Looking at the geometry, we instantly realize that we are used to assume everything is composed of straight lines. Or the mathematical analysis is full of linear assumptions here and there. However, in reality finding a straight line or a linearly interacting system is almost out of reach. This difference may seem abstract at the first sight. However, the effect of our mathematical assumption is perfectly vivid in manmade products, such that, by looking at a particular object we could easily distinguish manmade from natural. This deviation is clear since **all of manmade products are engineered based on the mathematics that does not share the same symmetry with the nature around us.**

This is also true, for our modeling. All of our models are linear interaction model, which absolutely is far from what happen in the real life. As it is nicely mentioned by Wigner, we are so lucky that our models can roughly explain what happen in the real life. Additionally, This type of thinking is not limited to the science or the engineering, but it is also extended to the social sciences such as philosophy. We should understand that sometimes** what we call perfect or ideal, is not necessarly the ideal of nature around us. **We should also note that** what we learn in the school is not necessarily what happen in the world.**

I finish this post by asking, can there be a different mathematics, more inline with the nature, where we can relax a straight line or linearity assumptions?

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I agree with the general message of your post, the other feature of our general mathematical models is that they are usually local. the linearity sometimes is caused by locality. generally non-local phenomena are highly non-linear too.

Furthermore, like you, I believe there can be an entirely new math describing such. Mathematicians and Physicists have traditionally considered these problems “hard”, these problem are also closely related to NP hard problems in Computer Science. The reason that we fail here, in my opinion is that, we have to change the language.

I have talked about this in my post here http://paymane.blogspot.com/2011/12/importance-of-language.html