Reviewing Mathimatical Linearity.

I consider that proportionality, often seen as a hallmark of linearity, can still be relevant within a more complex framework

While proportionality is a basic relationship, incorporating concepts like limits or asymmetry shouldn’t inherently contradict linearity.

I think we need to consider recognizing that every measurement carries uncertainty encourages us to account for variations and potential inaccuracies. This aligns with scientific practice where uncertainty is quantified to provide a clearer picture. Just as physical measurements can be imprecise, our conceptual frameworks may also need to adjust as new insights arise.

As systems become more complex, we may observe relationships that appear non-linear at specific scales but can still be understood as part of a broader linear framework when viewed holistically.

Systems can be linear even if they exhibit asymmetrical behaviors, as long as the underlying relationships can be described in a consistent manner. In math's we may apply limits and maximums to our linear values. Introducing limits doesn’t negate linearity; rather, it adds a layer of complexity that can be explored within a linear context.

Linearity should include A dynamic understanding of measurements and relationships that accounts for uncertainty and complexity. A broader, more inclusive view of linearity that allows for asymmetry and limits while still recognizing underlying linear relationships.

My idea of linearity encompasses relationships that can be understood as consistent and adaptable, even when incorporating limits, asymmetry, and dynamic adjustments to measurements. In contrast, non-linearity arises when values are perceived as lacking direct conveyance or proportionality, often due to hidden complexities or misinterpretations that prevent a clear understanding of the underlying relationships.

For an example Gravity is considered non-linear. However if we equate distance and mass as being the same thing, where mass is a measurement of inertia and inertia is a resistance to change and that resistance is slower time. Then time and distance interact linearly and explain that half the distance is four times the gravity because distance is four times the time or roughly speaking.

Generalized Linear System

1.There exists a decomposition of the domain into regions R_i such that f is approximately linear on each R_i.

2.The error in the linear approximation can be bounded and quantified.

3.There exist transformations T_i such that T_i(f) is linear in a classical sense.

4.The function preserves some notion of scaled addition: f(ax + by) ≈ af(x) + bf(y) + ε(a,b,x,y), where ε is a bounded error term.