Having opinions in public


[Written as part of Notebook Blog Month.]

I’m veering off the post ideas list today to talk about something that’s come up during the month. David MacIver’s been on a bit of a campaign recently to get people to try a daily writing practice, and has a good Twitter thread and blog post on how to get started. (His notebook blog is the main inspiration for my current notebook experiment.)

It turns out I have some opinions on this, focussed on a slightly different but complementary area: getting over emotional blocks around writing in public at all. If I had time I might try and rewrite this into a more generally applicable ‘advice’ type format. But I don’t, so I’m just going to ramble about what I did, and hope it’s possible to extract something useful out of that. Probably the main points are the classic start with something low-stakes and gradually ramp up, but maybe the details will turn out to be helpful too.

(I do still have an emotional block around anything that looks too much like ‘advice’ or ‘teaching’, actually. Like it’s claiming more authority than I have? I’m feeling some of that even writing this rambling sort of post – I mean, it’s not like I write some amazingly well-written mega-popular blog. But I do 1. regularly write posts that 2. some people read and get something useful out of, and that’s probably a more helpful reference point for people starting out anyway.)

The mechanics of writing blog posts came pretty easily to me. I know how to write in a fairly easy and unforced conversational voice, and have the result be coherent and entertaining enough that people will bother to read it. I have a decent intuitive grasp of how to explain why I care about a topic, and how to give enough background that people can follow along. I didn’t have to work on any of this deliberately and don’t have much insight into how I do it. I’m sure I could still improve a lot at these things, but it’s not been a focus for me.

Getting into a habit of writing frequently and coming up with topics to write about was hard at first, but over time both of these problems just solved themselves. I didn’t specifically put much thought into either, and David’s advice for getting round these at the start (minimal success criterion of ‘just write one sentence’, random book page to generate easy prompts) looks good to me.

What didn’t come easily for me, at all, was hitting the damn Publish button. Even under a pseudonym. I actually started from a level that seems extremely pathetic in retrospect, where I struggled to write comments on other people’s blogs under a consistent pseudonym. I’d write one comment under some name, and then I’d go back and nerve myself to look at it the next day, and it would look so cringily pointless and stupid that I’d never be able to make myself use that name again.

Come to think of it, I originally had this problem even with writing I didn’t publish. I’d write it, and the next day it would look atrociously bad, so I’d just delete it or bin it. So I have very little surviving writing from before age 25 or so. I’m not too sure how I solved that one, except that I kept going and eventually it looked less bad (combination of my writing improving and me dropping my standards way down from the very stupid ‘everything should be crafted carefully at the word level with no stale metaphors, Politics and the English Language style’ ones I’d picked up). I think this sort of ‘taste gap’ is very common when your ability to recognise good writing gets too far ahead of your ability to produce it, but I just had a really overly strong disgust reaction for some reason.

Solving writing in public was also quite accidental at first. I had a lot of time to waste and spent some of it going down the rabbit hole of something called rationalist-adjacent tumblr. I think it’s still going, but the peak was probably around 2015 or so. It’s hard to describe exactly what it was like, but a short version is ‘a bunch of clever but bored and unproductive people with fantastically distinctive writing styles and aesthetics having endless repetitive stupid arguments about dust specks and cupcakes and trying to befriend anybody who came along to join the argument.’ (Those two links give a better idea.) I never quite became part of the community there, more of a lurker and occasional commenter, but I did start writing. Mainly because it was incredibly low-stakes, and there was an easy ladder of increasing difficulty. First just reading and liking posts, then replying with the odd comment, then writing my own posts on low-controversy topics nobody was going to start a big fuss about. I started exploring my thoughts on mathematical intuition and discovering that I had something to say.

Around this time I started figuring out what was happening, and stretching my abilities deliberately. One big influence was Sarah Constantin’s post A Return To Discussion. This was aimed at people who were fleeing the spotlight of public discussion:

I have noticed personally is that people have gotten intimidated by more formal and public kinds of online conversation. I know quite a few people who used to keep a “real blog” and have become afraid to touch it, preferring instead to chat on social media. It’s a weird kind of locus for perfectionism — nobody ever imagined that blogs were meant to be masterpieces. But I do see people fleeing towards more ephemeral, more stream-of-consciousness types of communication, or communication that involves no words at all (reblogging, image-sharing, etc.) There seems to be a fear of becoming too visible as a distinctive writing voice.

But it also turned out to be useful for someone trying to learn how to do it in the first place. It called out some of my strategies and pushed me towards doing better:

You can preempt embarrassment by declaring that you’re doing something shitty on purpose. That puts you in a position of safety. You move to a space for trashy, casual, unedited talk, and you signal clearly that you don’t want to be taken seriously, in order to avoid looking pretentious and being deflated by criticism. I think that a lot of online mannerisms, like using all-lowercase punctuation, or using really self-deprecating language, or deeply nested meta-levels of meme irony, are ways of saying “I’m cool because I’m not putting myself out there where I can be judged. Only pompous idiots are so naive as to think their opinions are actually valuable.”

Very on point for someone with a tumblr called ‘drossbucket’! (That I’m-being-shitty-on-purpose thing did get me writing, though, even if it’s limiting in the long run. If you need it to start writing at all, I’d say go with it.)

That post also gets into the moral dimension of being able to have opinions in public, in terms of accountability and open debate. I’m not going to get into that, partly because it would take too long and partly because I don’t feel like I’m there yet. Still too conflict-averse to stick my neck out on most things that matter.

Still, I’ve kept working on it, increasing the difficulty level in small steps. I got this wordpress blog and moved over there, starting off by writing the same sort of short posts I wrote on tumblr. Then I started upping the quality standards and writing longer pieces that I’d obviously put time and thought into. No hiding behind the shitty-on-purpose label if it turned out bad. I got a Twitter account and started talking to people there. Then I attached the blog to my real name, but didn’t advertise that much. Then I added my real name and face to Twitter as well.

I was helped a lot by ending up in a fantastic corner of Twitter where people are really thoughtful and encourage each other with their writing projects, rather than trying to knock each other down and look clever all the time. Same for blog comments. I’d never have managed it otherwise. I’m not at the point where I could venture into some fraught culture war quagmire, or open up about anything deeply personal and upsetting. (I’m not even sure that I want to be able to do those things!) But by now there’s a pretty wide scope of topics where I’m able to blab out some thoughts with my name attached. And I want to keep pushing the scope of what I can do. Either directly on this blog, or by spinning up new alts to explore something different and merging them in.

So, yeah, I guess my advice did boil down to ‘start small and ramp up’ in the end. I hope the details are interesting to read though. Good luck to anyone trying this!

Thin technical terminology


[Written as part of Notebook Blog Month.]

Short one today on a weird aesthetic preference I have. It’s not particularly important but I’m curious whether anybody else has this, or whether it even makes sense to other people.

This relates back to the two types of symbol I was talking about a few posts back in Roses and traffic lights. Symbols as centres of clusters of rich associative meaning (‘rose symbolism in poetry’), vs symbols that are deliberately kept free of secondary associations so that they can stand for one ambiguous technical meaning (‘red traffic light means stop’).

