Fighting The Tempest

Derrida famously tried to replace aesthetic literary criticism with the analysis of “fault lines” in construction.  I do not generally endorse this for Shakespeare but in a few cases it makes sense.  I agree with Harold Bloom that The Merchant of Venice was intended as straightforward antisemitism, however compromised by Shakespeare’s genius, and so to endure that play one must regard it as a toxic laboratory sample to be diagnosed rather than enjoyed; a crystal of pure arsenic made horribly beautiful by the “flaws” of Shylock’s wonderful speeches.  Derrida’s approach is perfect for Merchant.

I have recently come to view The Tempest in a similar way.  Despite Prospero’s two magnificent soliloquies, the ever supple verse, and fine grotesquerie of Caliban, Stephano, and Trinculo, there are a few aspects of this play that render it insupportable to a modern audience.  With a more scientific approach we might regard it as a theorem demonstrating that vanity, prejudice, and simmering resentment can inspire great poetry.

Prospero is clearly a proto-fascist who would be at home in a white-supremacist militia movement.  That felt good.  Now let’s take it more slowly: first his vanity.

Of Milan:

    Through all the seigniories it was the first,
And Prospero the prime duke, being so reputed
In dignity, and for the liberal arts
Without a parallel;

Well, a once powerful man stranded on an island is bound to nurse fantasies of his former life.

I, thus neglecting worldly ends, all dedicated
To closeness and the bettering of my mind
With that which, but by being so retired,
O’erprized all popular rate

Natural enough to absolve himself of any guilt in his fall.

MIRANDA Wherefore did they not
That hour destroy us?
PROSPERO Well demanded, wench.
My tale provokes that question. Dear, they durst not,
So dear the love my people bore me

(Wench?)  Those many years of isolation have undoubtedly played tricks on his memory.

One can easily envision a heretical take on the events leading up to Prospero’s ousting: a threatening Naples, an arrogant and absentee duke, a popular brother with the political smarts needed for the situation, a few loyal retainers hustling Prospero away before he could be lynched.  Shakespeare did this himself for Homer in Troilus and Cressida, it’s time someone returned the favor.

Some have speculated on a pedaphilic interpretation of Prospero’s relationship with Ariel.  I don’t want to go that far, but it is odd that Prospero feels it necessary to hide Ariel from Miranda, and indeed everyone: Ariel never appears undisguised before anyone (at least when conscious) except Prospero.  Many Christians would have assumed that Ariel was a demonic entity who counterfeited spriteliness in order to lead Prospero into damnation.  The furtiveness of the dealings between the two suggest that Prospero was very alive to this interpretation.

The viciousness of Prospero’s reminder of Ariel’s past, and the hideous threat that fusillade culminates in, betoken much more than a lovers’ quarrel, and in fact betray a certain insecurity of control over Ariel.  It reminds me most of scolding a dog for having wet the rug.  And indeed after this their relation of master and pet/slave returns to an even keel and Prospero is continually petting Ariel verbally for the rest of the play.

Do you love me, master? No?
PROSPERO Dearly, my delicate Ariel.

One problem with a deus ex magiko plot is that, as Prospero himself says,

…but this swift business
I must uneasy make, lest too light winning
Make the prize light.

He may succeed with Ferdinand and Miranda, but I think Shakespeare has less success with the play as a whole.  Ariel and his “collaterals” are there to flesh out Prospero’s every revenge fantasy, and it’s hard not to feel sorry for Alonso at least, being forced to play mouse to Prospero’s cat.  There seems to be some indirect evidence that Shakespeare was conscious of this failing:  in I.ii we have

PROSPERO Do so, and after two days
I will discharge thee.

But by the end Shakespeare has evidently given up on producing the illusion of a long struggle and we have

How thou hast met us here, whom three hours since
Were wrecked upon this shore;

We have thus been witnessing the whole trial of the ship-wrecked in just about real time.

Prospero’s impatience with Ariel is bad enough, but his enmity with Caliban is pathological. Oh, Shakespeare provides us with the excuse that Caliban had attempted to “violate the honor of” Miranda, but Shakespeare in this period (? see below) loved the theme of lechery.  Later in this play he works up a scathing curse to scare the lovers into premarital chastity.

If thou dost break her virgin-knot before
All sanctimonious ceremonies may
With full and holy rite be ministered,
No sweet aspersion shall the heavens let fall
To make this contract grow; but barren hate,
Sour-eyed disdain, and discord shall bestrew
The union of your bed with weeds so loathly
That you shall hate it both.

