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I had a gigantic insight on my walk home tonight, which is clearly going to make me millions, but before I start on my self-help book empire I needed to write this rushed crappy blog post explaining it. And before that, I needed to do the dishes. Because my grand theory requires self-similar competence at all scales.

OK, so really this thing is not very profound or original at all. It’s pretty much the same as John Perry’s structured procrastination, but with a slightly different emphasis. (And probably this emphasis appears elsewhere too.)

If you somehow haven’t come across the structured procrastination essay before, it’s wonderful and you should read it. The key part:

Procrastinators often follow exactly the wrong tack. They try to minimize their commitments, assuming that if they have only a few things to do, they will quit procrastinating and get them done. But this approach ignores the basic nature of the procrastinator and destroys his most important source of motivation. The few tasks on his list will be, by definition, the most important. And the only way to avoid doing them will be to do nothing. This is the way to become a couch potato, not an effective human being.

I’m highly susceptible to this particular bad idea and end up doing nothing too often. Partly this is because I tend to have overambitious crackpot plans, so there’s always a good supply of ‘most important’ tasks to put at the top of the list. And partly it’s because I don’t seem to get bored as easily as most people and am unusually good at sitting around doing nothing very much, so it’s easy to slump into the couch potato ground state.

I do think sitting around doing nothing very much is highly underrated by a lot of people, but that would be a different post. In my case, I definitely need nudging towards actually getting shit done, instead of thinking idly about things I could do.

John Perry advocates avoiding this low-energy stuck state by filling up your to do list with ‘a hierarchy of the tasks you have to do, in order of importance from the most urgent to the least important’. The main mechanism he advances for why this works is that fear of the big intimidating tasks at the top drives you down the list, pushing you into actually completing many of the lower-ranked items.

I think this effect is somewhat important, but my thesis is that the most important mechanism is actually going the other way, from the bottom of the list up. Deadline fear is definitely useful, but I think that the energy and confidence created by completing the small tasks is the most important bit.

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My intuition is that energy tends to be created at the microscale and bubbles up from there. I definitely use this principle to try and build momentum at work when I have a seriously boring task to do. I don’t want to do the actual task, but maybe I can be bothered to open up the password manager and get out the password I need for the server, and then maybe I can be bothered to open up a terminal and log on. Then maybe I’ll type in some trivial command to get myself used to the fact that I’m going to be typing in some commands. I don’t actually care what files are in that particular directory, but listing them has enough of the flavour of ‘doing work’ that it’s often enough to push me over the threshold into doing real work.

I think this is all pretty uncontroversial at the microscale. Any grumpy old fart who writes a weekly column for the Telegraph on how The Kids These Days Have No Discipline could tell you that sitting up straight and making your bed in the morning (or whatever) will propagate through to getting more done in general.

Where it gets interesting is at the mid-scale – projects you’re spending weeks to months on, but that aren’t all that important, at least in comparison with Big Intimidating Project at the top of the list. These are the ones I find myself wanting to cross off the list, because they’re ‘wasting time’.

But I’m coming to realise that they play an extremely important role in the task ecosystem. In some sense these are the largest-scale projects that you know you can actually pull off. Really big intimidating projects tend to have some sort of ‘research’ type element, where you don’t know what would even constitute a solution when starting out. Mid-sized projects, on the other hand, take a considerable amount of effort but are much more well defined. You more-or-less know how you’re going to tackle them, and what a successful outcome will look like. Successful mid-sized projects give you the confidence and energy to keep going, gradually allowing you to push further and further up the scale.

(I think it’s also important that at least some of these are self-contained projects in their own right, rather than subtasks of Big Intimidating Project. Lopping chunks off of Big Intimidating Project and tackling them separately is an excellent strategy, but my intuition is that this can’t be the only thing. Probably this is something to do with needing a supply of new ideas to keep bubbling up at all scales, but I haven’t thought about it very carefully.)

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Here’s an example of an idea bubbling up. Last August I declared a Shitty Projects Month, as I could tell I needed some sort of break from more focussed work. It’s the kind of idea you can’t really fail at, and I did indeed do some shitty work on a couple of shitty projects, but I didn’t feel too pleased with how it went at the time. I suppose I was hoping that the results would be, well, less shitty.

