Thoughts on Zettelkasten numbering systems

I’ve seen variations of the beginner Zettelkasten question:

“What happens when you want to add a new note between notes 1/1 and 1/1a?”

asked at least a dozen times in the Reddit fora related to zettelkasten and note taking, on zettelkasten.de, or in other places across the web.

Dense Sets

From a mathematical perspective, these numbering or alpha-numeric systems are, by both intent and design, underpinned by the mathematical idea of dense sets. In the areas of topology and real analysis, one considers a set dense when one can choose a point as close as one likes to any other point. For both library cataloging systems and numbering schemes for ideas in Zettelkasten this means that you can always juxtapose one topic or idea in between any other two.

Part of the beauty of Melvil Dewey’s original Dewey Decimal System is that regardless of how many new topics and subtopics one wants to add to their system, one can always fit another new topic between existing ones ad infinitum.

Going back to the motivating question above, the equivalent question mathematically is “what number is between 0.11 and 0.111?” (Here we’ve converted the artificial “number” “a” to a 1 and removed the punctuation, which doesn’t create any issues and may help clarify the orderings a bit.) The answer is that there is an infinite number of numbers between these!

This is much more explicit by writing these numbers as:
0.110
0.111

Naturally 0.1101 is between them (along with an infinity of others), so one could start here as a means of inserting ideas this way if they liked. One either needs to count up sequentially (0, 1, 2, 3, …) or add additional place values.

Decimal numbering systems in practice

The problem most people face is that they’re not thinking of these numbers as decimals, but as natural numbers or integers (or broadly numbers without any decimal portions). Though of course in the realm of real numbers, numbers above 0 are dense as well, but require the use of their decimal portions to remain so.

The tough question is: what sorts of semantic meanings one might attach to their adding of additional place values or their alphabetical characters? This meaning can vary from person to person and system to system, so I won’t delve into it here.

One may find it useful to logically chunk these numbers into groups of three as is often done using commas, periods, slashes, dashes, spaces, or other punctuation. This doesn’t need to mean anything in particular, but may help to make one’s numbers more easily readable as well as usable for filing new ideas. Sometimes these indicators can be confusing in discussion, so if ever in doubt, simply remove them and the general principles mentioned here should still hold.

Depending on one’s note taking system, however, when putting cards into some semblance of a logical, sort-able order (perhaps within a folder for example), the system may choke on additional characters beyond the standard period to designate a decimal number. For example: within Obsidian, if you have a “zettelkasten” folder with lots of numbered and named files within it, you’ll want to give each number the maximum number of decimal places so that when doing an alphabetic sort within the folder, all of the numbered ideas are properly sorted. As an example if you give one file the name “0.510 Mathematics”, another “0.514 Topology” and a third “0.5141 Dense Sets” they may not sort properly unless you give the first two decimal expansions to the ten-thousands place at a minimum. If you changed them to “0.5100 Mathematics” and “0.5140 Topology, then you’re in good shape and the folder will alphabetically sort as you’d expect. Similarly some systems may or may not do well with including alphabetic characters mixed in with numbers.

If using chunked groups of three numbers, one might consider using the number 0.110.001 as the next level of idea between them and then continuing from there. This may help to spread some of the ideas out as surely one may have yet another idea to wedge in between 0.110.000 and 0.110.001?

One can naturally choose almost any any (decimal) number, so long as it is somewhat “near” the original behind which one places it. By going out further in the decimal expansion, one can always place any idea between two others and know that there will be a number that it can be given that will “work”.

Generally within numbers as we use them for mathematics, 0.100000001 is technically “closer” by distance measurement to 0.1 than 0.11, (and by quite a bit!), but somehow when using numbers for zettelkasten purposes, we tend to want to not consider them as decimals, as the Dewey Decimal System does. We also have the tendency to want to keep our numbers as short as possible when writing, so it seems more “natural” to follow 0.11 with 0.111, as it seems like we’re “counting up” rather than “counting down”.

