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Lexico gives an additional definition of "go non-linear" as:

go non-linear
informal

become very excited or angry, especially about a particular obsession
don't mention the drug problem or he'll go non-linear for hours.

What's the history of this sense?

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    Ask a physicist to explain it. After attempting to explain it for 15 minutes he'll go non-linear, and then you'll understand.
    – Hot Licks
    Apr 25 at 21:10

3 Answers 3

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William Safire, writing for the New York Times in 1990, gives us the article On Language; Hitting Today's Ceiling, which explains the origin:

Let us turn to physics and computer technology to help us into the 90's.

"When [Energy Secretary James D.] Watkins was first informed of the added cost," writes Physics Today, "he went 'nonlinear.'"

"The mere mention of multiple entry points," writes David M. Bulman in Computer Language, "would cause the typical structured programming advocate to go nonlinear." In Personal Computing, Michael Antonoff inserted bracketed definitions in a comment by the physicist Arno Penzias: "People say things like 'Sorry for giving you a core dump' [for giving you too much information at once] or 'I went nonlinear' or 'I blew my circuit' [for not making sense]."

In this new usage, two senses are emerging for nonlinear: the first is the classic hit-the-ceiling meaning, the second a deliberate rejection of reasonableness. John Leo, a writer for U.S. News & World Report finely tuned to language change, obituated Abbie Hoffman last year with "A fan of Marshall McLuhan's, he went 'nonlinear,' turning to arresting images and sound bites, on grounds that rational argument was dead anyway."

Ira Flatow of Stamford, Conn., who called this to my attention, explains: "Linear means traveling in a straight line; in science and math, it refers to a graph depicting behavior as smooth and predictable. A nonlinear graph shows a curving geometric progression as in a tremendous release of energy in a short time. An explosion is nonlinear." He adds, "What impacting did for the 70's and cusp for the 80's, going nonlinear may do for the 90's."

Linear thinking is generally a put-down, synonymous with "unimaginative" or "too logical," but linear programming tries to deal with the way all parts of a system interact with all the other parts over time. The adjective's opposite, nonlinear, can be used for wild and crazy or the angrier explosive; it beats the dated hitting the ceiling, but I wouldn't go ape over it. (Sorry for the core dump.)

As for first attestation, the best I've found so far is September 13, 1982, from Design News:

  • Encourage managers to exercise self-control and not go "non-linear" whenever something displeases them.

Earlier hits have the literal meaning. For example, this 1979 report on sonar probing:

It involves the use of a high frequency transducer driven to two frequencies that causes the salt itself to go nonlinear and generate the difference frequency which is comparable to that of the high frequency beam.

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The term derives from mathematics. Linear processes are ones that progress in a simple additive way. For example a linear series 1, 2, 3 … may be reasonably confidently predicted to develop as … 4, 5, 6 …

A non-linear process is one in which the progression is not so simple. It may be predictable but increasingly strong, as with 1, 2, 4, 8, 16… or it maybe unpredictable, as with 3, 23, 142, 28… ?

By analogy, if someone goes non-linear, it is suggested that their behaviour becomes increasingly intense, or becomes difficult or impossible to predict.

See for example Wikipedia:

Wikipedia

In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems.

Examples of the application of the linear/nonlinear concept to emotions are easily found. For instance:

psycnet

“In this chapter, the authors define what nonlinear dynamic systems are and show how emotions posses the characteristics of such systems. The authors then discuss the shortcomings of linear models and how linear dynamic models are better equipped to answer basic questions about the nature of emotion.”

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    How do you know ? Apr 25 at 14:03
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    I mean, how do you know that this is the reason that "he went non-linear" came to mean "he became very angry" Apr 25 at 21:30
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    This (also) seems speculative. This connection is the sort of thing that would only occur to someone pretty entrenched in math. Is there any evidence that "go nonlinear" is related like this (such as with the earliest known examples)?
    – Laurel
    Apr 25 at 21:54
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    @laurel it is not unusual for terms from a specialist field to diffuse into common usage. Consider “exponential” which is trotted out so often with no understanding of its technical meaning. “Sustainable” is another similarly treated word. However, I have added an example to help illustrate.
    – Anton
    Apr 25 at 22:16
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    This would have been my guess as well. But that's all it is—a guess.
    – GEdgar
    Apr 26 at 0:25
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It seems more likely to have come from stress tests in engineering than from mathematics or computing. When you put a material under increasing stress or strain, it will at first react in a linear way; this is the elastic phase, where the deformation of the material is linear and temporary. Beyond a certain point you reach the plastic phase, where the deformation becomes non-linear and permanent and ultimately results in catastrophic failure.

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  • The engineering use derives from the mathematical and physical usages. The behaviours of engineering systems are for example governed by various equations, some of which are linear and some non-linear. The maths came first.
    – Anton
    Apr 26 at 6:27
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    Tensile testing may seem more likely to be the origin but your answer does not offer any evidence to support it. The expression is also used in math, physics, quantum mechanics, computer science, and even in biology
    – Mari-Lou A
    Apr 26 at 6:29

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