Somehow, though, I found myself coming back to one of the projects a couple of months ago. I’d had an idea for a toy project I could try and do using the d3.js visualisation library – nothing useful, but it would look pretty if I got it right. I spent most of my time fighting my poor understanding of the library, and indeed of Javascript in general, and didn’t get very far.

Eventually it came back into my head, though, and this time I had the bright idea of prototyping in Inkscape. Once I could see something visually I was a lot more excited about the project and made rapid progress. I haven’t finished yet because there’s other stuff I have to do this month, but it looks likely that it’s going to be a major component in the visual design of the proper website I’m finally going to make, which will be my next mid-range non-physics project. If I don’t run into any more weird distractions.

And of course, the best example of a mid-range project bubbling up from triviality is this blog itself. I got the shittiest possible blog, a basic tumblr with the default design, and started writing with no particular plan. It turned out that what I wanted to write about was mathematical intuition (and chalk!? no idea about that one) so I went with that. And then got it off tumblr and turned it into something approximating a proper blog.

I haven’t run out of ideas yet, so hopefully this one can keep bubbling up. That’s my excuse for writing essentially the same post over and over again. Self-similar blogging at all scales!

I haven’t posted anything in a couple of weeks, not because I haven’t been writing but because I keep writing overambitious longer posts that get to a point where they seem something like 80% done and then die horribly. I’m hopeful that I can reanimate some of the dead posts but in the meantime it would be nice to keep a bit of momentum.

So I was looking at my folder of half-written draft crap (which starts with ‘academia_rant.txt’ and ‘asdfsdffsd.txt’ and doesn’t get any better) and found this thing I wrote for the tumblr blog and had half forgotten about, under the title ‘pretentious theme statement’. Maybe I decided it was too pretentious. But reading it back, I like it, and I think it’s accurate for at least part of what I want to do on this newer blog too:

 

If this blog has any sort of theme, beyond ‘let’s write the same boring post about mathematical intuition a thousand times’, it’s something like this:

Say you have some idea which can be written down in language in a more or less coherent and logical way. That’s the bit I’m mostly not interested in here. (Though these are really good! I definitely approve of coherent and logical thoughts. Sometimes I even manage to have one.)

Instead I find myself poking again and again at the cluster of stuff that’s packed around it that’s rather more difficult to get a hold on in language – the emotional tone the thought has, the mental images or bits of analogy that support it. Sort of like the ‘dressed’ thought rather than the ‘bare’ thought.

‘The role of intuition in maths’ is how I mostly approach it because it’s close to my own odd obsessions, it has a tiny fascinating literature that I’ve mostly read, and the divide seems particularly obvious there. It’s really common to have the experience of following a mathematical proof with several indisputably-correct steps and get to the end completely convinced of the result, but still have that feeling of urghh BUT WHY is this true?? And it’s really common to then find a reframing that makes it obvious.

But a bunch of my other posts seem to be about this too – there’s the assorted crap under the ‘tastes in the head’ tag, and some throwaway stuff like my new sort-of-interest in geology.

I’m definitely not talking about this because I understand it. Finding ways to talk about all this extra stuff is hard, there’s no one source of literature on it, and it’s possible that it varies so widely from person to person it’s essentially not even worth trying. Certainly people vary widely in their preferred mathematical learning styles. But the topic has some kind of, well, hard-to-describe quality that makes me keep returning to it.

(It’s also well-suited to tumblr because all I really know how to do is produce these sort of confused fragments. I’m definitely not going to be producing a 5000 word chunk of confidently-stated insight porn off the back of any of this any time soon.)

I grew up fascinated with this kind of thing, sort of improbably for a teenager in 2003 or so.

I’m going to write more about this; today I’m just taking bad photos while I’m at my parents’ house and have the materials to hand. But the point is that ‘systems of meaning all in flames’ isn’t just an abstract piece of history for me. I might not have understood the context very well, but the emotional tone got through anyway.

