Rephrasing the famous words on the electron and atom, it can be said that a hypocycloid is as inexhaustible as an ideal in a polynomial ring. But teaching ideals to students who have never seen a hypocycloid is as ridiculous as teaching addition of fractions to children who have never cut (at least mentally) a cake or an apple into equal parts. No wonder that the children will prefer to add a numerator to a numerator and a denominator to a denominator.
Vladimir Arnold, On teaching mathematics
I’ve still been really distractible this month and had my attention split between many things. In particular I haven’t done much physics, which isn’t great. On the plus side, I’ve at least made some slow progress instead of getting so distracted by the number of things that I don’t get anywhere with any of them.
I’ll stick to a couple of things in this newsletter, though. I’ll start with a long, meandering braindump wandering through a cluster of confused ideas to do with Derrida and the New Critics. Then I’ll say a bit about the Cognitive Reflection Test. No physics this time. The braindump took longer than expected and I ran out of time.
Nerrida the horrible Frenchman
A little while ago I wrote this:
… my biggest unusual pervasive influence is probably the New Critics: Eliot, Empson and I.A. Richards especially, and a bit of Leavis. They occupy an area of intellectual territory that mostly seems to be empty now (that or I don’t know where to find it). They’re strong contextualisers with a focus on what they would call ‘developing a refined sensibility’, by deepening sensitivity to tiny subtle nuances in expression. But at the same time, they’re operating in a pre-pomo world with a fairly stable objective ladder of ‘good’ and ‘bad’ art. (Eliot’s version of this is one of my favourite ever wrong ideas, where poetic images map to specific internal emotional states which are consistent between people, creating some sort of objective shared world.)
This leads to a lot of snottiness and narrow focus on a defined canon of ‘great authors’ and ‘minor authors’. But also the belief in reliable intersubjective understanding gives them the confidence for detailed close reading and really carefully picking apart what works and what doesn’t, and the time they’ve spent developing their ear for fine nuance gives them the ability to actually do this.
The continuation of this is probably somewhere on the other side of the ‘fake pomo blocks path’ wall in David Chapman’s diagram, but I haven’t got there yet, and I really feel like I’m missing something important.
I’ve been wanting to write more about this as a blog post for a while but it never comes right, so this time I’m going to just start writing with no preplanned structure at all, and see what comes out.
I spent a ridiculous amount of time staring at Chapman’s diagram I linked above when I first found it. I think the main thing that made it really sticky was my experience with the top row, the one with the brick wall marked ‘fake pomo blocks path’. My teenage autodidact blundering accidentally got me past the wall to the ‘Stage 4 via humanities education’ forbidden box while barely knowing that postmodernism existed.
I started out by reading books my dad had from his university course in the early sixties. This included a very wide-ranging multi-year course on literature, philosophy and general history of ideas called ‘The European Mind’. Even the name is brilliantly pre-pomo! There’s one unified mind, and it’s distinctively European, and you can learn about it by studying the classic Western canon.
I got particularly fixated on the early twentieth century. I was also reading a lot of pop science for the first time and learning about the insanely productive and disorientating revolution in physics, from Planck’s constant in 1900 up to the solidifying of the new quantum theory in the late 20s, with special and general relativity along the way. (Also a little bit about the crisis in foundations of mathematics, but I never got particularly interested in that at the time.)
It was easy to switch between science and humanities stuff from that era, because the tone and writing style was quite similar, in the Anglosphere anyway. The analytic philosophers had all got maths envy and were trying to adopt the language of logic and dig to the foundations. And even the literary critics wrote in a style that was easily accessible to a STEM nerd like me. Eliot, for instance, writes up his experiences in trying to revive verse drama like it’s a retrospective on some lab experiments that went wrong:
It was only when I put my mind to thinking what sort of play I wanted to do next, that I realized that in Murder in the Cathedral I had not solved any general problem; but that from my point of view the play was a dead end. For one thing, the problem of language which that play had presented to me was a special problem…
The style was similar to the scientists, but their main method was somewhat different. The New Critics tended to work via very detailed close reading of individual passages, really picking apart what makes specific examples work. For another Eliot example, here he talks about the vivid specificity of the images in Macbeth, and compares it to the artificial, conventional images of much eighteenth century poetry. The overarching ‘Shakespeare good, Milton bad’ moral might not be worth much, but it’s fantastic for pointing out what Shakespeare does that Milton can’t.
