Two types of mathematician reference list

(I posted this on Less Wrong back in April and forgot to cross post here. It’s just the same references I’ve posted before, but it’s worth reading over there for the comments, which are great.)

This is an expansion of a linkdump I made a while ago with examples of mathematicians splitting other mathematicians into two groups, which may be of wider interest in the context of the recent elephant/rider discussion. (Though probably not especially wide interest, so I’m posting this to my personal page.)

The two clusters vary a bit, but there’s some pattern to what goes in each – it tends to be roughly ‘algebra/problem-solving/analysis/logic/step-by-step/precision/explicit’ vs. ‘geometry/theorising/synthesis/intuition/all-at-once/hand-waving/implicit’.

(Edit to add: ‘analysis’ in the first cluster is meant to be analysis as opposed to ‘synthesis’ in the second cluster, i.e. ‘breaking down’ as opposed to ‘building up’. It’s not referring to the mathematical subject of analysis, which is hard to place!)

These seem to have a family resemblance to the S2/S1 division, but there’s a lot lumped under each one that could helpfully be split out, which is where some of the confusion in the comments to the elephant/rider post is probably coming in. (I haven’t read The Elephant in the Brain yet, but from the sound of it that is using something of a different distinction again, which is also adding to the confusion). Sarah Constantin and Owen Shen have both split out some of these distinctions in a more useful way.

I wanted to chuck these into the discussion because: a) it’s a pet topic of mine that I’ll happily shoehorn into anything; b) it shows that a similar split has been present in mathematical folk wisdom for at least a century; c) these are all really good essays by some of the most impressive mathematicians and physicists of the 20th century, and are well worth reading on their own account.

  • The earliest one I know (and one of the best) is Poincare’s ‘Intuition and Logic in Mathematics’ from 1905, which starts:

    “It is impossible to study the works of the great mathematicians, or even those of the lesser, without noticing and distinguishing two opposite tendencies, or rather two entirely different kinds of minds. The one sort are above all preoccupied with logic; to read their works, one is tempted to believe they have advanced only step by step, after the manner of a Vauban who pushes on his trenches against the place besieged, leaving nothing to chance.

    The other sort are guided by intuition and at the first stroke make quick but sometimes precarious conquests, like bold cavalrymen of the advance guard.”


    • Felix Klein’s ‘Elementary Mathematics from an Advanced Standpoint’ in 1908 has ‘Plan A’ (‘the formal theory of equations’) and ‘Plan B’ (‘a fusion of the perception of number with that of space’). He also separates out ‘ordered formal calculation’ into a Plan C.


    • Gian-Carlo Rota made a division into ‘problem solvers and theorizers’ (in ‘Indiscrete Thoughts’, excerpt here).


    • Timothy Gowers makes a very similar division in his ‘Two Cultures of Mathematics’ (discussion and link to pdf here).


    • Vladimir Arnold’s ‘On Teaching Mathematics’ is an incredibly entertaining rant from a partisan of the geometry/intuition side – it’s over-the-top but was 100% what I needed to read when I first found it.


  • Michael Atiyah makes the distinction in ‘What is Geometry?’:

    Broadly speaking I want to suggest that geometry is that part of mathematics in which visual thought is dominant whereas algebra is that part in which sequential thought is dominant. This dichotomy is perhaps better conveyed by the words “insight” versus “rigour” and both play an essential role in real mathematical problems.

    There’s also his famous quote:

    Algebra is the offer made by the devil to the mathematician. The devil says: `I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvellous machine.’

  • Grothendieck was seriously weird, and may not fit well to either category, but I love this quote from Récoltes et semailles too much to not include it:

    Since then I’ve had the chance in the world of mathematics that bid me welcome, to meet quite a number of people, both among my “elders” and among young people in my general age group who were more brilliant, much more ‘gifted’ than I was. I admired the facility with which they picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle – while for myself I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things I had to learn (so I was assured), things I felt incapable of understanding the essentials or following through to the end. Indeed, there was little about me that identified the kind of bright student who wins at prestigious competitions or assimilates almost by sleight of hand, the most forbidding subjects.

    In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still from the perspective or thirty or thirty five years, I can state that their imprint upon the mathematics of our time has not been very profound. They’ve done all things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they’ve remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have to rediscover in themselves that capability which was their birthright, as it was mine: The capacity to be alone.

  • Freeman Dyson calls his groups ‘Birds and Frogs’ (this one’s more physics-focussed).
  • This may be too much partisanship from me for the geometry/implicit cluster, but I think the Mark Kac ‘magician’ quote is also connected to this:

    There are two kinds of geniuses: the ‘ordinary’ and the ‘magicians.’ an ordinary genius is a fellow whom you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what they’ve done, we feel certain that we, too, could have done it. It is different with the magicians… Feynman is a magician of the highest caliber.

    The algebra/explicit cluster is more ‘public’ in some sense, in that its main product is a chain of step-by-step formal reasoning that can be written down and is fairly communicable between people. (This is probably also the main reason that formal education loves it.) The geometry/implicit cluster relies on lots of pieces of hard-to-transfer intuition, and these tend to stay ‘stuck in people’s heads’ even if they write a legitimising chain of reasoning down, so it can look like ‘magic’ on the outside.

  • Finally, I think something similar is at the heart of William Thurston’s debate with Jaffe and Quinn over the necessity of rigour in mathematics – see Thurston’s ‘On proof and progress in mathematics’.

Edit to add: Seo Sanghyeon contributed the following example by email, from Weinberg’s Dreams of a Final Theory:

Theoretical physicists in their most successful work tend to play one of two roles: they are either sages or magicians… It is possible to teach general relativity today by following pretty much the same line of reasoning that Einstein used when he finally wrote up his work in 1915. Then there are magician-physicists, who do not seem to be reasoning at all but who jump over all intermediate steps to a new insight about nature. The authors of physics textbook are usually compelled to redo the work of the magicians so they seem like sages; otherwise no reader would understand the physics.

A braindump on Derrida and close reading

I wrote this for a monthly newsletter I’ve been experimenting with. I feel a bit awkward about publishing this as a post, because it’s very meandering and unpolished and plain weird. But I did manage to cover a lot of ground, in a way that would be be really difficult and time-consuming to do in a normal post, and I quite like the result in some ways.

Also this is a blog, not some formal venue, and if I start fussing too much about quality  I should probably just get over myself.  Thanks to David Chapman for encouraging me to post it anyway.

I wasn’t sure I’d stick to the newsletter format, so I didn’t advertise it much, but it turns out I really like doing it. If you’re interested in getting a monthly email with more of this nonsense, please email me at bossdrucket(at)gmail(dot)com and I’ll add you to the list.  Fair warning: it’s normally a pretty disjointed mix of physics and whatever this braindump is.

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. 

Vladimir Arnold, On teaching mathematics

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 out 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 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 Tasić, which has a lot of 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 don’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 (quoted in the introduction of that book):

‘I feel very bad’, Empson wrote,

not to have answered you for so long, and not to have read those horrible Frenchmen you posted to me. I did go through the first one, Jacques Nerrida [sic], and nosed about in several others, but they seem to me so very disgusting, in a simple moral or social way, that I cannot stomach them. Nerrida does express the idea that, just as people were talking grammar before grammarians arose, so there are other unnoticed regularities in human language and probably in other human systems. This is what I meant by the book title *The Structure of Complex Words*, and it was not an out-of-the-way idea, indeed I may have got it from someone else, but of course it is no use unless you try to present an actual grammar, and actual grammar of the means by which a speaker makes his choice while using the language correctly. This I attempted to supply, and I do not notice that the French ever even try … They use enormously fussy language, always pretending to be plumbing the very depths, and never putting your toe into the water. Please tell me I am wrong.

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.