(The image is from the beginning of ‘Crisis in English Poetry’ by the excellently named Vivian De Sola Pinto, published 1951, which I picked out from a second-hand bookshop for 50p because I liked the doom-laden title. This stuff is easy to find once you’ve developed a taste for it.)

Related to the previous post, here is some free PhD advice for all three people who occasionally read the blog, none of whom it’s probably relevant to. I really did not excel in my PhD and then left academia, so this advice may not be worth having, but I felt like writing it down anyway.

I saw this really insightful answer on academia.stackexchange, in response to someone asking how they could attract more good applicants to a PhD programme in an ‘awesome’ but (implicitly) not super-top-level-wow-prestigious university. The core part:

So currently, you are getting two types of student: A) Those for whom you are accidentally special, e.g. they live in your city and don’t want to move, and B) those who dreamed to get into Harvard. A will contain the usual mix of brilliant and average students, while from B, Harvard picked all the chocolate chips from the cookie.

The solution is that you become top player by getting into a niche which has been overlooked. It may be completely new, or it may have 1-2 players which are in it accidentally, so you can beat them easily. Suddenly, you’ll start getting applications from C), the students who dream of being in that niche. Not only did you open yourself to a new set of students, but those who know early on what they know, and find out which university offers it, tend to be the best. This is a set of self-selected people who are motivated and effective.

I joined one of these sort of research groups and they are fantastic. They are obviously not as good for your future career as getting into Fancy Subfield at Imperial or Stanford. On the other hand, you won’t be expected to chew each others’ limbs off to get to the top of whichever bullshit status ladder is currently dominating the field. Also, nobody has gone there just to show off how amazingly brilliant they are, because if that was really important to them they’d have picked a trendier field/university/city. So you get a relaxed, collaborative atmosphere where people just really care about the subject and want to help each other learn.

Obviously the usefulness of this advice depends on the general intellectual health of your subject. If you reckon the existing status ladder in the field does line up nicely with actual useful progress, then it might be worth risking your limbs at the top groups. If instead you look at the ladder and think um, not so much, then you may as well go and have fun somewhere else.

There was one more thing I meant to port over from the old tumblr and forgot: a list of what I loved about my old research group. It was never under the ‘mathbucket’ tag, but goes a long way to explaining what I care about in maths and physics, what I missed horribly when I left and what I’m working towards finding again.

• Everyone is interested in a wide variety of things – other areas of maths and physics, other academic subjects, various sports and arts and hobbies. Nobody expects you to just be narrowly focussed on learning about your specialism.

• Getting better at these things is valued. A little bit of bragging is alright as long as you don’t get too obnoxious about it.

• Helping other people get better at these things is valued. Being able to explain your work in plain language is valued. Writing a clear paper, giving an entertaining talk or writing for a nonspecialist audience are all considered worthwhile, as well as technical competence in your own research area.

• (This one’s important) An almost total absence of that competitive one-upping thing where everyone spends their time proving how much smarter they are than everyone else, or looking down on other subdisciplines as less important/fundamental/difficult/rigorous than their own. This is all over the place in physics, I hate it, and I was very very lucky to avoid most of it.

• Playfulness, silliness, gurning, stupid repetitive injokes, awful songs played over and over again, pointless fun distracting projects with absolutely no relevance to anyone’s research.

• A kind of glorying in being stubbornly independent-minded and prepared to defend your own stupid opinion. ‘That is bollocks and I will tell you why.’ But always grinning as you say it, and sometimes you discover that it isn’t bollocks and admit you’ve changed your mind.

(Disclaimer I added a bit later: I’m not saying it was a perfect fit for me. It was more undisciplined and structureless and anarchic than I really knew how to deal with, and I was very lazy and unfocussed a lot of the time. This stored up problems for me in the long run, and finishing on time was a miserable ordeal. But there was a lot of good there.)

(Pictured: the inside of my head. This has been a pretty bad earworm recently.)

Figure out what your own cognitive style is. Embrace and develop it as your secret weapon; but try to learn and appreciate other styles as well.

