Why is linearity such a big deal?

its easy to work with

Everyone knows how to interpret a slope coefficient.

Many statistical models make assumptions about the data, such as linearity, because the models that don't make such assumptions are more difficult to compute.

What about quadratic etc coefficients, or trig coefficients? How do those apply to common problems like slope does?

related quote

>Classification of mathematical problems as linear and nonlinear is like classification of the Universe as bananas and non-bananas

>>8722826
Slope coefficients are more general. For instance, assume the relationship between money and happiness is perfectly linear and can be described as y=2x whith y being units of happiness and x being dollars of money. Then, for every one dollar increase in money, happiness increases by 2 units, regardless of x.

However, if this relationship were quadratic, then the increase in happiness for each additional dollar would depend on the amount of money you currently have. For instance, if y=2(x^2), then an increase from 1 to 2 dollars will increase happiness by 6 units whereas an increase from 2 to 3 dollars will increase happiness by 10 units.

In short, linearity provides a general result that you don't see with most other relationships. So we like linearity just because it makes things easy to deal with.

>>8722810
10 day countdown.

Linearity = simplest unit of interaction/measurement (Archimedes' Lever).

Mathematically this is the same as being able to make your equation balance to 0; meaning a highly understood/optimized function/expression.

Linear = 1d simplicity

Ratios = 2d simplicity (relations between number sets)

>>8722810
Linear = easy

Nonlinear = hard

ex.
Studying solutions of linear polynomial equations get you Linear Algebra. Studying solutions of nonlinear polynomial equations gets you Algebraic Geometry.

One of those is a lot easier than the other.