Happenings – 2010 July 3

My mathematical life continues to be fairly simple.

I am trying to put together a logic post about universal generalization etc. I’ve been meaning to do this for some time, but it was delayed for the obvious reason: I didn’t understand something.

“Real knowledge is to know the extent of one’s ignorance.” Confucius

Now I think I understand, and I want to put out two more logic posts. The second one will return to syllogisms. These will finish off my original projected posts on the subject.

In the meantime, I’ve learned a little bit about solving Boolean equations, and I’m looking forward to describing that, down the road. That is, the next two logic posts will not be the end of the subject.

If anything, I am not sure that I can finish the next logic post this weekend. Now that I understand this topic in principle, I’m busy looking at examples and counterexamples. That is to say, the potential material for the post is growing. Well, maybe it won’t fit into one post.

I feel badly if I can’t get a technical post out every weekend. Traffic on the blog peaks on Mondays, and I assume it’s people checking for a new post. I feel guilty if there isn’t one for them.

Still, publishing a technical post every weekend is a bit demanding. And the fact is, sometimes I just won’t get one done.

In the background, I have planned a set of posts about stepwise regression, and about regression diagnostics for outliers. I am intermittently looking at regression diagnostics for variance, normality, and independence. They seem to get relatively short shrift.

I’ll say this again when I get to the regression posts… I take a rather heuristic approach to regression analysis. Among the reasons for that are:

  • the residuals are not normal, even if the errors are – but we judge normality of the errors by testing the residuals because they’re all we have;
  • the residuals are not independent, even if the errors are;
  • I wouldn’t be surprised if the residuals do not have constant variance, even if the errors do.

(And I have another, more compelling, reason for my heuristic approach, but I’ll explain it when the time comes.)

Anyway, I’ve got plans for a fairly substantial number of posts about regression.

In addition, I have picked up control theory again… but I think it will be a while before I can post about it. Here’s a situation where I have a lot of facts, but I haven’t been able to organize them to my satisfaction. (That’s an understatement! But I don’t need to understand all of control theory – I just want more context for what I already know.)

Oh, after I get the next two logic posts out, I’ll pick up color once again. There are some nice things in Kang’s “Computational Color Technology”. Color appearance models, which are next after Kang on my color list, may get put off for a while.

Every once in a while I try to write a couple of posts about projectiles, since I did have fun playing with the math. If I don’t do them soon, they’ll never happen at all. It would be nice to have them in reserve for a weekend when my intended post can’t be completed.

And much of the impetus for the recent color posts and the planned logic posts is simply to finish off what I have already planned, before I go marching off with new stuff.

Well, I think it’s time to start working on logic. (Even the kid, my inner child, agrees.)


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