I keep thinking about this quote (from How To Think Real Good). And specifically about what my continuing adventures in being a terrible programmer are adding to my own toolkit, as it’s definitely quite a lot.

Of course everyone and their cat is now a programmer so these are not in any way hard-to-find insights. Actually most of what I read seems to be saturated with them. But my brain is quite resistant to learning any of this, so it’s only just starting to go in.

The ultimate aim would be to finally become passable at some of the tricks the current culture throws at me, and also hang on to my own weirdo cognitive style. Cognitive bilingualism!

Anyway let’s be specific. Here’s three related things that I’m starting to get a grip on.

‘Seeing the skull beneath the skin’.

As in, being able to isolate the structural skeleton of a problem, the bits that actually matter in this application, and mapping it on to some kind of data structure.

You’d think a maths degree would have taught me this already, but no. I was able to rely on intuition and good old rote memorisation for when that failed, and it worked just about OK. Now there’s nothing I can yet grasp well enough to visualise and not much to memorise either, so I suppose I have to learn how to do the thing.

This’ll be a slow one and I don’t yet have any strategies for getting better. I’m still in the process of ‘falling in love with the gears’, attempting to attach any sort of ‘positive affective tone’ to the idea so that I can be bothered to learn it at all. In that respect it’s interesting to listen to people who can do the thing. I joined my current job on some sort of graduate scheme thingy and there are some good CS graduates who were starting at the same time. Sometimes just in the pub or whatever they’ll mention the kinds of problems they idly think about for fun and they have this sort of quality. ‘How would I code this up?’ ‘What structure can I fit it to?’

I like these people so maybe I can like the thing? That always sounds dumb written out but it’s worked before.

(The ‘skull beneath the skin’ quote comes from here but even more I’m thinking of this bit from Watership Down:

“When we think of the downs, we think of the downs in daylight, as we think of a rabbit with its fur on. Stubbs may have envisaged the skeleton inside the horse, but most of us do not: and we do not usually envisage the downs without daylight, even though the light is not a part of the down itself as the hide is part of the horse itself.”

Seems like there are increasing numbers of people who are able to look for the skeleton inside the horse, which is interesting but also weird to me.)

‘Is there a process for that?’

I’m actually getting my head round this one quite nicely, as part of a general project of getting better at structure and discipline and organisation. (This has been way more successful than I would have expected — I actually get up at six and learn physics before going to work these days, which I’d never have imagined would work even a couple of years ago.)

The trick here is that if you’ve got something you need to do, you set up some kind of system so it happens automatically. My boss and his boss are both good at this and take it seriously – it’s worth having an in-depth dull conversation once for, say, how to keep track of emails in a shared inbox, because once you’ve got a good process it takes care of itself and you never need to think about it again.

Most productivity advice is of this form, but it took me a long time to start engaging with it. It just sounded so tedious and bean-county and I kind of liked the image of myself as an messy eccentric with piles of paper everywhere. But it turns out that getting shit done efficiently is extremely useful, and now I want to get more shit done efficiently.

I seem to pass as an organised person quite often these days, which is funny. My boss asked me if I had any thoughts on Trello, for example – I know nothing much about Trello, but it was nice to be considered as the sort of person who could plausibly have something useful to say.

Automate everything.

The general version of ‘is there a process for that?’ is the classic programmer tendency to ‘automate everything’, and it’s actually really hard for me to learn outside of a few special cases. I love repetition. I’m pretty sure there’s a gigantic lead flywheel in my brain which takes forever to spin up, but once it gets there I have enormous cognitive inertia and will happily do the same thing for ages. This is probably obvious from the contents of this blog, and even more obvious from my youtube music listening history. I’ve done many low-level menial admin temp jobs in the past because I have an unusually high tolerance for doing a rote task over and over again.

Whereas the programmer ideal seems to be to pick up a new task lightly, identify the abstract structure as cleanly as possible, and then automate the hell of the bastard so you never have to see it again. And then move on to the next one.

This is a massive nuisance for me! There’s no such thing picking up a task lightly when you have a lead flywheel to spin up, and once it’s spun up you’re properly invested. And then once you’re into that enjoyable flow state of knowing how to do something you’re supposed to rip it all up and make a computer have all the fun instead? Programmers are crazy!

