[This post is also crossposted on Less Wrong.]

The ‘research speedrun’ is a format that I’ve been playing with on here for the last year or so. It’s been more popular than I expected and it looks like there’s a lot more that could be done with the idea. So I thought I’d write it up here and see if anyone else wants to experiment with it themselves, or suggest different things to try.

The format

It’s a very simple format, so this section will be short:

• Pick a topic
• Set a one hour timer
• Find out as much as possible about the topic before the buzzer goes off while writing up a live commentary
• Do a very quick editing pass to fix the worst typos and then hit Publish

So far I’ve done speedruns on Marx on alienation, the Vygotsky Circle, sensemaking, the Prussian education system, abacus schools, Germaine de Staël, and mess.

What I’ve used it for so far

Obviously, there’s only so much you can learn in an hour – calling this ‘research’ is a little bit of a stretch. Sometimes I don’t even manage to leave Wikipedia! Even so, this technique works well for topics where the counterfactual is ‘I don’t read anything at all’ or ‘I google around aimlessly for half an hour and then forget it all’. Writing notes as I go means that I’m making enough active effort that I end up remembering some of it, but I know the process is timeboxed so it’s not going to end up being one of those annoying ever-expanding writing projects.

Here are a few rough categories of topics I’ve tried so far:

• ‘Sidequests’. Speedruns are great for topics that you find interesting but are never going to devote serious time to. I have a very minor side interest in the history of schools and universities, so if I come across something intriguing, like Renaissance abacus schools, it’s a good way to learn a few basic things quickly. I have one or two more ideas for speedruns in this area.
• Historical background. An hour is quite a good length of time to pick up a few fragments of background historical context for something you’re interested in. One hour won’t get you far on its own, but the good thing about historical context is that it builds nicely over time as you get a better picture of the timeline of different events and how they affect each other.
• Finding out what something is at a basic level. I did the ‘sensemaking’ speedrun because I’d heard that term a lot and had very little idea what it referred to.
• Dubious or simplistic claims. The Prussian education system post was in this category. If you read pop pieces about education by people who don’t like school very much, there’s often a reference to ‘the Prussian education system’ as the source of all evils, maybe alongside a claim that it was set up to indoctrinate citizens into being good factory workers. If you’re starting with an understanding this simplistic you can improve it significantly within an hour. (The Prussian education system really did introduce many of the elements of modern compulsory schooling, but the factory workers bit doesn’t really hold up.)
• Random curiosity. The Germaine de Staël one happened because I was reading Isaiah Berlin’s The Roots of Romanticism and she sounded like she might have had an interesting life (she did have an interesting life).

What I’ve got out of it

Sometimes the answer ends up being ‘not much’, but in that case I’ve only wasted an hour. I expect these to be pretty high variance. Some outcomes so far:

• I discover that a topic is more interesting or important than I realised, and decide to spend more time on it. This happened with the Vygotsky Circle post – the actual speedrun was frustrating because I didn’t find any good quality sources about the intellectual scene, but I did realise Vygotsky himself was more interesting than I’d realised and ended up reading and making notes on his book Thought and Language.
• I get good comments from more informed people and end up learning more after the speedrun as well. The sensemaking post was like this: in the speedrun itself I learned about the term’s origins in organisational studies, but not so much about the more recent online subculture that uses the term. After I posted it it ended up attracting a fair number of comments and twitter responses that explained the connection. (The root tweet is here, for people who have the patience to trawl through a branching twitter thread.)
• I get exactly what I bargained for: an hour’s worth of basic knowledge about a topic I’m mildly interested in.

Another minor benefit is that I keep my writing habit going by producing something. This was actually pretty useful in the depths of winter lockdown apathy.

Other possibilities

My sense is that there’s a lot more that could be done with the format. Some potential ideas:

Speedrun events. Tyler Alterman first suggested this on twitter:

I like this idea of a research speedruns

Party format:
5min everyone brainstorms topics of interest into a chat
1hr each person speedruns on one
1hr mini presentation from each person

I tried a tiny one with three people and it worked pretty well. I don’t love organising events and I doubt I’ll do this often myself, but if someone else wants to try it I’d probably be up for joining.

Chaining speedruns together. Multiple speedruns on the same topic would allow going into more depth while still having the ability to iterate every hour on exactly what you want to focus on.

Technical topics? I’m also interested in quantum foundations but I haven’t tried any maths- or physics-heavy speedrun topic yet. It sounds a lot harder, because that type of work tends to involve a lot more stopping and thinking, and maybe nothing would appear on the screen for long periods. Could still be worth trying.

Livestreamed speedruns. It could be funny to do an actual Twitch-style livestreamed speedrun. Or it could be atrociously dull. I’m not sure.

I’d like to hear suggestions for other ideas. I’d also be keen to hear from anyone who tries this as an experiment – please let me know how it goes!

This speedrun is a bit of an experiment and might go terribly. It’s a more open-ended topic than the ones I’ve tried before, and I’m not sure what I even want to know exactly.

The background is that I’m a big fan of Sarah Perry’s Tendrils of Mess in our Brains. This is a sketch of a satisfying theory of what mess is: interference from multiple conflicting ordering principles. (That’s probably too concise of a summary – see the post for more details and many good examples.)

I’d like to be able to contextualise this post, to have an idea about what other people have said about mess. Are there any other Big Theories of Mess? I’m not too sure where to start, even, but probably there is a Wikipedia article on mess. If not I’ll dredge Google Scholar. Let’s find out.

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There is no Wikipedia article on mess 😦 Unless you’re looking for the military term.

