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Before ChatGPT, the hype among productivity boosters was a PKMs or Personal knowledge management system.

It gained popularity through Tiago Forte’s book ‘Building a second brain’, and (for academics perhaps a more useful read) ‘How to take smart notes’ by Sönke Ahrens.

These books promote new techniques for note-taking (and for storing these notes) such as the PARA-method, the CODE-system, and Zettelkasten.

Unmistakable Creative has some posts on the principles behing the ‘second brain’ approach.

Your brain isn’t like a hard drive or a dropbox, where information is stored in folders and subfolders. None of our thoughts or ideas exist in isolation. Information is organized in a series of non-linear associative networks in the brain.

Networked thinking is not just a more efficient way to organize information. It frees your brain to do what it does best: Imagine, invent, innovate, and create. The less you have to remember where information is, the more you can use it to summarize that information and turn knowledge into action.

and

A network has no “correct” orientation and thus no bottom and no top. Each individual, or “node,” in a network functions autonomously, negotiating its own relationships and coalescing into groups. Examples of networks include a flock of birds, the World Wide Web, and the social ties in a neighborhood. Networks are inherently “bottom-up” in that the structure emerges organically from small interactions without direction from a central authority.

-Tiago Forte, Tagging for Personal Knowledge Management

There are several apps you can use to start building your second brain, the more popular seem to be Roam Research, LogSeq, and Obsidian.

These systems allow you to store, link and manipulate a large collection of notes, query them as a database, modify them in various ways via plugins or scripts, and navigate the network created via graph-views.

Exactly the kind of things we need to modify the simple system from the shape of languages-post into a proper topos of the unconscious.

I’ve been playing around with Obsidian which I like because it has good LaTeX plugins, powerful database tools via the Dataview plugin, and one can execute codeblocks within notes in almost any programming language (python, haskell, lean, Mathematica, ruby, javascript, R, …).

Most of all it has a vibrant community of users, an excellent forum, and a well-documented Obsidian hub.

There’s just one problem, I’m a terrible note-taker, so how can I begin to load my ‘second brain’?

Obsidian has several plugins to import data, such as your Kindle highlights, your Twitter feed, your Readwise-data, and many others, but having been too lazy in the past, I cannot use any of them.

In fact, the only useful collection of notes I have are my blog-posts. So, I’ve uploaded NeverEndingBooks into Obsidian, one note per post (admittedly, not very Zettelkasten-like), half a million words in total.

Fortunately, I did tag most of these posts at the time. Together with other meta-data this results in the Graph view below (under ‘Files’ toggled tags, under ‘Groups’ three tag-colours, and under ‘Display’ toggled arrows). One can add colour-groups based on tags or other information (here, red dots are posts tagged ‘Grothendieck’, the blue ones are tagged ‘Conway’, the purple ones tagged ‘Connes’, just for the sake of illustration). In Obsidian you can zoom into this graph, place a pointer on a node to highlight the connecting dots, and much more.

Because I tend to forget such things, and as it may be useful to other people running a WordPress-blog making heavy use of MathJax, here’s the procedure I followed:

1. Follow the instructions from Convert wordpress articles to markdown.

Export your WordPress posts to XML
Install Node.js
Run the wordpress-export-to-markdown script

In the wizard I’ve opted to go only for yearly folders, to prefix posts with the date, and to save all images.

2. This gives you a directory with one folder per year containing markdown versions of your posts, and in each year-folder a subfolder ‘img’ containing all images.

Turn this directory into an Obsidian-vault by opening Obsidian, click on the ‘open another vault’ icon (third from bottom-left), select ‘Open folder as vault’ and navigate to your directory.

3. You will notice that most of your LaTeX cannot be parsed because during the markdown-process backslashes are treaded as special character, resulting in two backslashes for every LaTeX-command…

A remark before trying to solve this: another option might be to use the wordpress-to-hugo-exporter, resulting in clean LaTeX, but lacking the possibility to opt for yearly-folders (it dumps all posts into one folder), and it makes a mess of the image-files.