So it’s difficult to take Prospero seriously on the topic of sex.  But surely as brilliant and powerful a wizard as he could find a better way to control the priapic urges of a feral teenage boy than by constant physical tortures. This xenophobic horror of “natives” is The Tempest‘s analogue of The Merchant of Venice‘s antisemitism, and by itself makes the play painful to experience.

The converse of Caliban the ugly recidivist is the buff, boyish hero, and Shakespeare is happy to give us that cliché as well.

MIRANDA  There’s nothing ill can dwell in such a temple.
If the ill spirit have so fair a house,

Prospero may take issue with this proposition, but surely the audience is meant to be on Miranda’s side here.  Ferdinand is the single best reason for doubting the conventional dating of this play.  Would the mature Shakespeare really have tried to foist this bubble-headed pretty boy on us?  I’d be willing to consider a date closer to that of A Midsummer Night’s Dream, though even that play has more psychological subtlety than The Tempest.

Ferdinand’s only virtue is that he is allowed to voice some common-sense criticisms of Prospero.

Oh, she is
Ten times more gentle than her father’s crabbed,
And he’s composed of harshness.

Indeed Prospero’s harshness can even take Miranda in its sight:

One word more
Shall make me chide thee, if not hate thee.

Here Prospero crosses a line which, while not surprising, is unforgivable: love for one’s children is supposed to be unconditional.  Perhaps it is anachronistic to hold him to that standard, but it is another reason this play can make us squirm.

Ferdinand’s insipidity also has the perhaps accidental effect of setting off every possible double-entendre:

MIRANDA   But this is trifling,
And all the more it seeks to hide itself
The bigger bulk it shows.  Hence, bashful cunning,
And prompt me, plain and holy innocence!,

Did Shakespeare plant this as wry self-mockery?  Could this juxtaposition of phallic and vulvic allusion really be a coincidence?  With the best Will in the world, I doubt it.

The early Shakespeare is continually deferring to conventional pieties and prejudices.  He is a believer in the class system, fights to become a gentleman, and accepts the innate superiority of the high born.  When we first meet the ship-wrecked nobles there’s an interesting interaction that prepares us for the final victory of class at the end of the play.

Antonio and Sebastian engage in a duel of wits with Gonzalo.  Though Shakespeare’s sympathies are ultimately with Gonzalo, the playwright allows the two young scoundrels to come off the better in this contest.  Indeed some of Shakespeare’s wittiest writing is given to that pair in this scene (II.i).  Evidently the audience is meant to have a grudging admiration for their intelligence and style.  For although they are the guiltiest curs in the whole play, at the end their nobility buys their acquittal.  The feckless low-born drunkards and their adopted feral companion do not fare so well.

O Setebos, these be brave spirits indeed!
How fine my master is! I am afraid
He will chastise me.
SEBASTIAN    Ha, ha!
What things are these, my lord Antonio?
Will money buy ’em?
ANTONIO    Very like. One of them
Is a plain fish, and no doubt marketble.

The two guilty of premeditating murder join in the mockery of the orphan freak.  Even in The Merchant of Venice I don’t know that Shakespeare ever sank so low.

The most touching relationship in the play remains that of Prospero and Ariel.

          Merrily, merrily shall I live now
Under the blossom that hangs on the bough.
Why, that’s my dainty Ariel! I shall miss thee,
But yet thou shalt have freedom.

Ariel is the only figure in the play with any influence over Prospero.

Your charm so strongly works ’em
That if you now beheld them your affections
Would become tender.
PROSPERO                   Dost thou think so, spirit?
ARIEL   Mine would, sir, were I human.
PROSPERO                             And mine shall.
Hast thou, which art but air, a touch, a feeling
Of their afflictions, and shall not myself,
One of their kind, that relish all as sharply
Passion as they, be kindlier moved than thou art?

Ariel, like a rich man’s dog licking a beggar, has the power to embarrass Prospero into charity.  After all this one hopes the play will climax in a touching scene of Prospero finally granting Ariel his freedom.  But either Shakespeare did not yet have the poetic chops to carry that off, or he saw the arc of the play very differently.

PROSPERO    I’ll deliver all;
And promise you calm seas, auspicious gales,
And sail so expeditious that shall catch
Your royal fleet far off. [Aside to Ariel] My Ariel, chick,
That is thy charge. Then to the elements
Be free, and fare thou well!
[To the others] Please you, draw near.

Thus ends The Tempest proper.  But there follow ten tetrameter couplets alerting the audience to the cessation of the drama, and the present necessity of applauding the performance.  I have never been one of those who found this speech touching, or even terribly competent versification.

