Thursday, October 16, 2008

Rosmini's Three Supreme Imperative Formulas

The first formula, which precedes the other three and is simply being, states: 'Acknowledge BEING for what it is.'

But BEING has three, supreme internal relationships, or forms, reality, ideality, and morality, in all of which it must be acknowledged. Hence three supreme imperative formulas.

Ideal being (ideality), which is itself light, reveals the other two. Through it we know real beings, which indicate in us the first imperative formula: 'Acknowledge real beings for what they are', that is, 'Esteem beings, love them, help them; rejoice in the being that they have, and desire for them the being they require according to their nature, and which perfects them.'

When we acknowledge moral being, that is, the essentially moral will, the will of God, the second moral imperative reveals itself in our spirit as: 'Make your will one with the essentially moral will.'

After making known real being and moral being, ideal being finally makes itself known by reflection as truth and gives rise to the third imperative which states: 'Acknowledge ideal being,' or 'Esteem the truth unreservedly,' or 'Follow the light of reason.'

All four formulas are equally supreme, but the three last are contained in the first, which is perfected by each of them.

[Antonio Rosmini, Conscience, Denis Cleary and Terence Watson, trs., Rosmini House (Durham: 1989) p. 92 [190-4], sections 191-193.] Like much of Rosmini, I find this approach to natural law an intriguing one, but am not really sure how it lines up with anything else. The basic idea is clear enough, though: the three 'internal relationships' are transcendental attributes of being (reality, goodness, truth), and it's unsurprising that Rosmini makes being the principle of morality, given how he understands its role in our cognition.

Wednesday, October 15, 2008

Krugman on Research

Paul Krugman, who recently won the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, has a piece online discussing his approach to research, which he boils down to four basic rules:

1. Listen to the Gentiles

2. Question the question

3. Dare to be silly

4. Simplify, simplify

(By (1) he means "Pay attention to what intelligent people are saying, even if they do not have your customs or speak your analytical language.") I think they are very good rules for approaching problems; the pressures to violate them are immense, and I think that, whatever our fields, these pressures must be resisted.

Tuesday, October 14, 2008

Peirce's Quincuncial

As you may know, C. S. Peirce worked for the USGS. One of the things he did while there was design a map projection that has come to be known as Peirce's quincuncial. In it one hemisphere is presented as a square, and the other hemisphere as four isosceles triangles around the sides, creating a map that is genuinely square and tiles nicely.

* Wikipedia has a good account of the basics

* Peirce's paper on it is available at Google Books. (Notice that he uses the tessellation property in the picture here.)

* Sean Carroll discussed it at Cosmic Variance a few years ago, as did John Baez.

* The same principles of projection can be used to make interesting pictures.

Light Streaming Through the Photocatalytic Air Purifier with Nanostructured Gold Catalyst

If this is true, it is just begging for someone to write a medieval SF romance about it. And, clunky scientific jargon aside, it would make for an excellent set of theological metaphors.

Restraining by Expanding

Jill Lepore at The New Yorker (ht):

And these men didn’t elect George Washington; they voted only for delegates to the Electoral College, an institution established to further restrain the popular will.

This seems to be the unkillable myth about the Electoral College, the one at the base of most of the unfounded complaints against it. (There are, of course, reasonably founded complaints against it, as against every system of election. You just don't hear about them much because the unfounded ones involve fewer dull details.) The Electoral College wasn't designed to "restrain the popular will"; it was explicitly designed to guarantee that the popular will had some say in the choice of the President, and to guarantee that that say was as reasonably clear and stable as could be hoped. There was, of course, a strong interest at the time in making sure that the President of the United States was chosen by the States; the Electoral College manages to do this while minimizing State-level abuses. But this wasn't a restraining of the popular will; it was a cautious expansion of it into new territory. Lepore tries to spin this in the opposite direction by saying that it was an "illbegotten compromise"; why it was illbegotten is never said, but it certainly was a compromise, as most things in the Constitution had to be. The compromise didn't, however, restrain anything; prior to the Constitution, there was nothing to restrain. It's like saying that if, after a period where the Senate didn't exist, the people were suddenly allowed to elect a Senator, this "restrains the popular will" because it doesn't allow you yourself to vote on every bill that comes up. There is no real meaning to the word 'restrain' here. One could, perhaps, call it a restrained expansion of the influence of popular will. But 'restrained expension of the power of popular will' and 'restrained popular will' are very different things.

