Venimus, Vidimus...

People have been noting here and there that this is the anniversary of the breaking of the Siege of Vienna in 1683. The Ottoman Empire had laid siege to Vienna in July; Vienna was in an almost perfect strategic spot for the purposes of the Empire, because of its key location with respect to the Danube and several trade routes. The Habsburgs had a treaty with Poland at the time; when the Ottoman Janissaries laid siege, the Polish king, Jan III Sobieski, came to its aid; Baden, Bavaria, Franconia, Saxony, and Swabia also supplied troops. Under Sobieski's leadership the disparate forces achieved a considerable amount of cohesion, a cohesion that the relatively disorganized Ottoman troops lacked. The result was a serious loss to the Ottoman Empire; the war went on for a good fifteen or sixteen years more, but Ottoman advance into Europe had been turned back, and before the war ended, the Empire had lost Hungary and Transylvania as well as any chance at ever capturing Vienna.

There is a common and certainly false legend that the Viennese invented the croissant to celebrate their deliverance.

Two Poem Drafts

Blossom

The blossom breathes light from the green of the leaf:
its colors are bright, and swift like a thief.
The songs of the birds cascade from the trees;
they mean without words in the tongue of the breeze.
Where is the plough and where is the sword?
They are flown away now like the migrating birds.
Where is the stream and where is the sea?
And where is the dream of the hope to be free?
They are gone and lost; nor can we know
the terrible cost of their death in harsh snow,
but still mid this blight is a tonic for grief:
the blossom breathes light from the green of the leaf.

The Hosts

The starlight bright upon the sea
takes shield and sword and conquers me;
with tide and wave it overcomes,
with rhythmic roll like sounding drums.
Who beneath the moon's bright sliver
would not fall, and quake and quiver
at the silver splendor fair
when burning argent lights the air?
For all this grim and silent host
of stars that shine on sea and coast
are marching in a dauntless manner,
terrible with spear and banner.

Progress

The great mistake of the Marxists and of the whole of the nineteenth century was to think that by walking straight on one mounted upwards into the air.

Simone Weil, Gravity and Grace, Crawford and von der Ruhr, tr. Routledge (New York: 2002) p. 174.

Elbereth

The poem I previously posted, Lingard's "Hail, Queen of Heaven, the Ocean Star," is usually seen as one of the major inspirations of another poem:

O Elbereth! Gilthoniel!
by J. R. R. Tolkien

Snow-white! Snow-white! O Lady clear!
O Queen beyond the Western Seas!
O Light to us that wander here
Amid the world of woven trees!

Gilthoniel! O Elbereth!
Clear are thy eyes and bright thy breath,
Snow-white! Snow-white! We sing to thee
In a far land beyond the Sea.

O stars that in the Sunless Year
With shining hand by her were sown,
In windy fields now bright and clear
We see your silver blossom blown!

O Elbereth! Gilthoniel!
We still remember, we who dwell
In this far land beneath the trees,
Thy starlight on the Western Seas.

You can hear Tolkien reciting the poem here. People have sometimes set it to music; my favorite setting, the one I think captures the mood of the poem best (one you can imagine someone singing sadly under the stars), is that of Helen Trevillion. Unfortunately, while you can hear it at YouTube, it's always with bad mash-ups of the Lord of the Rings movies. But you can ignore the video and hear that version here.

In Tolkien's Sindarin, Elbereth and Gilthoniel are names of Varda; Elbereth means 'Star-Queen' and Gilthoniel means 'The One Who Kindled the Stars'. And in the mythology, she is the Power who set the stars in the sky and in whose face shines most brightly the light of the Creator.

Maris Stella

Hail, Queen of Heaven, the Ocean Star
by John Lingard

Hail, Queen of heaven, the ocean star,
Guide of the wanderer here below,
Thrown on life's surge, we claim thy care,
Save us from peril and from woe.

Mother of Christ, O Star of the sea
Pray for the wanderer, pray for me.

O gentle, chaste, and spotless Maid,
We sinners make our prayers through thee;
Remind thy Son that He has paid
The price of our iniquity.

Virgin most pure, O star of the sea,
Pray for the sinner, pray for me.

