# The "Reality is not Linear Time Invariant" Fallacy

By Marc Gauvin (c) 24/12/2013

For the benefit of those that might be influenced by such arguments:

A reference is made to robotics and feed back control and how these systems are not linear in nature and therefore cannot correspond to linear models.  However what they don't say,  is that practically all such systems can and ARE modelled as linear (LTI) systems without "loss of generality", meaning that the outputs are generally accurate and precise.  The fallacy of this argument is that it confuses the non-linear nature of the system that performs the function with the logical linear nature of the function that the system is designed to perform.

To understand why this is the case,  we need to understand what a non-linear system is and how non linearity can affect the logical behaviour of a system.  A simple example is a scale that depends on a spring to produce a measure proportional (linear) to the weight being weighed within specified conditions of use.   The spring will gradually be deformed over time such that it will cease to produce a reading proportional to the weight for which we say that the apparatus is not linear nor time invariant,  but that does not mean that the correct logical function ceases to be a linear one,  it just says that a given physical apparatus will only behave linearly within a certain time and according to concrete physical specifications.   However, the reason we successfully apply linear modelling to such systems is because there is no loss of generality in that the linear model proves valid in general and for the specified use of the scale.

Essentially, the argument in question aims at negating money as a measure of value on the basis of the fact that the nature of the goods and services being evaluated are far more complex and contain far more non-linear information than can be recorded in the simpler non-linear evaluation represented by money.

"Value" is not a physical commodity,  it is in fact a non physical logical entity i.e. it has no necessary physical properties that make it susceptible to changes over time by virtue of corrosion, temperature, humidity, decay etc.   Money's function is to represent the relative value attributed to goods and services not the actual goods and services.

Thus, the comment that linear evaluations of non-linear phenomena are false or at best incomplete,  is tantamount to saying that tennis scores are invalid because they are simple linear systems while the act of scoring in tennis is very complex and non-linear in nature.  The implication is that we are being hoodwinked by tennis scores because not all successful unitary scores are equal, it could even go so far as to say that some missed "almost scored" scores are of greater value than some other trivial successful scores.  But what this argument leaves out, is that if we are to keep score we necessarily require using a linear system of score keeping and even if we were to provide a complex non-linear model capable of perfectly recording and representing every and all variables and their exact relations,  we would still end up with a linear record of won and lost matches.

I hope the fallacy is becoming unraveled,  we humans use all sorts of tools, knowledge and information about the non-linear nature of the goods and services we consume before we evaluate their relative value using a simple linear function of money, that is the complexity of the phenomenon is subsumed within the evaluation.  That that evaluation is imperfect is undeniable but the sum of many such evaluations is invaluable,  particularly in light of the broad array of different and specialised products that require different expertise to evaluate, the constant flow and implementation of these that generate a vast number of independent experiences, the constant exchange of data and information etc.  all this is subsumed in the relative measure of value of different products and options.