Another subtlety that one sees in numbering systems is the proper or improper use of the whole numbers in front of the decimal portions. For example, in Niklas Luhmann’s system, he has a section of cards that start with 3.XXXX which are close to a section numbered 35.YYYY. This may seem a bit confusing, but he’s doing a bit of mental gymnastics to artificially keep his numbers smaller. What he really means is 3000.XXXX and 3500.YYYY respectively, he’s just truncating the extra zeros. Alternately in a fully “decimal system” one would write these as 0.3000.XXXX and 0.3500.YYYY, where we’ve added additional periods to the numbers to make them easier to read. Using our original example in an analog system, the user may have been using foreshortened indicators for their system and by writing 1/1a, they may have really meant something of the form 001.001/00a, but were making the number shorter in a logical manner (at least to them).

The close observer may have seen Scott Scheper adopt the slightly longer numbers in the thousands (like 3500.YYYY) as a means of remedying some of the numbering confusion many have when looking at Luhmann’s system.

Those who build their systems on top of existing ones like the Dewey Decimal Classification, or the Universal Decimal Classification may wish to keep those broad categories with three to four decimal places at the start and then add their own idea number underneath those levels.

As an example, we can use the numbering for Finsler geometry from the Dewey Decimal Classification wikipedia page shown as:

500 Natural sciences and mathematics
   510 Mathematics
      516 Geometry
         516.3 Analytic geometries
            516.37 Metric differential geometries
               516.375 Finsler geometry

So in our zettelkasten, we might add our first card on the topic of Finsler geometry as “516.375.001 Definition of Finsler geometry” and continue from there with some interesting theorems and proofs on those topics.

Don’t Waste Time on Complex Classification Systems

Of course, while this is something one can do doesn’t mean that one should do it. Going too far down the rabbit holes of “official” forms of classification this way can be a massive time wasting exercise as in most private systems, you’re never going to be comparing your individual ideas with the private zettelkasten of others and in practice the sort of standardizing work for classification this way is utterly useless. Beyond this, most personal zettelkasten are unique and idiosyncratic to the user, so for example, my math section labeled 510 may have a lot more overlap with history, anthropology, and sociology hiding within it compared with others who may have all of their mathematics hiding amidst their social sciences section starting with the number 300. One of the benefits of Luhmann’s ad hoc numbering scheme, at least for him, is that it allowed his system to be much more interdisciplinary than using a more complicated Dewey Decimal oriented system which may have dictated moving some of his systems theory work out of his politics area where it may have made more sense to him in addition to being more productive on a personal level.

Of course if you’re using the older sort of commonplacing zettelkasten system that was widely in use before Luhmann’s variation, then perhaps using a Dewey-based system may be helpful to you?

A Touch of History

As both a mathematician working in the early days of real analysis and a librarian, I wouldn’t be surprised if some of these loose ideas may have occurred tangentially to Gottfried Wilhelm Leibniz (1646 – 1716), though I’m currently unaware of any specific instances within his work. One must note, however, that some of the earliest work within library card catalogs as we know and use them today stemmed from 1770s Austria where governmental conscription needs overlapped with card cataloging systems (Krajewski, 2011). It’s here that the beginnings of these sorts of numbering systems begin to come into use well before Melvil Dewey’s later work which became much more broadly adopted.

The German “file number” (aktenzeichen) is a unique identification of a file, commonly used in their court system and predecessors as well as file numbers in public administration since at least 1934. We know Niklas Luhmann studied law at the University of Freiburg from 1946 to 1949, when he obtained a law degree, before beginning a career in Lüneburg’s public administration where he stayed in civil service until 1962. Given this fact, it’s very likely that Luhmann had in-depth experience with these sorts of file numbers as location identifiers for files and documents. As a result it’s reasonably likely that a simplified version of these were at least part of the inspiration for his own numbering system. [] []

Your own practice

At the end of the day, the numbering system you choose needs to work for you within the system you’re using (analog, digital, other). I would generally recommend against using someone else’s numbering system unless it completely makes sense to you and you’re able to quickly and simply add cards to your system with out the extra work and cognitive dissonance about what number you should give it. The more you simplify these small things, the easier and happier you’ll be with your set up in the end.

References

Krajewski, Markus. Paper Machines: About Cards & Catalogs, 1548-1929. Translated by Peter Krapp. History and Foundations of Information Science. MIT Press, 2011. https://mitpress.mit.edu/books/paper-machines.

Munkres, James R. Topology. 2nd ed. 1975. Reprint, Prentice-Hall, Inc., 1999.