Book Review: The Reflective Practitioner

In my last two posts I’ve been talking about my experience of thinking through some website design problems. At the same time that I was muddling along with these, I happened to be reading Donald Schön’s The Reflective Practitioner, which is about how people solve problems in professions like architecture, town planning, teaching and management. (I got the recommendation from David Chapman’s ‘Further reading’ list for his Meaningness site.)

This turned out to be surprisingly relevant. Schön is considering ‘real’ professional work, rather than my sort of amateur blundering around, but the domain of web design shares a lot of characteristics with the professions he studied. The problems in these fields are context-dependent and open-ended, resisting any sort of precise theory that applies to all cases. On the other hand, people do manage to solve problems and develop expertise anyway.

Schön argues that this expertise mostly comes through building up familiarity with many individual examples, rather than through application of an overarching theory. He builds up his own argument in the same way, letting his ideas shine through a series of case studies of successful practitioners.

In the one I find most compelling, an established architect, Quist, reviews the work of a student, Petra, who is in the early stages of figuring out a design for an elementary school site. I’m going to follow Schön’s examples-driven approach here and describe this in some detail.

Petra has already made some preliminary sketches and come up with some discoveries of her own. Her first idea for the classrooms was the diagonal line of six rooms in the top right of the picture below. Playing around, she found that ‘they were too small in scale to do much with’, so she ‘changed them to this much more significant layout’, the L shapes in the bottom left.


I’m not sure I can fully explain why the L shapes are ‘more significant’, but I do agree with her assessment. There’s more of a feeling of spaciousness than there was with the six cramped little rectangles, and the pattern is more interesting geometrically and suggests more possibilities for interacting with the geography of the site.

At this point, we already get to see a theme that Schön goes back to repeatedly, the idea of a ‘reflective conversation with the materials’. The designer finds that:

His materials are continually talking back to him, causing him to apprehend unanticipated problems and potentials.

Petra has found a simple example of this. She switched to the L shapes on more-or-less aesthetic grounds, but then she discovers that the new plan ‘relates one to two, three to four, and five to six grades, which is more what I wanted to do educationally anyway.’ The materials have talked back and given her more than she originally put in, which is a sign that she is on to something promising.

After this early success, Petra runs into difficulties. She has learnt the rule that buildings should fit to the contours of the site. Unfortunately the topography of this particular site is really incoherent and nothing she tries will fit into the slope.

Quist advises her to break this rule:

You should begin with a discipline, even if it is arbitrary, because the site is so screwy – you can always break it open later.

Together they work through the implications of the following design:


This kicks off a new round of conversation with the materials.

Quist now proceeds to play out the imposition of the two-dimensional geometry of the L-shaped classrooms upon the “screwy” three-dimensional contours of the slope… The roofs of the classroom will rise five feet above the ground at the next level up, and since five feet is “maximum height for a kid”, kids will be able to be in “nooks”…

A drawing experiment has been conducted and its outcome partially confirms Quist’s way of setting the L-shaped classrooms upon the incoherent slope. Classrooms now flow down the slope in three stages, creating protected spaces “maximum height for a kid” at each level.

In an echo of Petra’s initial experiment, Quist has got back more than he put in. He hasn’t solved the problem in the clean, definitive way you’d solve a mathematical optimisation problem. Many other designs would probably have worked just as well. But the design has ‘talked back’, and his previous experience of working through problems like this has given him the skills to understand what it is saying.

I find the ‘reflective conversation’ idea quite thought-provoking and appealing. It seems to fit well with my limited experience: prototyping my design in a visual environment was an immediate improvement over just writing code, because it enabled this sort of conversation. Instead of planning everything out in advance, I could mess around with the basic elements of the design and ‘apprehend unanticipated problems and potentials’ as they came up.

I don’t find the other examples in the book quite as convincing as this one. Quist is unusually articulate, so the transcripts tell you a lot. Also, architectural plans can be reproduced easily as figures in a book, so you can directly see his solution for yourself, rather than having to take someone’s word for it. With the other practitioners it’s often hard to get a sense of how good their solutions are. (I guess Schön was also somewhat limited by who he could persuade to be involved.)

Alongside the case studies, there is some discussion of the implications for how these professions are normally taught. Some of this is pretty dry, but there are a few interesting topics. The professions he considers often have something like ‘engineering envy’ or ‘medicine envy’: doctors and engineers can borrow from the hard sciences and get definitive answers to some of their questions, so they don’t always have to do this more nebulous ‘reflective conversation’ thing.

It’s tempting for experts in the ‘softer’ professions to try and borrow some of this prestige, leading to the introduction of a lot of theory into the curriculum, even if this theory turns out to be pretty bullshit-heavy and less useful than the kind of detailed reflection on individual cases that Quist is doing. Schön advocates for the reintroduction of practice, pointing out that this can never be fully separated from theory anyway:

If we separate thinking from doing, seeing thought only as a preparation for action and action only as an implementation of thought, then it is easy to believe that when we step into the separate domain of thought we will become lost in an infinite regress of thinking about thinking. But in actual reflection-in-action, as we have seen, doing and thinking are complementary. Doing extends thinking in the tests, moves, and probes of experimental action, and reflection feeds on doing and its results. Each feeds the other, and each sets boundaries for the other. It is the surprising result of action that triggers reflection, and it is the production of a satisfactory move that brings reflection temporarily to a close… Continuity of enquiry entails a continual interweaving of thinking and doing.

For some reason this book has become really popular with education departments, even though teaching only makes up a tiny part of the book. Googling ‘reflective practitioner’ brings up lots of education material, most of which looks cargo-culty and uninspired. Schön’s ideas seem to have mostly been routinised into exactly the kind of useless theory he was trying to go beyond, and I haven’t yet found any good follow-ups in the spirit of the original. It’s a shame, as there’s a lot more to explore here.

Precision and slop together

[This was originally part of the previous post, but is separate enough of an idea that I spun it out into its own short post. As with the previous one, this is in no way my area of expertise and what I have to say here may be very obvious to others.]

‘Inkscape GUI plus raw XML editor’ turns out to be a really interesting combination, and I wish I had access to this general style of working more often. Normally I find I have a choice between the following two annoying options:

  • write code, no inbuilt way to visualise what it does
  • use a visual tool that autogenerates code that you have no control over

Visual tools give you lots of opportunity for solving problems ‘by doing’, moving things around the screen and playing with their properties. I find this style of problem solving intrinsically enjoyable, and finding a clever solution ‘by doing’ is extremely satisfying. (I gave a couple of examples in the previous post.)

Visual tools also tend to ‘offer up more of the world to you’, in some sense. They make it easy to enter a state of just messing around with whatever affordances the program gives you, without having to think about whatever symbolic representation is currently instantiating it. So you get a more open style of thinking without being tied to the representation.

A screen's worth of 'just mucking around'

On the other hand, of course, visual tools that don’t do what you want are the most frustrating thing. You have no idea what the underlying model is, so you just have to do things and guess, and the tool is normally too stupid to do anything sensible with your guesses. Moving an image in Microsoft Word and watching it trigger a cascade of other idiotic changes would be a particularly irritating example.

You also miss out on the good parts of symbolic tools. Precision is easier with symbolic tools, for example. The UI normally has some concessions to precision, letting you snap a rotation to exactly 45 degrees or 90 degrees, for example. But sometimes you just want exactly 123 degrees, and not 122 degrees or 124 degrees, and the UI is no help with that.

Most importantly, symbolic tools are much better for anything you’re going to automate or compose with other tools. (I don’t really understand how much this is inherent in the problem, and how much it’s just a defect of our current tools.) I knew that I was eventually going to move to coding up something that would dynamically generate random shapes, so I needed to understand the handles that the program would be manipulating. Pure visual mucking around was not an option.