And while to Him Who reigns above
In Godhead one, in Persons three,
The Source of life, of grace, of love,
Homage we pay on bended knee:

Do thou, bright Queen, O star of the sea,
Pray for thy children, pray for me.

Today is the feast of the nativity of our Lady. St. Andrew of Crete on the day:

This radiant and manifest coming of God to men most certainly needed a joyful prelude to introduce the great gift of salvation to us. The present festival, the birth of the Mother of God, is the prelude, while the final act is the fore-ordained union of the Word with flesh. Today the Virgin is born, tended and formed and prepared for her role as Mother of God, who is the universal King of the ages.

Whewell and Found Poetry

Found poetry, of course, is language that was not intended to be poetry but nonetheless bears the marks of it. William Whewell, whom I talk about quite a bit here, is actually the source of one of the most famous examples of it. In his 1819 work An Elementary Treatise of Mechanics, he wrote the following sentence (on p. 44, in the middle of a discussion of the equilibrium of forces on a point): "Hence no force however great can stretch a cord however fine into an horizontal line which is accurately straight: there will always be a bending downwards." Adam Sedgwick, the famous geologist, with a sharp eye recognized what happens if you rearrange it, like this:

No force however great
can stretch a cord however fine
into an horizontal line
which is accurately straight.

Apparently he quoted it when giving a speech at a dinner. I don't know what Whewell's immediate reaction was. The sentence doesn't appear in later editions, but he reworked the whole chapter in which it was found, so that perhaps had nothing to do with the sentence itself. However, if Whewell was embarrassed by it, it was too late. John Radford Young's The Elements of Mechanics (1834) quotes it in a similar discussion; it was given out to the public in magazines like Notes and Queries and Van Nostrand's Eclectic Engineering Magazine; everyone talking about involuntary versification from then on out has used it as an example; and, to take the cake, the Church of Christ, Scientist will be reading it for all time, because Mary Baker Eddy quotes it in Science and Health (attributing it to a "humorous poet" and using it as a metaphor for the relation between matter and spirit).* Whewell wrote serious poetry -- he has several volumes of it, including translations of German poetry, at which he was actually quite good -- but the poem people most associate with him is this one. People are tickled at the idea of a dignified philosopher, discussing a problem in physics, suddenly bursting out, quite by accident, in doggerel verse.

* ADDED LATER: Actually I find that I need to qualify this. Eddy did quote Whewell in Science and Health (Chapter 10), but the book went through many revisions between the first edition in 1875 and Eddy's death in 1910, and the lines don't seem to have lasted past the edition of 1889. But the metaphor, which originally was based on Whewell's sentence, still remains.

Newton's First and Second

As we usually learn it, Newton's second law of motion is:

F=ma

If we try to interpret Newton's first law of motion in terms of 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 that many physics textbooks state this.

This is quite right and reasonable if we mean by Newton's first and second laws what most physics textbooks mean. 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, if we take them in Newton's own formulation. Newton's own second law, of course, is not the equation F=ma.

It is easy enough to prove, however, that if we use the right combination of units, the first law, the second law, and the definition of quantity of motion (definition II), then F=ma for cases where mass is constant. To do it you use the method of construction The first law, as Newton states it, 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.

(1) Posit an alteration of motion.
(2) Use Law I to conclude that there is a force impressed upon the object whose motion is altered.
(3) Since Law II tells you how the change of motion is related to this impressed force, you can use Law II along with the definition of quantity of motion (Definition II) to infer F=ma. So F=ma follows from the second law plus some basic assumptions.

Definition II tells us that quantity of motion is the measure of motion from velocity and quantity of matter (mass). Therefore suppose we start at time t_i with a body of mass m_i whose motion is measured at a velocity v_i. And suppose it changes, so that at t_f we have m_f at v_f. Then (m_fv_f - m_iv_i)/(t_f-t_i) is our change of motion for those times. According to Law I, there is a force F for this; according to Law II, the change of motion is proportional to F. Let us assume that mass doesn't arbitrarily (or even non-arbitrarily) change: m_f=m_i, so both can just be called m, and m can be factored out, since it is unaffected by change of time, to get the claim that m((v_f-v_i)/(t_f-t_i)) is proportional to F. That's mass times change of velocity over change of time; change of velocity over change of time is acceleration, which gives ma, which is proportional to F. That should look familiar.