I’m not sure it’s worth tackling this one upfront. I also need to work on ways to get my existing abilities to help me out and route around obstacles, and I’m thinking about that too, but that will be another post sometime.

After the flight, I got a four hour coach back to Bristol, and the fun really started. While waiting in the airport I read a bit more of Keith Johnstone’s Impro, and got on to some pretty crazy-sounding free association exercises (the earlier part of this is what inspired my post about the pastebin of utter crap). Most of them required a partner, or at least a situation where you could talk out loud without sounding like a total nutter, but I thought I could at maybe try improvising stories in my head, allowing myself no pauses to think about what should come next.

I’ve forgotten most of what I came up with, and it was probably mostly crap anyway, but there were a few segments that were a) strange and memorable; b) somewhat in the style of those in the book; and c) nothing at all like what I would have expected to come up with, given what I normally think is in my head:

1. Plovers make their winter migration to the pole star, where all lines intersect. The surface of the pole star is covered in bulrushes, but the inner core is ice. Each plover brings a small amount of warmth to the star, and melts a bit of the ice. When the ice is fully melted, the universe ends and infinity returns.

2. Wolves are streaming down off the tundra in lines. In each line, each wolf carries the tail of the preceding wolf in its jaws. The air smells of lichen and wet feet.

3. There’s an internment camp for people who have forgotten the names of the four seasons. Most of them have internalised that they are stupid and deserve to die.

A man there gets angry and kicks his chair to bits. He makes a fire from the pieces. Staring into the ashes, he intuits new and better names for the seasons. He shouts them at the guards and they drop down dead. The inmates run out through the gates and all four seasons happen at once.

(These are sort of tidied up, but I think only slightly; the verbal content was almost exactly as I wrote it down, but there was a funny mix of visual imagery in there with it which I obviously can’t reproduce. This was interesting to me because I normally have a rather weak visual imagination. The reincorporation of the seasons at the end of the third one is probably because I’d just read the section on reincorporation. I’m pretty sure there were wolves in one of the Impro stories too.)

It’s fascinating to me that this stuff is just there. As Johnstone says, it all turns up when you stop fussing about whether the thoughts belong to or mesh well with you in any sense, and just let them come out with no particular owner. As ever, I wonder about whether mathematical intuition is made out of similar stuff.

After a while of this, I finally fell asleep and napped until Bristol.

Here’s an image of the seat pattern on Easyjet aircraft, which I stared at for an hour or so while sleep deprived yesterday:

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It’s been carefully designed to be maximally annoying to whatever kind of stupid brain I have, in that pretty much every element of the pattern almost but doesn’t quite repeat. Actually the segment in the photo isn’t too bad, but the bit I had in front of me had the ‘L’ shape appearing in three of the possible orientations but not the fourth one, and no ways to make larger squares using the grey squares as the corners, and some other incredibly frustrating feature that I have thankfully now forgotten.

Anyway this pattern ruined any chance I may have had of a good nap, but it did make me hazily realise that whatever this mental mode is is one of the key elements of my cognitive style, for better or worse. I normally label it as ‘synthesis’, which sounds kind of grand, but what I really mean is just this thing of idly mashing little bits of conceptual pattern together in a semi-conscious, automatic way, over and over and over until I maybe get something I can use.

It has a pretty similar subjective flavour to having an annoying tune or a bunch of odd word fragments stuck in your head, which is also something that I have going on all the sodding time.

OK, I’m maybe not selling this skill as an enjoyable one here, but actually I have a lot of affection for it. Whatever this skill is, it somehow manages to balance out my terrible ability at conscious rule-following and gives me a way to survive in mathematics.

it’s been abstracted too far for my tastes and stinks of algebra all over
that putrid stench? that would be the dead rotten hand of algebra

I dug out an interesting-ish writing experiment from a few years ago, where I just wrote out rubbish that came into my head as fast as possible over several evenings. I guess I should be horribly embarrassed by the result, but for some reason I like it, so I’m posting the whole lot to a pastebin here.