Anyway the thing I really viscerally dislike is when I’m trying to learn a new technical topic, and a word that has a rich set of associations in everyday life is suddenly being repurposed for the ‘traffic light’ type of thin technical meaning. It’s just… bleurgh… and slows me down when learning certain things.

I’ll give an example. One place I’ve noticed this strongly is reading about cryptography and networking protocols. The technical vocabulary of ‘keys’ and ‘certificates’ and ‘sockets’ takes very ordinary words that have vivid sensory associations, and abstracts out one very specific core property. A cryptographic key isn’t metallic or shiny or toothed like a ‘proper’ key, but it does have the core property of having to be exactly correct, or it won’t open the thing you want to get at. I agree that this is the abstract heart of being a key, but somehow the word is still unpleasant without its cloud of visual and tactile connotations.

(There’s a connection to the Bell Jar stuff I quoted in the cognitive decoupling elite post – it’s similar to Esther’s dislike of the physics class.)

I know that if I stuck with the topic it would become better again. I’d start developing associations between the technical words, and then they’d start to have this rich meaning again. If I do get to this other side then technical topics suddenly become REALLY INTERESTING, and I can get obsessive. But I have to put in a lot of activation energy to get over this initial phase, and a lot of the time I just can’t be bothered.

I have the feeling that some people do have the ability to rapidly get interested in stuff just based on thin meanings, like mathematical definitions or rules for puzzles… but I don’t really know. Maybe they are just quicker at converting to thick meaning?

Seeing like a stationery aisle


[Written as part of Notebook Blog Month.]

Back when this was a thing people did, I was waiting in the queue at the post office. There’s an aisle full of stationery where you queue up, and the phrase ‘all stationery is ambiguity reduction’ popped into my head. It’s not quite true – probably the more boring statement ‘a lot of stationery is ambiguity reduction’ is closer to the mark. But I haven’t really thought it through. This will be my first attempt.

Why do I even care? I can think of a couple of reasons. Part of it is that in the last year or two I started to get a deep appreciation for the fact that we engineer the world to conform better to rational systems. I’d undervalued this before, and I still need to read more on this subject – Sorting Things Out and Seeing Like A State seem like obvious choices – but today is going to be more just freeform thinking about specific examples.

The other reason is that a while back I was watching Brian Cantwell Smith’s talk on ‘The philosophy of computation: meaning, mechanism, mystery’, and he had something interesting to say about digitality:

Digitality… is an extraordinarily interesting metaphysical notion, poorly theorised, interestingly enough, there’s very little philosophy of digitality. What I think is powerful, that Haugeland [I think, audio is hard to hear] recognised, is that implementing something digitally is a fabulous way of providing insurance against the mess of the world below.

Stationery provides a lot of examples of ‘proto-digitality’, in a sense that should be made clearer by the examples below. They’re not as binary and noise-free as electronic bits, but the purpose of a lot of types of stationery is to carve the world into X and not-X in ways that are relevant for the current task. This is another kind of ‘insurance against the mess of the world below’. That’s why paper and envelopes and filing cabinets and staples are so important to any kind of pre-electronic bureaucracy.

I think this is all going to become a lot clearer if I stop waffling and start going through specific types of stationery like I’ve just wandered in from Mars and am trying to understand what they do for the first time. The rest of this post is just a list of them, in whichever order they come into my head.

Envelopes. This is a very simple kind of proto-digitality. Everything inside the envelope is X, and everything outside is not-X. The envelope provides a way to transport what we would normally consider to be several things, like individual sheets of paper, as one single thing.

Wrapping paper. This is similar to the envelope, but also needs…

Sellotape. This seals up the edges of the packages to complete the boundary between X and not-X. It can also attach two separate things together to become one thing (like sticking a worksheet into an exercise book, so that the worksheet becomes ‘part of the exercise book’).

Hole punches. You can punch holes into a bunch of individual sheets of paper you consider to be X to then add them to a…

Folder. Similar to an envelope again.

Staples. Also similar function to an envelope, but a minimalist one that just does the categorisation and doesn’t protect the item in transit.

Paper. The workhorse of bureaucracy. Already come up in several of the examples above. I think it’s more raw material for dividing things into categories, rather than category division itself? Rather than dividing up a pile of objects, which may be large and messy and intractable, you divide up pieces of paper that represent them in some way. These are repeatable and stackable in a way that the objects aren’t.

Pens and pencils. These have a lot of uses, not all of which are necessarily ambiguity reduction. Shoving all of writing into that category is probably a stretch. But consider a simple example where you mark some pieces of paper with a triangle, and some with a circle. (Or any other distinguishing marks you like.) Then you’ve created two categories.

Scissors. Sometimes used to cut one thing to make it into two things, or to cut round a border between ‘stuff you want’ and ‘stuff you don’t want’. But there are other uses, like snipping the edge off a pack of frozen peas or cutting out a Christmas snowflake, that don’t fit so obviously.

Eraser. Tool to repair deviations from intended categorisation. E.g. you meant to write ‘eraser’, but you wrote ‘ersaer’, which isn’t a thing, so you rub out the offending mistake and try again.

Pencil sharpener. I feel like this is just a tool for fixing another tool, rather than anything to do with ambiguity reduction itself.

Ruler. Creates straight lines… to separate things into rows and boxes, or just because you want to draw straight lines I guess.

Post-It note. Attaches metadata to an object, with the added feature that you can remove it later, unlike marking with a pen directly.

Highlighter. Distinguishes some areas of a page as ‘important’ by visually separating them from the rest.

OK that’ll do for now. Feel free to argue with any of these in the comments, or add more examples! I literally just typed them out and then hit Publish, so there will be a lot of subtleties that I missed out.

A heap of broken images


[Written as part of Notebook Blog Month.]

I’ve had these notes sitting around for ages now for some kind of pretentious essay on… The Waste Land and ‘oddly satisfying’ videos? Who even knows. I’m never going to write it up properly, so I may as well have a stab at it as part of this notebook project.

So, the original inspiration is David Chapman’s page on the atomised mode. This is mostly going to be an elaboration (or rip-off) of some of the ideas there. Particularly this bit:

In our present, atomized mode of meaningness, cultures, societies, and selves cannot hold together. They shatter into tiny jagged shards. We shake the broken bits together, in senseless kaleidoscopic, hypnotic reconfigurations, with no context or coherence.

Those ‘tiny jagged shards’ reminded me of something else, the ‘heap of broken images’ in The Waste Land:

What are the roots that clutch, what branches grow
Out of this stony rubbish? Son of man,
You cannot say, or guess, for you know only
A heap of broken images, where the sun beats,
And the dead tree gives no shelter, the cricket no relief,
And the dry stone no sound of water.

