Thursday, January 23, 2014

This is another post about "Gravitational Pull"

As I closed last time, "gravitational pull" tends not to produce collisions — at least, not in idealized circumstances, which I described with the phrase "essentially-two". In the old, "classical" physics setting, this is due to the particular (empirically-determined, but excellently predictive!) gravitational potential, which has a large group of symmetries. The model of a two-object interaction then looks like
\[ \frac{1}{2} \left( \frac{d}{dt} r \right)^2 + \frac{1}{2} r^2 \left(\frac{d}{dt} \Theta\right)^2 - \frac{g_0}{r} = H \qquad\mbox{is constant}\]
where $r$ is the (variable) distance between the two objects and $\Theta$ is a cleverly-composed something that describes the (variable) direction of the two objects' separation, and $g_0$ is a constant describing the gravitational attraction between the two things. It happens that another expression
\[ r \Theta \times r \frac{d}{dt} \Theta = L \] must also be a constant — this one having directional information.

The never-meeting of the two things is sumarized in the necessity that squares of real things be positive:
\[ H + \frac{g_0}{r} - \frac{1}{2r^2} L^2 = \frac{1}{2} \left( \frac{d}{dt} r \right) ^2 \geq 0 \]

Now, of course we know that things largely under the influence of gravity do occasionally hit one another, and so the Moon is a rather interesting thing to behold at night, and St. Laurence has his “tears” every year — these are instances of things having size, being more than geometric points — and so of not being “essentially-two”, in my strange turn of phrase. Another class of things exerting mutual gravitational pull that aren't “essentially-two” in this sense is that of binary stellar systems. A notable sub-class are the pairings of a red giant and a white dwarf, in relative proximity. Sometimes these sorts of collisions take the form of the dwarf partner gradually accumulating the loose hydrogen from off their red giant partner, untill it gets thick and hot enough to start fusing hydrogen into helium on its own account, which makes a kind of nova. I wonder if (and how) this picture might have been in Benedict's analogical thought when he spoke or wrote of "gravitational pull"?

Tuesday, January 21, 2014

This is a post about "Gravitational Pull"

It's a funny thing: the Church has Laws — these are in addition to the moral law, at least in the sense that one could reasonably not do what they prescribe under the counterfactual hypothesis that they didn't say it. Nonetheless the Law, justly proposed, itself imposes a moral character on acts that otherwise wouldn't suffer such character.

One such law, which pertains to Priests, accolytes, and cantors, is that Priests as such (accolytes, cantors...) have no authority either to set aside nor to add to the prescribed text and ceremonial of the Mass, except in narrowly described ways. There are good reasons for this on which we need not dwell, and there are annoying consequences of it.

One annoying consequence of it (for a Priest) is that the indulgence attached to the aspiration of "Doubting" Saint Thomas is not allowed him, even in the usual circumstances, at the First Elevation in a Mass he is himself celebrating — for this would be an illicit interruption of, or addition to, the Canon. An annoying consequence of it is that blue chasubles, dalmatics, and tunicles (which exist in plenty, and of which many are profoundly beautiful) are thoroughly outlawed. A most perplexing consequence of it, for the children of Summorum Pontificum is that there really isn't any way the Extraordinary Form can be made an excuse to depart from the edited text of the Missal for the Ordinary Form, nor vice-versa. The dressing of the altar, the vesting of the ministers, the words used and their order, have each their circumscriptions; the propers of a Sunday Mass (proper of the Season) may not be used for votive masses, but only on their own Sunday and feriae; there are more points, but these are enough to keep in mind (unless you are a priest, in which case you keep a fresh Ordo and GIRM and all the rest handy and what are you doing, in whose name, reading this waste of time?) So we're a bit funny, celebrating the Kingship of Our Lord twice a year, and calling 1st January both the Motherhood of Mary and the Circumcision of Our Lord... and for a time we will be funny. (We should always be some sort of funny!) It is not in any authority below the Supreme Pontiff to adjust these counterpoints.

Do we want to unify the Calendars? Perhaps we do, and so why not compose ideas for how to do so; or better: consider sound principles whereupon the Church might do so. Why not write a thesis on the matter together with an example revised biformal Calendar and send it to His Holiness — I understand he answers surprisingly many letters, so the odds are better than at other times that, if he doesn't approve the thing ad experimendum for your oratory, at least he might give you a good reason why.

It's another funny thing altogether (one on which our continued experiences of any kind in this Creation largely depend) that if essentially-two things exert a mutual gravitational pull out of parallel with their relative motion, they never meet.