I really like the close reading method. If I study one example in depth, I normally come away with some new ability to read the situation, in a way that grand abstract theorising can’t match. (I do also really like sloppy big-picture grand theorising, but in my case it’s normally motivated by trying to mash examples together.) Examples are inexhaustible, like Arnold’s hypocycloid in the quote at the start. In fact, ‘close reading’ has become my idiosyncratic mental label for any kind of heavily example-driven work, not just the detailed study of written texts. Toy models in maths and physics also count, for example.
Once I’d got my ear in for the New Critical style, it was pretty easy to find more of it in secondhand bookshops and never really read anything that went beyond it, so the ‘wall of fake pomo’ wasn’t a problem. (I knew what postmodernism was anyway! It was that stupid rubbish that Sokal made fun of, where people make word salad out of hermeneutics and deconstruction and logocentrism. I wasn’t going to fall for any of that!)
Now, funnily enough, I seem to be back with the New Critics for different reasons. Something like ‘well, I’m in the right place to follow that ‘genuine pomo critique’ arrow, so let’s give it a go’. This time I got there by reading the text of this fantastic talk on Derrida by Christopher Norris. Norris is a literary critic who wrote about Empson as well – I’ll get to that in a minute. But first I’ll talk about that linked Norris piece, especially the bit on Rousseau and Rameau. (I did warn you that this is going to be a rambling braindump.)
I learned a lot from the Norris talk. The first thing I picked up was that Derrida is not the vague sort of waffler I’d imagined from the Science Wars stereotype. He does have a weird writing style that I find a complete pain to read (I have started wading through Of Grammatology now, and I’m not particularly enjoying the process), but it’s not a vague style. He’s actually a close reader with a similar method to the New Critics, even if the tone is completely different, and he works by going through specific examples in detail. Which is actually my favourite way of learning!
Derrida’s main targets for the close reading treatment in Of Grammatology are Rousseau, Saussure and Lévi-Strauss. A very French list which doesn’t mean a whole lot to me, so I’m having to read backwards too. But I was able to understand the part about Rousseau’s fight with the musician Rameau. Norris explains it here:
Rousseau was himself a musician, a performer and composer, and he wrote a great deal about music history and theory, in particular about the relationship between melody and harmony… One way of looking at Rousseau’s ideas about the melody/harmony dualism is to view them as the working-out of a tiff he was having with Rameau. Thus he says that the French music of his day is much too elaborate, ingenious, complex, ‘civilized’ in the bad (artificial) sense — it’s all clogged up with complicated contrapuntal lines, whereas the Italian music of the time is heartfelt, passionate, authentic, spontaneous, full of intense vocal gestures. It still has a singing line, it’s still intensely melodious, and it’s not yet encumbered with all those elaborate harmonies.
This was really accessible to me because of my weird music listening habits. I listen to a lot of baroque music, and I specifically like the Italian baroque, pretty much for the reasons Rousseau lists above. It’s very different to Bach’s sort of baroque music, which is very harmonically and structurally complex, and it sticks much closer to its roots in dance music. The melodies are straightforwardly, immediately appealing, instead of being subsumed into some big contrapuntal structure. It’s not simple folk music, though – the complexity is instead in the very delicate, constantly changing mood and texture.
