Math has been rather slow lately, with much going on in my other, commercial work that is taking my time up. I have been reviewing some material I may not have learned well the first time: tangents and secants and their segments in circles, solving non-right triangles with the sine and cosine formulae, and areas of triangles found through trigonometric formulas. Geometry shows me tangents and secants, but I have yet to figure out why tangent and secant are also names of trigonometric ratios. None of my trig books have seen fit to tell me. In fact Barron's Ruritanians were misleading, talking about "going off on a tangent" rather than explaining how the geometry led to trigonometry.

I feel the need to know this material well enough so that if I see it again next year or later on, I'll at least recognize it and be able to look it up in my reference books. Some important formulae, I must remember forever and always have available, just as I learned the quadratic formula in years past. All told, trigonometry has featured a lot of formula-crunching, with more to come.

Spring is really here now, with the leaves finally on the trees in that ever-so-brief color of brilliant chartreuse, which seems so bright as to be unnatural. But then, the blasting pink and red of azaleas also seems unnatural, and those colors are there too. There are certain colors of paint (or markers) which you can only use unaltered, at this time of year.

The urban spaces are filled with birdsong at dawn and dusk, and sometimes all through the night as well. There is an indefatigable mockingbird who sings all night long in back of my residence, when it is warm enough. He goes on for hours. As a birdwatcher trained from childhood in song identification, I can recognize almost all of the birdsongs he repeats. Some of his imitations are so good that they are indistinguishable from the real thing, such as his red-bellied woodpecker "barks" or his carolina wren calls. Other imitations, such as his "robin," are too loud and frantic to match the sweeter tones of the real bird. This mockingbird also imitates baby birds, crickets, frogs, and even a car alarm siren.

Listening to him for an hour or so, I charted his "song list" to see whether he followed any pattern. I was interested to see that he continued to vary his song imitations, in length, complexity, and dynamics (loudness or softness). For instance he would follow a loud, repetitive carolina wren chant with single soft notes of a woodpecker call, then the squeaky tweets of a titmouse, then the chattering of a robin alert call. It was as if he had some sort of variety generator which reminded him not to go on too long with the same type of call. He reminded me of a jazz trumpeter, riffing away in syncopated rhythms in a long solo. And like that jazz player, it seemed as though Mockingbird had an aesthetic sense about it all — he knew what to play at what time, when to play soft and slow or when to shout it out.

Can a bird have an aesthetic sense? Perhaps he can. Or perhaps, as is more probable, the variations of the mockingbird song are evolutionarily determined as the best strategy to win the attention of female mockingbirds and proclaim one's territory. I suppose one could say the same thing about the jazz musician.

Posted at 1:47 am | link