Higgs Boson possibly found.

[drewC.]

The problem is not the root of mathematics itself, but the fact we haven't discovered a way to solve it. It has taken major discoveries in math to further develop our understanding of the physical world (imagine how physics would be if calculus was never discovered)

I definitely agree that the advancement of math has opened many doors to a solution for physical problems. I was incorrect when I said that the issue is math. I was trying to talk more along the lines of our inability to solve extremely complex problems. The issue is not math, but the fact that we have created models to describe things which we cannot yet solve with math due to the huge amount of time required (and money).

Don't confuse nonlinearity to mean non-analytical. There are many nonlinear models that have exact solutions. As with your example with turbulence, we do have a a model to describe it (The Navier-Stokes eqs), but we don't have and exact solution. For now, numerical methods work, but we are always trying to find ways to simplify enormously complex situations to solves things quickly and on much greater scales.

Many models include both nonlinear and non-analytical equations. There are indeed many nonlinear models with exact solutions. There are also many nonlinear models with no exact solution. Turbulence is one of these due to its highly random nature. The NS equations can be applied to fluid flow in general, but at high Reynold's numbers we cannot make the assumptions (steady, incompressible for air) required to simplify the equations into a solution which can be solved by hand. Depending on the Reynold's number, this solution can be highly nonlinear to the extent that it passes current computer's computational ability for analytical or numerical methods.

And in most cases, linearity is a simplification of a nonlinear problem. As an example, F=ma is the sum of the forces acting on an object, and doesn't model the individual components of the system.

I was wrong here as well with what I wrote, bad example.

here's a question.

is anything in the universe truly random? is it possible that a non-linearity problem can never be solved?

This is basically what I was trying to explain before. On the macro scale, a lot of the unknown problems we have today are because we are trying to predict random events. Some examples are turbulence and weather prediction. The prediction of weather patterns has gotten significantly better over the years, but it is not always correct. Some issues can be solved to a fairly accurate degree by using statistics to simplify the random variables that are roadblocks, but the calculations sometimes are still too complex that it takes a huge amount of time to solve.

[penguinofsleep]

drew puts it well.

[hondarider525]

I think I understand what he's saying, but what can I for to which that is while the boson isn't when it doesn't?