Unusually, though, I didn’t have to choose between visual immersion and symbolic manipulation, at least at the prototyping stage. This was a rare example of a domain where I could use a mix of both. On the symbolic side, I understood the underlying model (paths and transformations for scalable vector graphics) reasonably well, and wasn’t trying to do anything outlandish that it would struggle to cope with. At the same time, it was also an inherently visual problem involving a load of shapes that could be moved and edited and transformed with a GUI tool. So I could switch between open-ended playing and structural manipulation whenever I wanted. I wish I got to do this more often!

Practical Design for the Idiot Physicist

I’ve recently started getting a personal website together for maths and physics notes, somewhere that I can dump work in progress and half-baked scraps of intuition for various concepts.

For no good reason, I decided that this should also incorporate a completely irrelevant programming idea I’d been playing around with, where I dynamically generate kaleidoscope patterns. Like this:

Kaleidoscope pattern

(There’s a click-to-change version over on the website itself.)

I’d been working on this on and off for some time. It’s obviously not the most important problem I could be thinking about, but there was something about the idea that appealed to me. I originally thought that this would be a programming project, and that the problems I would need to solve were mostly programming ones. The open questions I had before I started were things like:

  • how would I represent the data I needed to describe the small shapes?
  • how would I generate them uniformly within the big triangles?
  • how would I make sure they didn’t overlap the boundaries of the big triangles?

I would say that in the end these sort of questions took up about 10% of my time on the project. Generally they were easy to solve, and generally it was enough to solve them in the simplest, dumbest possible way (e.g. by generating too many shapes, and then discarding the ones that did overlap the boundaries). That side of the project is not very interesting to describe!

Maybe another 30% was the inevitable annoying crap that comes along with web programming: fixing bugs and dodgy layouts and dealing with weird browser inconsistencies.

What surprised me, though, was the amount of time I spent on visual design questions. Compared to the programming questions, these were actually quite deep and interesting. I’d accidentally given myself a design project.

In this post I’m going to describe some of my attempts to solve the various problems that cropped up. I don’t know anything much about design, so the ‘discoveries’ I list below are pretty obvious in retrospect. I’m writing about them anyway because they were new to me, and I found them interesting.

There’s also a strong connection to some wider topics I’m exploring. I’m interested in understanding the kind of techniques people use to make progress on open-ended, vaguely defined sort of projects, and how they tell whether they are succeeding or not. I’ve been reading Donald Schön’s The Reflective Practitioner, which is about exactly this question, and he uses design (in this case architectural design) as a major case study. I’ll put up a review of the book in a week or so, which should be a good complement to this post.

I’m going to go for a fairly lazy ‘list of N things’ style format for this one, with the headings summarising my various ‘discoveries’. I think this fits the topic quite well: I’m not trying to make any deep theoretical point here, and am more interested in just pointing at a bunch of illustrative examples.

Get the models out of your head

I actually started this same project a couple of years ago, but didn’t get very far. I’d immediately tried coding up the problem, spent a while looking at some ugly triangles on a screen, got frustrated quickly with a minor bug and gave up.

I”m not sure what made me return to the problem, but this time I had the much more sensible idea of prototyping the design in Inkscape before trying to code anything up. This turned out to make a huge difference. First I tried drawing what I thought I wanted in Inkscape, starting with the initial scene that I’d reflect and translate to get the full image:

Bad first attempt at initial scene

It looked really crap. No wonder I’d hated staring at those ugly triangles. I tried to work out what was missing compared to a real kaleidoscope, and progressively tweaked it to get the following:Better attempt at initial scene
Suddenly it looked enormously better. In retrospect, making the shapes translucent was absolutely vital: that’s how you get all the interesting colour mixes. It was also necessary to make the shapes larger, or they just looked like they’d been scattered around the large triangle in a sad sort of way, rather than filling up the scene.

(My other change was to concentrate the shapes at the bottom of the triangle to imitate the effect of gravity. That turned out to be pretty unimportant: once I got round to coding it up I started by distributing them uniformly, and that looked fine to me, so I never bothered to do anything cleverer.)

Fast visual feedback makes all the difference

Once I knew what this central part looked like, I was ready to generate the full image. I could have done this by getting a pen and paper out and figuring out all the translations, rotations and reflections I’d need. But because I was already prototyping in Inkscape, I could ‘just play’ instead, and work it out as I went.

I quickly figured out how to generate one hexagon’s worth of pattern, by combining the following two sets of three rotated triangles:

Rotated and reflected triangles

Once I had that I was pretty much done. The rest of the pattern just consisted of translating this one hexagon a bunch of times:

Tiling hexagons

I generated that picture using the do-it-yourself method of just copying the hexagons and moving them round the page. I was still just playing around, and didn’t want to be dragged out of that mode of thinking to explicitly calculate anything.

I was really happy with the result. Having even this crude version of what I wanted in front of me immediately made me a lot more excited about the project. I could see that it actually looked pretty good, even with the low level of effort I’d put in so far. This sort of motivating visual feedback is what had been missing from my previous attempt where I’d jumped straight into programming.

You can often solve the same problem ‘by thinking’ or ‘by doing’

I gave a simple example of this in my last post. You can solve the problem of checking that the large square below has a side length of 16 by counting the small squares. Instead of putting in this vast level of mental effort, I instead added the four-by-four squares around it as a guide:

16 by 16 square, with 4 by 4 squares around it as a guide

Four is within subitizing range, and sixteen is well outside of mine, so this converts a problem where I have to push through a small amount of cognitive strain into a problem where I can just think ‘four four four four, yep that’s correct’ and be done with it. (‘Four fours are sixteen’ also seems to ‘just pop into my head’ as a fairly primitive action without any strain.)

Now admittedly this not a difficult problem, and solving in ‘by thinking’ would probably have been the right choice – it would have been quicker than drawing those extra squares and then deleting them again. I just have a chronic need to solve ‘by doing’ wherever I can instead.

Sometimes this actually works out quite well. In an earlier iteration of the design I needed to create a translucent overlay to fit over a geometric shape with a fairly complicated border (part of it is shown as the pinkish red shape in the image below). I could have done this by calculating the coordinates of the edges – this would have been completely doable but rather fiddly and error prone.

Drawing a line around the rough border of the shape

Instead, I ‘made Inkscape think about the problem’ so that I didn’t have to. I opened up the file containing the shape I wanted to make an overlay of, and drew a rough bodge job of the outline I needed by hand, with approximate coordinates (this is the black line in the image). Then I opened up Inkscape’s XML editor containing the raw markup, and put in the right numbers. This was now very easy, because I knew from previous experience playing around that the correct numbers should all be multiples of five. So if the number in the editor for my bodged version was 128.8763, say, I knew that the correct number would actually be 130. The need to think had been eliminated.

For me, at least, this was definitely quicker than calculating. (Of course, that relied on me knowing Inkscape well enough to ‘just know’ how to carry out the task without breaking immersion – if I didn’t have that and had to look up all the details of how to draw the outline and open the XML editor, it would have been quicker to calculate the numbers.)

Go back to the phenomena

Once I got the rough idea working, I had to start thinking about how I was actually going to use it on the page. For a while I got stuck on a bunch of ideas that were all kind of unsatisfying in the same way, but I couldn’t figure out how to do anything better. Everything I tried involved a geometric shape that was kind of marooned uselessly on a coloured background, like the example below:

Bad initial design for page

All I seemed to produce was endless iterations on this same bad idea.

What finally broke me out of it was doing an image search for photos of actual kaleidoscopes. One of the things I noticed was that the outer rings of the pattern are dimmer, as the number of reflections increases:

Actual kaleidoscopes


That gave me the idea of having a bright central hexagon, and then altering the opacity further out, and filling the whole screen with hexagons. This was an immediate step-change sort of improvement. Every design I’d tried before looked rubbish, and every design I tried afterwards looked at least reasonably good:

Improved design for page

Which leads to my final point…

There are much better ideas available – if you can get to them

I find the kind of situation above really interesting, where I get stuck in a local pocket of ‘crap design space’ and can’t see a way out. When I do find a way out of it, it’s immediately noticeable in a very direct way: I straightforwardly perceive it as ‘just being better’ without necessarily being able to articulate a good argument for why.