Featured photo by Manson Yim on Unsplash

NaNoWriMo with Zettelkasten Approach for an AcWriMo Non-Fiction Writing

Using Niklas Luhmann’s rough average of six zettels per day working full time for 8 hours a day versus writing approximately 1,667 words in an hour’s work (~28 words written per minute, which seems a reasonable average), I’ve created a zettelkasten word count equivalent for reading, research, and note making.

  • 28 words for every minute spent reading and making fleeting notes.
  • 415 words for every well-formed, fully written out permanent note
  • 500 words for every well-formed, fully written out and installed permanent note (includes work to install it in the box)
  • 84 words for every cross link created from one note to another
  • 140 words for every bibliographic card created
  • 56 words for every index entry created

If you’re diligently working at any or all of the above, instead of measuring all the small pieces, you could just use a 28 word/minute measure for your zettelkasten-based work.

If you’re not a full time research-only academic (without a teaching load or other administrative obligations) and for fun want to measure your NaNoWriMo for non-fiction work on a card per day basis using Niklas Luhmann as a guide/measure, then you should do the reading, research and note taking work to produce 0.75 cards per day (that is, well written permanent notes installed, indexed, and well-linked; we’re not keeping track of the indexing cards, bibliographic cards, or other fleeting notes here, which you’ll also be doing along the way) to keep pace for an equivalent 50,000 words during the month. This is about 5.25 cards per week or about 23 cards for the entire month.

The goal here is, instead of churning out raw words, to churn out reading, research, and note making towards material you can reasonably use to write journal articles, book chapters, or a full non-fiction book.

If you’re using an index card-based system for fiction writing the way Vladimir Nabokov did, then you really should do a traditional word count as that’s more closely in line with the workflow of the standard NaNoWriMo work.

N.B. This probably overshoots the mark, as the 6 cards/day number for Luhmann probably includes all cards and not just permanent notes in his entire collection over his entire lifetime’s work. It also doesn’t take into account the possibility that he carried a teaching load, administrative work, fundraising work, or other nonsense required of professors.) Of course this is is all just for fun anyway, so… quit worrying and start researching and writing a little bit every day.

Bookmarked ‘Mere chips from his workshop’: Gotthard Deutsch’s monumental card index of Jewish history by Jason Lustig (History of the Human Sciences | Sage Journals)
Gotthard Deutsch (1859–1921) taught at Hebrew Union College in Cincinnati from 1891 until his death, where he produced a card index of 70,000 ‘facts’ of Jewish history. This article explores the biography of this artefact of research and poses the following question: Does Deutsch’s index constitute a great unwritten work of history, as some have claimed, or are the cards ultimately useless ‘chips from his workshop’? It may seem a curious relic of positivistic history, but closer examination allows us to interrogate the materiality of scholarly labor. The catalogue constitutes a total archive and highlights memory’s multiple registers, as both a prosthesis for personal recall and a symbol of a ‘human encyclopedia’. The article argues that this mostly forgotten scholar’s work had surprising repercussions: Deutsch’s student Jacob Rader Marcus (1896–1995) brought his teacher’s emphasis on facticity to the field of American Jewish history that he pioneered, catapulting a 19th-century positivism to the threshold of the 21st century. Deutsch’s index was at an inflection point of knowledge production, created as historians were shifting away from ‘facts’ but just before new technologies (also based on cards) enabled ‘big data’ on a larger scale. The article thus excavates a vision of monumentality but proposes we look past these objects as monuments to ‘heroic’ scholarship. Indeed, Deutsch’s index is massive but middling, especially when placed alongside those of Niklas Luhmann, Paul Otlet, or Gershom Scholem. It thus presents a necessary corrective to anointing such indexes as predecessors to the Internet and big data because we must keep their problematic positivism in perspective.
In honor of Yom Kippur today, I’m celebrating with acknowledgement of Gotthard Deutsch’s “monumental card index [zettelkasten] of Jewish history”. I hope everyone had an easy fast.

Zettelkasten Method State of the Art in 1898

Many people mistakenly credit Niklas Luhmann with the invention of the zettelkasten method, so I’ve been delving into historical note taking practices. I’ve recently come across a well known and influential book on historical method from the late 1800s that has well described version of the slip (box) method.