This isn’t just a random similarity. The Waste Land is about the same process of the fragmentation into shards of meaning, but from an earlier phase of the process. (In as much as it’s about anything, I mean. I realise it’s a poem, not a lecture, and reading it in just the reductive way I’m going to in this post would be a bad idea.) Eliot is writing in 1922, against the backdrop of systems of meaning all in flames. In the third section of the poem, The Fire Sermon, he uses the Thames and its centuries of accreted histories to explore this unravelling. He compares mythic imagery of the past:

Elizabeth and Leicester
Beating oars
The stern was formed
A gilded shell
Red and gold
The brisk swell
Rippled both shores
Southwest wind
Carried down stream
The peal of bells

to random bits of incoherent junk in modernity:

The river’s tent is broken: the last fingers of leaf
Clutch and sink into the wet bank. The wind
Crosses the brown land, unheard. The nymphs are departed.
Sweet Thames, run softly, till I end my song.
The river bears no empty bottles, sandwich papers,
Silk handkerchiefs, cardboard boxes, cigarette ends
Or other testimony of summer nights. The nymphs are departed.

Only fragments of meaning remain, and the poem is made up from a disconnected collage of these. “Sweet Thames, run softly” is from Spenser’s Prothalamion. Possibly more echoes in there I don’t recognise.

(Not going to track down references because notebook blog, but my memory is that the coherence of meaning in the Elizabethan age is a recurring theme in Eliot’s critical essays as well. E.g. vividness and immediacy of imagery in Shakespeare and then the Metaphysical poets. Something like a ‘phoenix age’ in John Michael Greer’s retelling of Vico, to chuck in another reference.)

Anyway, it’s now nearly a century later, and we’ve hit new levels of incoherence. David Chapman’s example is Gangnam Style, which was current when he started writing the page:

Gangnam Style has been watched 2.9 billion times on YouTube. Even counting repeat views, it’s probably well-known to most young people on the planet. Its genre is, in fact, K-pop; but may be the only K-pop song most Westerners have ever heard.

Genre — which defined many subcultures — has disintegrated. Atomization seemed at first like subculturalism taken to an extreme, but it is a qualitatively new mode. K-pop may be a subculture in Korea, but in America it’s just YouTube. It’s normal for a Top 40 hit to mash up country-style pedal steel guitar with bubble-gum-pop vocals, hip-hop rapping, EDM bass, and black metal blast beats. “Authenticity”—the aesthetic ideal of subculturalism—is impossible because there are no standards to be authentic to.

I think atomisation goes one level deeper again, though. Gangnam Style lasts for whole minutes, after all, and is recognisably a song. It has a relatively stable theme, a recurring chorus, and similar images crop up throughout the music video. I’m interested in stuff that’s fragmented nonsense right down to the five-second level.

My favourite examples are from this wonderful article by John Mahoney in The Awl on chumboxes. Chumboxes are those ‘related article’ boxes full of terrible clickbait at the bottom of news sites, supplied by the likes of Taboola and Outbrain. The analogy is to buckets of chum: chopped up bits of fish chucked in the water to attract larger fish. Chumbox chum is designed to appeal at this same shark-brain level:

Like everything else on the internet, traffic flowing through chumboxes must be tracked in order for everyone to be paid. Each box in the grid’s performance can be tracked both individually and in context of its neighbors. This allows them to be highly optimized; some chum is clearly better than others. As a byproduct of this optimization, an aesthetic has arisen. An effective chumbox clearly plays on reflex and the subconscious. The chumbox aesthetic broadcasts our most basic, libidinal, electrical desires back at us. And gets us to click.

Mahoney clicked through chumbox after chumbox to get to the absolute worst chum possible, and analysed common themes. Here’s a couple of examples:

Top left: Sexy Thing and Localized Rule. We won’t dwell on the efficacy of a Sexy Thing in advertising. But do note this Sexy Thing, enhanced with a chummy sprinkle of sinister context (crime? Young women in handcuffs?). Here the Sexy Thing is combined with a more digital-age enhancement, the Localized Rule. Scouring a visitor’s IP for its geographic location, anxiety can be created by informing you of a brand new reason to find yourself handcuffed in the back of a squad car in your neighborhood.

Upper Middle: Oozing Food/Egg. A trend without an immediately recognizable psychological precedent? Oozing eggs are extremely common, and are possibly deployed under similar principles as Disgusting Invertebrates or Globular Masses Presented as Weird Food. Or perhaps the resemblance to an oozing pustular sore brings us back into the familiar realm of the Skin Thing?

The only aim of chum is to hit one-note reactions of disgust, body horror, horniness, nosiness, fear and greed, so that you click through. There’s no need to make sense at all. This isn’t confined to chum, of course. Other examples include:

  • those videos aimed at toddlers of opening Kinder eggs etc
  • ‘Oddly satisfying’ videos
  • ASMR
  • Some bits of TV Tropes would fit. Some of it is longer, more coherent narrative patterns, but some is just recognisable fragments of plot that appear on screen for a few seconds
  • Argument theatre. Short clips of the moment where ‘X DESTROYS liberal snowflake’, or whatever the 2020 version of this 2018 pattern is
  • Almost anything that’s bad on purpose to make you click

Surely this is the end of the line? I feel like we must be right out in the estuary of this process… can we even get much more fragmented than this? (Probably we can, and I just can’t see it.) This looks like the famous lines from the end of The Fire Sermon:

On Margate Sands.
I can connect
Nothing with nothing.
The broken fingernails of dirty hands.

Broken fingernails of dirty hands would make a pretty good chumbox image, actually.

Maybe this post looks like I think this fragmentation is purely a bad thing. Chumboxes are pretty gross, and there there’s all the Waste Land comparisons. Eliot’s response was essentially reactionary, looking backwards towards an Anglo-Catholic traditionalism that he hoped could hold the line against incoherence. His friend and Waste Land editor Ezra Pound later turned to outright fascism.

Actually, I think atomisation is a lot more interesting and positive than that. Again, I’m ripping off Chapman’s take here:

This may sound like a problem. Overall, my description of the atomized mode may sound like a panicked condemnation. However, there is much to like about atomization, and—I will suggest—it provides vital resources for constructing the next, fluid mode.

Now I have some examples of my own to think about, this is making much more sense to me. Maybe they can help to illustrate what these ‘vital resources’ are?

There’s enormous power down at the chumbox level of meaning. All the fragments have been liberated from any top-down need to make conceptual sense on a timescale greater than ten seconds, and appeal directly at the visceral level. Everything is very vivid and raw.

Still, to do anything useful with these fragments we need to build with them. We need to figure out how to recombine them skilfully from the bottom up, while keeping the energy. The kaleidoscope is maybe not the ideal metaphor here; it makes sense of the heap of broken images by imposing a rigid geometric scheme. We need something more local, provisional and reconfigurable. I don’t really know what, or I’d be writing that post instead of this one! But ‘build upwards from the fragments’ at least points towards the right direction.

Marx on alienation speedrun


[Written as part of Notebook Blog Month.]

This is a bit of an experiment to see how ‘set a timer for an hour and see what you find’ works for finding out basic information about a topic. Why Marx on alienation specifically? Well, it’s been in the back of my mind as something where I’ve wanted to know more for a while now, but not to the point where I could ever be bothered to, you know, put the work in. At least this way I’ll put some half-arsed work in, and find out something.

Before I set the timer, I’ll give some quick background. I first got curious about this when I was reading The World Beyond Your Head by Matthew Crawford. This book is in large part about the skilful use of physical tools, often in the context of work, and how modern life degrades the ability to form these craftsman-like relationships with your materials. (Ugh, that’s a horribly abstract and clunky sentence. I don’t want to spend ages writing this intro, so I’m not going to spend time making it into a concrete one. But I do include a lot of examples in that linked review.)

