Understanding: The Challenge Understanding is a concept that is difficult to communicate. Everyone knows what knowing is so it presents no problem in communication regarding what is known. This fact I think points toward the reality of ‘understanding’; it is a very personal and very subjective phenomenon. I have recently had the experience of digging out the root system of a tree that I had cut down. I think this experience might be useful as an analogy for communicating my understanding of ‘understanding’. I would say that cutting down a tree might be comparable to ‘knowing’ and digging out the root system might be comparable to ‘understanding. Not everyone has had the pleasure of digging out tree roots but I suspect few will have any difficulty in immediately understanding the analogy. I think that it is appropriate to describe philosophy as a domain of knowledge directed toward understanding. I suspect that understanding what mathematics is really about is very difficult but knowing addition, subtraction, division, calculus, etc. are relatively simple. I would say understanding the nature of mathematics is a matter of understanding but ‘doing’ math is a matter of skilful application of knowledge. I suspect you could ask any engineer if s/he knows math and they would quickly reply, yes. I think they would be far more hesitant in such a reply if you asked them if they understood math. We can look out our plane window when flying over the Grand Canyon and truthfully say we know the Grand Canyon. We might spend three months living in and exploring the length of the Grand Canyon before we would be willing to say we understood the Grand Canyon. Understanding Newton’s Mechanics is much easier, I think, than understanding Quantum Mechanics. The parameters Newton deals with are such things as distance, time, momentum, acceleration, velocity, etc., all parameters that we live with in our daily lives. From what little I know about QM no one really expresses their confidence that they understand it even though they have the knowledge necessary to predict the behavior of the phenomenon with startling accuracy.