I still don’t have a good explicit argument for why the second design is ‘just better’, but looking at actual kaleidoscopes definitely helped. This was pretty similar to what I found back when I was playing with the individual shapes – adding the translucency of actual kaleidoscope pieces made all the difference.

I don’t have any great insight in how to escape ‘crap design space’ – the problem is pretty much equivalent to the problem of ‘how to have good ideas’, which I definitely don’t have a general solution to! But maybe going back to the original inspiration is one good strategy.

20 Fundamentals

I was inspired by John Nerst’s recent post to make a list of my own fundamental background assumptions. What I ended up producing was a bit of a odd mixed bag of disparate stuff. Some are something like factual beliefs, some of them are more like underlying emotional attitudes and dispositions to act in various ways.

I’m not trying to ‘hit bedrock’ in any sense, I realise that’s not a sensible goal. I’m just trying to fish out a few things that are fundamental enough to cause obvious differences in background with other people. John Nerst put it well on Twitter:

It’s not true that beliefs are derived from fundamental axioms, but nor is it true that they’re a bean bag where nothing is downstream from everything else.

I’ve mainly gone for assumptions where I tend to differ with the people I to hang around with online and in person, which skews heavily towards the physics/maths/programming crowd. This means there’s a pretty strong ‘narcissism of small differences’ effect going on here, and if I actually had to spend a lot of time with normal people I’d probably run screaming back to to STEM nerd land pretty fast and stop caring about these minor nitpicks.

Also I only came up with twenty, not thirty, because I am lazy.

  1. I’m really resistant to having to ‘actually think about things’, in the sense of applying any sort of mental effort that feels temporarily unpleasant. The more I introspect as I go about problem solving, the more I notice this. For example, I was mucking around in Inkscape recently and wanted to check that a square was 16 units long, and I caught myself producing the following image:


    Apparently counting to 16 was an unacceptable level of cognitive strain, so to avoid it I made the two 4 by 4 squares (small enough to immediately see their size) and then arranged them in a pattern that made the length of the big square obvious. This was slower but didn’t feel like work at any point. No thinking required!

  2. This must have a whole bunch of downstream effects, but an obvious one is a weakness for ‘intuitive’, flash-of-insight-based demonstrations, mixed with a corresponding laziness about actually doing the work to get them. (Slowly improving this.)

  3. I picked up some Bad Ideas From Dead Germans at an impressionable age (mostly from Kant). I think this was mostly a good thing, as it saved me from some Bad Ideas From Dead Positivists that physics people often succumb to.

  4. I didn’t read much phenomenology as such, but there’s some mood in the spirit of this Whitehead quote that always came naturally to me:

    For natural philosophy everything perceived is in nature. We may not pick and choose. For us the red glow of the sunset should be as much part of nature as are the molecules and electric waves by which men of science would explain the phenomenon.

    By this I mean some kind of vague understanding that we need to think about perceptual questions as well as ‘physics stuff’. Lots of hours as an undergrad on Wikipedia spent reading about human colour perception and lifeworlds and mantis shrimp eyes and so on.

  5. One weird place where this came out: in my first year of university maths I had those intro analysis classes where you prove a lot of boring facts about open sets and closed sets. I just got frustrated, because it seemed to be taught in the same ‘here are some facts about the world’ style that, say, classical mechanics was taught in, but I never managed to convince myself that the difference related to something ‘out in the world’ rather than some deficiency of our cognitive apparatus. ‘I’m sure this would make a good course in the psychology department, but why do I have to learn it?’

    This isn’t just Bad Ideas From Dead Germans, because I had it before I read Kant.

  6. Same thing for the interminable arguments in physics about whether reality is ‘really’ continuous or discrete at a fundamental level. I still don’t see the value in putting that distinction out in the physical world – surely that’s some sort of weird cognitive bug, right?

  7. I think after hashing this out for a while people have settled on ‘decoupling’ vs ‘contextualising’ as the two labels. Anyway it’s probably apparent that I have more time for the contextualising side than a lot of STEM people.

  8. Outside of dead Germans, 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.

  9. I don’t understand what the appeal of competitive games is supposed to be. Like basically all of them – sports, video games, board games, whatever. Not sure exactly what effects this has on the rest of my thinking, but this seems to be a pretty fundamental normal-human thing that I’m missing, so it must have plenty.

  10. I always get interested in specific examples first, and then work outwards to theory.

  11. My most characteristic type of confusion is not understanding how the thing I’m supposed to be learning about ‘grounds out’ in any sort of experience. ‘That’s a nice chain of symbols you’ve written out there. What does it relate to in the world again?’

  12. I have never in my life expected moral philosophy to have some formal foundation and after a lot of trying I still don’t understand why this is appealing to other people. Humans are an evolved mess and I don’t see why you’d expect a clean abstract framework to ever drop out from that.

  13. Philosophy of mathematics is another subject where I mostly just think ‘um, you what?’ when I try to read it. In fact it has exactly the same subjective flavour to me as moral philosophy. Platonism feels bad the same way virtue ethics feels bad. Formalism feels bad the same way deontology feels bad. Logicism feels bad the same way consequentialism feels bad. (Is this just me?)

  14. I’ve never made any sense out of the idea of an objective flow of time and have thought in terms of a ‘block universe’ picture for as long as I’ve bothered to think about it.

  15. If I don’t much like any of the options available for a given open philosophical or scientific question, I tend to just mentally tag it with ‘none of the above, can I have something better please’. I don’t have the consistency obsession thing where you decide to bite one unappealing bullet or another from the existing options, so that at least you have an opinion.

  16. This probably comes out of my deeper conviction that I’m missing a whole lot of important and fundamental ideas on the level of calculus and evolution, simply on account of nobody having thought of them yet. My default orientation seems to be ‘we don’t know anything about anything’ rather than ‘we’re mostly there but missing a few of the pieces’. This produces a kind of cheerful crackpot optimism, as there is so much to learn.

  17. This list is noticeably lacking in any real opinions on politics and ethics and society and other people stuff. I just don’t have many opinions and don’t like thinking about people stuff very much. That probably doesn’t say anything good about me, but there we are.

  18. I’m also really weak on economics and finance. I especially don’t know how to do that economist/game theoretic thing where you think in terms of what incentives people have. (Maybe this is one place where ‘I don’t understand competitive games’ comes in.)

  19. I’m OK with vagueness. I’m happy to make a vague sloppy statement that should at least cover the target, and maybe try and sharpen it later. I prefer this to the ‘strong opinions, weakly held’ alternative where you chuck a load of precise-but-wrong statements at the target and keep missing. A lot of people will only play this second game, and dismiss the vague-sloppy-statement one as ‘just being bad at thinking’, and I get frustrated.

  20. Not happy about this one, but over time this frustration led me to seriously go off styles of writing that put a strong emphasis on rigour and precision, especially the distinctive dialects you find in pure maths and analytic philosophy. I remember when I was 18 or so and encountered both of these for the first time I was fascinated, because I’d never seen anyone write so clearly before. Later on I got sick of the way that this style tips so easily into pedantry over contextless trivialities (from my perspective anyway). It actually has a lot of good points, though, and it would be nice to be able to appreciate it again.

The cognitive decoupling elite

[Taking something speculative, running with it, piling on some more speculative stuff]

In an interesting post summarising her exploration of the literature on rational thinking, Sarah Constantin introduces the idea of a ‘cognitive decoupling elite’:

Stanovich talks about “cognitive decoupling”, the ability to block out context and experiential knowledge and just follow formal rules, as a main component of both performance on intelligence tests and performance on the cognitive bias tests that correlate with intelligence. Cognitive decoupling is the opposite of holistic thinking. It’s the ability to separate, to view things in the abstract, to play devil’s advocate.