This sounds a lot like alienation, to me, but Crawford never mentions Marx. This isn’t surprising, because Marx is very much Not His Tribe and it’s a very tribal sort of book. But it seemed like an omission I should follow up.

(I suppose it’s possible he does talk about him in Shop Class As Soul Craft, his other book on the topic. I haven’t read that one.)

The other reason I’m interested in this is pretty silly. I’m fascinated by this meme:


There’s something quite deep buried in there, I think. The two computers look different – the work one is more of a utilitarian enterprise-edition black box, the home one is a friendlier silver laptop. But I suspect that even if you worked at a trendy startup with a Macbook covered in stickers, you’d still get a lot of the same effect. The two computers are going to be used in very different ways.

Bad Screen is embedded in a work culture with distanced, ‘professional’ norms. You’re expected to turn up at set times, put in a certain number of hours, and do tasks that you quite frankly don’t care about either way, and wouldn’t look at for five minutes if you weren’t being paid. If you’re feeling any strong emotions that day, you’re mostly expected to leave them at home to the extent that they’d interfere with your job.

Good Screen is much more deeply connected to your whole life – you might stare at it at weird hours of the night and morning, rather than ‘office hours’. You use it to further instrinsically motivated projects that you chose yourself, like overanalysing stupid internet memes. If you’re miserable while looking at Good Screen you can just cry about it, or get angry, or whatever. Good Screen reaches tendrils right out into your whole life, while Bad Screen is much more weakly connected to a smaller, professional self. That difference in contexts is going to leak right down to the perceptual level. You’re alienated from Bad Screen in a way that you aren’t from Good Screen.

I suspect Marx’s interest will be structural – the conditions that lead to this alienation – rather than phenomenological – what alienation feels like on the inside. So might not be as directly relevant as I’d like. But still… I’m not going to know either way if I don’t read anything.

OK, that’s enough blathering about background. Timer time. I’ll tidy up and add in links afterwards, but the majority of writing is done during the hour.

OK. Type ‘marx on alienation’ into Google, get pull quote:


Oh dear, two long German words already. Entfremdung (alienation/estrangement) looks fine I think. Gattungswesen (species-essence) is going to take more work to understand.

Fine I’ll read the Wikipedia article. It continues:

The theoretical basis of alienation within the capitalist mode of production is that the worker invariably loses the ability to determine life and destiny when deprived of the right to think (conceive) of themselves as the director of their own actions; to determine the character of said actions; to define relationships with other people; and to own those items of value from goods and services, produced by their own labour. Although the worker is an autonomous, self-realized human being, as an economic entity this worker is directed to goals and diverted to activities that are dictated by the bourgeoisie—who own the means of production—in order to extract from the worker the maximum amount of surplus value in the course of business competition among industrialists.

No massive surprises there. OK lets find out what the source texts are:

In the Economic and Philosophic Manuscripts of 1844 (1932), Karl Marx expressed the Entfremdung theory—of estrangement from the self. Philosophically, the theory of Entfremdung relies upon The Essence of Christianity (1841) by Ludwig Feuerbach which states that the idea of a supernatural god has alienated the natural characteristics of the human being. Moreover, Max Stirner extended Feuerbach’s analysis in The Ego and its Own (1845) that even the idea of “humanity” is an alienating concept for individuals to intellectually consider in its full philosophic implication. Marx and Friedrich Engels responded to these philosophic propositions in The German Ideology (1845).

So probably want to read about that first one. Open in new tab. Feuerbach sounds kind of interesting but different rabbit hole.

Next is type of alienation. Here’s Marx himself (from “Comment on James Mill”):

Let us suppose that we had carried out production as human beings. Each of us would have, in two ways, affirmed himself, and the other person. (i) In my production I would have objectified my individuality, its specific character, and, therefore, enjoyed not only an individual manifestation of my life during the activity, but also, when looking at the object, I would have the individual pleasure of knowing my personality to be objective, visible to the senses, and, hence, a power beyond all doubt. (ii) In your enjoyment, or use, of my product I would have the direct enjoyment both of being conscious of having satisfied a human need by my work, that is, of having objectified man’s essential nature, and of having thus created an object corresponding to the need of another man’s essential nature … Our products would be so many mirrors in which we saw reflected our essential nature.

So you affirm yourself in two ways – you manifest your individuality by what you choose to make, and also by directly enjoying seeing your work be useful to another person. Marx identifies four ways that industrial production breaks this:

Alienation of the worker. Design of the product is fixed by the capitalist class, worker is just implementing a fixed model. More detailed stuff I’ll read if I get time.

Alienation of the worker from the act of production. The product itself is made in some repetitive way that gives little psychological satisfaction.

Alienation of the worker from their Gattungswesen (species-essence). Now we get the long German word. Open in new tab. Described below as:

Conceptually, in the term “species-essence” the word “species” describes the intrinsic human mental essence that is characterized by a “plurality of interests” and “psychological dynamism”, whereby every individual has the desire and the tendency to engage in the many activities that promote mutual human survival and psychological well-being, by means of emotional connections with other people, with society. The psychic value of a human consists in being able to conceive (think) of the ends of their actions as purposeful ideas, which are distinct from the actions required to realize a given idea.

I’d need to read more to grasp the subtleties. For now, imagine it something like ‘human potential’ or ‘actualisation’. Mix of individual and societal, individual determination over your work and also connection to others.

This is thwarted by industrial production by turning the worker into a interchangeable, mechanised part.

Alienation of the worker from other workers. Workers are competing in the labour market and turned against each other.

Shit that’s already 25 minutes gone. I’d like to get further than one wiki article. Skim the rest for interesting bits. Ignore Hegel. OK the rest of this is mostly Hegel. Tiny criticism section which is all Althusser.

References: Marx originals, some university lecture notes. Maaybe follow the lecture notes if time.

Go back to that other wiki article on Economic and Philosophic Manuscripts of 1844. OK maybe Feuerbach is more important than I realised and not separate rabbit hole:

Marx expounds his theory of alienation, which he adapted (not without changes) from Feuerbach’s The Essence of Christianity (1841).

Another version of four types of alienation. Bit about Aristotle:

He refers to Aristotle’s praxis and production, by saying that the exchange of human activity involved in the exchange of human product, is the generic activity of man. Man’s conscious and authentic existence, he states, is social activity and social satisfaction.

Moreover, he sees human nature in true common life, and if that is not existent as such, men create their common human nature by creating their common life. Furthermore, he argues similarly to Aristotle that authentic common life does not originate from thought but from the material base, needs and egoism. However, in Marx’s view, life has to be humanly organized to allow a real form of common life, since under alienation human interaction is subordinated to a relationship between things. Hence consciousness alone is by far not enough.

Labour value of value. Everything reduced to its exchange rate, causing further alienation.

Marx is of the opinion that alienation reaches its peak once labour becomes wage labour.

OK that’s the end of the two wiki articles. Back to Google. Stanford Philosophy is next. See how far I get through this.