Newton's first law can't be a special case of his second because they aren't in the same category. What Law I in effect does is tell us that an alteration of motion requires a particular kind of cause, namely, an impressed force, or a combination of impressed forces; and (depending on how it is read) it tells us that we do not need to look for such a cause unless the motion is altered. Law II extends this by telling us how, precisely, the alteration of motion is related to the impressed force causing it, assuming that there is both an alteration of motion and an impressed force. 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; he needs Law I to do this properly. But if we interpret them in this light, Law I is not a special case of Law II; it simply tells us when a certain sort of cause exists, while Law II tells us how the effect is related to that cause when it does exist. These are two completely distinct things, and you have to use both of them to get the usual equations. If we took Law I simply to say that when force is zero, acceleration is zero, it would be a special case of F=ma; but Law I as Newton formulates it doesn't say that. It tells us when we must appeal to forces and when we don't need to do so. We need to know this before equations about forces are even possible. This is something I think even physicists sometimes forget: equations are never fundamental. We don't start with equations; we start with rules of inference and means of measurement, then use those to get equations.

It's interesting in this light to look at William Whewell's interpretation of Newton's laws of motion, because Whewell is very sensitive to the fact that we start with rules of inference. Whewell argues in his Philosophy of the Inductive Sciences and in his 1834 essay, "On the Nature and Truth of the Laws of Motion," that the laws of motions are actually general causal principles to which we add certain experimental facts to obtain more restricted causal principles suitable for discussing physical motion. Thus Newton's First Law is, on his view, nothing other than the claim Every change is produced by a cause, given that we have experimentally ruled out certain things as causes for motion (time is the major one that needs to be ruled out; but location, which Whewell considers but takes to be ruled out by the fact that we are considering no external forces, and the object's own mass, which Whewell does not, also need to be ruled out). That is, Law I is just "Velocity does not change without a cause" plus "The time for which a body has already been in motion is not a cause of change of velocity." With the specific causal inferences provided by Newton's three laws, we can then produce the whole of Newtonian dynamics (add rules governing how we reason about equilibrium and you have statics as well).

In any case, the case of Newton's laws of motion shows one way in which science changes by drifting: because of the usefulness of F=ma, over time it has come to be treated as indistinguishable from Law II, even though they are logically distinct.

Modality and the Third Way III

Perhaps the way to think of the modality in the Third Way is to think of it not as 'able' or 'possible' but as 'can'. What I mean is this: we can ask of a given thing, given what we know about its duration, "Can it have come to be and can it come to fail to be?" I will only focus on the "Can it have come to be?" (i.e., can it have been generated?) since the Aristotelian position is that anything that can come to be can come to fail to be, i.e., anything generable is corruptible. Also, it will have to be kept in mind that when I say, "come to be" I mean "come to be in the sense that is in view in Aristotle's account of generation". Then we have the following cases:

(1) Something that always exists.
Can it have come to be? No: Since it has always been, there is no point at which it could come to be (be generated). This is necessity in the relevant sense: it cannot be generated or corrupted given that it always is.

(2) Something that never exists.
Can it have come to be? No: Since it never existed, there is no point at which it could come to be (be generated). This is impossibility in the relevant sense: it cannot be generated or corrupted given that it never is.

(3) Something that exists but does not always eixst.
Can it have come to be? Yes: It was not, then it was, there was a point when it could come to be (be generated). It is possible-to-be-and-not-to-be.

Then the basic line of thought in the Third Way would be:

(1) Some things can have come to be (be generated).
: We know this because there are things that came to be.

(2) What can have come to be, at some point was not.
: That is, things that can have come to be cannot always have existed.
: Because if they always existed, there was never a point at which they could come to be.

(3) If the whole world (i.e., everything, taken collectively) can have come to be, at some point nothing existed.
: From (2)

(4) What does not exist can only exist if it is caused by something that exists.

(5) If the whole world (taken all together) can have come to be, nothing exists now.
: From (3) and (4)

(6) Something exists now.
: Look around you.

(7) It is not the case that the whole world (taken all together) can have come to be.
: From (3), (5), (6).

(8) Something or other must have always been.
: Or, to be more precise, something or other exists that has not been generated (=something ingenerable exists).

