2.3

1. The most difficult part for me is following using the dot product for probabilities. The reasons follow...

2. It's interesting to me when a mathematical operation is taken out of the context that probably motivated its creation and put in a different one. Of course, we're a long way from geometric interpretations in any advanced math course. If we're looking for intuition (which I am), we might consider the 26-dimensional vector space which W exists in. A higher dot product would mean the vectors are more "coincident", right? As one shifts the vector, one is actually shifting the components into adjacent dimensions. Of course, I am conditioned to think of vector spaces when we use dot products. I am probably shoehorning this concept into an entirely unrelated framework that would not only give no more insight into the problem, it would also destroy creativity.