… Speculatively, we might imagine that there is a “cognitive decoupling elite” of smart people who are good at probabilistic reasoning and score high on the cognitive reflection test and the IQ-correlated cognitive bias tests.

It’s certainly very plausible to me that something like this exists as a distinct personality cluster. It seems to be one of the features of my own favourite classification pattern, for example, as a component of the ‘algebra/systematising/step-by-step/explicit’ side (not the whole thing, though). For this post I’m just going to take it as given for now that ‘cognitive decoupling’ is a real thing that people can be more or less good at, build on that assumption and see what I get.

It’s been a good few decades for cognitive decoupling, from an employment point of view at least. Maybe a good couple of centuries, taking the long view. But in particular the rise of automation by software has created an enormous wealth of opportunities for people who can abstract out the formal symbolic exoskeleton of a process to the point where they can make a computer do it. There’s also plenty of work in the interstices between systems, defining interfaces and making sure data is clean enough to process, the kind of jobs Venkatesh Rao memorably described as ‘intestinal flora in the body of technology’.

I personally have a complicated, conflicted relationship with cognitive decoupling. Well, to be honest, sometimes a downright petty and resentful relationship. I’m not a true member of the elite myself, despite having all the right surface qualifications: undergrad maths degree, PhD in physics, working as a programmer. Maybe cognitive decoupling precariat, at a push. Despite making my living and the majority of my friends in cognitive-decoupling-heavy domains, I mostly find step-by-step, decontextualised reasoning difficult and unpleasant at a fundamental, maybe even perceptual level.

The clearest way of explaining this, for those who don’t already have a gut understanding what I mean, might be to describe something like ‘the opposite of cognitive decoupling’ (the cognitive strong coupling regime?). I had this vague memory that Sylvia Plath’s character Esther in The Bell Jar voiced something in the area of what I wanted, in a description of a hated physics class that had stuck in my mind as somehow connected to my own experience. I reread the passage and was surprised to find that it wasn’t just vaguely what I wanted, it was exactly what I wanted, a precise and detailed account of what just feels wrong about cognitive decoupling:

Botany was fine, because I loved cutting up leaves and putting them under the microscope and drawing diagrams of bread mould and the odd, heart-shaped leaf in the sex cycle of the fern, it seemed so real to me.

The day I went in to physics class it was death.

A short dark man with a high, lisping voice, named Mr Manzi, stood in front of the class in a tight blue suit holding a little wooden ball. He put the ball on a steep grooved slide and let it run down to the bottom. Then he started talking about let a equal acceleration and let t equal time and suddenly he was scribbling letters and numbers and equals signs all over the blackboard and my mind went dead.

… I may have made a straight A in physics, but I was panic-struck. Physics made me sick the whole time I learned it. What I couldn’t stand was this shrinking everything into letters and numbers. Instead of leaf shapes and enlarged diagrams of the hole the leaves breathe through and fascinating words like carotene and xanthophyll on the blackboard, there were these hideous, cramped, scorpion-lettered formulas in Mr Manzi’s special red chalk.

I knew chemistry would be worse, because I’d seen a big chart of the ninety-odd elements hung up in the chemistry lab, and all the perfectly good words like gold and silver and cobalt and aluminium were shortened to ugly abbreviations with different decimal numbers after them. If I had to strain my brain with any more of that stuff I would go mad. I would fail outright. It was only by a horrible effort of will that I had dragged myself through the first half of the year.

This is a much, much stronger reaction than the one I have, but I absolutely recognise this emotional state. The botany classes ground out in vivid, concrete experience: ferns, leaf shapes, bread mould. There’s an associated technical vocabulary – carotene, xanthophyll – but even these words are embedded in a rich web of sound associations and tangible meanings.

In the physics and chemistry classes, by contrast, the symbols are seemingly arbitrary, chosen on pure pragmatic grounds and interchangeable for any other random symbol. (I say ‘seemingly’ arbitrary because of course if you continue in physics you do build up a rich web of associations with x and t and the rest of them. Esther doesn’t know this, though.) The important content of the lecture is instead the structural relationships between the different symbols, and the ways of transforming one to another by formal rules. Pure cognitive decoupling.

There is a tangible physical object, the ‘little wooden ball’ (better than I got in my university mechanics lectures!), but that object has been chosen for its utter lack of vivid distinguishing features, its ability to stand in as a prototype of the whole abstract class of featureless spheres rolling down featureless inclined planes.

The lecturer’s suit is a bit crap, too. Nothing at all about this situation has been designed for a fulfilling, interconnected aesthetic experience.

I think it’s fairly obvious from the passage, but it seems to be worth pointing out anyway: ‘strong cognitive coupling’ doesn’t just equate to stupidity or lack of cognitive flexibility. For one thing, Esther gets an A anyway. For another, she’s able to give very perceptive, detailed descriptions of subtle features of her experience, always hugging close to the specificity of raw experience (‘the odd, heart-shaped leaf in the sex cycle of the fern’) rather than generic concepts that can be overlaid on to many observations (‘ah ok, it’s another sphere on an inclined plane’).

Strong coupling in this sense is like being a kind of sensitive antenna for your environment, learning to read as much meaning out of it as possible, but without necessarily being able to explain what you learn in a structured, explicit logical argument. I’d expect it to be correlated with high sensitivity to nonverbal cues, implicit tone, tacit understanding, all the kind of stuff that poets are stereotypically good at and nerds are stereotypically bad at.

I don’t normally talk about my own dislike of cognitive decoupling. It’s way too easy to sound unbearably precious and snowflakey, ‘oh my tastes are far too sophisticated to bear contact with this clunky nerd stuff’. In practice I just shut up and try to get on with it as far as I can. Organised systems are what keep the world functioning, and whining about them is mostly pointless. Also, I’m nowhere near the extreme end of this spectrum anyway, and can cope most of the time.

When I was studying maths and physics I didn’t even have to worry about this for the most part. You can compensate fairly well for a lack of ability in decoupled formal reasoning by just understanding the domain. This is very manageable, particularly if you pick your field well, because the same few ideas (calculus, linear algebra, the harmonic oscillator) crop up again and again and again and have very tangible physical interpretations, so there’s always something concrete to ground out the symbols with.

(This wasn’t a conscious strategy because I had no idea what was happening at the time. I just knew since I was a kid that I was ‘good at maths’ apart from some inexplicable occasions where I was instead very bad at maths, and just tried to steer towards the ‘good at maths’ bits as much as possible. This is my attempt to finally make some sense out of it.)

It’s been more of an issue since. Most STEM-type jobs outside of academia are pretty hard going, because the main objective is to get the job done, and you often don’t have time to build up a good picture of the overall domain, so you’re more reliant on the step-by-step systematic thing. A particularly annoying example would be something like implementing the business logic for a large enterprise CRUD app where you have no particularly strong domain knowledge. Maybe there’s a tax of 7% on twelve widgets, or maybe it’s a tax of 11.5% on five hundred widgets; either way, what it means for you personally is that you’re going to chuck some decontextualised variables around according to the rules defined in some document, with no vivid sensory understanding of exactly what these widgets look like and why they’re being taxed. There is basically no way that Esther in The Bell Jar could keep her sanity in a job like that, even if she has the basic cognitive capacity to do it; absolutely everything about it is viscerally wrong wrong wrong.

My current job is rather close to this end of the spectrum, and it’s a strain to work in this way, in a way many other colleagues don’t seem to experience. This is where the ‘downright petty and resentful’ bit comes in. I’d like it if there was a bit more acknowledgment from people who find cognitive decoupling easy and natural that it is in fact a difficult mode of thought for many of us, and one that most modern jobs dump us into far more than we’d like.