Introductory definitional stuff. Alienation as a kind of separation that is sin some way problematic.

Disclaimers. Not going to be much about historical development but mentions some names. More Hegel. Rousseau.

Two adjacent concepts ‘drawn from Hegelian and Marxist traditions’: fetishism and objectification.

‘Fetishism’ refers here to the idea of human creations which have somehow escaped (inappropriately separated out from) human control, achieved the appearance of independence, and come to enslave and oppress their creators… Consider, for instance, the frequency with which ‘market forces’ are understood and represented within modern culture as something outside of human control, as akin to natural forces which decide our fate.

Feuerbach had some similar argument about Christianity:

the Christian God demands real world sacrifices from individuals, typically in the form of a denial or repression of their essential human needs.

Similar to Marx’s alienation, but not all alienation is fetishism. E.g. alienation can come from our ‘our ruthlessly instrumental treatment of nature, rather than in nature’s tyranny over us’.

Next objectification. Not the feminist version.

In the present context, objectification refers rather to the role of productive activity in mediating the evolving relationship between humankind and the natural world.

i.e. humans make stuff and collectively shape the world.

These world transforming productive activities, we might say, embody the progressive self-realisation of humankind.

Marx would say that this doesn’t always take an alienated form. E.g. meaningful work that is freely chosen, that develops your capabilities and is useful to others. So different to say:

what is sometimes called the ‘Christian’ view of work. On this account, work is seen as a necessary evil, an unpleasant activity unfortunately required for our survival. It owes its name to its embrace of the claim that it was only after the Fall that human beings were required to work by the sweat of their brows

OK next we have subjective and objective alienation. Subjective – experiencing life as lacking meaning, feeling estranged from the world. Objective – potential is frustrated by conditions of the world.

Then there is a table of

subjective + objective present
objective present, not subjective
subjective present, not objective

and how different thinkers fit in. E.g. ‘I take it that existentialists think of (something like) objective alienation as a permanent feature of all human societies.’ Potentially interesting but will skip for now.

Haha I’m slow. Just realised this article is alienation in general, not just Marx. That’s why all these other people keep cropping up! D’oh! Ah well at least I’m getting some background. Still 15 minutes to go. Will skim for Marxy bits.

Something about the positive side of alienation, as an expression of individuality and differentiation. Hard to be too alienated in premodern tribe where you have no choice about what you have to do with life. In this view it should be an intermediate stage:

By a dialectical progression is meant only a movement from a stage characterised by a relationship of ‘undifferentiated unity’, through a stage characterised by a relationship of ‘differentiated disunity’, to a stage characterised by a relationship of ‘differentiated unity’.

Future communist societies will get to the wonderful world of ‘differentiated unity’ and then we’ll all be happy.

The suggestion here is that internal to the second stage, the stage of alienation, there is both a problematic separation from community and a positive liberation from engulfment.

Interesting sounding bit on morality as alienation. All those shoulds alienating you from your own taste.

certain conceptions of morality might embody or encourage a problematic division of self, and a problematic separation from much that is valuable in our lives.

Utilitarianism as example. Again this isn’t really Marx but alienation in general.

Unresolved issues. How much alienation in pre-capitalist societies? Religion alienation as another flavour.

Its plausibility is scarcely incontrovertible, given the amount of sheer productive drudgery, and worse, in pre-capitalist societies.

How much can we be free of systematic alienation?

Marx’s view about communism rests crucially on the judgement that it is the social relations of capitalist society, and not its material or technical arrangements, which are the cause of systematic forms of alienation.

OK that’s the end of the article. What can I do with the remaining 6 minutes? Not much. Back to Google. Next listing is from something called marxists.org. Really short but has a big reference list. More Hegel 😦

Some university lecture notes. Nothing is jumping out at me. Try this blog post. A little bit more about the species-being concept:

Because humans are biological beings, and not merely free-floating immaterial minds, we, like all other biological beings, must interact with and transform the natural world in order to survive. But what distinguishes us from all other animals, like bees, spiders, or beavers, which all transform the world based on instinct, is that we transform the world consciously and freely.5 Thus, the essence of a human being – what Marx calls our species-being – is to consciously and freely transform the world in order to meet our needs. Like many other philosophers, Marx believes that excellently doing what makes us distinctively human is the true source of fulfillment.

3 minutes. Next page of results. Now I’m on Issue 79 of International Socialism. Long and not a riveting read. OK here’s an example:

Peter Linebaugh in his history of 18th century London, The London Hanged, explained that workers considered themselves masters of what they produced. It took great repression, a ‘judicial onslaught’, in the late 18th century to convince them that what they produced belonged exclusively to the capitalists who owned the factories. During the 18th century most workers were not paid exclusively in money. ‘This was true of Russian serf labour, American slave labour, Irish agricultural labour and the metropolitan labour in London trades’

Reading some concrete history would be a lot more interesting. Thinking back to Lark Rise and Enclosure.

Time’s up! That was fun, and I learned a few things. A lot of it was just ‘in the water’, so that I vaguely knew it already, but I did learn some new terminology, and I have an idea of where to find the primary sources and go deeper if I want to.

Writing and searching in the same hour was a bit difficult and tended to bias towards spending longer on each link. Maybe an hour of just going down link rabbit holes and writing up afterwards would be worth trying too? Still, I think this format is promising.

Roses and traffic lights


[Written as part of Notebook Blog Month.]

I read Iain McGilchrist’s The Master and His Emissary last year, and I’m still digesting what I think of the book as a whole (see this thread for a few thoughts), but I’ve already got a lot of use out of some of the ideas I picked up along the way. One of the most surprising things I learned is that there are two very different ways we use the word ‘symbol’, and I’d never noticed! This observation is probably not unique to McGilchrist, and may be obvious to others anyway, but it was news to me.

The first sense is roughly what we mean by symbolism in poetry. The power of a poetic symbol lies in the strength of its associations to other ideas, objects and symbols, both direct and culturally specific. The rose is a canonical (western?) example:

In one sense of the word, a symbol such as the rose is the focus or centre of an endless network of connotations which ramify through our physical and mental, personal and cultural, experience in life, literature and art: the strength of the symbol is in direct proportion to the power it has to convey an array of implicit meanings, which need to remain implicit to be powerful. In this it is like a joke that has several layers of meaning – explaining them destroys its power.

The other sense is a more technical, practical one, that applies to the sort of symbols you see on clothes labels, maps and airport signs. These symbols need to be unambiguous. In this case secondary associations are useless at best and may be actively dangerous. A red traffic light needs to mean one thing only:

The other sort of symbol could be exemplified by the red traffic light: its power lies in its use, and its use depends on a 1:1 mapping of the command ‘stop’ onto the colour red, which precludes ambiguity and has to be explicit.

In the book these two quotes are bookended by a couple of sentences linking this back to his hemisphere model. I left those out because this point stands whether he’s right or not. I’m more interested in the implications, which I haven’t thought through very much yet.  I can’t think of any situations where we mistake one kind of symbol for the other – we generally know whether we’re reading poetry or a clothes label – so maybe this is something we just know how to navigate in practice, and the mixing together of concepts doesn’t matter very much.