Google Scholar is giving me articles written by people called Mess. This isn’t going well…

‘Theory of mess’ maybe? All sorts of things are coming up, mostly uninteresting. Maybe this paper on ‘Attuning to mess’? Oh it’s a book chapter, in some kind of military strategy context. Doesn’t look that promising for what I want.

Ok, try ‘What is mess’. Now I’ve found a paper that’s just called ‘Mess‘, by Tanggaard and Tue Juelsbo.

This text is about mess, feelings of loneliness and loss, and their potential creative power. In a recent paper on collaborative writing, Wegener (2014) shares her experience with the reader on how a writing refuge almost turned into a prison. Having spent two days at the refuge, piles of papers with interview transcripts and field-notes were in a total mess. The themes in the writing seemed irrelevant and boring. Feeling lost, Wegener realised that she needed to break free and do something, and so she eventually decided to leave the research files behind and enjoy life in the sun outside the dirty windows in her room (Figure 10.1). She walked out along the beach and, when she came back, she began reading A. C. Bryatt’s A Biographer’s Tale, which she found by chance in her messy suitcase. The book was just meant to be a leisurely read and not intended to serve as a research tool and yet, soon, Wegener found herself writing a fictional dialogue with the protagonist Phineas from the tale about feeling lost and in need of creative inspiration (see also Chapter 8).

Getting warmer, still not really what I want.

Further down there’s a book called A Perfect Mess: The Hidden Benefits of Disorder, by Abrahamson and Freedman. The book preview looks kind of entertaining, but probably not going to get into any deep theory of mess. Hm, though I did just find this bit:

Mess Isn’t Necessarily an Absence of Order. Often a system is messy to some extent because of the lack of one specific type of order, even though other forms of order are present in abundance… What’s more, mess often arises from a failed order rather than from an absence of order.

This is sort of close to Perry’s thesis. But the book seems to be mostly more first-principles musings on mess, rather than helping me find more standard references. (Are there standard references? Where are the Established Theorists of Mess hanging out?)

There’s a categorisation of types of mess that may be worth returning to later, I’ll just add a screenshot in:

That’s probably all I’ll get out of this source for now. None of the other search results look useful. What about a general google search? Nope, totally useless, pages of dictionary definitions and other useless crap.

Hmm. This is not easy. It’s a mess, in fact. 41 minutes left, what to try next? Let’s search the Stanford Encyclopedia of Philosophy for the word ‘mess’. Nothing really about mess as such, just the word cropping up in various unrelated contexts. Where’s my Grand Theory of Mess??

OK I’ll go back to the original blog post and check for leads there. Oh OK there’s Alan Watts:

When you look at the clouds they are not symmetrical. They do not form fours and they do not come along in cubes, but you know at once that they are not a mess. A dirty old ashtray full of junk may be a mess but clouds do not look like that. When you look at the patterns of foam on water they never make an artistic mistake and they are not a mess. They are wiggly but in a way, orderly, although it is difficult for us to describe that kind of order.

Alan Watts, The Tao of Philosophy, p. 27.

I’ve always got some weird resistance to reading Alan Watts that I don’t fully understand but if this is the source I’d better go there. I don’t know though, I’m googling this quote and the context is sort of more first principles talking about mess. I’m still unclear what I do want but this isn’t really it. Ugh.

Back on Google Scholar looking up various combinations of ‘mess’ and ‘aesthetics’. Haha I just found a paper called ‘Chocolate or shit: aesthetics and cultural poverty in art therapy with children’. Not what I want either but… interesting I guess? I’m over half way through now and getting nowhere.

Hmm, this isn’t particularly promising but I just searched ‘theory of mess’ in google and found a review of something called Cooking with Mud: The Idea of Mess in Nineteenth-Century Art and Fiction by David Trotter. This at least seems to have some links to other works:

The only strange feature of this admirable book is its title. Baudelaire, the writer who pre-eminently characterized the creation of art in terms of the culinary and the cosmetic, described the metamorphosis of raw reality into crafted artefact, as the transformation of mud into gold, in a way which the anecdote from the childhood of Mary Butts, cited by David Trotter, barely encompasses. The sub-title of the book gives a far clearer picture of its range and content: the poetics and politics of “mess-theory” in Western fiction and painting, from approximately 1860 to 1900. “Mess” is to be understood in Samuel Beckett’s use of the term, in his 1961 interview with Tom Driver, when he spoke of seeking in art “a form that accommodates the mess.” Beckett, however, equated this activity with “chaos,” whereas Trotter, in his book, differentiates between the two. More precisely, Trotter makes a distinction between a theory of “waste” and a theory of “mess” (17). “Waste” is an effect which can be traced back to its cause and, ultimately, to human agency: it can be recycled and can be linked to renewal. Philosophically, in terms of order and disorder, it is related to determinism. By contrast, “mess” is governed by chance. It can be “good,” in that it may mark the beginning of an illusion (as in desire), or “bad,” in that it may mark the shattering of an illusion. It may be creative, as in the clutter of the studios of Edgar Degas or Francis Bacon, who each, in their different ways, produced some of their finest works in an environment of extreme “messiness.” Philosophically, it is linked to the concept of contingency and is, aesthetically, the harbinger of modernism.

But ‘mess’ as ‘governed by chance’ isn’t really what I’m looking for.

Now I’ve found a book called Making the Most of Mess by Emery Roe, which seems to be about policy and management. Quotes the Trotter piece: ‘Those interested in the role of mess in other fields should begin with mess theory in literary criticism (Trotter 2000), rubbish theory in anthropology (Thompson 1979), or the heap paradox in philosophy’.