It starts out stilted and self-conscious and pretentious and derivative and crap, and then eventually relaxes a bit into being, well, still very pretentious but vaguely worth reading. And every so often there’s an odd little section I’d never have imagined I could write, based on my normal output.

This was a year or so before I started reading SSC, got a tumblr and got fascinated with the whole odd rationalist-adjacent world, so in a lot of ways the prevailing weather in my head was pretty different. I mean, some things never change – as well as the algebra bit there’s another maths rant 500 lines or so in, this time about terminology in differential geometry. But I was finishing up my thesis and was utterly sick of it, and winter was hanging around a lot longer than usual, and the main loops in my head were these sort of miserable ones linked up somehow with M. John Harrison’s Viriconium series and the Anatomy of Norbiton blog. The Pastel City and the Ideal City. And of course underneath it The Waste Land and the Unreal City, my longest-lived and most faithful source of brain noise (that and some Empson stuff).

There was some kind of depressing economics-related news around too, whatever this Harrison post was soaked in. I honestly can’t remember what particular thing it was now that the whole of the news is such a shitshow, but it may have been something about automation/’the post-work future’? “Outside it’s minus ten & you have no idea what’s happening on the old housing estates by the river.” That image of boiling an egg in the same water is completely lodged anyway, even if the specifics have gone out of my head.

Anyway it’s been interesting to read back. I’m a lot more cheerful right now despite the news, and my brain is currently working around some new loops, so maybe I should try this exercise again.

Note: these posts are copied over from the ‘mathbucket’ section of my old tumblr blog and I haven’t put much effort into this, so there is likely to be context or formatting missing.

[I don’t really know where I’m going with this post, but my brain seems to be fixated on writing it. It never comes out right, so this time I’m just going to push it out the door in whatever confused form I can manage, and then hopefully my brain will shut up.]

Tastes in the head is some idiosyncratic piece of mental furniture I have cluttering up the place. I’m not even sure where the best place to look is if I want to find a better vocabulary for this sort of thing (phenomenology? meditation practice? do I have to drag my way through Heidegger or something? ugh). I first got it from Empson’s Seven Kinds of Ambiguity:

“… what the poet has conveyed is no assembly of grammatical meanings, capable of analysis, but a ‘mood’, an ‘atmosphere’, a ‘personality’, an attitude to life, an undifferentiated mode of being. Probably it is in this way, as a sort of taste in the head, that one remembers one’s own past experiences, including the experience of reading a particular poet.”

He obviously liked the phrase, because he uses it again a bit later to snark about the Romantic poets:

“They admired the poetry of previous generations, very rightly, for the taste it left in the head, and, failing to realize that the process of putting such a taste into a reader’s head involves a great deal of work which does not feel like a taste in the head while it is being done, attempting, therefore, to conceive a taste in the head and put it straight on to their paper, they produced tastes in the head which were in fact blurred, complacent, and unpleasing.”

I don’t know if I’m that close to what he meant, but I interpret his ‘tastes in the head’ as that kind of preverbal emotional tone ideas have – once you have some description in language you can manipulate that and catch some of the meaning, but there is also some qualitative essence that is harder to get at. I’m not going to give any examples now, because 1. that ‘preverbal’ bit makes it really hard, 2. the ones I tried were really distracting and ended up taking over the post, but I will quote a couple of sources further along that hopefully clarify it a bit.

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This is a bit of an aside, but I’m really not aiming for clear structure in this one: while I’m talking about the the New Critics, there’s an interesting link here to the idea of the ‘objective correlative’ popularised by T.S. Eliot. I often see this used to mean just, like, imagery in literature that helps to convey the emotional tone of the piece, but iirc he originally used it to make a much stronger, wrong-but-interesting claim: that each image in literature maps to a distinct ‘taste in the head’ – a specific nonverbal emotional tone – that is ‘objective’, i.e. the same for each person (provided they have cultivated the Correct level of literary sensitivity, is the disclaimer at this point.)

