This is a fascinating article about the late 19th century/early 20th century studies in set theory and infinity. I particularly like the accompanying picture. Since I’m not sure the link will work (TNR might be behind a paywall), I’ll reproduce it here:
To keep up the trend of making what are not actual posts, I give you a quotation I recently came across which I think well expresses the idea of what I call “the mathematical sublime.”
Mathematics, rightly viewed, possesses not only truth but supreme beauty — a beauty cold and austere, like that of a sculpture, without appeal to any part of our weaker nature, without the gorgeous trapping of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.
— Bertrand Russell
This isn’t exactly the same as the scientific sublime I used a few weeks ago when discussing Andrew Bird, but it is related. There are two primary differences; first, science, while abstracted from humanity, still deals with the natural world, while mathematics is removed even from that, residing entirely in the realm of logic. This means that while the scientific sublime offers a way of looking at humans as cogs in a machine, the mathematical does not even offer the machine or the cogs — only the rules by which they would, in theory, operate, if they existed.
Second, unlike science, mathematics actually wrestles with infinity. People often go on about “infinity” when they just mean vastness; mathematics actually attempts to quantify the unquantifiable.
Few writers have a true feel for the mathematical sublime, I think (many more can grasp the scientific); the only positive example I can give is Jorge Luis Borges, many of whose stories offer excellent examples of it; see “The Library of Babel.”
Cormac McCarthy’s epic 1985 novel Blood Meridian, or the Evening Redness in the West, contains shockingly detailed descriptions of gruesome acts of violence, and perhaps more disturbing than the violence itself is that by the end of the book the violence has become routine, and the reader barely notices. None of the novel’s characters are truly sympathetic, though some are less loathsome than others, and the plot consists of a band of scalp-hunters roaming around the American Southwest slaughtering people until they’re not doing it any more, a shoot-the-shaggy-dog story if there ever was one.
It’s also an amazing book. It’s like Moby-Dick, but more nihilistic, with whaling replaced by scalp-hunting, and Moby-Dick made a member of Ahab’s crew (i.e. Glanton’s gang) in the form of Judge Holden. The Judge is perhaps the most disturbing example of the sublime ever; a giant of a man, hairless, and pure white, he kills for pleasure and desires to possess all knowledge in the universe so that he can control (and destroy) the universe. To that end carries around a notebook in which he makes detailed scientific observations before destroying the things he is observing. He may be a pedophile. He claims that “War is god.” He seems some sort of Gnostic deity, though he cannot be traced back to any “atavistic egg.” Perhaps he represents Death. He is a skilled dancer.
I have a hard time saying more than this about the novel. This is partially because it’s so overwhelming on a first reading – it’s like Moby-Dick in this regard as well – that I am completely aware that I do not understand it, at all. The Judge is by far the most fascinating character, but the rest of the gang are interesting as well — the captain, the expriest, Toadvine, the Delawares (are they like Fedallah and his men?), the kid himself, who never receives a name. One gets the feeling each of them can be examined individually in much the same way as Ahab, Starbuck, Stubb, Flask, Queequeg, Tashtego, Dagoo, and Ishmael. But I have not done so yet.
I did wonder, while reading the book, whether or not Cormac McCarthy is capable of describing anything as being red without comparing it to fire or blood. It’s an effective descriptive technique, but every once in a while I sat back and said, really? Again? The sunset is bloodred. Is it ever any other color?
I’ve also read recently that there are plans to make it into a movie. Now, three of McCarthy’s books have already been filmed – All The Pretty Horses, No Country for Old Men, and The Road – but those are children’s books compared to Blood Meridian. It would be completely impossible to show all the violence described in the book without getting an NC-17 rating. And omitting the violence somewhat defeats the point. So, to say the least, I’m skeptical, though I’m willing to give it a chance.
I haven’t said anything here about music for a while. With this post I intend to rectify that. My subject will be Andrew Bird, an indie-baroque-pop artist, whom I only started listening to in the last few months (probably since January), but who has quickly become one of my favorite musicians. I have three of his albums, “Andrew Bird & The Mysterious Production of Eggs,” “Armchair Apocrypha,” and “Noble Beast”; all three have many good songs on them, some of which I’ll mention over the course of this post.
Andrew Bird has several things going for him. To start with, I find his intricate musical style quite appealing; he plays guitar, violin (pizzicato and arco), and whistles, as well as other instruments, and layers them all together in a way that doesn’t overwhelm – in fact, his music has a quite minimalistic feel to it, until you pay attention and realize how complex it really is. The whistling in particular makes it unlike most other music I’ve listened to. Andrew Bird songs often give me the feeling of being in a white room looking at a complex yet not chaotic contraption, a clock or perhaps a circuit.
A related strength is his use of his voice and the sound of his lyrics. He doesn’t have an amazingly strong voice, but he uses it to his advantage. It’s melodic yet matter-of-fact, occasionally plaintive, which fits with the precise minimalism of the instrumentals. Then there are the lyrics. The words of his songs always sound as if they mean something, merely by their sound, even if they don’t. For example, he has a song called “Fake Palindromes,” the first few lines of which are, “my dewy-eyed disney bride, what has tried / swapping your blood with formaldehyde?” No one else would try to rhyme with a scientific word like “formaldehyde.”