Gentle breath of yours my sails
Must fill, or else my project fails,
Which was to please. Now I want
Spirits to enforce, art to enchant,
And my ending is despair,
Unless I be relieved by prayer,
Which pierces so that it assaults
Mercy itself, and frees all faults.
As you from crimes would pardoned be,
Let your indulgence set me free.

“…my project fails / which was to please”, what an awkward enjambment.  And prayer “pierces so that it assaults”, like a hardened round from an AK-47.  Either this was appended to the play later or it is indeed a very early play.

There is in fact a book which promotes the thesis that The Tempest was written earlier (1603) than usually thought (1611).  I’m all for it, though that new date may not be radical enough.

But let’s return the theorems.  Shakespeare first proves the lemma that long years of hopelessness + egocentrism + self-pity + poetry →

You do look, my son, in a moved sort,
As if you were dismayed. Be cheerful, sir.
Our revels now are ended. These our actors,
As I foretold you, were all spirits and
Are melted into air, into thin air;
And, like the baseless fabric of this vision,
The cloud-capped towers, the gorgeous palaces,
The solemn temples, the great globe itself,
Yea, all which it inherit, shall dissolve,
And, like this insubstantial pageant faded,
Leave not a rack behind. We are such stuff
As dreams are made on, and our little life
Is rounded with a sleep.

Then he establishes the main result that vanity + self-deception + nostalgia + resignation →

Ye elves of hills, brooks, standing lakes, and groves,
And ye that on the sands with printless foot
Do chase the ebbing Neptune, and do fly him
When he comes back; you demi-puppets that
By moonshine do the green sour ringlets make,
Whereof the ewe not bites; and you whose pastime
Is to make midnight mushrooms, that rejoice
To hear the solemn curfew; by whose aid,
Weak masters though ye be, I have bedimmed
The noontide sun, called forth the mutinous winds,
And twixt the green sea and the azured vault
Set roaring war; to the dread rattling thunder
Have I given fire, and rifted Jove’s stout oak
With his own bolt; the strong-based promontory
Have I made shake, and by the spurs plucked up
The pine and cedar; graves at my command
Have waked their sleepers, oped, and let ’em forth
By my so potent art. But this rough magic
I here abjure, and when I have required
Some heavenly music—which even now I do—
To work mine end upon their senses that
This airy charm is for, I’ll break my staff,
Bury it certain fathoms in the earth,
And deeper than did ever plummet sound
I’ll drown my book.

Those results are perhaps worth the violence needed to obtain them.

[Quotes from the play have been taken from the Bevington edition on Pelican.]



I’ve been reading about the Black-Scholes formula for the past two months.  It turns out to be a lot less impressive than I thought it was when I didn’t know anything about it.  Here’s a brief overview of the arguments that have been given for it and where I think it might be improved.

Why Metaphysics is Impossible

As far as I know there are no persuasive theories in metaphysics. By “persuasive” I mean one around which a consensus forms. There used to be some – for example in times past the majority of philosophers would assent to the principle of the first cause or the omnipotence of God. But all those theories are now seen as specious and metaphysical systems are as variegated as fingerprints.

The only form of explanation that humans have ever developed is to start with some agreed upon terms and principles, and then work up to new terms and principles by applying basic logic, essentially unchanged since Aristotle. This is the system crystallized in first order logic: some undefined terms, some axioms, and rules of inference; thence theorems.

The trouble with metaphysics is that everything, absolutely everything, is up for grabs, even the basic terms and axioms. Unlike the situation in number theory and geometry, there is no agreement among humans about what the fundamental objects of the theory are, much less what properties they have. Evidently evolution has provided us with strong and reliable intuitions about space and time, but not about the nature of being. After thousands of years of thought metaphysics is still stuck at square one: what are the basic objects under discussion?

The Christian scholastics tried to make God the basic undefined term, and proceeded to paint themselves into corners. Since God was to be unexplained, God had to be “simple”. This use of “simple” is not encountered much any more; evidently to a scholastic God was simpler than peanut butter, since my jar of Jif contains peanuts, sugar, and vegetable oils, which can be further broken down into hydrogen, carbon, oxygen, etc., but God is just God all the way through. Thus we got the self-caused cause and negative theology.

Eventually philosophers realized that if they were willing to suspend the Principle of Sufficient Reason for God, why not suspend it earlier in the grand causal chain of Being? Why not an uncaused universe rather than an uncaused First Cause? After all, despite the effort of the scholastics to reify otherwise, everyone realizes that an omnipotent, omniscient, eternal deity isn’t really any “simpler” than the universe as a whole.