Still, I find this confusion deeply weird, and I’m left with a few questions:

  • Who else has written about this point? Any good references?
  • Do other languages split these two concepts up into separate words?
  • Are there good examples of intermediate cases? Emoji seem like one potential good place to look. They need a fairly fixed meaning to work, but often pull a network of secondary meanings along with them (which sometimes – as with the eggplant/aubergine – end up overshadowing the original intended meaning). They’re often conveying squishy human emotions, and haven’t been as rigorously pruned for the purposes of technical rationality as airport signs. This would be an interesting topic to explore in itself.
  • Does being unaware of this distinction ever cause trouble in practice? Maybe emoji are the place to look again.

If you have any thoughts, let me know!

Five jobs meme, post-PhD edition

IMG_20200603_163119957 (2)

[Written as part of Notebook Blog Month.]

There was a ‘first five jobs’ meme going around in March when I first started compiling this list of potential posts. This is my favourite entry:

I’m going to do this but with the first five jobs I did immediately after getting a PhD in physics, because the answer is funnier. I had a sort of unmotivated directionless phase after I finished, and did a bunch of weird temporary jobs in the absence of any better ideas. Exactly five in fact. I haven’t made anything up here, the jobs really were that odd. Here’s the list:

1. Walking round hospitals measuring things

I really wanted to do something mindless straight after I finished, and I’d done some temporary admin work before, so I signed up with a temp agency. They really excelled themselves and came up with something more mindless than I could ever have imagined.

The job was seriously weird. There were two hospitals being merged together on a new site, and the project management office needed to collect data on how much storage space the new hospital would need for medical supplies. I’m not sure what the best way of doing this would be, but maybe it would involve, I don’t know, some Fermi estimates based on their current storage requirements, plus some efficiencies for the single site. What they actually did was make a giant spreadsheet of every sort of item ordered by the hospital (bandages, prosthetics, tiny orthopaedic screws) and then employ EIGHT OF US to go round the hospitals with tape measures FOR WEEKS tracking down and measuring every individual item on the list, including the tiny orthopaedic screws. It was a kind of bizarre treasure hunt round the wards and cupboards and operating theatre storerooms, and I sometimes got to scrub up and go into the theatres themselves for the more obscure items. I genuinely enjoyed this job, because I like walking and exploring and being nosy, but also wtf??

I was so talented at this challenging job that I was kept with one other guy for an even tougher assignment – weighing things. We went round finding all the different types of surgical kits and putting them on scales for… reasons, I guess.

I have no idea if any of this data was ever useful for anything.

2. Following medical secretaries around

After this I had a few weeks off for some reason I forget, and then I phoned the temp agency again. They had more work at the same place! This time they were collecting data on the space they’d need for admin work, and my job was to follow people round and tick a box saying what they were doing every five minutes. Most people were understandably pretty unhappy about being seen like a state, and were grumpy at first, but when they realised I wasn’t too irritating they’d soon warm up, often to the point of offering me office cake.

I discovered Slate Star Codex some time in this job (this was early 2014) and obsessively read my way through the whole back catalogue on a tiny phone screen in between ticking boxes. That was my first step down the rabbit hole of becoming an extremely online person, so I guess it’s notable in retrospect.

3. Receptionist in a soup factory

I only did this one for two weeks, which is good because it was deadly boring. I was on the reception desk signing visitors in and out of a soup factory in an industrial estate on the outskirts of Bristol. Not many people visit soup factories in industrial estates unless they’re bringing a lorry of soup ingredients, so this wasn’t very taxing. To pass the rest of the time I was given a big pile of soup batch reports (temperature, density, etc) to enter into some spreadsheet.

Not much else to say about this one. The soup smelled quite nice in the morning I guess.

4. Numeracy drop-in sessions for nurses

After this I stumbled into a job that actually used some of my mathematical knowledge. This wasn’t really due to any effort on my part – my landlord, a research chemist, knew some people at the maths department of a local university and passed my name on. It’s not a big research university with an army of PhD students to do all the bits of marking and tutoring that crop up, so I took some of these on.

This is the only one where I’ve tweaked the title for comic effect, because I did a lot of more normal stuff too, marking Fourier series engineering coursework and running computer labs. But the best thing they gave me was the numeracy drop-in sessions. There’d been a high profile case somewhere where a patient had been given X milligrams of something instead of X micrograms and died, and now nursing students had to pass a test to show understanding of unit conversions along with some other basic maths. It was a nice walk along the river to the nursing hospital, which was in a converted Victorian lunatic asylum, and I’d sit in their fancy barrel-vaulted canteen and help people out if a numeracy test was coming up, and get on with whatever I wanted if it wasn’t. Pretty enjoyable job.

5. Sorting the post in a law firm

This was about as exciting as it sounds. The post would come in early in the morning, and then we’d open it, sort it, scan it, email it out, and file the originals. Sometimes people would request the original documents, so in the afternoon we’d pick those out of the files. For some added excitement we’d do a trolley run to other offices to fetch the post.

The most fun I had on this job was when I got put on ‘destruction’ for a week. This is still a lot less fun than it sounds, and involved chucking old documents into bags for shredding after rescuing any stray passports and birth certificates. Still, it wasn’t supervised much, and a leisurely week of listening to music while throwing things in bags is quite relaxing.

After a couple of months of this I finally decided I’d had enough of this, and started looking for a more normal job. Since then I’ve been working as a programmer, like everybody else who left academia after a STEM PhD and didn’t have any other ideas. So that was that was the end of my prestigious career in weird temp work. Though I guess there’s still time to become a duck roper.

Synthesising foggy pearls



[Written as part of Notebook Blog Month.]

Very short one to start things off. I have a new twitter bio and I wanted to explain it.


Like everything else in my head it comes from mashing two things together and deciding that they are the same thing. First, here’s an alternative definition of ‘metascience’, from… whatever this game is:

I’m not sure ‘metascience’ has much of an agreed-on definition beyond the obvious ‘ideas that extend around or beyond science’, but the conference mentioned in the tweet expands on it with the following:

During this decade, we have witnessed the emergence of a new discipline called metascience, metaresearch, or the science of science. Most exciting was the fact that this is emerging as a truly interdisciplinary enterprise with contributors from every domain of research. This symposium served as a formative meeting for metascience as a discipline. The meeting brought together leading scholars that are investigating questions related to themes such as:

  • How do scientists generate ideas?
  • How are our statistics, methods, and measurement practices affecting our capacity to identify robust findings?
  • Does the distinction between exploratory and confirmatory research matter
  • What is replication and its impact and its value?
  • How do scientists interpret and treat evidence?
  • What are the cultures and norms of science?

I think that ‘synthesising foggy pearls’ is actually weirdly appropriate, especially for the first point about idea generation. You go into the fog — vague, contextual, disorienting swirls of untheorised confusing stuff — and try to condense out something more structured, durable and reusable. This process fascinates me more than almost anything. I want to understand how we do it, and I want to understand how to do it better.

