What Does Nonlinear Mean?

Nonlinear is a mathematical term. It is a very specific thing. First consider the linear: In the figure to the right one observes a graphic representation of a linear equation. It’s clearly straight in progression with no discontinuities.

It is important to recognize for every x there is exactly one and only one corresponding y value in that graph.

A digression: Saying there is one and only one y value for every x value is not a trivial thing. In Pure Algebra there’s a lot of attention given to the principles that insure and define the proper behavior of functions; that something maps a value from one domain to another domain whether that is R1 space to R1, or R2 space to a R3 space. All that is rigorously studied.

Science – mathematics – are very serious studies. Remember Giordana Bruno was burned at the stake in the 16th century by the Catholic Church for his belief that the Universe was infinite and that there could be other solar systems.  Cecco d’Ascoli of the 13th century was the first university professor executed during the Inquisistion.  There are many other historical figures executed in the name of science. My point: that defining valid constructs is a very important concept in our world yet most never think of this.

Things as mundance as the number systems such as the natural numbers, integers, real numbers, etc are rigorously proven even as abstract as these concepts are. While many New Agers don’t want to be hung-up about the “validity” of experience or highjacking science terms in an attempt to substantiate their jargon, the proof of many fundamental concepts in our world were in fact life and death matters at one time and even now they are life and death matters when one considers the science in the mechanical engineering behind the construction of a bridge or the electrical engineering used in developing a heart pacemaker.

Back to business: now consider the illustration of three graphs below. Each graph shows a plot which is clearly not straight, what one would call nonlinear or the opposite of linear. Notice in these examples that again for every x valve there is exactly one and only one corresponding y value. These corresponding to well known mathematical functions (exponential, trigometric, and polynomial expressions).


Now consider the graph below and to the right. One clearly recognizes the shape of a crashing wave in the illustration; we see this in nature – a shock wave. This is the graph of the solution for a nonlinear differential wave equation. In this case one readily observes that for every x on the graph there may be more than one unique value of y; in this case as many as three.


Are any of these nonlinear expressions what TMI had in mind as a time representation for F15? I don’t think so.

Below is another example of a possible nonlinear graph, maybe a trajectory in some chaotic domain. This is not known to be real or represent any known equation. It’s just an example for the purpose of this discussion.  In the graph below note the ascending squiggly line. In this case let’s consider the x axis as position and the verticle axis as time.

What could this represent? In the 2016 movie Arrival twelve alien craft visit Earth. Louise Banks, a linguist, is hired by the military to communicate with the aliens. During the 33D003BA-F005-475C-8552-722C570BFAF4course of her interations with that species she has numerous experiences with her future daughter Hanna, at different points in the future timeline of Hanna’s life. Those momentary intersecting future experiences in Louise’s timeline could represent the graph on the left. It is interesting to note that in the movie Lousie’s experience were not a function of some space construct but rather due to an ability of the aliens.

To read my notes about Sa-Tash one should appreciate what nonlinear means.