I probably understand where you are coming from. But, you are may be missing the point? > The visual explanation of the Markov chains on that web site looks el

I probably understand where you are coming from. But, you are may be missing the point? > The visual explanation of the Markov chains on that web site looks elegant and simple because... it is I strongly resonate with this statement. However, I disagree with the claim the "You are replacing the active intellectual process". In fact, it is the opposite - it is stimulating. Let me present an anecdote which will perhaps resonate with many people. Often times, when venturing into a new topic, one tends to read the reference texts. Let us be frank - reference texts are not beginner friendly no matter how much they claim (they are reference for a reason). To get to the meat of the story, a reader has to hold lot of context from past knowledge. This is hard and often towards reaching the actual results, the reader is already exhausted. Instead, such intuitive visualizations provide context to a new reader. The next time the reader goes back to the reference text, this "lookahead" (from the visualization) is valuable. It is easier to internalize that where in the grand scheme of things a particular topic lies. > Of course, this doesn't mean that visualizations are useless, but they should be carefully designed with some learning goal in mind. Not easy! For example, the visualization could slowly gray out states that are not visited. In that way, the student could get a feeling for concepts like recurrence etc. This I believe is nitpicking.