Osculating Circles, Serenade, Reverse Video, and all that Jazz (Not)

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Well, dear readers, I’m blowing my own horn here once again, mostly because I want to drum up some viewers for a little YouTube video I put up which, I think (but I’m biased), is a particularly nice piece of work, and because I think there’s so much to talk about.

On second thoughts, I’m not going to talk very much about all that has to be talked about.  At time of writing, the Republican dominated Congress has voted to Sequester, which is a system of automatic and arbitrary cuts in the Federal budgets and services settled upon a couple of decades ago.  The branches of the Federal Government that are cut are those considered inessential, such as Food Stamps, the Federal Parks (certain forest preserves and recreation areas, for those of you who are so lucky as to live abroad), and such things that do not actually discomfit actual Members of Congress, some of whom are among the most vile individuals on the face of the Earth, both ignorant and vicious, while others are merely team players, who have found themselves on the wrong team.

The reason for the Sequester is that the new Health Plan put in place by Democrats and President Obama to provide reasonable health care for most members of American society (and still provide a handsome profit for Insurance Companies) needs a certain amount of government funding to get started.  (As will all insurance schemes, you have to provide a certain amount of startup money.)

Here is an explanation of what is going on through one possible interpretation:


And why do the Republicans want to not fund the health plan?  One reason, supposedly, is because it provides government funding for birth control.  The Pope has declared that religious preoccupation with birth control is disproportionate to its importance.  But certain (very small, but vociferous) sectors of American society are outspoken about the Principle that the government should not participate in birth control.  Ironically, the USA funds birth control in foreign countries.

There has been an onslaught of media advertising that provides a mixture of misleading information and outright lies about the new health plan, urging private individuals to stay away from it.  But it appears that large numbers of people are signing up nevertheless, which means that government funding is not as important as it might have been if people did not sign up.  The American people seem to have weighed in on the side of the new health plan, called the Affordable Care Act, officially, and Obamacare unofficially.  If it goes on to be a great success, the next step for the Republicans, who are now in the majority (the Act was passed in the previous session of Congress, which was dominated by the Democrats) will be to make some minor changes in the law, and relabel it the American Apple Pie Act, or something like that, and take credit for its success.  The changes might be as little as allowing condoms, but not contraceptives, or something equally stupid.  When private companies use marketing tricks to deceive customers it is irritating, but when Congress plays with words and tinkers with the truth, it is truly disgusting.  I sincerely hope the Democrats never indulge in Marketing.

Osculating Circles

An osculating circle is a simple thing.  Suppose we have a curve C, and some point P on the curve.  If you pick three points on the curve, you can easily make a circle pass through those three points.  Now if you make the three points all move to P, the circle gradually becomes the osculating circle at P, which is a circle that matches the shape of the curve perfectly just at the point P.  The radius of this circle is called the radius of curvature of the curve C at the point P.

In the figure we have a curve, in pale blue, unfortunately, and three points F, G, and H.  We also show the circle through those points, and how it was made, using perpendicular bisectors, and so forth.  Now imagine F and H moving towards G.  As you can see, the circle will not change very much, and becomes the osculating circle at G.  This can be done at any point, really; at flat points of the curve, such as F, the circle will be large; at point where the curve turns rapidly, such as A, the circle will be very tight.  In fact, it will be precisely the circle along which you would be driving, briefly, if the curve was a road.

I forgot to say: wherever the curve turns sharply, the Osculating Circle will be small, wherever the road curves hardly at all, the Osculating Circle will be enormous.  The smaller the radius, the tighter the curve.  (Each point has its own osculating circle.)  The video was made by tracing the osculating circles; in other words, the circles remain as the point moves on, so that there are hundreds of circles, which were set to fade gradually (but don’t seem to fade at all, unfortunately). [Added later: I figured out why there was no fading; I had forgotten to click in an important box.]

In the video below, the point A moves along the curve, taking the osculating circle with it.




Meanwhile, down at the farm, my friend is a horn player, and I had visited their home back in the Fall of 2010 --Rally to Restore Sanity, remember?-- and played them a MIDI version of my Serenade, my only original composition --except for an early Chorale-prelude.  Just the other day, my friend said that she had begun playing in a wind quintet (Flute, Oboe, Clarinet, French Horn, and Bassoon), and may she play my Serenade with her gang, just for fun?

A typical woodwind quintet:
the Berlin Philharmonic Wind Quintet

To have my Serenade really played live!  OMG!  Of course, I had to make it worth playing by a quintet, which meant that it had to be rewritten in true 5-voice form.  (The piece I had written was in four parts, which is the easiest thing to do, with the bass being doubled.  That doesn’t really count as 5 parts.)

For the first time I found myself actually engaging with issues of instrumentation: how high can a bassoon go, how low, how long can they play without taking a breath?  Suffice it to say that I had to rewrite the harmony extensively to keep it more or less the same, and to make sure all the parts were within the ranges of the instruments, and that each of the parts was fairly interesting to play.  So that’s what you’re hearing, going on behind the osculating circles.  No, not a live performance, but the new rewritten composition, played by MIDI sequencer.  If and when the live performance actually takes place (possibly even this weekend), and if the parts are all in feasible ranges, and if they happen to record the performance, I will post it here!!!

[Added later:  The Quintet was performed, but it sounded so bad that they never recorded it.  So I have to be content with the version played by software :( ]

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Under Attack: Obamacare!

The far right extreme of the GOP (or SOP: Silly Old Party) is attacking the Affordable Care Act, commonly known as Obamacare, furiously.  There was a 21-hour address by Ted Cruz of Texas, that brought in such relevant themes as Naziism, and Eggs and Green Ham, and Freedom, all to speak in favor of de-funding the Act.