This would be amazing if true: we could generate a load of poetic imagery, discover exactly what impossible-to-convey-with-normal-language emotional tone it mapped to, and then produce a giant lookup table that people could use to reliably convey the background texture of their thoughts, and then nobody would ever misunderstand each other ever again. E.g., taking the latest SSC post as an example, Scott digs up the image that exactly corresponds to lived-experience-sympathy-for-the-plight-of-overworked-junior-doctors (it’s probably some kind of whale), sticks it in the post, and we all understand it on an intuitive level and none of us ever need to argue about it again. This sounds like the ultimate rationalist project, but unfortunately we’re going to fail given the obvious problem that the same image provokes very different responses in different people. (And even in the same person at different times.) It’s actually hard for me to believe that this idea was even on the table, but, well, behaviourism was popular at one point, and this is a good deal less reductionist.

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Normally I approach this stuff through my endless droning on about the role of intuition in maths. In that case I sometimes also think of the feeling as ‘falling in love with the gears’. This comes from the intro to Seymour Papert’s Mindstorms (pdf) where he talks about his early fascination with cars, and how playing with gears helped his early intuition for maths:

“I believe that working with differentials did more for my mathematical development than anything I was taught in elementary school. Gears, serving as models, carried many otherwise abstract ideas into my head. I clearly remember two examples from school math. I saw multiplication tables as gears, and my first brush with equations in two variables (e.g., 3x + 4y = 10) immediately evoked the differential. By the time I had made a mental gear model of the relation between x and y, figuring how many teeth each gear needed, the equation had become a comfortable friend.

“Assimilating equations to gears certainly is a powerful way to bring old knowledge to bear on a new object. But it does more as well. I am sure that such assimilations helped to endow mathematics, for me, with a positive affective tone that can be traced back to my infantile experiences with cars.

“A modern-day Montessori might propose, if convinced by my story, to create a gear set for children. Thus every child might have the experience I had. But to hope for this would be to miss the essence of the story. I fell in love with the gears.”

That ‘positive affective tone’ is what I mean by ‘taste in the head’, and for me learning maths is all about the process of finding that kind of tone in new areas:

As an example I’ve been going on about a lot, for me at the moment differential geometry is strongly associated with a positive tone, and abstract algebra most definitely isn’t. (This hasn’t always been true, so hopefully one day I can like both!) Lie groups provide one natural bridge, as an algebraic object that is also a differentiable manifold. Using that I can start to see a path to more “unpleasantly algebraic” components, like, I don’t know, classifying Lie algebras or something, and hopefully later I can move further along it.

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So this has mostly just been a lot of quoting various links. I was going to try and make some rambling ill-defined claims at this point, but I don’t think I’m going to be able to manage that this time so I’ll just wave vaguely at one of them.

I must be unusual in that one part of Less Wrong that I actually like is all the stuff about ‘akrasia’ and reducing procrastination – I don’t get a whole lot of practical use out of this, but the vocabulary of ‘ugh fields’ works very well at communicating the pre-verbal feel of what’s going on. Some of Alicorn’s ‘Living Luminously’ posts are even closer to what I’m interested in, including a much more developed idea of ‘hacking yourself’ to like things (like my Lie group example, but she seems to manage a greater level of control.)

When I read this stuff (also the parts about cognitive biases, Kahneman’s System One, etc., but there I haven’t read so much of the LW content), LW seems really good at taking all this preverbal substructure seriously. And then suddenly, bam!, I’ll be reading something else and it’s all about fitting everything into some incredibly restrictive language-based formal structure. I don’t know, I am possibly just missing the part of my brain that can get anything out of philosophical discussions of ethics, but this part of LW in particular gives me this strong feeling of “how the hell have have you reduced this gigantic mess of tastes in the head to a clean conceptual system, which in certain versions is clean enough to actually take values in the real numbers? This is worse than the T. S. Eliot Emotional Lookup Table! And more importantly, what the hell have you left out by doing this?”

I don’t know, sometimes formal systematizing does work, really well. I would be very surprised if this is one of those times.

OK, I’m going to finish here, and push it out the door like I said I would. Hopefully this has got some of what I wanted out of my head.