Paradisal roots: Canto 15

Paradiso 15 puts in place an elaborate setting for the meeting of Dante and Cacciaguida, the root (radice) of his Florentine stock. The great-great-grandfather invokes organic imagery, which we've seen elaborated in the Sun with the tale of St. Dominic, but radically simplified here:

“O fronda mia in che io compiacemmi 

pur aspettando, io fui la tua radice”

"O leaf of mine, in whom I pleasure took
E'en while awaiting, I was thine own root!" (15.88-89)

Dante discovers that the root of his life was ahead of him, waiting for his arrival. Normally in organic systems, the leaves don't meet the roots. Here, on Mars, they connect. 

Faithful to the system of nourishment and energy that comes from a solar myth of gardens and flowers -- Cacciaguida emboldens the poet to let his voice resound secure, bold, and joyous:

la voce tua sicura, balda e lieta 

suoni la volontà, suoni 'l disio,

Now let thy voice secure and frank and glad
Proclaim the wishes, the desire proclaim,) (15.67-68)

Cacciaguida - the guide to the hunt - will go on to give Dante a view of the past of his city, how it changed as it absorbed people around it, and then divulge what the poet can expect in his future, which will involve a radical break with Florence. 

All of this -- the organic sense of growth, of a family and a city as a living thing -- forms a strong metaphorical armature for these central cantos of Paradiso. But there is another kind of root, another skein of imagery interwoven throughout these cantos, and it begins with Cacciaguida's first speech -- the language of number:

Tu credi che a me tuo pensier mei 

da quel ch'è primo, così come raia 

da l'un, se si conosce, il cinque e 'l sei;

Thou thinkest that to me thy thought doth pass  

From Him who is the first, as from the unit,  

If that be known, ray out the five and six; (15.55-57) 

Dante believes, Cacciaguida says, that he need not speak, because all his thoughts radiate from that which is primal, or at the root, even as 5 and 6 derive from 1. All numbers are implicated in 1 -- so long as you have 1, you can produce the rest.

Numbers appear even earlier -- with the first thing Dante understands Cacciaguida to say;

“Benedetto sia tu,” fu, “trino e uno, 

che nel mio seme se' tanto cortese!”

"Benedight be Thou, O Trine and One,
Who hast unto my seed so courteous been!" (15.47-48)

The poet in turn speaks of the central mystery of the Trinity in noting how mortals differ from those with a vision of the triune God:

Poi cominciai così: “L'affetto e 'l senno, 

come la prima equalità v'apparse, 

d'un peso per ciascun di voi si fenno,

Then in this wise began I: "Love and knowledge, 

When on you dawned the first Equality, 

Of the same weight for each of you became; (15.73-75)

Clearly the language of numbers and geometric figures (in 17 Dante will say he's tetragono -- foursquare, or four-angled -- against the whims of Fortune) present a second set of images, parallel to the organic metaphors of plants, seeds, roots and leaves, but quite different.

Getting to the "root" of this dual series of figures -- one, organic, rich in natural attributes of nourishment, sunlight, and strength, the other a purely formal system that is nothing like Nature, and presents conceptions that Nature is incapable of -- is beyond this post. 

The only point to make here is that this second motif relates to the fact -- much remarked on in the canto -- that everyone who is moving along the radials of the cross is looking into a mirror that reflects what Dante thinks before he thinks it.

The poet will be emboldened to speak even though these thousands of militant warriors of the Church have already heard it. What's more, they will all grow silent in order to give him the will to speak:

Come saranno a' giusti preghi sorde 

quelle sustanze che, per darmi voglia 

ch'io le pregassi, a tacer fur concorde?

How unto just entreaties shall be deaf 

Those substances, which, to give me desire 

Of praying them, with one accord grew silent? (15.7-9)

The very act of speech is rendered unnecessary even as it it dramatically heightened by the vast, silent attention that presents itself. These armies present a thunderous silence. Radiating from one center, they will to hear Dante, redundant.

The irony and surprise, true to the Commedia, makes the ruddy martial sphere into that scene where the intimate, familial connectedness of all rises to our attention.

Non Bacco, non Peana: Glimpsing Par. 14

A brief look back at the Sun, and a quick look ahead to Mars.

