I've sketched it out elsewhere but let's memorialize the broad strokes here because we're inspired at the moment... come back later and add in quotes from Luhmann and other sources (@Heyde1931).

Luhmann was balancing the differences between topically arranged commonplaces and the topical nature of the Dewey Decimal System (a standardized version across thousands of collections) and building neighborhoods of related ideas.

One of the issues with commonplace books, is planning them out in advance. How might you split up a notebook for long term use to create easy categories when you don't know how much room to give each in advance? (If you don't believe me, stop by r/commonplacebooks where you're likely to see this question pop up several times this year.) This issue is remedied when John Locke suggests keeping commonplaces in chronological order of their appearance and cross-indexing them.

This creates a new problem of a lot of indexing and increased searching over time as the commonplace book scales. Translating to index cards complicates things because they're unattached and can potentially move about, so they don't have the anchor effectuated by their being bound up in a notebook. But being on slips allows them to be more easily shuffled, rearranged, and even put into outlines, which are all fantastic affordances when looking for creativity or scaffolding things out into an article or book for creation.

As a result, numbering slips creates a solid anchor by which the cards can be placed and always returned for later finding and use. But how should we number them? Should it be with integers and done chronologically? (1, 2, 3, ..., n) This is nice, but makes a mish-mash of things and doesn't assist much in indexing or finding.

Why not go back to Dewey, which has been so popular? But not Dewey in the broadest sense of using numbers to tie ideas to concrete categories. An individual's notes are idiosyncratic and it would be increasingly rare for people to have the same note, much less need a standardized number for it (and if they were standardized, who does that work and how is it distributed so everyone could use it?) No, instead, let's just borrow the decimal structure of Dewey's system. One of the benefits of his decimal structure is that an infinity of new books can be placed on ever-expanding bookshelves without needing to restructure the numbering system. Just keep adding decimal places onto the end when necessary. This allows for immense density when necessary. But, importantly, it also provides some fantastic level of serendipity.

Let's say you go to learn about geometry, so you look up the topic in your trusty library card catalog. Do you really need to look at the hundreds of records returned? Probably not. You only need the the Dewey Decimal Number 516. Once you're at the shelves, you can browse through that section to see what's there and interesting in the space. You might also find things on the shelves above or below 516 and find the delights of topology and number theory or abstract algebra and real analysis. Subjects you might not necessarily have had in mind will suddenly present themselves for your consideration. Even if your initial interest may have been in Zhongmin Shen's Lectures on Finsler geometry (516.375), you might also profitably walk away with James E. Humphreys' Introduction to Lie Algebras and Representation Theory (512.55).

So what happens if we use these decimal numbers for our notes? First we will have the ability to file things between and amongst each other to infinity. By filing things closest to things which seem related to each other, we'll create neighborhoods of ideas which can easily grow over time. Related ideas will stay together while seemingly related ideas on first blush may slowly grow away from each other over time as even more closely related ideas move into the neighborhood between them. With time and careful work, you'll have not only a breadth of ideas, but a massive depth of them too.

The use of decimal numbering provides us with a few additional affordances:

1 (Neighborhoods of ideas) 1.1 combinatorial creativity Neighborhoods of ideas can help to fuel combinatorial creativity and forge new connections as well as insight over time. 1.2 writing One might take advantage of these growing neighborhoods to create new things. Perhaps you've been working for a while and you see you have a large number of cards in a particular area. You can, to some extent, put your hand into your box and grab a tranche of notes. By force of filing, these notes are going to be reasonably related, which means you should be able to use them to write a blog post, an article, a magazine piece, a chapter, or even an entire book (which may require a few fistfuls, as necessary.)

2 (Sparse indexing) We don't need to index each and every single topic or concept into our index. Because we've filed things nearby, if a new card about Finsler geometry relates to another and we've already indexed the first under that topic, then we don't need to index the second, because our future selves can easily rely on the fact that if we're interested in Finsler geometry in the future, we can look that up in the index, and go to that number where we're likely to see other cards related to the topic as well as additional serendipitous ideas related to them in that same neighborhood.