From this point, of course, we have an ordinary causal argument, on the principle that something that has always been could have always been either because its own nature is such that if it exists it must always be, or because it was caused always to exist by something that has always been.

Incidentally, you'll notice that I keep taking "all beings" and "everything" collectively to mean "the whole world". In this context, I think that is the most natural interpretation: the roots of the Third Way are in Aristotle's De Caelo, and Aquinas very clearly (and plausibly) reads De Caelo as a work of natural philosophy discussing the universe as a whole. Aquinas identifies three subjects of the De Caelo:

(1) the entire corporeal universe, considered as prior to its parts;
(2) simple bodies, considered as prior to mixed bodies;
(3) the first simple body (i.e., the heavens), considered as prior to other simple bodies

If we were to read the first part of the Third Way with purely Aristotelian eyes, it looks like an argument for heavenly body; that is, the part of Aristotelian cosmology it looks most like is Aristotle's argument that the heavenly body is neither generable nor corruptible. Aristotle, as Aquinas interprets him, holds that every form has a power to exist: and everything exists for the extent of time this power to exist covers. The heavenly body, having the most perfect corporeal form, can have no privation of form (it is only capable of privation, and therefore change, of place), and thus always is. Aquinas, of course, doesn't think the heavens have actually existed always; but, as he says, the Catholic view is not that the heavens were generated in the proper Aristotelian sense but that they were caused to exist by the first principle at some point in time. On Aquinas's view, the ingenerable heavens were caused to exist; 'ingenerability' like 'generability' in this context presupposes existence. Given that the heavens exist they cannot have been generated. But although there is no cause of their coming to exist, there still can be a cause of their existence.

However, you will notice a conspicuous lack of any of this in the actual Third Way: the heavens or heavenly body finds no mention at all. This fits with a noticeable pattern throughout the Five Ways: all of them take Aristotelian principles but treat them in a more generalized way than Aristotle himself does. This may have something to do with the fact that they are summaries; it makes sense to put them in the more general form, to avoid potential disputes over details that won't change the main point. In the Third Way it's very likely that Aquinas doesn't want to focus on the heavens alone: another kind of ingenerable is the incorporeal ingenerable (separate substances -- angels, planetary intelligences), and there's no good reason to leave them out in this context. Some have suggested that he's also thinking of matter itself. But strictly, Aquinas doesn't need the specifics: all he needs is that there is something ingenerable because it always exists. This gets him to the point at which he can ask about the reason for its ingenerability; then rejection of infinite regress brings us to a first ingenerable that causes other ingenerables to exist always.

Gaberbocchus -- Oh! Frabiusce Dies!

Gaberbocchus
by Hassard Dodgson

Hora aderat briligi. Nunc et Slythreia Tova
Plurima gyrabant gymbolitare vabo ;
Et Borogovorum mimzebant undique formae,
Momiferique omnes exgrabuere Rathi.

"Cave, Gaberbocchum moneo tibi, nate cavendum
(Unguibus ille rapit. Dentibus ille necat.)
Et fuge Jubbubbum, quo non infestior ales,
Et Bandersnatcham, quae fremit usque, cave."

Ille autem gladium vorpalem cepit, et hostem
Manxonium longa sedulitate petit;
Turn sub tumtummi requiescens arboris umbra
Stabat tranquillus, multa animo meditans.

Dum requiescebat meditans uffishia, monstrum
Praesens ecce ! oculis cui fera flamma micat,
Ipse Gaberbocchus dumeta per horrida sifflans
Ibat, et horrendum burbuliabat iens !

Ter, quater, atque iterum cito vorpalissimus ensis
Snicsnaccans penitus viscera dissecuit.
Exanimum corpus linquens caput abstulit heros
Quocum galumphat multa, domumque redit.

" Tune Gaberbocchum potuisti, nate, necare ?
Bemiscens puer ! ad brachia nostra veni.
Oh! frabiusce dies ! iterumque caloque calaque
Laetus eo" ut chortlet chortla superba senex.

Hora aderat briligi. Nunc et Slythseia Tova
Plurima gyrabant gymbolitare vabo ;
Et Borogovorum mimzebant undique formae,
Momiferique omnes exgrabuere Rathi.

A Latinate rendering of a more famous Anglo-nonsense poem, by the uncle of the man who wrote the latter.