The article above just proved it's possible using math. From an intuitive standpoint it's also easy to see why entropy can decrease. However the problem is, most people don't have a good intuition of what entropy is....

Entropy is a probabilistic phenomena. Meaning that entropy can go lower, it's just that there is a low probability of it happening.

So for example random particles in a closed system do have the potential of self organizing into a cube but it's just a very very low probability.

Even the sentence above distracts from what entropy truly is because our solar system is an example of particles self organizing into spheres rather than cubes.

Here's another example: Flat cylindrical Magnets will self organize into stacks. When the magnets are scattered entropy is lower, when the magnets self organize into a stack entropy has reached it's highest equilibrium point.

Once you understand why the above occurs in the context of entropy than you truly understand the concept. Until then most people don't understand it at all and explain away the self organization with some temperature increase happening somewhere else in the system.

The logic above holds the flaw that the system is still self organizing by shifting temperature to other regions in the system. Moving temperature or disorder to specific regions in a system is still self organization.