I’m out of better ideas so let’s look up ‘rubbish theory in anthropology’. OK the book is Rubbish Theory: The Creation and Destruction of Value by Michael Thompson. Seems to be about waste and not particular about mess.

Oh god, 12 minutes left. Back on Scholar looking at stuff to do with mess and aesthetics. Debris, Mess and the Modernist Self? Making Sense of Mess. Marginal Lives, Impossible Spaces? This last one seems to theroise about mess at least a bit:

In the following few paragraphs I sketch some of the main concepts that animate our understanding of ‘mess’, as a way of attempting to outline a tradition of thinkers that were fascinated by lack of formal order, by chaos or filth; I hope
then to draw a constellation of keywords which help us clarify the connotations of the term we intend to use as a guiding idea running throughout this issue.

In its comparative understanding, as the opposite or ‘lack’ of order, balance, and clarity, mess reminds us of the canonical Dionysian/Apollonian dialectic as famously articulated by Nietzsche’s The Birth of Tragedy (1872).

… Fast-forwarding to more recent times, it is noticeable that postmodern culture is certainly deeply fascinated by mess, by simultaneity and overlapping, by directionless hyperactivity and the overcrowded physical scenarios of mass society
and conspicuous consumption.

Bla bla Lyotard, bla bla entropy. Doesn’t go too deep, seems to just be an introduction to a book of essays with a fairly typical pomo-ish inverting-the-order theme: ‘It also contributes, I believe, to questioning the rationale behind a value system that prioritizes order and rational organization of space, objects, and people.’

I just found another potentially interesting reference: Thomas Leddy, “Everyday Surface Aesthetic Qualities: ‘Neat,’ ‘Messy,’ ‘Clean,’ ‘Dirty,'” This is in something called ‘Everyday Aesthetics’ by Yuriko Saito. I’ve only found the first page of the Leddy so far and don’t have long left, and it looks like it probably won’t go deep on mess, though it might be worth reading anyway.

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Ding! Ok, yeah, that did go pretty terribly. But my lack of success is least suggestive that there really isn’t a lot of deep theory of mess out there. There’s still a chance that I’m missing the right search terms, but I have no idea what the right ones would be. If you have any good ideas, let me know…

(This is a speedrun post, where I set a one hour timer to see what I can find out about a subject. See the category tag for more examples.)

I’m currently reading Catarina Dutilh Novaes’s Formal Languages in Logic, and one part of the section on the historical development of mathematical notation jumped out at me as potentially interesting. Abbaco (‘abacus’) schools were a kind of practical school in medieval southern Europe that trained the sons of merchants and artisans in useful mathematics for bookkeeping and business. Apparently the mathematical culture associated with these schools actually went beyond the university education of the time in some respects, and helped push forward the development of algebra:

Indeed, modern algebra (and its notation) will ultimately emerge from the sub-scientific tradition of the abbaco schools, rather than the somewhat solidified academic tradition taught at the medieval universities.

I find these sort of semi-informal institutions on the edges of academia intriguing… I’m not sure how much I care about the details, but it seems worth an hour of investigation at least. There’s also a mention of Leonardo da Vinci and Danti Alighieri attending these schools, which could be interesting to follow up.

This speedrun session is also a bit different because we’re trying out a group speedrun event, and David MacIver and Eve Bigaj have also joined. Let’s see how it goes… As usual I typed this as I went and have done only minor tidying up afterwards, so there may be a bunch of typos and dodgy formatting.

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There’s a wikipedia article, but it isn’t very long. Looks like there are a few other useful links though

Abacus school is a term applied to any Italian school or tutorial after the 13th century, whose commerce-directed curriculum placed special emphasis on mathematics, such as algebra, among other subjects. These schools sprang after the publication of Fibonacci’s Book of the Abacus and his introduction of the Hindu-Arabic numeral system. In Fibonacci’s viewpoint, this system, originating in India around 400 BCE, and later adopted by the Arabs, was simpler and more practical than using the existing Roman numeric tradition. Italian merchants and traders quickly adopted the structure as a means of producing accountants, clerks, and so on, and subsequently abacus schools for students were established.

So, yep, practical education for merchants and traders.

Significant for a couple of reasons. First they got rid of Roman numerals.

The number of Roman characters a merchant needed to memorize to carry out financial transactions as opposed to Hindu-numerals made the switch practical. Commercialists were first introduced to this new system through Leonardo Fibonacci, who came from a business family and had studied Arabic math. Being convinced of its uses, abacus schools were therefore created and dominated by wealthy merchants, with some exceptions

Also they were instrumental in rising literacy levels.

Nothing about algebra here! Another thing on the search page mentioned Cardano though so hopefully there will be a link.

Then there’s a bunch of stuff about the school system.

Italian abacus school systems differed more in their establishment than in their curriculum during the Middle Ages. For example, institutions and appointed educators were set up in a number of ways, either through commune patronage or independent masters’ personal funds. Some abbaco teachers tutored privately in homes. All instructors, however, were contractually bound to their agreement which usually meant that they could supplement their salary with tuition fees or other rates.

Could be an overlap here with medieval guild funding of universities (e.g. in Bologna), another subject I’m considering speedrunning on.

Independent teachers could also be hired by the commune, but for lower wages.[19] Most times, free-lance masters were contracted by a group of parents in a similar fashion to that of communal agreements, thus establishing their own school if the number of students being tutored was significant in size.[20] Abbaco apprentices training to become masters could also tutor household children and pay for their studies simultaneously.

Last (short) section is on the curriculum.

