of the Specious' for Robin Fox, The Passionate Mind: Sources of Destruction and Creativity (2000), xxi.
Science quotes on:  |  Continue (179)  |  Labor (200)  |  Man (2252)  |  Mass (160)  |  Produced (187)  |  Reproduction (74)  |  Unskilled (4)  |  Wholly (88)

The problem with linear theory is that it is not nonlinear.
Epigraph in Mathematics in Nature: Modeling Patterns in the Natural World (2003), 173. Quoting from his own first professional presentation as a first-year graduate student.
Science quotes on:  |  Linear (13)  |  Problem (731)  |  Theory (1015)

In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
Sitewide search within all Today In Science History pages:
Visit our Science and Scientist Quotations index for more Science Quotes from archaeologists, biologists, chemists, geologists, inventors and inventions, mathematicians, physicists, pioneers in medicine, science events and technology.

Names index: | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

Categories index: | 1 | 2 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
Thank you for sharing.

# Science T-Shirts from Amazon

See more at Amazon

by Ian Ellis