The main story of the five cantos of the Sun delineates in great detail the solar force of the Church. It composes itself before our eyes as a series of layers, creating a complex image of a chariot of the Sun. Like the actual sun, it nurtures life through heat and light. But these attributes of the Church are not merely physical, nor do they rest upon philosophical first principles. From the first, the cantos of the Sun debunk the power of logic as the arbiter of judgment and basis of wisdom.

Rather than axioms, the true first principles of the Church are individual lives -- specifically, Francis and Dominic -- they are at one point called principi, and are the living embodiments of primal ardor and intellect. They are the wheels of the Church's solar chariot at work in historical time, and their 24 disciples actively extend their powers (even those who preceded them chronologically, apparently).

As the set of five solar cantos concludes, we see even more clearly how pattern recognition, which is basic to knowledge, is both insisted upon and shown to be utterly imperfect as a model or sign of the truth. The necessary imperfection of the sublunar world is the way things are, and nothing the human mind can construct or imagine will offer more than an approximation. The 24-line opening of canto 13 ends with:

poi ch'è tanto di là da nostra usanza,
quanto di là dal mover de la Chiana
si move il ciel che tutti li altri avanza.

Because it is as much beyond our wont,
As swifter than the motion of the Chiana
Moveth the heaven that all the rest outspeeds.

In discussing, we didn't address what immediately comes after this awareness of the sketchiness of our awareness:

Lì si cantò non Bacco, non Peana,
ma tre persone in divina natura,
e in una persona essa e l'umana.

There sang they neither Bacchus, nor Apollo,
  But in the divine nature Persons three,
  And in one person the divine and human.  (13.25-27)

The canto opened, we recall, with numbers -- the 15 stars, the 7, the 2 -- we combined them to get the sum of the disciples of Francis and Dominic. This is arithmetically coherent. But now, here's a new math, in which three persons can be one, which in turn can be two. The austere, rigorous system elucidated by every mathematician from Euclid to Fibonacci is scrambled. Our rational capacity to count is broken.

The Trinity was evoked by Thomas, but here it seems to mark a rupture with everyday reality. Not Apollo, not Dionysus. A song beyond anything the ancients imagined, Revelation outside number, beyond ecstatic dream.

Canto 14 will conclude the enlightenment of the Sun with an account of the resurrection of the body, after which Dante and Beatrice will be translated (translato - used at 14.81 for the only time) to the next realm of Paradiso, to a vast red galaxy that sweeps us into the sublime:

Come distinta da minori e maggi
lumi biancheggia tra ' poli del mondo
Galassia sì, che fa dubbiar ben saggi;

Even as distinct with less and greater lights
Glimmers between the two poles of the world
The Galaxy that maketh wise men doubt . . .

Antigone 141-154: Mathematics and the Dance

ἑπτὰ λοχαγοὶ γὰρ ἐφ᾽ ἑπτὰ πύλαις 
ταχθέντες ἴσοι πρὸς ἴσους ἔλιπον 
Ζηνὶ τροπαίῳ πάγχαλκα τέλη, 
πλὴν τοῖν στυγεροῖν, ὣ πατρὸς ἑνὸς 
145μητρός τε μιᾶς φύντε καθ᾽ αὑτοῖν 
δικρατεῖς λόγχας στήσαντ᾽ ἔχετον 
κοινοῦ θανάτου μέρος ἄμφω.

[141] For the seven captains, equal number stationed against an equal number at the seven gates, left behind their brazen arms in tribute to Zeus the turner of battle—all but the accursed pair who, born of one father and one mother, set against each other their double-slaying spears, both victorious, and who now share in a common death.

In bold are the specific numerical terms as well as some that involve a mathematical operation like adding or averaging. The language is markedly formal, a spectacle of mirroring symmetries - seven against seven, of course, but also the idea of one generating two who fight and share one death. So there are symmetries of space as well, we could say, of time, (and unity of plot): beginning (1), middle (2), end (1). Common to both the seven and the pair of brothers is the moment of mutual-annihilation -- a fateful act that first showed itself when Cadmus, sowing the dragon's teeth, witnessed the symmetric mutual destruction of all but five of the spartoi.