From the other side, I’m sure that the decouplers would also appreciate it if we stopped chucking around words like ‘inhuman’ and ‘robotic’, and did a bit less hating on decontextualised systems that keep the world running, even if they feel bad from the inside. I think some of this stuff is coming from a similar emotional place to my own petty resentment, but it’s not at all helpful for any actual communication between the sides.

I’m seeing a few encouraging examples of the kind of communication I would like. Sarah Constantin looks to be in something like a symmetric position to me on the other side of the bridge, with her first loyalty to explicit systematic reasoning, but enough genuine appreciation to be able to write thoughtful explorations of the other side:

I think it’s much better to try to make the implicit explicit, to bring cultural dynamics into the light and understand how they work, rather than to hide from them.

David Chapman has started to write about how the context-heavy sort of learning (‘reasonableness’) works, aimed at something like the cognitive decoupling elite:

In summary, reasonableness works because it is context-dependent, purpose-laden, interactive, and tacit. The ways it uses language are effective for exactly the reason rationality considers ordinary language defective: nebulosity.

And then there’s all the wonderful work by people like Bret Victor, who are working to open up subjects like maths and programming for people like me who need to see things if we are going to have a hope of doing them.

I hope this post at least manages to convey something of the flavour of strong cognitive coupling to those who find decoupling easy. So if the thing I’m trying to point at still looks unclear, please let me know in the comments!

Imagination in a terrible strait-jacket

I enjoyed alkjash’s recent Babble and Prune posts on Less Wrong, and it reminded me of a favourite quote of mine, Feynman’s description of science in The Character of Physical Law:

What we need is imagination, but imagination in a terrible strait-jacket. We have to find a new view of the world that has to agree with everything that is known, but disagree in its predictions somewhere, otherwise it is not interesting.

Imagination here corresponds quite well to Babbling, and the strait-jacket is the Pruning you do afterwards to see if it actually makes any sense.

For my tastes at least, early Less Wrong was generally too focussed on building out the strait-jacket to remember to put the imagination in it. An unfair stereotype would be something like this:

‘I’ve been working on being better calibrated, and I put error bars on all my time estimates to take the planning fallacy into account, and I’ve rearranged my desk more logically, and I’ve developed a really good system to keep track of all the tasks I do and rank them in terms of priority… hang on, why haven’t I had any good ideas??’

I’m poking fun here, but I really shouldn’t, because I have the opposite problem. I tend to go wrong in this sort of way:

‘I’ve cleared out my schedule so I can Think Important Thoughts, and I’ve got that vague idea about that toy model that it would be good to flesh out some time, and I can sort of see how Topic X and Topic Y might be connected if you kind of squint the right way, and it might be worth developing that a bit further, but like I wouldn’t want to force anything, Inspiration Is Mysterious And Shouldn’t Be Rushed… hang on, why have I been reading crap on the internet for the last five days??’

I think this trap is more common among noob writers and artists than noob scientists and programmers, but I managed to fall into it anyway despite studying maths and physics. (I’ve always relied heavily on intuition in both, and that takes you in a very different direction to someone who leans more on formal reasoning.) I’m quite a late convert to systems and planning and organisation, and now I finally get the point I’m fascinated by them and find them extremely useful.

One particular way I tend to fail is that my over-reliance on intuition leads me to think too highly of any old random thoughts that come into my head. And I’ve now come to the (in retrospect obvious) conclusion that a lot of them are transitory and really just plain stupid, and not worth listening to.

As a simple example, I’ve trained myself to get up straight away when the alarm goes off, and every morning my brain fabricates a bullshit explanation for why today is special and actually I can stay in bed, and it’s quite compelling for half a minute or so. I’ve got things set up so I can ignore it and keep doing things, though, and pretty quickly it just goes away and I never wish that I’d listened to it.

On the other hand, I wouldn’t want to tighten things up so much that I completely stopped having the random stream of bullshit thoughts, because that’s where the good ideas bubble up from too. For now I’m going with the following rule of thumb for resolving the tension:

Thoughts can be herded and corralled by systems, and fed and dammed and diverted by them, but don’t take well to being manipulated individually by systems.

So when I get up, for example, I don’t have a system in place where I try to directly engage with the bullshit explanation du jour and come up with clever countertheories for why I actually shouldn’t go back to bed. I just follow a series of habitual getting-up steps, and then after a few minutes my thoughts are diverted to a more useful track, and then I get on with my day.

A more interesting example is the common writers’ strategy of having a set routine (there’s a whole website devoted to these). Maybe they work at the same time each day, or always work in the same place. This is a system, but it’s not a system that dictates the actual content of the writing directly. You just sit and write, and sometimes it’s good, and sometimes it’s awful, and on rare occasions it’s genuinely inspired, and if you keep plugging on those rare occasions hopefully become more frequent. I do something similar with making time to learn physics now and it works nicely.

This post is also a small application of the rule itself! I was on an internet diet for a couple of months, and was expecting to generate a few blog post drafts in that time, and was surprised that basically nothing came out in the absence of my usual internet immersion. I thought writing had finally become a pretty freestanding habit for me, but actually it’s still more fragile and tied to a social context that I expected. So this is a deliberate attempt to get the writing flywheel spun up again with something short and straightforward.

Seeing further

In November and December I’m going to shut up talking nonsense here, and also have a break from reading blogs, Twitter, and most of my usual other internet stuff. I like blogs and the internet, but being immersed in the same things all the time means I end up having the same thoughts all the time, and sometimes it is good to have some different ones. I’ve seen a big improvement this year from not being on tumblr, which mostly immerses you in other people’s thoughts, but stewing in the same vat of my own ones gets a bit old too. Also I have a bunch of stuff that I’ve been procrastinating on, so I should probably go do that.

I’ve pretty much accepted that I am in fact writing a real blog, and not some throwaway thing that I might just chuck tomorrow. That was psychologically useful in getting me started, but now writing just seems to appear whether I want it to or not. So I might do some reworking next year to make it look a bit more like a real blog and less like a bucket of random dross.

The topic of the blog has spread outwards a bit recently (so far as there is a topic — I haven’t made any deliberate effort to enforce one), but there does seem to be a clear thread connecting my mathematical intuition posts with my more recent ramblings.

One of the key things I seem to be interested in exploring in both is the process of being able to ‘see’ more, in being able to read new meaning into your surroundings. I’ve looked at examples in a couple of previous posts. One is the ‘prime factors’ proof of the irrationality of the square root of two, where you learn to directly ‘see’ the equation \frac{p^2}{q^2} = 2 as wrong (both p^2 and q^2 have an even number of each prime factor, so dividing one by the other is never going to give a 2 on its own).

Another is the process of noticing interesting optical phenomena after reading Light and Colour in the Outdoors. I see a lot of sun dogs, rainbows and 22° halos that I’d have missed before. (No circumzenithal arcs yet though! Maybe I’m not looking up enough.)

They are sort of different: the first one feels more directly perceptual — I actually see the equation differently — while the second feels like more of a disposition to scan my surroundings for certain things that I’d previously have missed. I’m currently doing too much lumping, and will want to distinguish cases more carefully later. But there seems to be some link there.

I’m interested in the theoretical side of how this process of seeing more might work, but currently I’d mostly just like to track down natural histories of what this feels like to people from the inside. This sort of thing could be distributed all over the place — fiction? the deliberate practice literature? autobiographies of people with unusual levels of expertise? — so it’s not easy to search for; if you have any leads please pass them on.

I hadn’t really thought to explicitly link this to philosophy of science, even though I’d actually read some of the relevant things, but now David Chapman is pointing it out in his eggplant book it’s pretty obvious that that’s somewhere I should look. There is a strong link with Kuhn’s scientific revolutions, in which scientists learn to see their subject within a new paradigm, and I should investigate more. I used to hang around with some of the philosophy of science students as an undergrad and liked the subject, so that could be fun anyway.