Jim DeMint who recently abandoned running for the Senate in favor of taking the reins of the Heritage Foundation (a conservative think-tank) has had the Foundation put up an enormous billboard in New York City that decries Obamacare, and urges readers to support de-funding it.  The list of Republican spokesmen (and women) calling for erasing Obamacare is too long to enumerate.

Why is Obamacare such a cause for concern among conservatives?
It is hard to guess.  What they claim is their reason for opposing it need not have a lot to do with why they actually want it destroyed.  I have a few guesses.

(*) Obamacare is a huge Democrat achievement, and if it works as it was planned (and remember, its success was estimated probabilistically, and a lot depends on behavior trends, as most insurance initiatives do; a lot of people acting irrationally can derail it), it will be a huge issue on the credit side for the Dems, and you can see Democrats, both great and small (mostly small, unfortunately) running on the strength of it for a decade.  "We brought you Obamacare!  Vote for me!" 

Obamacare is also a Republican loss.  They fought like dogs to sabotage it, and if they fail, it will be an enormous dent in their reputation.  They brought up everything from Freedom of Choice, motherhood and apple pie, and had to go to the extreme of painting the Insurance Industry as the saviours of the nation, to vilify the Bill (but of course they went right back and said, no, the Insurance Industry is the very devil incarnate, and the Bill was written by them, and is a piece of crap, etc, etc).  So in the puerile world of political point-scoring, Obamacare could be a huge smudge on the GOP scoresheet.

(*) The GOP has been heavily lobbied by the Insurance Industry.  This is senseless, really, because the Industry does not really lose such a lot.  There are controls of runaway profit-taking, I suppose, but it seems to me that the new law strengthens the industry, while reining in its lucrativity.  If the Insurance Industry fights the law, they are really making things harder for themselves.  After a year or two of Obamacare, I believe that the population will look at the Insurance Industry with a very jaundiced eye, but nevertheless I believe it will be in a comfortable position, if not going like gangbusters.

(*)  A few small businesses, and small-business organizations, have been persuaded early that the new law is to their disadvantage.  As far as I understand, while all businesses are given new responsibilities for the health care of their employees, they have also been given new financial help for that purpose.  In all fairness, I have to say that this is inappropriate; I am strongly of the opinion that Health Care is the responsibility of the State (the government, at any rate), but Congress —as it was constituted in 2004-2005— distrusted the Government bureaucracy, and decided that small businesses were more to be trusted with providing health care for the population.  This attitude has been nurtured by Business itself, and Business has only itself to blame for promulgating the myth that Business is more to be trusted than Government.  Yeah, right.  At any rate, now that various sectors of the Small Business whatchamacallit have taken the view that Obamacare is bad for Small Businesses, those who lied to Small Business in the first place have begun to believe it themselves.  Isn't that amazing?

(*)  Healthy young people have been incited to protest against the law, because it requires everyone to carry health insurance.  Some of the young people in my extended family were railing about the new law, and moaning that they could not afford to carry insurance (especially since some of them were unemployed), and, as you can imagine, young people are, generally speaking, not subject to the health problems of older people.  Furthermore, young people are perfectly happy to ignore whatever health problems they have.  And again, young people looking for employment are eager to present themselves as being in almost amazingly good health, even if they suspect that they might have a chronic condition, which of course must be kept from their prospective employers at all cost.

(*)  The people leading the Republican Party at the moment are some of the dimmest bulbs we have had in government for a century.  Let's face it: Health Care is a complex issue, and of all solutions to the problem of National Health Care, the one that was in fact adopted (by a Coalition of idealistic liberals, scaredy-cat Democrats who were nervous about the fallout from the bill —with good reason, in hindsight— cooperative Republicans, who were afraid of the backlash from their more conservative fellow-party members —with good reason— and meddling members of the Insurance Industry Lobby, who were anxious to make sure the law would not debilitate the Industry) is a compromise, and so even harder to figure out than such a law would have been if it was simple in design.  So, not too many people are able to read the law in its entirely and make sense of it.  We liberals —and forgive me for including you in this category— for the most part endorse the law because we have some faith in Obama and his team.  I have not read the law, and I'm afraid to start reading it now.  But such people as Rand Paul, Ted Cruz, and Rick Santorum (who isn't anything connected with any government body, at the moment) and the members of the conservative media have no hope of understanding it.  They do not have the mental equipment for it, and possibly not the vocabulary.  All they can do is to spot an isolated sentence here and there, and cling to them with furious indignation, misinterpret its intention and its consequences, and run to proclaim their hostility to it, and to the Act as a whole.

A big mistake that congressmen make, in poking holes in the law, is that they have of course forgotten what it was like before they had the fabulous health plan they enjoy as member of congress.  They object to the law because it makes it possible that a person may have to change their doctor.  Well, if your health plan is like my health plan, I have been forced to change my doctor any number of times, because my employer changes insurance providers every once in a while, and sometimes a health plan has a list of Preferred Providers, which means a new doctor.  We went to the extent of hanging on to our non-preferred doctor, just for the sake of continuity, despite the very real antipathy between our doctor and our insurance.  So far, so good.

A few Republicans, notably John McCain, have said that de-funding Obamacare is not a possibility.  Who knows; perhaps McCain has been in sympathy with a unified health care system for the USA all along, and simply did not bring it up for fear of being accused of being UnAmerican.  It seems to me that anyone who has served in the Armed Forces can only be in favor of Health Care Reform, both because of the health care they get as members of the Armed Forces, and the miserable health care they get once they're discharged.  Both Kerry and McCain and any real veterans (unlike George W. Bush) are likely to have their heads screwed on well enough to know a good thing when they see it.  There is no going back from Obamacare, unless we want bigger chaos than we have now.

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