Mathematical symmetry (equality, ἰσότης) is the root of ratio that allows for laws, alliances, and the balances of nature, Jocasta tells her sons in Euripides' Phoenician Women:

Equality . . . always joins friend to friend, city to city, allies to allies; for Equality is naturally lasting among men; but the less is always in opposition to the greater, [540] and begins the dawn of hatred. For it is Equality that has set up for man measures and divisions of weights, and has determined numbers. Night's sightless eye, and radiant sun proceed upon their yearly course on equal terms, [545] and neither of them is envious when it has to yield.

Even as Jocasta says these lines, her sons are preparing to kill one another. Equality at Thebes seems doomed to yield mutual annihilation.

After this militant display of numbers, the first Ode of the Antigone concludes with the chorus of elders turning to Bacchus and to forgetting:

ἀλλὰ γὰρ ἁ μεγαλώνυμος ἦλθε Νίκα 
τᾷ πολυαρμάτῳ ἀντιχαρεῖσα Θήβᾳ, 
150ἐκ μὲν δὴ πολέμων 
τῶν νῦν θέσθαι λησμοσύναν, 
θεῶν δὲ ναοὺς χοροῖς 
παννυχίοις πάντας ἐπέλθωμεν, ὁ Θήβας δ᾽ ἐλελίχθων 
Βάκχιος ἄρχοι.

[148] But since Victory whose name is glory has come to us, smiling in joy equal to the joy of chariot-rich Thebes, let us make for ourselves forgetfulness (λησμοσύναν) after the recent wars, and visit all the temples of the gods with night-long dance and song. And may Bacchus, who shakes the earth of Thebes, rule our dancing! 

The earth shaking -- ἐλελίχθων -- of Bacchus comes from ἐλελίζω - to whirl round, to cause to vibrate, to turn.  Dionysus here stands counterposed to Ζηνὶ τροπαίῳ -- Zeus turner of battle -- in the preceding strophe.

Where Zeus's tropism powered a decisive victory for Thebes against the Argives, the city-shattering power of Bacchus is bound up with music and rhythm, which the god is said to lead. There is no equality here, just the power of the ruling god, leading mortals to forget the strife of wars, ambition and mathematics as they turn in the dance.

Mario Livio on the enigma of knowledge

Excerpt from a longer, fascinating interview here:

Ms. Tippett: … and you end up with all these puzzles or mysteries that feel to me that they're verging on the philosophical and the theological as well, right, by implication. So you can say that our minds give rise to mathematics but then mathematics are found to explain the physical world.

Mr. Livio: That's right.

Ms. Tippett: Which is a very mysterious thing to think about.

Mr. Livio: Yeah. You're absolutely right. And, you know, my colleague Roger Penrose, I don't know if you've ever interviewed him …

Ms. Tippett: I haven't, but I know his work. Yeah.

Mr. Livio: Yeah. So he's a very famous mathematical physicist. So he once said that there are at least three worlds and three mysteries.

Ms. Tippett: Mm-hmm.

Mr. Livio: So the three worlds are, one is the physical world. You know, this is the world where we exist. There are chairs, tables, there are stars, there are galaxies, and so on. Then there is a second world, which is the world of our consciousness, if you like. You know, a mental world, a world where this is where we love, where we hate, you know, and so on. All our thoughts are there and so on. And then there is the third world, which is this world of mathematical forms. This is the world where all of mathematics is there. You know, the theorem of Pythagoras and so on and so forth, all the imaginary numbers and all that. So these are the three worlds. And now come these three mysteries. One mystery is that somehow, out of the physical world, our world of consciousness has emerged. That's one mystery.

Ms. Tippett: Right. Right.

Mr. Livio: A second mystery is that somehow our world of consciousness or mental world gained access to this world of mathematical form. You know, that we were able to invent and discover all these mathematics. And third, and maybe most amazing mystery, is that we find that this world of mathematics provides the explanations for the physical world.

Ms. Tippett: Right. Right. So it's that circle again.

Mr. Livio: Right. So there are these three worlds and three mysteries which, you know, of course at the end of the day they are all part of one universe, right? But it's an interesting way of posing the question.