We ended up discussing a specific case study on Twitter (Storify link to the whole conversation here): ‘The Work of a Discovering Science Construed with Materials from the Optically Discovered Pulsar’, by Harold Garfinkel, Michael Lynch and Eric Livingston. This is an account based on transcripts from the first observations of the Crab Pulsar in the optical part of the spectrum. There’s a transition over the course of the night from talking about the newly discovered pulse in instrumental terms, as a reading on the screen…

In the previous excerpts projects make of the optically discovered pulsar a radically contingent practical object. The parties formulate matters of ‘belief’ and ‘announcement’ to be premature at this point.

…to ‘locking on’ to the pulsar as a defined object:

By contrast, the parties in the excerpts below discuss the optically discovered pulsar as something-in-hand, available for further elaboration and analysis, and essentially finished. … Instead of being an ‘object-not-yet’, it is now referenced as a perspectival object with yet to be ‘found’ and measured properties of luminosity, pulse amplitude, exact frequency, and exact location.

This is high-concept, big-question seeing further!

I’m currently more interested in the low-concept, small-question stuff, though, like my two examples above. Or maybe I want to consider even duller and more mundane situations than those — I’ve done a lot of really low-level temporary administrative jobs, data entry and sorting the post and the like, and they always give me some ability to see further in some domain, even if ‘seeing further’ tends to consist of being able to rapidly identify the right reference code on a cover letter, or something else equally not thrilling. The point is that a cover letter looks very different once you’ve learned do the thing, because the reference code ‘jumps out’ at you. There’s some sort of family resemblance to a big fancy Kuhnian paradigm shift.

The small questions are lacking somewhat in grandeur and impressiveness, but make it up in sheer number. Breakthroughs like the pulsar observation don’t come along very often, and full-scale scientific revolutions are even rarer, but millions of people see further in their boring office jobs every day. There’s much more opportunity to study how it works!

Followup: messy confusions

My last post was a long enthusiastic ramble through a lot of topics that have been in my head recently. After I finished writing it, I had an interesting experience. I’d temporarily got all the enthusiasm out of my system and was sick of the sight of the post, so that what was left was all the vague confusions and nagging doubts that were sitting below it. This post is where I explore those, instead. (Though now I’m getting excited again… the cycle repeats.)

Nothing in here really invalidates the previous post, so far as I can tell. I’ve just reread it and I’m actually pretty happy with it. It’s just… more mess. Things that don’t fit neatly into the story I told last time, or things that I know I’m still missing background in.

I haven’t bothered to even try and impose any structure on this post, it’s just a list of confusions in more-or-less random order. I also haven’t made much effort to unpack my thoughts carefully, so I don’t know how comprehensible all of this is.

I probably do have to read Heidegger or something

My background in reading philosophy is, more or less, ‘some analytic philosophers plus Kant’. I’ve been aware for a long time now that that just isn’t enough to cover the space, and that I’m missing a good sense of what the options even are.

I’m slowly coming round to the idea that I should fix that, even though it’s going to involve reading great lumps of text in various annoying writing styles I don’t understand. I now have a copy of Dreyfus’s Being-in-the-World, which isn’t exactly easy going in itself, but is still better than actually reading Heidegger.

Also, I went to the library at UWE Bristol, my nearest university, the other weekend, and someone there must be a big Merleau-Ponty fan. It looks like I can get all the phenomenology I can eat reasonably easily, if that’s what I decide I want to read.

One thing: worse than two things

Still, reading back what I wrote last time about mess, I think that even at my current level of understanding I did manage to extricate myself before I made a complete fool of myself:

There is still some kind of principled distinction here, some way to separate the two. The territory corresponds pretty well to the bottom-up bit, and is characterised by the elements of experience that respond in unpredictable, autonomous ways when we investigate them. There’s no way to know a priori that my mess is going to consist of exercise books, a paper tetrahedron and a kitten notepad. You have to, like, go and look at it.

The map corresponds better to the top-down bit, the ordering principles we are trying to impose. These are brought into play by the specific objects we’re looking at, but have more consistency across environments – there are many other things that we would characterise as mess.

Still, we’ve come a long way from the neat picture of the Less Wrong wiki quote. The world outside the head and the model inside it are getting pretty mixed up. For one thing, describing the remaining ‘things in the head’ as a ‘model’ doesn’t fit too well. We’re not building up a detailed internal representation of the mess. For another, we directly perceive mess as mess. In some sense we’re getting the world ‘all at once’, without the top-down and bottom-up parts helpfully separated.

The main reason I was talking about not having enough philosophical background to cover the space is that I’ve no idea yet how thoroughgoing I want to be in this direction of mushing everything up together. There is this principled distinction between all the autonomous uncontrollable stuff that the outside world is throwing at you, and the stuff inside your head. Making a completely sharp distinction between them is silly, but I still want to say that that it’s a lot less silly than ‘all is One’ silliness. Two things really is better than one thing.

Sarah Constantin went over similar ground recently:

The basic, boring fact, usually too obvious to state, is that most of your behavior is proximately caused by your brain (except for reflexes, which are controlled by your spinal cord.) Your behavior is mostly due to stuff inside your body; other people’s behavior is mostly due to stuff inside their bodies, not yours. You do, in fact, have much more control over your own behavior than over others’.

This is obvious, but seems worth restating to me too. People writing in the vague cluster that sometimes gets labelled postrationalist/metarationalist are often really keen on the blurring of these categories. The boundary of the self is fluid, our culture affects how we think of ourselves, concepts don’t have clear boundaries, etc etc. Maybe it’s just a difference in temperament, but so far I’ve struggled to get very excited by any of this. You can’t completely train the physicist out of me, and I’m more interested in the pattern side than the nebulosity side. I want to shake people lost in the relativist fog, and shout ‘look at all the things we can find in here!’

How important is this stuff for doing science?

One thing that fascinates me is how well physics often does by just dodging the big philosophical questions.

Newtonian mechanics had deficiencies that were obvious to the most sophisticated thinkers of the time — instantaneous action at a distance, absolute acceleration — but worked unbelievably well for calculational purposes anyway. Leibniz had most of the good arguments, but Newton had a bucket, and the thing just worked, and pragmatism won the day for a while. (Though there were many later rounds of that controversy, and we’re not finished yet.)

This seems to be linked to the strange feature that we can come up with physical theories that describe most of the phenomena pretty well, but have small holes, and filling in the holes requires not small bolt-on corrections but a gigantic elegant new superstructure that completely subsumes the old one. So the ‘naive’ early theories work far better than you might expect having seen the later ones. David Deutsch puts it nicely in The Fabric of Reality (I’ve bolded the key sentence):

…the fact that there are complex organisms, and that there has been a succession of gradually improving inventions and scientific theories (such as Galilean mechanics, Newtonian mechanics, Einsteinian mechanics, quantum mechanics,…) tells us something more about what sort of computational universality exists in reality. It tells us that the actual laws of physics are, thus far at least, capable of being successively approximated by theories that give ever better explanations and predictions, and that the task of discovering each theory, given the previous one, has been computationally tractable, given the previously known laws and the previously available technology. The fabric of reality must be, as it were, layered, for easy self-access.

One thing that physics has had a really good run of plugging its ears to and avoiding completely is questions of our internal perceptions of the world as it appears to us. Apart from some rather basic forms of observer-dependence (only seeing the light rays that travel to our eyes, etc.), we’ve mostly been able to sustain a simple realist model of a ‘real world out there’ that ‘appears to us directly’ (the quotes are there to suggest that this works best of all if you interpret the words in a common sense sort of way and don’t think too deeply about exactly what they mean). There hasn’t been much need within physics to posit top-down style explanations, where our observations are constrained by the possible forms of our perception, or interpreted in the light of our previous understanding.

(I’m ignoring the various weirdo interpretations of quantum theory that have a special place for the conscious human observer here, because they haven’t produced much in the way of new understanding. You can come up with a clever neo-Kantian interpretation of Bohr, or an awful woo one, but so far these have always been pretty free-floating, rather than locking onto reality in a way that helps us do more.)