4. So, we will need to do a lot of search&replaces in all files, and need a convenient tool for this.

First option was the Sublime Text app, which is free and does the search&replaces quickly. The problem is that you have to save each of the files, one at a time! This may take hours.

I’ve done it using the Search and Replace app (3$) which allows you to make several searches/replaces at the same time (I messed up LaTeX code in previous exports, so needed to do many more changes). It warns you that it is dangerous to replace strings in all files (which is the reason why Sublime Text makes it difficult), you can ignore it, but only after you put the ‘img’ folders away in a safe place. Otherwise it will also try to make the changes to these files, recognise that they are not text-files, and drop them altogether…

That’s it.

I now have a backup network-version of this blog.

As we mentioned in the previous post a first attempt to construct the ‘topos of the unconscious’ might be to start with a collection of notes (the ‘conscious’) and work on the semantics of text-snippets to unravel (a part of) the unconscious underpinning of these notes. We also mentioned that the poset-structure in that post should be replaced by a more involved network structure.

What interests me most is whether such an approach might be doable ‘in practice’, and Obsidian looks like the perfect tool to try this out.

What we need is a sufficiently large set of notes, of independent interest, to inject into Obsidian. The more meta it is, the better…

(tbc)

Previously in this series:

Next:

The enriched vault

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Last May, the meeting Lacan et Grothendieck, l’impossible rencontre? took place in Paris (see this post). Video’s of that meeting are now available online.

Here’s the talk by Alain Connes and Patrick Gauthier-Lafaye on their book A l’ombre de Grothendieck et de Lacan : un topos sur l’inconscient ? (see this post ).

Let’s quickly recall their main ideas:

1. The unconscious is structured as a topos (Jacques Lacan argued it was structured as a language), because we need a framework allowing logic without the law of the excluded middle for Lacan’s formulas of sexuation to make some sense at all.

2. This topos may differs from person to person, so we do not all share the same rules of logic (as observed in real life).

3. Consciousness is related to the points of the topos (they are not precise on this, neither in the talk, nor the book).

4. All these individual toposes are ruled by a classifying topos, and they see Lacan’s work as the very first steps towards trying to describe the unconscious by a geometrical theory (though his formulas are not first order).

Surely these are intriguing ideas, if only we would know how to construct the topos of someone’s unconscious.

Let’s go looking for clues.

At the same meeting, there was a talk by Daniel Sibony: “Mathématiques et inconscient”

Sibony started out as mathematician, then turned to psychiatry in the early 70ties. He was acquainted with both Grothendieck and Lacan, and even brought them together once, over lunch, some day in 1973. He makes a one-line appearance in Grothendieck’s Récoltes et Semailles, when G discribes his friends in ‘Survivre et Vivre’:

“Daniel Sibony (who stayed away from this group, while pursuing its evolution out of the corner of a semi-disdainful, smirking eye)”

In his talk, Sibony said he had a similar idea, 50 years before Connes and Gauthier-Lafaye (3.04 into the clip):

“At the same time (early 70ties) I did a seminar in Vincennes, where I was a math professor, on the topology of dreams. At the time I didn’t have categories at my disposal, but I used fibered spaces instead. I showed how we could interpret dreams with a fibered space. This is consistent with the Freudian idea, except that Freud says we should take the list of words from the story of the dream and look for associations. For me, these associations were in the fibers, and these thoughts on fibers and sheaves have always followed me. And now, after 50 years I find this pretty book by Alain Connes and Patrick Gauthier-Lafaye on toposes, and see that my thoughts on dreams as sheaves and fibered spaces are but a special case of theirs.”

This looks interesting. After all, Freud called dream interpretation the ‘royal road’ to the unconscious. “It is the ‘King’s highway’ along which everyone can travel to discover the truth of unconscious processes for themselves.”

Sibony clarifies his idea in the interview L’utilisation des rêves en psychothérapie with Maryse Siksou.