A couple of months later I saw this tweet:

It turns out that there’s a beetle that synthesises pearls from fog already! Maybe it can teach us how to do metascience…

Notebook Blog Month

I’m going to try an experiment in June: writing lots of short notebook-style posts, roughly in the style of David MacIver’s notebook blog. I’ve been thinking of testing whether this format works for me for ages, and it seems like a good time to finally do it.

I crashed most of my writing routines in late 2019 by getting a new job with a long bus commute and dropping my monthly newsletter for a while to readjust. That was the main engine driving new post drafts, so once that crashed the blog went with it. Then 2020 came along and crashed everything else. I’ve been doing a lot of weird half-baked physics stuff but not really writing anything up properly, and I’ve sort of forgotten how to by now. This is my attempt to flywheel up some writing energy again, starting with some easier raw material than badly organised physics notes.

If I like it I may continue with something like this, if not I’ll probably go back to the newsletter format. Or combine both somehow? Don’t know yet.

Anyway… I’ve made a list. I’ve dredged through old drafts and newsletter notes and incomprehensible shower-thought emails to myself, and managed to pull together 50 topics I could potentially write about. And I’m going to make quick low-res attempts at a bunch of these. Some of these are pretty constrained in scope anyway, others would be a serious research project to do well, but either way I’ll just sit down for an hour or two and see what I can bash out in that time. I might also veer off the list if any good ideas come up during the month.

My goal is 20 posts but I’m not going to beat myself up if I don’t get there. I don’t have a good sense of how difficult this is going to be, and the idea is to have fun rather than kicking myself through a miserable obstacle course. Ten would be fine.

I wanted to call this Shitty Blog Posts Month, which is a funnier name, but I’m trying to wean myself off this sort of self-deprecation. It is quite likely that many of the posts will be shitty, given the time constraints. But I want to avoid the whole thing of saying ‘oh I’m not really trying, look I’ve labelled it ‘shitty’ and put it on a blog called Drossbucket, don’t judge me’. That was very effective several years ago for getting past my defences and starting to write at all, but I don’t need it any more.

OK, here’s the list. There’s no meaning behind the order, I just came up with a whole load of ideas and then randomised the list afterwards. In practice I’m likely to do a mix of the ones I’m most excited about and the ones I can phone in quickly, but I’d also be interested to know which ones look appealing to people – it’d be more fun to write for an audience!

Edit to add: I’m crossing these off as I do them. Also if I have more ideas I’m adding them to the end after the original fifty.

  1. Cognitive dancing! cognitive style! followup post
  2. Pullman – alethiometer/marionette theatre essay
  3. Debugging resources – just a list of blog posts etc people suggested in that twitter thread.
  4. The way mathematicians name variables is actually good and not bad. Notes from November: “I had a good thought about… something… but lost it before I opened this document 😦 Possibly it was connected to that John Cook thing David Chapman mentioned about how everything in probability is P… was connecting it to that thing people say about meaningless variable names in mathematics. I don’t think this is such a big deal because mathematical symbols end up richly saturated with meaning when you use them… they tend to represent recurring concepts not arbitrary bags-of-crap like in programming.”
  5. Bret Victor Kill Math
  6. Mane 6 as Mitford sisters
  7. Talking About Machines Kindle highlights
  8. Examples only
  9. Whiny post about why I find debugging hard
  10. Redraft Wittgenstein newsletter stuff as post
  11. “Neoliberalism”
  12. Something on ‘accountability’ narratives e.g. that Meaningness gluing goldfish crackers to ceiling example.
  13. I don’t like the ‘bullshit jobs’ classification, too binary. Attempt to bullshit out a better taxonomy.
  14. Programmer envy
  15. Old ‘fragmentation’ draft
  16. Something about that vague thing I was just thinking about on intellectually understanding vs viscerally understanding – the visceral one feels a lot ‘more real’ so it is really tempting (coming from a sort of rational worldview) to think there is a clean theory behind it. whereas actually that visceral sense is coming out of the background of previous engagement with the thing, which is complicated and specific, and isn’t ever going to resolve to a clean theory. need to sort out what I’m even trying to say.
  17. Do something with all those Tasic postmodern mathematics notes I made
  18. Bristol bridge walk tweets in blog post form
  19. Rewilding physics
  20. Too many cooks spoil the global section
  21. Marx on alienation speedrun. Feel like I should know what he has to say but I can’t be arsed. So set a timer for one hour to research and read, then write up what I find.
  22. Pebbles and sheep as an example of the middle distance thing. If they are an example of the middle distance thing. Write the post and find out.
  23. Something like Dan Luu’s ‘HN: The Good Parts’ post where I dig out comments I really like from various places. or maybe exceptional comment threads? i dunno.
  24. Rubik’s cube learning notes
  25. Write out that twitter thread on McGilchrist/Derrida/whatever with some words between it
  26. Thinking on the page’/ writing, fast and slow
  27. Old draft on my dislike of ‘thin’ technical terminology
  28. Trailing clouds of glory’ ramble from August 2019 notes
  29. Crackpot time 3
  30. That thing I was thinking about in the stationery aisle in the post office. Something like ‘most stationery is ambiguity reduction’. Is it true? Write the post and find out.
  31. Some shit on going all out on your natural strengths vs getting to mediocre on your weaknesses.
  32. Worse than quantum mechanics. (PR box and Piponi’s machine are both ‘worse than QM’ in some way. Is there any deep connection there?)
  33. Something to do with the banana’s indexicality post
  34. You Are Not An Artisan thoughts
  35. David MacIver’s book prompt notebook post thing
  36. Taste
  37. Pretentious essay on The Waste Land and oddly satisfying videos
  38. Close to the Machine Kindle highlights
  39. The Well Wrought Urn / Heresy of Paraphrase
  40. The middle distance post comments are good enough that I could probably make a post by summarising them.
  41. Seven Types of Ambiguity Kindle highlights
  42. diff mcgilchrist.txt chapman.txt
  43. Two types of symbols bit from McGilchrist
  44. Keep your identity embodied and *maybe* also illegible.
  45. Five jobs meme: post-PhD edition
  46. Ben Hoffman on LW has a good comment… somewhere… about how we end up doing ‘accidental deliberate practice’ on things we already like, e.g. improving writing by monologuing in your head while walking. Find it and give more examples.
  47. Practical Criticism book thoughts
  48. AU where Derrida trolled mathematicians instead and writing/speech became algebra/geometry
  49. Bristol study hall – what it is + why it’s good
  50. ‘Eating fog’ (Namib desert beetle)
  51. Having opinions in public
  52. Motive power
  53. Universities are still good
  54. Dig out that Garfinkel pulsar thread and do something with it
  55. Doing things on purpose
  56. Some rambling thoughts on visual imagery


Grabiner on eighteenth century mathematics

These are some notes I wrote a couple of years ago on Judith Grabiner’s paper ‘Is Mathematical Truth Time Dependent?’ David Chapman suggested I put them up somewhere public, so here they are with a few tweaks and comments. They’re still notes, though – don’t expect proper sentences everywhere! I’m not personally hugely interested in the framing question about mathematical truth, but I really enjoyed the main part of the paper, which compares the ‘if it works, do it’ culture of eighteenth century mathematics to the focus on rigour that came later.