But the article does a good job of laying out the often-overlooked Australian innovation to the ballot system, standardized ballots, and the advantages and disadvantages it introduced.

Sunday, October 12, 2008

Some Poem Drafts

Some smaller, rougher pieces.

Winds Bitter-Cold

Winds bitter-cold, bold and biting,
cross over the sea, free and wild,
never meeting shore, nor touching stone,
catching all sails, failing never,
brining cold gloom, doom and darkness.
Sailors ship out, south their sailing,
seeking out warmth, storms avoiding;
they hope for land, sand on beaches,
lasses in ports courting free sailors,
and drams of wet fire. 'Dire' does not daunt:
danger is kin when you sail the high seas.

Black Ant on a Black Rock on a Black Night

Black ant on a black rock on a black night,
and still God sees;
truth upon truth brings terror
and still it frees.
The doors have locks on locks,
but God yet has the keys:
black ant, black rock, black night--
but still God sees.

The Mirror

The mirror flatters itself clear, exact,
but this is far from sterling fact;
its preconceptions on every side
manifest its misty pride.
With cruel disdain it mocks the truth,
turns youth to age and age to youth,
swallows all things with dishonest game
while pretending always to be the same.

Sor Juana's Apologia

Why persecute me, World, behind a thousand faces?
In what do I offend you, when all I am demanding
Is to put graces into my understanding
And not my understanding into these graces?
I regard not treasures nor mundane riches,
And so I always have tranquillity bought
By putting riches into my thought,
Not giving my thought to those riches.
And I do not regard beauties that, taken,
Are imperial spoils for long centuries;
Nor treacherous wealth can my pleasure waken;
Holding it better, in my clear verities,
To let the vanities of life be shaken
Than to waste my life in vain vanities.

Elm the Undertaker

Elm the undertaker spoke to me,
half in waking, half in dream,
his branches swaying in the wind
above the gravestones shaped for men:
"I have a coffin made for you,
grown from rain and earth and dew,
shaped by God with living life
to wait until your death is nigh."

Newton's Own Laws

The recent discussion in the comments box of the book list post has had me thinking about the differences between Newtonian physics as found in Newton and Newtonian physics at a much later date. Here's a simple but striking instance. As we usually learn it, Newton's second law of motion is:


Trying to interpret Newton's first law of motion in algebraic equations, it's very natural to take it as simply describing the case where the acceleration, and thus the resultant force, is zero. The first law then becomes a special case of the second law; and you will find many physics textbooks stating this.

This is quite right and reasonable given the way the two laws are usually understood. But it's worth noting that if we take the laws as actually stated in the Principia, this conclusion is impossible: the first law can't be a special case of the second law on the reasoning shown, if we take them in Newton's own formulation. One minor but important point is that Newton's own second law is not the equation F=ma. I say 'minor' because it is, in fact, easy enough to prove that if we use the right combination of units, F=ma for cases where mass is constant and time is not, given the first law, the second law, and the definition of quantity of motion (definition II). To do it you use the method of construction: you posit an alteration of motion, use the first law to conclude that there is a force, and use the second law and the definition of quantity of motion to infer that the change of velocity divided by the change of time is equal to some constant times the impressed force, divided by the mass. The constant can be set to one with the right combination of units, and we therefore have an equation equivalent to the standard one. So F=ma follows from the second law; but this is not the same as to say that it is the second law -- in part because you need to assume things besides the second law to make the proof work.

More importantly, however, Newton's first law can't be a special case of his second because they don't discuss the same thing. The first law is:

Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.

The second law is:

The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

What the first law in effect does is tell us that an alteration of motion requires a cause, namely, an impressed force, or a combination of impressed forces. The second law extends this by telling us how, precisely, the alteration of motion is related to the impressed force causing it. (One of Newton's major projects in the Principia is to develop a method for properly accounting for the difference between true and apparent motions and the causes underlying that difference.) But if we interpret them in this light, the first law is not a special case of the second law; it simply tells us when a certain sort of cause exists, while the second law tells us how the effect is related to that cause when it does exist. These are two completely distinct things, and when you try to do proofs with them, you have to use both of them to get the usual equations. If we took the first law simply to say that when force is zero, acceleration is zero, it would be a special case of F=ma; but the first law doesn't simply say that, but gives a causal role to forces.

This is a very small sort of change, since it doesn't change anything structurally speaking -- you can get the same equations, in somewhat different ways, on both interpretations. But it is a striking example of how the role Newton himself assigns to a feature of his physics might be somewhat different from that assigned by later physicists with somewhat different interests.