Arithmetic, geometry, bookkeeping, reading and writing in the vernacular were the basic elementary and secondary subjects in the abbaco syllabus for most institutions, which began in the fall, Mondays through Saturdays.

… Mathematical problems dealt with the everyday exchange of different types of goods or monies of differing values, whether it was in demand or in good quality, and how much of it was being traded. Other problems dealt with distribution of profits, where each member invested a certain sum and may have later withdrawn a portion of that amount

Well that wasn’t a very informative article. There isn’t one in Italian either, just Arabic (same info as English) and Persiian (a stub where I’m not going to even bother to hit translate). So I need to leave wikipedia very early.

OK, this looks good and more what I was after. ‘Solving the Cubic with Cardano – Aspects of Abbaco Mathematics’ by William Branson.

To understand the abbaco mathematics used by Cardano, we have to step back and look at the medieval tradition of abbaco schools and their masters. Though the subject is a fascinating and deep one, there is one particular aspect of this tradition that is crucial in the following account: abbaco masters thought in terms of canonical problems, and one particular canonical problem, the “Problem of Ten,” arises in the solution of the cubic that we will examine.

Quick summary of what they were, similar to wikipedia.

Abbaco mathematics was rhetorical—in Cardano’s time, most of the algebraic symbols with which we are so familiar were either recently invented, concurrent with the Ars Magna, or were well in the future. For example, ‘(+)’ and ‘(–)’ were first recorded in the 1480s, and were not in common use in 1545, when the Ars Magna was published. Robert Recorde would not invent the equals sign until 1557, and the use of letters and exponential notation would have to await Francois Viete in the 1590s and the Geometrie of Rene Descartes of 1637 [Note 2]. What Descartes would write as (x^3=ax+b,) Cardano wrote as “cubus aequalis rebus & numero” [Cardano 1662, Chapter 12, p. 251].

OK this is similar to what Dutilh Novaes was saying, people were solving problems that were algebraic in nature with unknowns to solve for, but the notation was still very wordy.

Rhetorical formulas can be difficult to remember, so algebraic rules were presented with canonical examples, which encoded the rules as algorithms within the examples. Thus, the mind of the abbaco master was a storehouse of such canonical examples, to which he compared the new problems that he came across in his work. When he recognized a parallel structure between the new problem and a canonical problem, he could solve the new problem by making appropriate substitutions into the canonical example.

So these ‘wordy’ forms still had some kind of canonical structures, it wasn’t just free text but was a kind of notation.

Such canonical examples occurred even in the foundational texts of abbaco mathematics, including the Algebra of al-Khwarizmi. An important example for us, one that occurs implicitly in Cardano’s solution to the cubic, is the “problem of ten” [Note 3]. Most abbaco texts had such problems, and one from Robert of Chester’s 1215 translation of al-Khwarizmi’s Algebra into Latin [al-Khwarizmi, p. 111] ran as follows:

Denarium numerum sic in duo diuido, vt vna parte cum altera multiplicata, productum multiplicationis in 21 terminetur. Iam ergo vnam partem, rem proponimus quam cum 10 sine re, quae alteram partem habent, multiplicamus…

In his translation of this passage into English, Louis Karpinski used (x) for ‘rem’ (thing), and so I offer my own translation, without symbols [Note 4]:

Ten numbers in two parts I divide in such a way, in order that one part with the other multiplied has the product of the multiplication conclude with 21. Now therefore one part we declare the thing, and then, with 10 without the thing, which the other part is, we multiply…

My god I can’t even be bothered to read all of that that… very glad we don’t do maths like that now…

The structure of the “problem of ten” was that of a number (a) broken into two parts (x) and (y,) with a condition on the parts; symbolically: [x+y=a\,\,{\rm and}\,\,f(x,y)=b] for some function (f(x,y)) and number (b.) The usual method of solution was to express the two parts as “thing” and “number minus thing” and then to substitute into the condition, as al-Khwarizmi did above. The “problem of ten” was canonical for quadratic problems, and served as a way to remember the rules for solving such problems.

This was used in Cardano’s solution to the cubic, apparently, but there’s no more detail on this page, it just ends there. Looks like a book extract or something.

There’s another MAA page on abbaco schools, though, so I’ll read that next. This is ‘Background: The Abbaco Tradition’ by Randy K. Schwarz.

Bit more detail on where these schools were:

They arose first in northern Italy, whose economy was the most vibrant in Europe during this period (Spiesser 2003, pp. 34-35). A banker and official in Florence, Italy, reported that in 1345 at least 1,000 boys in that city alone were receiving instruction in abbaco and algorismo (Biggs 2009, p. 73). Such schools also began to appear in neighboring southern France, and a few in Catalonia (the area around Barcelona, Spain) and coastal North Africa. These four regions of the western Mediterranean had extensive trade and cultural ties with one another at the time, so it isn’t surprising that they shared methods of practical mathematics and its instruction (Høyrup 2006).

Mentions the Fibonacci book again as a common ancestor. Ah so this is why Fibonacci knew this stuff:

He was only a boy, he reports, when his father, a customs official representing Pisan merchants at their trading enclave of Bugia, in what is now Algeria, brought him to the customs house there to be taught Hindu-Arabic numerals and arithmetic (Sigler 2002, pp. 3, 15)

This article is part of a series on something called the Pamiers manuscript, which translated some of this into French maybe? or some language in modern France anyway. look up later if time.

Nice picture of teaching in an abbaco school here.

