(Yes, the title used to say April 29. My bad.)
Okay, it’s later than usual for my weekly math diary post. I’ve been distracted so far today — by nothing bad, but distracted nonetheless by life.
My newsgroup browsing this morning turned up an interesting read: “What Is Mathematics For?”
And since Lockhart’s Lament (at the bottom of this link) discusses the same issue, it seems appropriate to have provided its link again.
Oh, and I was searching my own blog for something — and shocked to discover that command-F isn’t very useful anymore, because I have split the posts into a small portion which is displayed, and another portion which is not… command-F only works on what is displayed.
Well, I always wondered why WordPress offered me a “search” widget; I thought command-F was all we needed. Now I know: the widget will select every post — heck, it will select everything! — containing a search string.
It won’t go so far as to expand a post which contains the search string… we have to do that ourselves, and then use command-F. But at least we are guaranteed that the post we are expanding does contain the search term.
It was simply not feasible to expand every post on the blog — one at a time — in order to apply command-F to it; for a search string that is known to be only in several posts, it’s not too bad.
So there’s a search box for the blog, over on the right.
Last week’s conundrum with the projectile problem — the fort versus the ship — turned out to have a simple enough solution: use the right numbers! The algebra was correct… in the limit, the ship is unable to fire back over a distance equal to twice the height of the fort… and once I used the correct numbers everywhere for the ship, rather than half the time (!), my computed answer was also twice the height.
As for the FFT, and the possible correction I was considering last week — no, there was no correction necessary…. I thought I was wrong, but I was mistaken.
But my surprising results still stands… so I’ll have to keep thinking about it.
And because I know how to pinpoint multi-collinearity in a data set, I really should put out some posts about regression (OLS, ordinary least squares) in general and multi-collinearity in particular.
And I have figured out why the drawing of a particular modular function is a disc… it hinges on the fact that the Mathematica function which is our starting point is defined only on the upper half plane. Maybe I’ll get around to explaining this… but maybe not, because I do believe it depends specifically on the Mathematica definition.
Color stands just where it did: I need to assemble the details to describe the nonlinearity of my monitor.
And orbital mechanics stands just where it did: I know what the next example is… although there is auxiliary information that I have to figure out how best to present (“canonical units”, and a handful of additional equations for the scalar orbit).
Logic, however, has moved around a little bit. Yes, I should be working on universal generalization etc.
But a new book came in, and I find it intensely absorbing. It may provide me with the modern tools to work out George Boole’s original stuff. (How’s that for a precise technical term?)
As I think I said before, there are three eras in the history of logic: syllogistic, Boole, the predicate calculus. Okay, I didn’t phrase it that way before. Until about 1850, the goal was to represent as much reasoning as possible in terms of syllogisms. For about the next 70 years, the goal was to extract as much information as possible from given premises. Finally and presently, logic seems to be devoted to the foundations of mathematics.
Unless you’re an electrical engineer designing switching circuits. Then it turns out that much of what Boole originally did — seasoned and dressed — is extremely useful.
While I have a book on switching theory… and it goes much further than my introduction to IC design (the un-named electrical engineering book that listed only one distributive law, mentioned at the end of this post; if I decide it’s a good book, I’ll list it, but until then) …a great find turned out to be “Boolean Reasoning” by Frank Markham Brown. It actually came in 10 days ago, but I forgot to mention it last week. And it was cheap, a Dover paperback.
Look, what I really want to be able to do — at least one of the things that Boole did — is to solve a logical equation for any of its variables. This is not something we usually do nowadays. Apparently.
This book might show me how to do that… and I can’t put it down long enough to do anything else in logic, although I have been doing other things.