(If you want to get an idea of the kind of music I’m thinking of, the Youtube channel Ispirazione Barrocca is my best source for obscure but brilliant Italian composers. For a specific example, at the moment I keep listening to the ciaccona and rondeau here. The ciaccona is the simplest thing possible harmonically, it’s just the same chords over and again. The melody is pretty straightforward too, and there’s no fancy structure. But I love the shadings in mood, and that fantastic change in energy at 7:00 as it transitions into the rondeau.)
So I’m probably the right sort of person to be persuaded by Rousseau’s argument. But actually, as Norris/Derrida tells it, it doesn’t work at all. I’m just going to quote this big glob of Norris’s text, because I can’t possibly explain it any better myself:
What’s more, Rousseau says, this is where writing came in and exerted its deleterious effect, because if you have a complex piece of contrapuntal music, by Rameau let’s say, then you’ve got to write it down. People can’t learn it off by heart; you can quite easily learn a folk tune, or an unaccompanied aria, or perhaps a piece of plainchant, or anything that doesn’t involve harmony because it sinks straight in, it strikes a responsive chord straight away. But as soon as you have harmony then you have this bad supplement that comes along and usurps the proper place of melody, that somehow corrupts or denatures melody, so to speak, from the inside. Now the interesting thing, as Derrida points out, is that Rousseau can’t sustain that line of argument, because as soon as he starts to think harder about the nature of music, as soon as he begins to write his articles about music theory, he recognizes that in fact there is no such thing as melody without harmony. I think this is one of the remarkable things about Derrida’s reading of Rousseau, that it carries conviction as a matter of intuitive rightness as well as through sheer philosophical acuity and close attention to the detail of Rousseau’s text. His arguments seem to be very cerebral, very technical and even counter-intuitive, but in this case they can be checked out against anyone’s – or any responsive listener’s – first-hand experience of music. Thus even if you think of an unaccompanied folk song, or if you just hum a tune or pick it out in single notes on the piano, it will carry harmonic overtones or suggestions. What makes it a tune, what gives it a sense of character, shape, cadence, etc., is precisely this implicit harmonic dimension.
Derrida brings out this contradiction through his characteristic method (again I’ll just quote a glob of Norris’s talk):
Derrida gets to this point through a close reading of Rousseau’s text which shows it to concede – not so much ‘between the lines’ but in numerous details of phrasing and turns of logico-semantic implication – that there is no melody (nothing perceivable or recognizable as such) without the ‘bad supplement’ of harmony. Thus, for instance, Rousseau gets into a real argumentative pickle when he say – lays it down as a matter of self-evident truth – that all music is human music. Bird-song just doesn’t count, he says, since it is merely an expression of animal need – of instinctual need entirely devoid of expressive or passional desire – and is hence not to be considered ‘musical’ in the proper sense of that term. Yet you would think that, given his preference for nature above culture, melody above harmony, authentic (spontaneous) above artificial (‘civilized’) modes of expression, and so forth, Rousseau should be compelled – by the logic of his own argument – to accord bird-song a privileged place vis-à-vis the decadent productions of human musical culture. However Rousseau just lays it down in a stipulative way that bird-song is not music and that only human beings are capable of producing music. And so it turns out, contrary to Rousseau’s express argumentative intent, that the supplement has somehow to be thought of as always already there at the origin, just as harmony is always already implicit in melody, and writing – or the possibility of writing – always already implicit in the nature of spoken language.
Birdsong is an awkward case for Rousseau, because it really is melody without the implicit harmonic dimension. It’s mostly missing the exact, ‘engineered’ side of human music – the precise, repeatable harmonic intervals and lengths of notes and bars. But this is the same structure that makes a tune sound like a tune, rather than a loose cascade of pitches. Even Rousseau didn’t want music that was that structureless and undifferentiated, so he gets himself tied in knots trying to exclude this case that ruins his argument.