Originally published in French in 1897 as Introduction aux études historiques and then translated into English by George Godfrey Berry, Henry Holt and Company published Introduction to the Study of History in 1898 by authors Charles Victor Langlois and Charles Seignobos. Along with Ernst Bernheim’s popular Lehrbuch der historischen Methode mit Nachweis der wichtigsten Quellen und Hülfsmittelzum Studium der Geschichte (Leipzig: Duncker & Humblot, 1889), Langlois and Seignobos’ text is one of the first comprehensive manuals discussing the use of scientific techniques in historical research.

Primarily written by Seignobos, Book II, Chapter IV “Critical Classification of Sources” has several sections on the zettelkasten method under the section headings:

  • Importance of classification—The first impulse wrong—Thenote-book system not the best—Nor the ledger-system—Nor the “system” of trusting the memory
  • The system of slips the best—Its drawbacks—Means ofobviating them—The advantage of good “private librarian-ship”

This section describes a slip method for taking notes which is ostensibly a commonplace book method done using slips of paper (fiches in the original French) instead  of notebooks. Their method undergirds portions of the historical method they lay out in the remainder of the book. Seignobos calls the notebook method “utterly wrong” and indicates that similar methods have been “universally condemned” by librarians as a means of storing and maintaining knowledge. Entertainingly he calls the idea of attempting to remember one’s knowledge using pure memory a “barbarous method”. 

The slip method is so ubiquitous by the time of his writing in 1897 that he says “Every one admits nowadays that it is advisable to collect materials on separate cards or slips of paper.”

The Slip Method

The book broadly outlines the note taking process: 

The notes from each document are entered upon a loose leaf furnished with the precisest possible indications of origin. The advantages of this artifice are obvious : the detachability of the slips enables us to group them at will in a host of different combinations ; if necessary, to change their places : it is easy to bring texts of the same kind together, and to incorporate additions, as they are acquired, in the interior of the groups to which they belong. As for documents which are interesting from several points of view, and which ought to appear in several groups, it is sufficient to enter them several times over on different slips ; or they may be represented, as often as may be required, on reference-slips.

Seignobos further advises, as was generally common, “to use slips of uniform size and tough material” though he subtly added the management and productivity advice “to arrange them at the earliest opportunity in covers or drawers or otherwise.”

In terms of the form of notes, he says

But it will always be well to cultivate the mechanical habits of which professional compilers have learnt the value by experience: to write at the head of every slip its date, if there is occasion for it, and a heading in any case; to multiply cross-references and indices; to keep a record, on a separate set of slips, of all the sources utilised, in order to avoid the danger of having to work a second time through materials already dealt with.

Where the Luhmann fans will see a major diversion for the system compared to his internal branching system is in its organization. They describe a handful of potential organizations based on the types of notes and their potential uses, though many of these use cases specific to historical research are now better effected by databases and spreadsheets. As for the broader classes of more traditional literature-based textual notes, they recommend grouping the slips in alphabetical order of the words chosen as subject headings. Here, even in a French text translated to English, the German word Schlagwörter is used. It can be translated as “headwords”, “catchwords” or “topical headings” though modern note takers, particularly in digital contexts, may be more comfortable with the translation “tags”.

While there are descriptions of cross-linking or cross-referencing cards from one to another, there is no use of alpha-numeric identifiers or direct juxtaposition of ideas on cards as was practiced by Luhmann.

The authors specifically credit Ernst Bernheim’s Lehrbuch der historischen Methode several times in the book. While a lot of the credit is geared toward their broader topic of historical method, Bernheim provides a description of note taking very similar to their method. I’ve found several copies of Bernheim’s text in German, but have yet to find any English translations. 

Both Bernheim and Langlois/Seignobos’ work were influential enough in the areas of history specifically and the humanities in general that Beatrice Webb (an influential English sociologist, economist, socialist, labour historian, and social reformer who was a co-founder of the London School of Economics, the Fabian Society, and The New Statesman) cites their work in Appendix C “The Art of Note-Taking” in her 1926 autobiographical work My Apprenticeship, which was incredibly popular and went through multiple reprintings in the nearly full century since its issue. Her personal use of this note taking method would appear to pre-date both books (certainly the Langlois/Seignobos text), however, attesting to its ubiquity in the late 1800s.

What is the “true” zettelkasten method?