Which brings me to what I find really interesting about Bird; the subjects of his songs. Given his complex, layered, precise, even scientific, aural aesthetic, it shouldn’t be a surprise that he often takes as his subject science and mathematics. What he is most interested in are the aesthetic and ethical implications of the scientific way of looking at things. He wants to believe in beauty, to have free will, but the fact that we can quantify the universe threatens to make these things impossible. In the song “Masterfade,” he says to his lover that “when you look up at the sky / all you see are zeros / all you see are zeros and ones.” That way of looking at the world, he fears, make a true appreciation of the wonders of the world impossible. In “Imitosis,” he reports (a lot of Andrew Bird songs have the feeling of being reports, perhaps even scientific abstracts) that “What was mistaken for closeness / Was just a case of mitosis.” If we’re just organisms like any other, than whatever meaningful relationships we may have, whatever rights and duties to others we may think we have, are actually just our genetic code controlling us.
But Bird doesn’t go from here to a rejection of science; he loves science and math and logic. You can tell from listening to his songs, to his use of complex latinate words and bizarre conceits and language games. He rejects any attempt, religious or otherwise, to feel better by ignoring what science seems to be saying. In “The Privateers,” he asks of us, “Don’t sell me anything / Your one time offer, so uncalled for / You call it piece of mind.” In “Measuring Cups,” perhaps my favorite Andrew Bird song, he asks, “when you talk about the hand of glory / a tale that’s rather grim and gory / is it just another children’s story that’s been de-clawed? / when the tales of brothers Grimm and Gorey have been outlawed.”
So Bird doesn’t want us to look for meaning by rejecting science. What, then, does he turn to? In the end, I think, he never answers that question in full. If he could, he wouldn’t have to make songs about it. But I think he finds a partial answer in the very scientific aesthetic that resulted from his worrisome interest in science. His songs, after all, though often sounding plaintive and questioning, rarely sound despairing. Instead they revel in their own precision. Rather than seeking beauty outside of science, he finds it in the patterning, of numbers and of sound. This is what the best Andrew Bird songs show us; the precise use of language and sound can conjure images of what they describe that make us feel almost like we’re watching a nature documentary, like with with sea aenenome of “Anonanimal.”
But beauty, I think, might be the wrong word here. He finds aesthetic pleasure in patterns, and beauty is defined as proportion; but more precisely, beauty is found in things being proportionate relative to the viewer. Beauty requires something to be on a human scale. Bird doesn’t find the science beautiful for it’s relationship to humans (in fact, that’s what scares him about it); he finds pleasure in it for its own sake. That sounds to me more like the sublime. And indeed, I think there’s an aspect of reveling in the infinite going on here. Bird is probably one of the few songwriters who would completely understand what it means to say that the world itself is not infinite – it is very large, but bounded. When we draw general laws from it – which is what science does – we are inductively drawing the infinite out of the finite. Bird already intuits this, I think; in “Tenuousness,” he talks about the world, which is “tenuous at best,” coming “just shy of infinity.” The world itself is beyond our grasps and finite; strangely, what is infinite, what is in our minds, is less tenuous.
I’ve been thinking a lot about the finitude of the world recently. What I mean by that is this: While we interact with the physical world as if it were infinitely variable – everything can be subdivided, including time and space – it seems scientifically quite likely that this is not in fact the case, that rather the world is finite, that there are finitely many particles in the universe, that each of them has finitely many positions, and thus that the universe has finitely many possible states – an absurdly large number, but still finitely many.
This possibility disturbs me, and I think I’ve figured out why. Mathematically speaking, if we have infinitely many points, we can find only one equation that fits it, for it is a smooth curve, a definite function – the universe would have only one explanation. But if we have finitely many points, there are infinitely many equations that would fit the given data – for example, if we just have the points (0,0) and (1,1), the equations y=x and y=x^2 both equally well describe the data. If we have (0,0), (1,1), and (2,0), both y=-(x-1)^2+1 and y=-(x-1)^4+1 work. Et cetera. And those were all just polynomials – there’s lots of other kinds of equations out there. So a finite universe means that the universe has many possible explanations, and even at the end of time, when all is said and done, there’s no way to know which one was correct.
So finitude somewhat scares me. Then again – if the universe is finite, there are many possible explanations, but one will, I hope, be much more elegant than the others, and that will be the “true” one… that, or, since by “the universe is finite” I really mean only the physical world, the atoms and quarks and leptons and dimensions of space and time, meaning will in the end be found not in the physical, but the metaphysical. That is, I suppose, what I believe – but I’d would like to be able to find meaning in both.
Does finitude scare anyone else, or is it just me?
I don’t mean for this blog to turn into just a bunch of book reviews, but I’ve been reading a lot lately, alright? I do hope to post soon about “copyright and the pirate bay trial”, and perhaps something philosophically oriented as well. But no promises.
