I definitely like thoughts that are simple to explain but that raise elementary questions. Thus, I always have this great feeling of true joy once I get to know a new idea of this kind. My most recent discovery is the Kac ring model. Amazingly, a google search will get you mostly very specific scientific papers.
A quick introduction: This model was introduced by Mark Kac (a Polish mathematician). It is a very simple model to illustrate parts of Ludwig Boltzmann‘s work in statistical mechanics. You can find a description in “Probability and related topics in physical sciences” by Mark Kac on p. 99ff. The most interesting about it is, that the second law of thermodynamics raises some questions (not exactly of the intelligent design kind). The most intriguing is the reversability paradox (or arrow of time paradox). Imaging, you start from a rather ordered state (e.g., some unequal distribution of natural gas). The problem is (or actually it is questionably whether it actually is a problem) that according to thermodynamics the entropy will increase in both directions of time — forward and backward. The increase for the backward case is the problem here. Imaging a drop of milk in your coffee. If you wait some time (forward), it will diffuse and you end up with a great (well, maybe cold) white coffee. If you would travel back in time, the exact same thing would happen according to thermodynamics. Well, should the drop have flown back into the milk jug? Is thermodynamics incomplete or wrong? Using Kac’s model this can be investigated with a very simple model (much simpler than a cup of coffee…).
Well, I’m not getting into details here. This was just to challenge you. If you are interested you might want to have a look into this thesis or Ilya Prigogine‘s work. Have fun! 