Scott Scheper has recently written that personal communication with Luhmann’s youngest son Clemmens Luhmann indicated that Luhmann learned his method in 1951 from the Johannes Erich Heyde text Technik des wissenschaftlichen Arbeitens (with several German editions from 1931 onward). This book’s note taking method is broadly similar to that of the long held commonplace book maintained on index cards as seen in both Langlois/Seignobos (1897) and Webb (1926). One of the few major differences in Heyde was the suggestion to actively make and file multiple copies of the same card under different topical headings potentially using carbon copy paper to speed up the process. While it’s possible that Luhmann may have either learned the modifications of his particular system from someone or modified it himself, it is reasonably obvious that there is a much longer standing tradition as early as Konrad Gessner in 1548 to the middle of the 20th century of a zettelkasten tradition that is more similar to the commonplace book tradition effectuated with index cards (or slips “of a similar size”). Luhmann’s system, while seemingly more popular and talked about since roughly 2013, is by far the exception rather than the rule within the broader history of the “zettelkasten method”. With these facts in mind, we should be talking about a simpler, historical zettelkasten method and a separate, more complex/emergent Luhmann method.

Call for Model Examples of Zettelkasten Output Processes

Perhaps too much of the resurgence of the zettelkasten idea and the online space about it is focused on what a zettelkasten is or how it should be done. After this, descriptions of the process of collecting material for one’s zettelkasten is followed by using it to generate new ideas and thought, though this last part is relatively sparce in comparison. Very little of the discussion or examples I’ve seen in online fora, social media, websites, and the blogosphere is focused on actively using them for creating actual long form output.

As Luhmann’s (all-too-frequently used) example is so powerful, I think it would be massively helpful if users had stronger examples of what these explicit creation workflows looked like, particularly at the longer end of creation of chapters or even book length spaces. Are there any detailed posts, videos, other media about how one approached this problem? What worked well? What didn’t? What would you do differently next time? Have you done this multiple times and now settled into something you feel is most efficient? Is your process manual/digital? What tools helped along the way for laying out and doing the actual stitching together and editing? Would you use them again or try something else? Have you experimented with different methods or practices?

Here, I’m looking for direct and actual experience; I’m explicitly not looking for “this is how I would do it” responses.

Because it’s much easier and far more successful for humans to imitate the practice of others than to innovate it for themselves, I’m ultimately looking not for outlines of what people recommend, but public examples of the practices in progress. Who can show their actual “receipts” and in a reasonably linear and practical way for others to follow? We suffer from a lack of these practices being visible online as most aren’t. Further even the digital ones aren’t public, or if they are, they aren’t well known.

As an example of the broader problem, I’ve yet to see a week go by that someone doesn’t read Ahrens’ generally excellent book, but in posting online they still seem lost in attempting to put the lowest level ideas into active practice.

Personally, I use Hypothes.is as a digital tool for the majority of my note taking. One could follow my feed and see it in real time if they choose. There are benefits for this public practice and I’m aware that many people follow this feed of notes out of curiosity. I’ve even gotten emails from folks indicating that they’ve learned some interesting things for use in their own practices. Sadly, the follow up of revision, cross linking, active indexing, and subsequent growth isn’t public (yet), though the platform I’m using is open to active public conversation and commentary, which is a useful side benefit. I have seen a few other public examples of others’ practices, some in video form, though this can be dull as the time and effort is work and doesn’t make for powerful entertainment because it isn’t. Still these public examples can be far more powerful than some of the explanations I’ve seen, especially for beginners who don’t comprehend the long term benefits (surprise, serendipity, insight, emergent creativity) and who generally focus on the minutiae for lack of direct experience.

On the creation portion, I’m currently experimenting with carrying out the original  instructions of Konrad Gessner, an early zettelmacher, as laid out in his book Pandectarum sive Partitionum Universalium. (1548. Zurich: Christoph Froschauer) and hope to report back shortly about the experience. 

Call for explicit examples

So where are the examples? Show us your receipts. Who’s doing this in public that people can follow? Who can be imitated until people have the experience(s) to do this more easily on their own? Let’s collect some of the best (or at least extant) examples for sharing with others. 

Once we’ve got some concrete examples then we can study them and iterate on them.

Too many people seem intent on potentially wasting their time by innovating on a practice they haven’t even tried because someone in the productivity space (who usually hasn’t tried it either) wrote a page long post saying it would be a good idea. I know we can do far better.