This is really just a sideline in the book. Derrida’s main interest is not the tension between harmony and melody, but that between writing and speech. The argument goes through in a similar way, though. Speech is presumed to be the fundamental one of the pair, and writing is derivative – what Saussure called ‘a signifier of a signifier’. But Derrida points out that speech also has a structural element, using repeatable components and arbitrary conventions. The possibility of writing is inherent in speech from the start, in the same way that harmonic structure is inherent in the simplest folk tune:
For Derrida, ‘writing’ should rather be defined as a sort of metonym for all those aspects of language – or of human culture generally – that set it apart from the realm of natural (that is, pre-social, hence pre-human) existence. That is to say, it encompasses not only writing in the usual, restricted (graphematic) sense but also speech in so far as spoken language likewise depends on structures, conventions, codes, systems of relationship and difference ‘without positive terms’, and so forth.
Derrida was in the right time and place to take both sides of the writing/speech opposition seriously. He’d started out in phenomenology, with a deep study of Husserl and his emphasis on the immediacy of raw experience. And then structuralism had been in the air in France at the time, and he’d picked up its insights through Saussure and Lévi-Strauss. He could see that either on its own was not enough:
What Derrida does, essentially, is juxtapose the insights of structuralism and phenomenology, the two great movements of thought that really formed the matrix of Derrida’s work, especially his early work. Phenomenology because it had gone so far – in the writings of Husserl and Merleau-Ponty after him – toward describing that creative or expressive ‘surplus’ in language (and also, for Merleau-Ponty, in the visual arts) that would always elude the most detailed and meticulous efforts of structuralist analysis. Structuralism because, on its own philosophic and methodological terms, it revealed how this claim for the intrinsic priority of expressive parole over pre-constituted langue would always run up against the kind of counter-argument that I have outlined above.
This might be a good point to briefly try and explain my other reason for being interested in this Derrida stuff, beyond ‘trying to understand the New Critics’. This goes back to my normal pet topic. There’s a very similar tension in mathematics between the structural, ‘algebraic’ element, where the individual symbols are arbitrary and only their relations matter, and the ‘geometric’ side where these symbols become grounded in our perceptual experience, and are experienced as being ‘about’ curved surfaces or nodes in a graph or whatever. I’m scare-quoting ‘algebra’ and ‘geometry’ because I’m using them in a weird way – there is of course a structural component to any geometric problem, and a perceptual component to any algebraic one. But algebra tends to be closer to the structuralist style, and geometry to the phenomenological one, so they work quite well as labels for the two sides of the opposition. This is actually pretty similar to Derrida’s weird use of ‘writing’ and ‘speech’.
I really want to understand this parallel story, and how the ‘algebra’/’geometry’ tension played out in the twentieth century. I can figure out who a lot of the main characters are: Bourbaki on the structuralist side, for a start, and Poincare and Weyl on the phenomenology one, in very different ways. Also Brouwer and the intuitionist weirdos must fit in there somewhere. But I’m struggling to find much in the way of good secondary material. About the only thing I’ve found is Mathematics and the Roots of Postmodern Thought by Vladimir Tasic, which has some good material but is kind of all over the place. It’s very different to the situation with Derrida, where there’s an overabundance of crappy secondary sources, mostly teaching literature students how to make up bullshit ‘deconstructions’ of any text that comes their way. I’m glad the maths students didn’t have to suffer in the same way, but it would be nice if there was more to read.
Finally, I’m going to wrench this braindump back to the New Critics where I started. Reading Norris on Derrida made me think of Empson. Empson was particularly keen on the close reading technique, particularly early on when he wrote Seven Types of Ambiguity. Here’s a short example where he goes over a few lines of The Waste Land in minute detail. His main interest in this is trying to track down all the fleeting associations that words in a poem pull with them:
As a rule, all that you recognise as in your mind is the one final association of meanings which seems sufficiently rewarding to be the answer—‘now I have understood that’; it is only at intervals that the strangeness of the process can be observed. I remember once clearly seeing a word so as to understand it, and, at the same time, hearing myself imagine that I had read its opposite. In the same way, there is a preliminary stage in reading poetry when the grammar is still being settled, and the words have not all been given their due weight; you have a broad impression of what it is all about, but there are various incidental impressions wandering about in your mind; these may not be part of the final meaning arrived at by the judgment, but tend to be fixed in it as part of its colour.