In general, the abbaco texts offered practical, simplified treatments in which mathematical techniques were distilled into easy-to-remember rules and algorithms. The focus was on how to carry these out rather than on justifying the theory behind them. At the same time, the books were often innovative in their solutions to particular problems and especially in their pedagogical approach: their presentation was popular, and they introduced the use of illustrations and vernacular languages to the history of mathematics textbooks.

Reference here to something called Swetz 1987, ‘Capitalism and Arithmetic: The New Math of the 15th Century’.

OK this article finishes here too… and I still have 34 minutes, this might be a difficult speedrun for finding information. I may as well skim the intro page and find out what the Pamiers manuscript is while I’m here.

Pamiers is in the far south of France, south of Toulouse near the Pyrenees. Written in the Languedocian language.

One of the striking features of the Pamiers manuscript is the fact that it includes the world’s earliest known instance in which a negative number was accepted as the answer to a problem for purely mathematical reasons. The fact that this occurred in the context of a commercial arithmetic, rather than a more scholastic or theoretical work, is a surprise.

Ah, nice, this is the sort of thing I was hoping for, new ideas coming up in the context of practical problems.

Back to wikipedia for now, what else can I find?

I found a pdf by Albrecht Heeffer which is very short but does mention one interesting book.

The abbaco or abbacus tradition (spelled with double b to distinguish it from the material calculating device called ‘abacus’) has the typical characteristics of a so-called ‘sub-scientific’ tradition of mathematical practice (coined by Jens Høyrup). It is supported by lay culture, e.g. merchants, artisans and surveyors. Knowledge is disseminated through master-apprentice relationships, often within family relations. Texts, as far as they are extant, are written in the vernacular. The tradition is open to foreign influences, including cross-cultural practices. Typically, the tradition is underrepresented in the history of mathematics.

Dutilh Novaes also mentioned the Høyrup book so maybe that is what I should really be reading. It’s this ‘sub-scientific’ angle that I’m interested in.

Abbaco masters made subtle but important contributions to the development of early symbolism. Their two centuries of algebraic practice paved the road for the development of symbolic algebra during the sixteenth century. They introduced mathematical techniques such as complete induction which is believed to have emerged a century later

Yeah, ok, so this is an interesting subject but I probably need to be reading books to find the good bits, rather than skimming the internet. Similar to Vygotsky speedrun maybe.

Let’s find out what this Høyrup book is called. Ah it must be this book mentioned on his wikipedia page: ‘Jacopo da Firenze’s Tractatus algorismi and early italian abacus culture.’ Yes I’m definitely going to buy these chapters off Springer for 25.95 euros each, sounds like a great idea.

Ah here’s a copy of a pdf by Høyrup! It’s 34 pages so I don’t have time to go into the details, but I can skim it. Hm also it looks like it’s mainly arguing about the centrality of Fibonacci in the tradition, I’m not interested in that, I’m interested in the sub-scientific thing.

First though I’d like to chase up that thing about Dante and da Vinci.

20 minutes left.

Search ‘da Vinci abbacco school’, oh god the results are full of random schools named after him and references to The Da Vinci Code. Must include: abbaco.

I have found another vaguely useful paper though, ‘The Market for Luca Pacioli’s Summa Arithmatica’ by Alan Sangster and others. Something here about the two-track nature of education in Renaissance Italy, with these schools at the practical end.

The curriculum of the vernacular schools emerged from the merchant culture and was designed to prepare sons of merchants and craftsmen for their future working lives [Grendler, 1990]. There was another parallel set of schools, the Latin (either scholastic or humanist) schools, where the sons of the privileged were taught in Latin.

The two sets of schools taught very different subjects. The Latin schools sought to teach the future leaders of society and those that aided them, e.g., secretaries and lawyers [Grendler,1989, p. 311]. They specialized in the trivium of grammar, rhetoric, and logic… On the rare occasions when mathematics was taught in these schools, it took the form of “classical or medieval Latin mathematics” [Grendler, 1989, p. 309]. In contrast to the vernacular schools, boys leaving the humanist schools often went to university.

Hang on, why don’t I just look on da Vinci’s wikipedia page? It just says the following:

Despite his family history, Leonardo only received a basic and informal education in (vernacular) writing, reading and math, possibly because his artistic talents were recognized early.

which would at least be consistent with going to one of these schools. And Dante Alighieri:

Not much is known about Dante’s education; he presumably studied at home or in a chapter school attached to a church or monastery in Florence.

Hm, so what did Dutilh Novaes say? Ah, it’s a quote from Heeffer 2007, ‘Humanist Repudiation of Eastern Influences in Early Modern Mathematics’. Pdf is here. Should have looked this up to start with!

Actually I’m confused because, although this is very relevant looking, it doesn’t have the quote in it at all. Ah well, I may as well read it for the rest of the time anyway (only 5 minutes left!). The thing about Dante and da Vinci isn’t really important.

Here’s some more on the sub-scientific idea:

Jens Høyrup coined the term sub-scientific mathematics for a long tradition of practice which has been neglected by historians. As a scholar working on a wide period of mathematical practice, from Babylonian algebra to the seventeenth century, Høyrup has always paid much attention to the more informal transmission of mathematical knowledge which he calls sub-scientific structures.

This is pretty complicated to skim quickly.

The sub-scientific tradition was a cross-cultural amalgam of several traditions. Merchant type arithmetic and recreational problems show a strong similarity with Indian sources. Algebra descended from the Arabs. By the time Regiomontanus learned algebra in Italy it was practiced by abbaco masters for more than 250 years. The tradition of surveying and mensuration within practical geometry goes back to Babylonian times.

Some stuff on ‘proto-algebraic rules’.

