A recent run of too many articles on the same topic (exhibits: A, B and C) puts me in a position where I feel the need to explain my motivation. Which itself becomes yet another article related to the original topic. The explanation I offer is: this is the way mathematicians think. To us mathematicians the tension is that there are far too many observable patterns in the world to be attributed to mere chance. So our dilemma is: for which patterns/regularities should we derive some underlying law and which ones are not worth worrying about. Or which conjectures should try to work all the way to proof or counter-example? Continue reading
We describe the “the local to global principle.” It is a principle used to break algorithmic problem solving into two distinct phases (local criticism followed by global solution) and is an aid both in the design and in the application of algorithms. Instead of giving a formal definition of the principle we quickly define it and discuss a few examples and methods. We have produced both a stand-alone PDF (more legible) and a HTML/blog form (more skimable).