The problem of consciousness is similar. Our mental worlds are ungrounded. Before any mental concept we can always ask Why or What or How?, recursively. The metaphysics of consciousness seems equally at square one. The current hot idea is to ground the system in the undefined terms of qualia, which evidently are “simple” conscious experiences.  No thought is ever given to how qualia themselves can be explained.  Another problem with this is that we would need at least a small library of qualia to ground human consciousness.   Perhaps this notion should be combined with Chomsky’s idea that evolution has engineered human conceptual space into more or less fixed lexical units. That wouldn’t satisfy the qualiists, but it does me.

It suggests that human consciousness is in one sense logically grounded in axioms implicit in the brain, and  in another sense ungrounded – when viewed from the inside. From the inside our consciousness is circular.  We are never at loss to explain an idea, but we frequently have to use more complicated concepts to do so.  (Johnson used “reticular” to define “net”.)  That doesn’t really bother most people, just lexicographers and philosophers.

For me consciousness is best viewed as a a relational system, which is “grounded” in emotions.  When your brain gets tired of explaining itself it just broadcasts pleasure or pain, or some other emotional qualia.  Emotion has the virtue of stopping thought and motivating action.

This deflationary view of consciousness is the one I’m drawn to intellectually, but emotionally I still like the idea of immortal souls.  So I don’t begrudge the qualiists their fun; I actually hope they’re right.

Colin McGinn is certainly right to think that the “hard” problem of conscious cannot be solved, and just about anyone who has thought seriously about it for five minutes will agree.  In my terms, there is no way the brain can give an inner explanation for the Chomskian elemental concepts that the mind cannot account for reductively but feels it understands heuristically.  In more general metaphysical or logical terms, there is no way to explain qualia in that doesn’t invite further questions that demand further explanations.

The Reluctant Nihilist

Meta-Theorem 2:  No rational argument for the existence of the mind-body problem is possible.

Proof:  Any rational argument could and would be made by a zombie. Since zombies by hypothesis are unconscious any such argument would be logically invalid.

Corollary:  No rational solution of the mind-body problem is possible.

Proof:  A problem that cannot be stated can certainly not be solved.

Priority for the corollary goes to Colin McGinn in his 1989 paper “Can We Solve the Mind–Body Problem?” The theorem may be original with me.

The theorem I think demonstrates that the mysterian position on consciousness is beyond the realm of phlogiston, it’s right in “how many angels can dance on the head of a pin?” territory.

I’m saddened by that. I would really like to defend the ineffability of consciousness but reason keeps getting in the way. The best I can do presently is to say that it may be an illusion, but it’s an extraordinary and precious illusion.

Flame Seeks Moth: Haskell’s Monads

To borrow a turn of phrase from Norman Mailer, a programming language that prides itself on handling IO via category theory, has a problem.  But I share that problem, to an extent.

I understand the seductive power of abstraction, but I think the Haskellians made a huge PR mistake in going all in on category theory.  CT is by construction both bland and general: any formal system can be parsed into CT, but CT usually brings nothing new to the discussion.  CT is abstraction for abstraction’s sake, i.e. pure mathematics, and there is no need for computer scientists to make a fetish of it.

Here’s my 10,000 ft view of monads.  A monad is a derived type.  For example, for any type t,  F t might be a framed portrait of elements of type t.  B t might be an element of type t produced by code partially written by a Beatles fan.  More realistically C t might be container type for objects of type t, or a warning type that an object of type t has been contaminated by an impure procedure (e.g., IO).

Haskell provides some utilities to facilitate working with derived types.  All the programmer has to do when defining a monad M is provide (1) a method for turning an object of type t into an object of type M t; (2) a method for turning a function defined on type t into a function defined on type M t.

This sort of thing is easy enough in Lisp, Mathematica, etc, and doable in any modern language.  It’s perhaps easiest in Haskell but the fear and trembling surrounding monads are silly, and mostly result from poor explanations.

I lost most of my enthusiasm for Haskell when I discovered it has no good mechanism for memoizing recursive functions.  By “good” I mean: it ought to be  possible to define an operator memo so that “memo fun” yields a memoized version of the function fun.  This can be done in Lisp and Python, to mention two extreme examples, but not in Haskell.  The culprit seems to be immutability: the memo operator would have to be able to redirect recursive calls to fun to the new version, but that kind of redefinition is forbidden in Haskell.  Please let me know if I’m wrong.

Circles of Apollonius

Circle of Apollonius and one of its orthogonal circles.

A circle of Apollonius with respect to given foci O and P and real number r is the locus of points B with BO/BP = r.  The upper half of the image diagrams the proof.

Any circle through the foci O and P will be orthogonal to the circle of Apollonius.  The lower half of the image diagrams the proof.

Note that the green and red angles are bisected by the segments through A.