Our main hypothesis is that many recipes or precepts for arithmetical problem solving, in abbaco texts and arithmetic books before the second half of the sixteenth century, are based on proto-algebraic rules. We call these rules proto-algebraic because they are, or could be based originally on algebraic derivations. Yet their explanation, communication and application do not involve algebra at all. Proto-algebraic rules are disseminated together with the problems to which they can be applied. The problem functions as a vehicle for the transmission of this sub-scientific structure. Little attention has yet been given to sub-scientific mathematics or proto-algebraic rules.

Ding! Time’s up.

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Hm, that was kind of annoying to do a speedrun on, because the Wikipedia article was so short and I had to jump quickly to a bunch of other sources which all either had very limited detail or way too much detail. I never did get to the bottom of the Dante and da Vinci thing.

I’m also still not that clear on the details of exactly what new techniques they introduced, but looks like they were relevant to Cardano’s solution of the cubic, and also to the use of negative numbers in problems. They also introduced a bunch of schematic templates for solving problems, which later developed into modern algebraic notation.

The idea of ‘sub-scientific’ traditions sounds interesting more generally too, maybe I should look up the Høyrup book. Overall this looks like a topic where I’m better off reading books and papers than skimming random web pages.

I did a ‘speedrun’ post a couple of months ago where I set a one hour timer and tried to find out as much as I could about Marx’s theory of alienation. That turned out to be pretty fun, so I’m going to try it again with another topic where I have about an hour’s worth of curiosity.

I saw a wikipedia link to something called ‘the Vygotsky Circle’ a while back. I didn’t click the link (don’t want to spoil the fun!) but from the hoverover it looks like that includes Vygotsky, Luria and… some other Russian psychologists, I guess? I’d heard of those two, but I only have the faintest idea of what they did. Here’s the entirety of my current knowledge:

• Vygotsky wrote a book called Thought and Language. Something about internalisation?
• Luria’s the one who went around pestering peasants with questions about whether bears in the Arctic are white. And presumably a load of other stuff… he pops up in pop books with some frequency. E.g. I think he did a study of someone with an extraordinary memory?

That’s about it, so plenty of room to learn more. And also anything sounds about ten times more interesting if it’s a Circle. Suddenly it’s an intellectual movement, not a disparate bunch of nerds. So… let’s give this a go.

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OK first go to that wiki article.

The Vygotsky Circle (also known as Vygotsky–Luria Circle[1][2]) was an influential informal network of psychologists, educationalists, medical specialists, physiologists, and neuroscientists, associated with Lev Vygotsky (1896–1934) and Alexander Luria (1902–1977), active in 1920-early 1940s in the Soviet Union (Moscow, Leningrad and Kharkiv).

So who’s in it?

The Circle included altogether around three dozen individuals at different periods, including Leonid Sakharov, Boris Varshava, Nikolai Bernstein, Solomon Gellerstein, Mark Lebedinsky, Leonid Zankov, Aleksei N. Leontiev, Alexander Zaporozhets, Daniil Elkonin, Lydia Bozhovich, Bluma Zeigarnik, Filipp Bassin, and many others. German-American psychologist Kurt Lewin and Russian film director and art theorist Sergei Eisenstein are also mentioned as the “peripheral members” of the Circle.

OK that’s a lot of people! Hm this is a very short article. Maybe the Russian one is longer? Nope. So this is the entirety of the history of the Circle given:

The Vygotsky Circle was formed around 1924 in Moscow after Vygotsky moved there from the provincial town of Gomel in Belarus. There at the Institute of Psychology he met graduate students Zankov, Solov’ev, Sakharov, and Varshava, as well as future collaborator Aleksander Luria.[5]:427–428 The group grew incrementally and operated in Moscow, Kharkiv, and Leningrad; all in the Soviet Union. From the beginning of World War II 1 Sept 1939 to the start of the Great Patriotic War, 22 June 1941, several centers of post-Vygotskian research were formed by Luria, Leontiev, Zankov, and Elkonin. The Circle ended, however, when the Soviet Union was invaded by Germany to start the Great Patriotic War.

However, by the end of 1930s a new center was formed around 1939 under the leadership of Luria and Leontiev. In the after-war period this developed into the so-called the “School of Vygotsky-Leontiev-Luria”. Recent studies show that this “school” never existed as such.

There are two problems that are related to the Vygotsky circle. First was the historical recording of the Soviet psychology with innumerable gaps in time and prejudice. Second was the almost exclusive focus on the person, Lev Vygotsky, himself to the extent that the scientific contributions of other notable characters have been considerably downplayed or forgotten.

This is all a bit more nebulous than I was hoping for. Lots of references and sources at least. May end up just covering Vygotsky and Luria.

OK Vygotsky wiki article. What did he do?

He is known for his concept of the zone of proximal development (ZPD): the distance between what a student (apprentice, new employee, etc.) can do on their own, and what they can accomplish with the support of someone more knowledgeable about the activity. Vygotsky saw the ZPD as a measure of skills that are in the process of maturing, as supplement to measures of development that only look at a learner’s independent ability.

Also influential are his works on the relationship between language and thought, the development of language, and a general theory of development through actions and relationships in a socio-cultural environment.

OK here’s the internalisation thing I vaguely remembered hearing about:

… the majority of his work involved the study of infant and child behavior, as well as the development of language acquisition (such as the importance of pointing and inner speech[5]) …

Influenced by Piaget, but differed on inner speech:

Piaget asserted that egocentric speech in children “dissolved away” as they matured, while Vygotsky maintained that egocentric speech became internalized, what we now call “inner speech”.