I haven’t read all that much history of mathematics, so I don’t have a lot of context to put this in. If something looks off or oversimplified let me know.

I found this essay in an anthology called New Directions in the Philosophy of Mathematics, edited by Thomas Tymoczko. I picked this book up more or less by luck when I was a PhD student and a professor was having a clearout, and I didn’t have high hopes – nothing I’d previously read about philosophy of mathematics had made much sense to me. Platonism, logicism, formalism and the rest all seemed equally bad, and I wasn’t too interested in formal logic and foundations. However, this book promised something different:

The origin of this book was a seminar in the philosophpy of mathematics held at Smith College during the summer of 1979. An informal group of mathematicians, philosophers and logicians met regularly to discuss common concerns about the nature of mathematics. Our meetings were alternately frustrating and stimulating. We were frustrated by the inablility of traditional philosophical formulations to articulate the actual experience of mathematicians. We did not want yet another restatement of the merits and vicissitudes of the various foundational programs – platonism, logicism, formalism and intuitionism. However, we were also frustrated by the difficulty of articulating a viable alternative to foundationalism, a new approach that would speak to mathematicians and philosophers about their common concerns. Our meetings were most exciting when we managed to glimpse an alternative.

There’s plenty of other good stuff in the book, including some famous pieces like Thurston’s classic On proof and progress in mathematics, and a couple of reprinted sections of Lakatos’s Proofs and Refutations.

Anyway, here are the notes. Anything I’ve put in quotes is Grabiner. Anything in square brackets is some random tangent I’ve gone off on.

Two “generalizations about the way many eighteenth-century mathematicians worked”:

  1. “… the primary emphasis was on getting results”. Huge explosion in creativity, but “the chances are good that these results were originally obtained in ways utterly different from the ways we prove them today. It is doubtful that Euler and his contemporaries would have been able to derive their results if they had been burdened with our standards of rigor”.
  2. “… mathematicians placed great reliance on the power of symbols. Sometimes it seems to have been assumed that if one could just write down something which was symbolically coherent, the truth of the statement was guaranteed.” This extended to e.g. manipulating infinite power series just like very long polynomials.

Euler’s Taylor expansion of \cos(nz) starting from the binomial expansion as one example. He takes z as infinitely small and n as infinitely large, and is happy to assume their product is finite without worrying too much. “The modern reader may be left slightly breathless”, but he gets the right answer.

Trust in symbol manipulation was “somewhat anomalous in the history of mathematics”. Grabiner suggests it came from the recent success of algebra and the calculus. E.g. Leibniz’s notation, which “does the thinking for us” (chain rule as example). This also extended out of maths, e.g. Lavoisier’s idea of ‘chemical algebra’.

18th c was interested in foundations (e.g. Berkeley on calculus being insufficiently rigorous) but this was “not the basic concern” and generally was “relegated to Chapter I of textbooks, or found in popularizations”, not in research papers.

This changed in the 19th c beginning with Cauchy and Bolzano – beginnings of rigorous treatments of limits, continuity etc.

Why did standards change?

“The first explanation which may occur to us is like the one we use to justify rigor to our students today: the calculus was made rigorous to avoid errors, and to correct errors already made.” Doesn’t really hold up – there were surprisingly few mistakes in the 18th c stuff as they “had an almost unerring intuition”.

[I’ve been meaning to look into this for a while, as I get sick of that particular justification being trotted out, always with the same dubious examples. One of these is Weierstrass’s continuous-everywhere-differentiable-nowhere function. This is a genuine example of something the less rigorous approach failed to find, but it came much later, so isn’t what got people started on rigour.

The other example normally given is about something called “the Italian school of algebraic geometry”, which apparently went off the rails in the early 20th c and published false stuff. There’s some information on that in the answers to a MathOverflow question by Kevin Buzzard and the linked email from David Mumford – from a quick read it looks like it was one guy, Severi, who really lost it. Anyway, this is also a lot later than the 18th century.]

It is true though that by the end of the 18th c they were getting into topics – complex functions, multivariable calculus – where “there are many plausible conjectures whose truth is relatively difficult to evaluate intuitively”, so rigour was more useful.

Second possible explanation – need to unify the mass of results thrown up in the 18th c. Probably some truth to this: current methods were hitting diminishing returns, time to “sit back and reflect”.

Third explanation – prior existence of rigour in Euclid’s geometry. Berkeley’s attack on calculus was on this line.

One other interesting factor she suggests – an increasing need for mathematicians to teach (as they became employees of government-sponsored institutions rather than being attached to royal courts). École Polytechnique as model for these.

“Teaching always makes the teacher think carefully about the basis for the subject”. Moving from self-educated or apprentice-master set-ups, where you learn piecemeal from examples of successful thinking, to a more formalised ‘here are the foundations’ approach.

Her evidence – origins of foundational work often emerged from lecture courses. This was true for Lagrange, Cauchy, Weierstrass and Dedekind.

[I don’t know how strong this evidence is, but it’s a really interesting theory. I’ve had literalbanana‘s blog post on indexicality thoroughly stuck in my head for the last month, so I’m seeing that idea everywhere – this is one example. Teaching a large class forces you to take knowledge that was previously highly situated and indexical – ‘oh yes, you need to do this’ – and pull it out into a public form that makes sense to people not deeply immersed in that context. Compare Thurston’s quote in Proof and progress in mathematics: “When a significant theorem is proved, it often (but not always) happens that the solution can be communicated in a matter of minutes from one person to another within the subfield. The same proof would be communicated and generally understood in an hour talk to members of the subfield. It would be the subject of a 15- or 20-page paper, which could be read and understood in a few hours or perhaps days by members of the subfield.”]

How did standards change?

Often 18th c methods were repurposed/generalised. E.g. haphazard comparisons of particular series to the geometric series became Cauchy’s general convergence tests. Or old methods of computing the error term epsilon for the nth approximation get turned round, so that we are given epsilon and show we can always find n to beat that error term. This is essentially the definition of convergence we still use today.


Goes back to original question: is mathematical truth time-dependent? Sets up two bad options to knock down…

  • Relativism. “‘Sufficient unto the day is the rigor thereof.’ Mathematical truth is just what the editors of the Transactions say it is.” This wouldn’t explain why Cauchy and Weierstrass were ever unsatisfied in the first place.

  • MAXIMAL RIGOUR AT ALL TIMES. The 18th c was just sloppy. “According to this high standard, which textbooks sometimes urge on students, Euler would never have written a line.”

[A lot of my grumpiness about rigour is because it was exactly what I didn’t need as a first year maths student. I was just exploring the 18th century explosion myself and discovering the power of mathematics, and what I needed right then was to be able to run with that and learn more cool shit, without fussing over precise epsilon-delta definitions. Maybe it would have worked for me a couple of years later, if I’d seen enough examples to have come across a situation where rigour was useful. This seems to vary a lot though – David Chapman replied that lack of rigour was what he was annoyed by at that age, and he was driven to the library to read about Dedekind cuts.]

… then suggests “a third possibility”:

  • A Kuhnian picture where mathematics grows “not only by successive increments, but also by occasional revolutions”. “We can be consoled that most of the old bricks will find places somewhere in the new structure”.