When I look back over the past year, I see that I do not have all that many posts about the doing of mathematics — almost none, in fact. If anything, the introductory material for my “books added” posts is the closest I have come to talking about the doing of mathematics. Even those are more about “here’s what I don’t know and where I think I might be able to learn about it”. Fair enough, they’re something like what I had hoped to do; I’ll try to keep on writing non-trivial introductions to the “books added” posts.
I can point out that many of my “Davis” posts on PCA / FA are, in retrospect, mostly about my learning to use the SVD (singular value decomposition). They were as much about learning mathematics as doing it, and are a rare example – in public, on the blog, I hope! – of my blundering through something. I daresay the calculations were correct, but my assessment of issues was not very clear. It took me a while to decide what was important in that work.
So let’s see if I can do something else, too, to show the process. Let me try posting the questions I’m working on. Now, not everything I am doing is the answering of a clearly stated question. All too often my question is the all too general “what the hell is going on?” In that situation, there isn’t much I can say until I make some progress. In fact, some of the following questions are still a bit vague.
And I will confess that I am a little afraid of making these questions public. For one thing, they may seem silly. I expect that most of them will certainly be simple. By publishing them, I may make myself look foolish and ignorant; and lazy, too, because surely I should have been able to answer the questions in less time than it took to publish them. (Yes and no.)
And how long will it take me to answer them? Will the list of questions grow so long as to become unmanageable? Will my readers start throwing the answers at me? (Hmm. Wouldn’t that be a good thing?)
Okay. Let me just dive in. I have three sets of questions: mechanics, principal components, and simplical coordinates.
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