Not sure I’ve picked a good topic this time, pulls in way too many directions so this is going to be very shallow and skip around. And ofc there’s lots of confusing turbulent historical background, and all these pages refer to various controversies of interpretation 😦 Skip to Luria, can always come back:

Alexander Romanovich Luria (Russian: Алекса́ндр Рома́нович Лу́рия, IPA: [ˈlurʲɪjə]; 16 July 1902 – 14 August 1977) was a Russian neuropsychologist, often credited as a father of modern neuropsychological assessment. He developed an extensive and original battery of neuropsychological tests during his clinical work with brain-injured victims of World War II, which are still used in various forms. He made an in-depth analysis of the functioning of various brain regions and integrative processes of the brain in general. Luria’s magnum opus, Higher Cortical Functions in Man (1962), is a much-used psychological textbook which has been translated into many languages and which he supplemented with The Working Brain in 1973.

… became famous for his studies of low-educated populations in the south of the Soviet Union showing that they use different categorization than the educated world (determined by functionality of their tools).

OK so this was early on.

Some biographical stuff. Born in Kazan, studied there, then moved to Moscow where he met Vygotsky. And others:

During the 1920s Luria also met a large number of scholars, including Aleksei N. Leontiev, Mark Lebedinsky, Alexander Zaporozhets, Bluma Zeigarnik, many of whom would remain his lifelong colleagues.

Leontiev’s turned up a few times, open in another tab.

OK the phrase ‘cultural-historical psychology’ has come up. Open the wikipedia page:

Cultural-historical psychology is a branch of avant-garde and futuristic psychological theory and practice of the “science of Superman” associated with Lev Vygotsky and Alexander Luria and their Circle, who initiated it in the mid-1920s–1930s.[1] The phrase “cultural-historical psychology” never occurs in the writings of Vygotsky, and was subsequently ascribed to him by his critics and followers alike, yet it is under this title that this intellectual movement is now widely known.

This all sounds like a confusing mess where I’d need to learn way more background than I’m going to pick up in an hour. Back to Luria. Here’s the peasant-bothering stuff:

The 1930s were significant to Luria because his studies of indigenous people opened the field of multiculturalism to his general interests.[12] This interest would be revived in the later twentieth century by a variety of scholars and researchers who began studying and defending indigenous peoples throughout the world. Luria’s work continued in this field with expeditions to Central Asia. Under the supervision of Vygotsky, Luria investigated various psychological changes (including perception, problem solving, and memory) that take place as a result of cultural development of undereducated minorities. In this regard he has been credited with a major contribution to the study of orality.

That last bit has a footnote to Ong’s Orality and Literacy. Another place I’ve seen the name before.

In 1933, Luria married Lana P. Lipchina, a well-known specialist in microbiology with a doctorate in the biological sciences.

Then studied aphasia:

In his early neuropsychological work in the end of the 1930s as well as throughout his postwar academic life he focused on the study of aphasia, focusing on the relation between language, thought, and cortical functions, particularly on the development of compensatory functions for aphasia.

This must be another pop-science topic where I’ve come across him before. Hm where’s the memory bit? Oh I missed it:

Apart from his work with Vygotsky, Luria is widely known for two extraordinary psychological case studies: The Mind of a Mnemonist, about Solomon Shereshevsky, who had highly advanced memory; and The Man with a Shattered World, about a man with traumatic brain injury.

Ah this turns out to be late on in his career:

Among his late writings are also two extended case studies directed toward the popular press and a general readership, in which he presented some of the results of major advances in the field of clinical neuropsychology. These two books are among his most popular writings. According to Oliver Sacks, in these works “science became poetry”.[31]

In The Mind of a Mnemonist (1968), Luria studied Solomon Shereshevskii, a Russian journalist with a seemingly unlimited memory, sometimes referred to in contemporary literature as “flashbulb” memory, in part due to his fivefold synesthesia.

In The Man with the Shattered World (1971) he documented the recovery under his treatment of the soldier Lev Zasetsky, who had suffered a brain wound in World War II.

OK 27 minutes left. I’ll look up some of the other characters. Leontiev first. Apparently he was ‘a Soviet developmental psychologist, philosopher and the founder of activity theory.’ What’s activity theory?

Activity theory (AT; Russian: Теория деятельности)[1] is an umbrella term for a line of eclectic social sciences theories and research with its roots in the Soviet psychological activity theory pioneered by Sergei Rubinstein in 1930s. At a later time it was advocated for and popularized by Alexei Leont’ev. Some of the traces of the theory in its inception can also be found in a few works of Lev Vygotsky,[2]. These scholars sought to understand human activities as systemic and socially situated phenomena and to go beyond paradigms of reflexology (the teaching of Vladimir Bekhterev and his followers) and classical conditioning (the teaching of Ivan Pavlov and his school), psychoanalysis and behaviorism.

So maybe he founded it or maybe he just advocated for it. This is all a bit of a mess. But, ok, it’s an umbrella term for moving past behaviourism.

One of the strengths of AT is that it bridges the gap between the individual subject and the social reality—it studies both through the mediating activity. The unit of analysis in AT is the concept of object-oriented, collective and culturally mediated human activity, or activity system.

This all looks sort of interesting, but a bit vague, and will probably take me down some other rabbithole. Back to Leontiev.

After Vygotsky’s early death, Leont’ev became the leader of the research group nowadays known as the Kharkov School of Psychology and extended Vygotsky’s research framework in significantly new ways.