Eddington, who had a complex and bizarre idealist metaphysics of his own, discusses this in The Nature of the Physical World (my bolds again):

The synthetic method by which we build up from its own symbolic elements a world which will imitate the actual behaviour of the world of familiar experience is adopted almost universally in scientific theories. Any ordinary theoretical paper in the scientific journals tacitly assumes that this approach is adopted. It has proved to be the most successful procedure; and it is the actual procedure underlying the advances set forth in the scientific part of this book. But I would not claim that no other way of working is admissible. We agree that at the end of the synthesis there must be a linkage to the familiar world of consciousness, and we are not necessarily opposed to attempts to reach the physical world from that end…

…Although this book may in most respects seem diametrically opposed to Dr Whitehead’s widely read philosophy of Nature, I think it would be truer to regard him as an ally who from the opposite side of the mountain is tunneling to meet his less philosophically minded colleagues. The important thing is not to confuse the two entrances.

This is all very nice, but it doesn’t seem much of a fair division of labour. When it comes to physics, Eddington’s side’s got those big Crossrail tunnelling machines, while Whitehead’s side is bashing at rocks with a plastic bucket and spade. The naive realist world-as-given approach just works extraordinarily well, and there hasn’t been a need for much of a tradition of tunnelling on the other side of the mountain.

Where I’m trying to go with this is that I’m not too sure where philosophical sophistication actually gets us. I think the answer for physics might be ‘not very far’… at least for this type of philosophical sophistication. (Looking for deeper understanding of particular conceptual questions within current physics seems to go much better.) Talking about ‘the real world out there’ just seems to work very well.

Maybe this only holds for physics, though. If we’re talking about human cognition, it looks inescapable that we’re going to have to do some digging on the other side.

This is roughly the position I hold at the moment, but I notice I still have a few doubts. The approach of ‘find the most ridiculous and reductive possible theory and iterate from there’ had some success even in psychology. Behaviourism and operant conditioning were especially ridiculous and reductive, but found some applications anyway (horrible phone games and making pigeons go round in circles).

I don’t know much about the history, but as far as I know behaviourism grew out of the same intellectual landscape as logical positivism (but persisted longer?), which is another good example of a super reductive wrong-but-interesting theory that probably had some useful effects. Getting the theory to work was hopeless, but I do see why people like Cosma Shalizi and nostalgebraist have some affection for it.

[While I’m on this subject, is it just me or does old 2008-style Less Wrong have a similar flavour to the logical positivists? That same ‘we’ve unmasked the old questions of philosophy as meaningless non-problems, everything makes sense in the light of our simple new theory’ tone? Bayesianism is more sophisticated than logical positivism, because it can accommodate some top-down imposition of order on perception in the form of priors. But there’s still often a strange incuriosity about what priors are and how they’d work, that gives me the feeling that it hasn’t broken away completely from the unworkable positivist world of clean logical propositions about sense-impressions.

The other similarity is that both made an effort to write as clearly as possible, so that where things are wrong you have a hope of seeing that they’re wrong. I learned a lot ten years ago from arguing in my head with Language, Truth and Logic, and I’m learning a lot now from arguing in my head with Less Wrong.]

Behaviourism was superseded by more sophisticated bad models (‘the brain is a computer that stores and updates a representation of its surroundings’) that presumably still have some domain of application, and it’s plausible that a good approach is to keep hammering on each one until it stops producing anything. Maybe there’s a case for the good old iterative approach of bashing, say, neural nets together until we’ve understood all the things neural nets can and can’t do, and only then bashing something else together once that finally hits diminishing returns.

I’m not actually convincing myself here! ‘We should stop having good ideas, and just make the smallest change to the current bad ones that might get us further’ is a crummy argument, and I definitely don’t believe it. But like Deutsch I feel there’s something interesting in the fact that dumb theories work at all, that reality is helpfully layered for our convenience.

The unreasonable effectiveness of mathematics

Just flagging this one up again. I don’t have any more to say about it, but it’s still weird.

The ‘systematiser’s hero’s journey’

This isn’t a disagreement, just a difference in emphasis. Chapman is mainly writing for people who are temperamentally well suited to a systematic cognitive style and have trouble moving away from it. That seems to fit a lot of people well, and I’m interested in trying to understand what that path feels like. The best description I’ve found is in Phil Agre’s Toward a Critical Technical Practice: Lessons Learned in Trying to Reform AI. He gives a clear description of what immersion in the systematic style looks like…

As an AI practitioner already well immersed in the literature, I had incorporated the field’s taste for technical formalization so thoroughly into my own cognitive style that I literally could not read the literatures of nontechnical fields at anything beyond a popular level. The problem was not exactly that I could not understand the vocabulary, but that I insisted on trying to read everything as a narration of the workings of a mechanism. By that time much philosophy and psychology had adopted intellectual styles similar to that of AI, and so it was possible to read much that was congenial — except that it reproduced the same technical schemata as the AI literature.

… and the process of breaking out from it:

My first intellectual breakthrough came when, for reasons I do not recall, it finally occurred to me to stop translating these strange disciplinary languages into technical schemata, and instead simply to learn them on their own terms. This was very difficult because my technical training had instilled in me two polar-opposite orientations to language — as precisely formalized and as impossibly vague — and a single clear mission for all discursive work — transforming vagueness into precision through formalization (Agre 1992). The correct orientation to the language of these texts, as descriptions of the lived experience of ordinary everyday life, or in other words an account of what ordinary activity is like, is unfortunately alien to AI or any other technical field.

I find this path impressive, because it involves deliberately moving out of a culture that you’re very successful in, and taking the associated status hit. I don’t fully understand what kicks people into doing this! It does come with a nice clean ‘hero’s journey’ type narrative arc though: dissatisfaction with the status quo, descent into the nihilist underworld, and the long journey back up to usefulness, hopefully with new powers of understanding.

I had a very different experience. For me it was just a slow process of attrition, where I slowly got more and more frustrated with the differences between my weirdo thinking style and the dominant STEM one, which I was trained in but never fully took to. This reached a peak at the end of my PhD, and was one of the main factors that made me just want to get out of academia.

I’ve already ranted more than anybody could possibly want to hear about my intuition-heavy mathematical style and rubbishness at step-by-step reasoning, so I’m not going to go into that again here. But I also often have trouble doing the ‘workings of a mechanism’ thing, in a way I find hard to describe.

(I can give a simple example, though, which maybe points towards it. I’m the kind of computer user who, when the submit button freezes, angrily clicks it again twenty times as fast as I can. I know theoretically that ‘submitting the form’ isn’t a monolithic action, that behind the scenes it has complex parts, that nobody has programmed a special expediteRequestWhenUserIsAngry() method that will recognise my twenty mouse clicks, and that all I’m achieving is queuing up pointless extra requests on the server, or nothing at all. But viscerally it feels like just one thing that should be an automatic consequence of my mouse click, like pressing a physical button and feeling it lock into place, and it’s hard to break immersion in the physical world and consider an unseen mechanism behind it. The computer’s failure to respond is just wrong wrong wrong, and I hate it, and maybe if I click this button enough times it’ll understand that I’m angry. The calm analytic style is not for me.)

(… this is a classic Heideggerian thing, right? Being broken out of successful tool use? This is what I mean about having to read Heidegger.)

On the other side, I don’t have any problem with dealing with ideas that aren’t carefully defined yet. I’m happy to deal with plenty of slop and ambiguity in between ‘precisely formalized’ and ‘impossibly vague’. I’m also happy to take things I only know implicitly, and slowly try and surface more of it over time as an explicit model. I’m pretty patient with this, and don’t seem to be as bothered by a lack of precision as more careful systematic thinkers.

This has its advantages too. Hopefully I’m getting to a similar sort of place by a different route.