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¶ Intuitive explanations
Some of the greatest moments in learning for me have been when, after spendings hours or days or even months trying to figure out a particularly difficult concept, I am presented with a simple but intuitive explanation that makes everything suddenly click into place. The world becomes clear, and the concept, which seemed so daunting and challenging before, appears as simple as elementary algebra. Such moments of tribulation are typically followed by massive confusion, wondering why nobody brought forth that simple explanation in the first place. Sometimes it even makes me feel that if I armed myself with an encyclopaedia of these simple explanations, that I could singlehandedly raise the world's awareness by an order of magnnitude (this feeling is usually quite short-lived).

A recent example - I had been trying to do some reading on my own and figure out what Markov Random Fields are. They are used heavily in computer vision research, and I thought it would be useful to know what they are and why they are used. It was a complete failure on my part. Paper after paper, I just couldn't figure it out. Frustration reigned supreme and battered my tormented ego. Then one day, I found out that a Markov Random Field is nothing more than a Bayesian network with undirected edges. Like a Bayesian network, it exists to allow the user to estimate the hidden state of a system by inferring the most probable state from the set of observed variables. But instead of using directed edges to express causal relationships and conditional probabilities, a MRF uses undirected edges to express compatibilities and joint probabilities ( assumptions about the probabilities that two variables have certain states rather than assumptions about the probability of one variable given the value of its parents ). Instantly, Markov Random Fields made sense to me and I could see why they're being used so much.

So here's the kicker. Intuitive as that was to me, unless you're an AI specialist or have taken a reasonably challenging course in probability theory, that probably (haha) made no sense to you at all. The generalization of this is that simple, intuitive explanations for a subject certainly exist, but each "intuitive" explanation is intuitive only for a certain, possibly extremely small, audience. One of the major challenges that a teacher faces is knowing exactly which audience she is preaching to, and which of those explanations is exactly the right one to give. The best teachers can read their students and refine their estimates of both which kind of audience their students fall into, and which explanations are best.

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