“The dream brings blocks of words, of “compacted” meanings, and we question, according to the good old method, each of these blocks, each of these points and which we associate around (we “unblock” around…), we let each point unfold according to the “fiber” which is its own.

I introduced this notion of the dream as fibered space in an article in the review Scilicet in 1972, and in a seminar that I gave at the University of Vincennes in 1973 under the title “Topologie et interpretation des rêves”, to which Jacques Lacan and his close retinue attended throughout the year.

The idea is that the dream is a sheaf, a bundle of fibers, each of which is associated with a “word” of the dream; interpretation makes the fibers appear, and one can pick an element from each, which is of course “displaced” in relation to the word that “produced” the fiber, and these elements are articulated with other elements taken in other fibers, to finally create a message which, once again, does not necessarily say the meaning of the dream because a dream has as many meanings as recipients to whom it is told, but which produces a strong statement, a relevant statement, which can restart the work.”

Key images in the dream (the ‘points’ of the base-space) can stand for entirely different situations in someone’s life (the points in the ‘fiber’ over an image). The therapist’s job is to find a suitable ‘section’ in this ‘sheaf’ to further the theraphy.

It’s a bit like translating a sentence from one language to another. Every word (point of the base-space) can have several possible translations with subtle differences (the points in the fiber over the word). It’s the translator’s job to find the best ‘section’ in this sheaf of possibilities.

This translation-analogy is used by Daniel Sibony in his paper Traduire la passe:

“It therefore operates just like the dream through articulated choices, from one fiber to another, in a bundle of speaking fibers; it articulates them by seeking the optimal section. In fact, the translation takes place between two fiber bundles, each in a language, but in the starting bundle the choice seems fixed by the initial text. However, more or less consciously, the translator “bursts” each word into a larger fiber, he therefore has a bundle of fibers where the given text seems after the fact a singular choice, which will produce another choice in the bundle of the other language.”

This paper also contains a pre-ChatGPT story (we’re in 1998), in which the language model fails because it has far too few alternatives in its fibers:

I felt it during a “humor festival” where I was approached by someone (who seemed to have some humor) and who was a robot. We had a brief conversation, very acceptable, beyond the conventional witticisms and knowing sighs he uttered from time to time to complain about the lack of atmosphere, repeating that after all we are not robots.

I thought at first that it must be a walking walkie-talkie and that in fact I was talking to a guy who was remote control from his cabin. But the object was programmed; the unforeseen effects of meaning were all the more striking. To my question: “Who created you?” he answered with a strange word, a kind of technical god.

I went on to ask him who he thought created me; his answer was immediate: “Oedipus”. (He knew, having questioned me, that I was a psychoanalyst.) The piquancy of his answer pleased me (without Oedipus, at least on a first level, no analyst). These bursts of meaning that we know in children, psychotics, to whom we attribute divinatory gifts — when they only exist, save their skin, questioning us about our being to defend theirs — , these random strokes of meaning shed light on the classic aftermaths where when a tile arrives, we hook it up to other tiles from the past, it ties up the pain by chaining the meaning.

Anyway, the conversation continuing, the robot asked me to psychoanalyse him; I asked him what he was suffering from. His answer was immediate: “Oedipus”.

Disappointing and enlightening: it shows that with each “word” of the interlocutor, the robot makes correspond a signifying constellation, a fiber of elements; choosing a word in each fiber, he then articulates the whole with obvious sequence constraints: a bit of readability and a certain phrasal push that leaves open the game of exchange. And now, in the fiber concerning the “psy” field, chance or constraint had fixed him on the same word, “Oedipus”, which, by repeating itself, closed the scene heavily.

Okay, we have a first potential approximation to Connes and Gauthier-Lafaye’s elusive topos, a sheaf of possible interpretation of base-words in a language.

But, the base-space is still rather discrete, or at best linearly ordered. And also in the fibers, and among the sections, there’s not much of a topology at work.

Perhaps, we should have a look at applications of topology and/or topos theory in large language models?

(tbc)

Next:

The shape of languages

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Tag: books

Loading a second brain

The topology of dreams