In any case, even if I never posted book reviews, I would post one for Moby-Dick, because it has leaped to the front of my list of great books. That’s right – I think Moby-Dick is almost certainly the best novel ever written in the English language, and might even be the best thing ever written in the English language, period. But I’m not going to explore the question of whether it’s better than Shakespeare’s best.
I didn’t really expect this – I came into Lit Trad IV expecting to love Crime and Punishment, really like Go Down Moses, like Moby-Dick, and tolerate Mansfield Park. We haven’t read Go Down Moses yet, but so far all my predicts are right except for Moby-Dick. I don’t just like it; it’s simply amazing.
What makes it so great? A large part of it is simply its scope. It tries to be the modern epic, and succeeds admirably. Some people find the “encyclopedic” portions of the book boring; I thought they were really well done, and was surprised to find myself enjoying reading for ten pages of tiny text about “cetology” so I can learn about how nature can’t be fit in a box or “the whiteness of the whale” so I can learn about the terrifying sublime. And those parts are necessary to do what an epic is supposed to – explore all of human life, religion, politics, economics, social interactions, etc.
(Interlude: This business about the “modern epic” I actually find somewhat fascinating. As technology has progressed, the primary literary form has changed, and epics are normally done in the primary literary form – but there are only a few works in the history of mankind that deserve the term “epic”. In the days of oral traditions, we had oral epics, such as the Iliad and Odyssey, because verse is easier to remember. When writing came about but there wasn’t really any way to publish something, we got literary epics like the Aeneid and the Divine Comedy. When printing first came about but wasn’t that widespread, we got Shakespeare, none of whose plays are themselves an epic, but of whom I’m willing to say his entire corpus composes something “epic”. Milton’s Paradise Lost is an interesting abberation, but it still makes sense, since printing wasn’t that widespread at that point. When books become widespread, we get the novel, and Moby-Dick.)
But its scope is not all that makes Moby-Dick amazing, even if that’s the easiest thing to describe about it. There’s also the fact that its characters are so compelling – there’s only perhaps a dozen real characters, and by my count six major ones (Ishmael, Ahab, Quigqueg, Starbuck, Stubb, Flask) – but they all seem at the same time immensely real and perfect “psychic projections” of a single consciousness.
And then there’s just the quality of the prose. The entire book is worth reading just to get this monologue:
Ahab is forever Ahab, man. This whole act’s immutably decreed. ‘Twas rehearsed by thee and me a billion years before this ocean rolled. Fool! I am the Fates’ lieutenant; I act under orders. Look thou, underling! that thou obeyest mine.
I’d also recommend the Demons & Wizards song “Beneath These Waves”, from their album Touched by the Crimson King. It’s actually about Moby-Dick. Don’t you love power metal bands singing about great literature? I’m just waiting for the first concept album about the Divine Comedy, or perhaps about the Bible itself (now that’s be interesting, if perhaps slightly blasphemous).
A damsel with a dulcimer
In a vision once I saw :
It was an Abyssinian maid,
And on her dulcimer she played,
Singing of Mount Abora.
Could I revive within me
Her symphony and song,
To such a deep delight ‘twould win me,
That with music loud and long,
I would build that dome in air,
That sunny dome ! those caves of ice !
And all who heard should see them there,
And all should cry, Beware ! Beware !
His flashing eyes, his floating hair !
Weave a circle round him thrice,
And close your eyes with holy dread,
For he on honey-dew hath fed,
And drunk the milk of Paradise.
I just wrote a paper for my Romantic Tradition class, and I’m in a poetical mood; plus I had too much coffee and so am still awake at 2:30 AM. Hence this post.
The above is an excerpt from “Kubla Khan”, by Samuel Taylor Coleridge, a celebration of raw poetic power. The first half of the poem is simply a description of an incredibly sublime scene, Kubla Khan’s pleasure dome, with its sacred river Alph that “ran / Through caverns measureless to man / Down to a sunless sea”, and assorted other wonders. The second half, reproduced above, reveals that this description is a vision the poet had.
What I love about this poem is how, with its irregular rhyme scheme, lilting rhythm, and constant use of alliteration, it propels the reader forward, almost as if it were a magic spell or incantation. Its power is irresistible, sweeping us along whether we want it or not. And that’s what the poem is about; how poetry is power, how the poet is a magician whom all others should “beware! beware!”
What I can’t understand is how the same poet that wrote the above also wrote poems like “Frost at Midnight” or “This Lime-tree Bower my Prison” – poems which, though well-written, are not at all sublime or powerful. I can’t really enjoy them as poems, because, well, they don’t strike me as poetic; I may sound like a philistine saying this, but they’re for the most part just prose descriptions of not that interesting events with line-breaks every ten syllables.
I don’t insist that poetry must rhyme or alliterate, but I do think it has to use words as if they were something magical, as if words had power, or else its words will not have power, the form of the poem will not matter as much as the content, and it will not be poetry. Perhaps that’s how I define poetry – as something written so that the way the words fit together is as important to the meaning as the literal meaning of the words.