Replied to a thread by Scott P. Scheper and Alexandra Graßler (Twitter)
I’ll go you one better with the likely historical precedent for Niklas Luhmann’s zettelkasten numbering system: conscription numbers on Viennese houses in 1770s! https://hypothes.is/users/chrisaldrich?q=austria+tag%3A%22Niklas+Luhmann%22

Alberto Cevolini & Markus Krajewski have relevant research. There are still a few missing puzzle pieces however.

Tiago, I’ve started into an advanced copy of your forthcoming book and at the end of the introduction you have a footnote:

Other popular terms for such a system include Zettelkasten (meaning “slipbox” in German, coined by influential sociologist Niklas Luhmann), Memex (a word invented by American inventor Vannevar Bush), and digital garden (named by popular online creator Anne-Laure Le Cunff)

Please know that the zettelkasten and its traditions existed prior to Niklas Luhmann. He neither invented them nor coined their name. It’s a commonly repeated myth on the internet that he did and there’s ample evidence of their extensive use prior to his well known example. I’ve documented some brief history on Wikipedia to this effect should you need it: https://en.wikipedia.org/wiki/Zettelkasten

The earliest concept of a digital garden stems from Mark Bernstein’s essay Hypertext Gardens: Delightful Vistas in 1998. This torch was picked up by academic Mike Caulfield in a 2015 keynote/article The Garden and The Stream: A Technopastoral.

Anne-Laure Le Cunff’s first mention of “digital garden” was on April 21, 2020

Which occurred just after Maggie Appleton’s mention on 2020-04-15

And several days after Justin Tadlock’s article on 2020-04-17 

Before this there was Joel Hooks by at least 2020-02-04 , though he had been thinking about it in late 2019.

He was predated by Tom Critchlow on 2018-10-18 who credits Mike Caulfield’s article from 2015-10-17 as an influence.

Archive.org has versions of the phrase going back into the early 2000’s: https://web.archive.org/web/*/%22digital%20garden%22

Hopefully you’re able to make the edits prior to publication, or at least in an available errata.

For those who’ve been waiting for it to show up, the digitized version of box 9 of Niklas Luhmann’s second zettelkasten is now available online. It contains many of his notes on the zettelkasten itself.
https://niklas-luhmann-archiv.de/bestand/zettelkasten/zettel/ZK_2_NB_9-8g_V
For those in the back: Niklas Luhmann did not invent the Zettelkasten.
If this is something you have a penchant to forget there are bumper stickers now.

White bumper sticker with a cartoon image of Luhmann  with text that reads "Niklas Luhmann did not invent the zettelkasten"
 
Or if you need a mug for drinking your coffee as you process your permanent notes…
 
White coffee mug with cartoon image of Niklas Luhmann staring at the viewer
 

Does Spirit hide in the filing cabinet?

On a slip in his zettelkasten (a card catalog or filing cabinet of personal notes), entitled “Does Spirit hide in the filing cabinet?”, Niklas Luhmann wrote a note about people who came to see his system:

“People come, they see everything and nothing more than that, just like in porn movies; consequently, they leave disappointed.”

This is a telling story about people’s perception of the simplicity of the idea of a slip box (zettelkasten, card catalog, commonplace book or whatever you want to call your note taking system).

yellowed index card with the identifier 9/8,3 with almost illegible handwriting in German Niklas Luhmann, Zettelkasten II, index card no. 9/8,3

It’s also a testament to the fact that the value of a zettelkasten is in the upfront work that is required in making valuable notes and linking them. Many people end up trying out the simple looking system and then wonder why it isn’t working for them. The answer is that they’re not working for it.

Just as sex can be fun, working with a system of notes can be fun. (“Just” can be a problematic word, n’cest pas?)  In either framing, both partners need to do some work—neither necessarily the same work. The end result can be magic.

As Potter Stewart might have said, “I may not be able to define proper note taking, but I know it when I see it.”

A quick note to the personal knowledge management fanatics: Niklas Luhmann positively did NOT invent the Zettelkasten. The idea predates him by quite a bit and had even earlier forms. He’s also not the only significant example.

https://boffosocko.com/2021/07/03/differentiating-online-variations-of-the-commonplace-book-digital-gardens-wikis-zettlekasten-waste-books-florilegia-and-second-brains/