At times he seems pretty close to Derrida, at least as Norris tells it, in the way he combines structural critique (he later wrote a book called The Structure of Complex Words, which I haven’t read) with an interest in the phenomenology of how a poem is experienced.
I did some research and discovered that Norris has written a lot about Empson as well. In fact he edited a whole book about him. So maybe that isn’t so surprising! I looked to see if he wrote anything specifically about both Empson and Derrida, and it turns out that Norris actually sent Empson a copy of one of Derrida’s essays, along with some other stuff by de Man and Barthes, to see whether he liked it. He got this very funny response:
That’ll be a no, then. I don’t blame him about the writing style. But I have convinced myself that I want to read Derrida anyway.
The Cognitive Reflection Test
I’m writing up a blog post on the Cognitive Reflection Test, which I’ve been interested in for a while, so hopefully I’ll get that done and finally close a mental loop that’s been open too long. I’ve finally gone and read some of the literature, and the story that emerges is more complicated than the ‘spontaneous and intuitive thought bad, effortful thought good’ of the original paper.
My favourite thing I found was this (apparently unpublished) ‘extremely rough draft’ revisiting the bat and ball problem. The intuitive-but-wrong answer turns out to be extremely sticky, and the paper is basically a series of increasingly desperate attempts to get people to actually think about the question. After a few more subtle attempts, they resorted to these huge warnings:
These were still only mildly effective, so they gave up and just flat out added “HINT: 10 cents is not the answer.” This worked reasonably well, though there was still a hard core of 13% who persisted in writing down 10 cents.
There’s a connection to close reading here, too. The original paper is in that generic social science style where you define a new metric and then see how it correlates with a bunch of other factors (time preference, risk preference, gender). There’s no discussion of why he picked those specific questions and no attempt to model what was making the intuitive-but-wrong answer appealing.
The later paper is much more interesting to me. It really starts to pick apart the specifics of the bat and ball problem. Is an easier question getting substituted? Can participants reproduce the correct question from memory? I still want more detail, though, on the methods people use when they try to solve the problem. But I’ll get to that in the blog post.
- One thing I discovered when googling around is that the people I’ve always thought of as the New Critics – Empson, Eliot, Richards and co – are maybe more like ‘the people who influenced the New Critics’, and the label itself applies most accurately to the American critics who came along a bit later. So I’ve been reading a classic of ‘actual’ New Criticism, Cleanth Brooks’s The Well Wrought Urn. It’s pretty good – doesn’t feel hugely different to the ‘old’ New Criticism I’ve read before, but it’s nice to see the techniques applied to a wider range of poets, and it’s helped me read a few things with a better eye. The last chapter, ‘The Heresy of Paraphrase’, looks promising – it’s about how it doesn’t make sense to think of poetry to have ‘a meaning’ with some ‘poetic decoration’ pasted over the top. Sense and expression are much more closely tied together than that.
- @ryan_nayr_ on Twitter posted a link to this email by Phil Agre, which is fascinating. Also has a section on Derrida and close reading. That definitely seemed to be the theme this month.
- I found this paper by Leo Corry on exactly how structuralist Bourbaki were. I skimmed this when I was bored at work and it looks interesting, but I should read it properly.
- Less Wrong has mostly got boring again, but this piece on developing scientific intuition was good. Thanks to David Chapman for pointing it out!
I’ll finish that bat and ball blog post, hopefully. Also maybe I’ll actually do some physics. Who knows.
Also, I haven’t said it in a while, so it’s probably worth repeating that I’m very happy to get comments on these newsletters. I am sometimes very slow at replying, but I do reply! Also if you no longer want these, let me know and I’ll take you off the list.