Oh shit completely missed the whole thing about Vygotsky’s early death. Back to him… died aged 37! Of tuberculosis. Mostly became famous after his death, and through the influence of his students. Ah this bit on his influence might be useful. Soviet influence first:

In the Soviet Union, the work of the group of Vygotsky’s students known as the Vygotsky Circle was responsible for Vygotsky’s scientific legacy.[42] The members of the group subsequently laid a foundation for Vygotskian psychology’s systematic development in such diverse fields as the psychology of memory (P. Zinchenko), perception, sensation, and movement (Zaporozhets, Asnin, A. N. Leont’ev), personality (Lidiya Bozhovich, Asnin, A. N. Leont’ev), will and volition (Zaporozhets, A. N. Leont’ev, P. Zinchenko, L. Bozhovich, Asnin), psychology of play (G. D. Lukov, Daniil El’konin) and psychology of learning (P. Zinchenko, L. Bozhovich, D. El’konin), as well as the theory of step-by-step formation of mental actions (Pyotr Gal’perin), general psychological activity theory (A. N. Leont’ev) and psychology of action (Zaporozhets).

That at least says something about what all of those names did. Open Zinchenko tab as first.

Then North American influence:

In 1962 a translation of his posthumous 1934 book, Thinking and Speech, published with the title,Thought and Language, did not seem to change the situation considerably.[citation needed] It was only after an eclectic compilation of partly rephrased and partly translated works of Vygotsky and his collaborators, published in 1978 under Vygotsky’s name as Mind in Society, that the Vygotsky boom started in the West: originally, in North America, and later, following the North American example, spread to other regions of the world.[citation needed] This version of Vygotskian science is typically associated with the names of its chief proponents Michael Cole, James Wertsch, their associates and followers, and is relatively well known under the names of “cultural-historical activity theory” (aka CHAT) or “activity theory”.[45][46][47] Scaffolding, a concept introduced by Wood, Bruner, and Ross in 1976, is somewhat related to the idea of ZPD, although Vygotsky never used the term.[

Ah so Thought and Language was posthumous.

Then a big pile of controversy about how his work was interpreted. Now we’re getting headings like ‘Revisionist movement in Vygotsky Studies’, think I’ll bail out now. 16 minutes left.

OK let’s try Zinchenko page.

The main theme of Zinchenko’s research is involuntary memory, studied from the perspective of the activity approach in psychology. In a series of studies, Zinchenko demonstrated that recall of the material to be remembered strongly depends on the kind of activity directed on the material, the motivation to perform the activity, the level of interest in the material and the degree of involvement in the activity. Thus, he showed that following the task of sorting material in experimental settings, human subjects demonstrate a better involuntary recall rate than in the task of voluntary material memorization.

This influenced Leontiev and activity theory. That’s about all the detail there is. What to do next? Look up some of the other people I guess. Try a few, they’re all very short articles, give up with that.

Fine I’ll just google ‘vygotsky thought and language’ and see what i get. MIT Press description:

Vygotsky’s closely reasoned, highly readable analysis of the nature of verbal thought as based on word meaning marks a significant step forward in the growing effort to understand cognitive processes. Speech is, he argues, social in origins. It is learned from others and, at first, used entirely for affective and social functions. Only with time does it come to have self-directive properties that eventually result in internalized verbal thought. To Vygotsky, “a word is a microcosm of human consciousness.”

OK, yeah that does sound interesting.

Not finding great sources. 8 minutes left. Zone of proximal development section of Vygotsky’s page:

“Zone of Proximal Development” (ZPD) is a term Vygotsky used to characterize an individual’s mental development. He originally defined the ZPD as “the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers.” He used the example of two children in school who originally could solve problems at an eight-year-old developmental level (that is, typical for children who were age 8). After each child received assistance from an adult, one was able to perform at a nine-year-old level and one was able to perform at a twelve-year-old level. He said “This difference between twelve and eight, or between nine and eight, is what we call the zone of proximal development.” He further said that the ZPD “defines those functions that have not yet matured but are in the process of maturation, functions that will mature tomorrow but are currently in an embryonic state.” The zone is bracketed by the learner’s current ability and the ability they can achieve with the aid of an instructor of some capacity.

ZPD page itself:

Zygotsky spent a lot of time studying the impact of school instruction on children and noted that children grasp language concepts quite naturally, but that math and writing did not come as naturally. Essentially, he concluded that because these concepts were taught in school settings with unnecessary assessments, they were of more difficulty to learners. Piaget believed that there was a clear distinction between development and teaching. He said that development is a spontaneous process that is initiated and completed by the children, stemming from their own efforts. Piaget was a proponent of independent thinking and critical of the standard teacher-led instruction that was common practice in schools.

But also:

… He believed that children would not advance very far if they were left to discover everything on their own. It’s crucial for a child’s development that they are able to interact with more knowledgeable others. They would not be able to expand on what they know if this wasn’t possible.

OK 3 minutes left. Let’s wildly skip between tabs learning absolutely nothing. Hm maybe this would have been interesting? ‘Vygotsky circle as a personal network of scholars: restoring connections between people and ideas’.

Ding! Didn’t get much past reading the title.

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Well that didn’t work as well as the alienation one. Sprawling topic, and I wasn’t very clear on what I wanted to get out of it. History of the Circle itself or just some random facts about what individual people in it did? I mostly ended up with the second one, and not much insight into what held it together conceptually, beyond some vague idea about ‘going beyond behaviourism’/’looking at general background of human activity, not just immediate task’.

Still, I guess I know a bit more about these people than I did going in, and would be able to orient more quickly if I wanted to find out anything specific.