You may have heard that as Luhmann progressed on his decades long project, broadly on society and within the area of sociology, he managed to amass 90,000 index cards. How many do you suppose he indexed under the topic of sociology? Certainly he had 10s of thousands relating to his favorite subject, no? Of course he did, but what would happen over time as a collection grows? Having 20,000 indexed entries about sociology doesn't scale well for your search needs. Even 10 indexed entries may be a bit overwhelming as once you find a top level card, hundreds to thousands around it are going to be related. 10 x 100 = 1,000 cards to flip through. So if you're indexing, be conservative. In the roughly 45 years of creating 90,000 slips, Luhmann only indexed two cards with the topic of "sociology". If you look through his index, you'll find that most of his topical entries only have pointers to one or two cards, which provide an entryway into those topics which are backed up with dozens to hundreds of cards on related topics. In rarer, instances you might find three or four, but it's incredibly rare to find more than that.

Over time, one will find that, for the topics one is most interested in, the number of ideas and cards will grown without bound. Here it makes sense to use more and more specific topics (tags, categories, taxonomies) all of which are each also sparsely indexed. Ultimately one finds that in the limit, the categories get so fractionalized that the closest category one idea has with another is the fact that they're juxtaposed closely by number. The of the decimal expansion might say something about the depth or breadth of the relationship between ideas.

Something else arises here. At first one may have the tendency to associate their numbers with topical categories. This is only natural as it's a function at which humans all excel. But are those numbers really categories after a few weeks? Probably not. Treat them only as address numbers or GPS coordinates to be able to find your way. Your sociology section may quickly find itself with invasive species of ideas from anthropology and archaeology as well as history. If you treat all your ideas only at the topical level, they'll be miles away from where you need them to be as the smallest level atomic ideas collide with each other to generate new ideas for you. Naturally you can place them further away if you wish and attempt to bridge the distance with links to numbers in other locations, but I suspect you'll find this becomes pretty tedious over time and antithetical when it comes time to pull out a handful and write something. It's fantastically easier to pull out a several dozen and begin than it is to go through and need to pull out linked cards in a onesy-twosies manner or double check with your index to make sure you've gotten the most interesting bits. This becomes even more important as your collection scales.

—Georg Christoph Lichtenberg, Notebook E, #46, 1775–1776

In this single paragraph quote Lichtenberg, using the model of Italian bookkeepers of the 18th century, broadly outlines almost all of the note taking technique suggested by Sönke Ahrens in How to Take Smart Notes. He's got writing down and keeping fleeting notes as well as literature notes. (Keeping academic references would have been commonplace by this time.) He follows up with rewriting and expanding on the original note to create additional "explanations" and even "connections" (links) to create what Ahrens describes as permanent notes or which some would call evergreen notes.

Lichtenberg's version calls for the permanent notes to be "separated and ordered" and while he may have kept them in book format himself, it's easy to see from Konrad Gessner's suggestion at the use of slips centuries before, that one could easily put their permanent notes on index cards ("separated") and then number and index or categorize them ("ordered"). The only serious missing piece of Luhmann's version of a zettelkasten then are the ideas of placing related ideas nearby each other, though the idea of creating connections between notes is immediately adjacent to this, and his numbering system, which was broadly based on the popularity of Melvil Dewey's decimal system.

It may bear noticing that John Locke's indexing system for commonplace books was suggested, originally in French in 1685, and later in English in 1706. Given it's popularity, it's not unlikely that Lichtenberg would have been aware of it.

Given Lichtenberg's very popular waste books were known to have influenced Leo Tolstoy, Albert Einstein, Andre Breton, Friedrich Nietzsche, and Ludwig Wittgenstein. (Reference: Lichtenberg, Georg Christoph (2000). The Waste Books. New York: New York Review Books Classics. ISBN 978-0940322509.) It would not be hard to imagine that Niklas Luhmann would have also been aware of them.

Open questions: <br /> - did Lichtenberg number the entries in his own waste books? This would be early evidence toward the practice of numbering notes for future reference. Based on this text, it's obvious that the editor numbered the translated notes for this edition, were they Lichtenberg's numbering? - Is there evidence that Lichtenberg knew of Locke's indexing system? Did his waste books have an index?

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 note taking and zettelkasten, 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:<br /> 0.110<br /> 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 it 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.XXX and 3500.YYY 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.

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 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, 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.

While Heyde outlines using keywords/subject headings and dates on the bottom of cards with multiple copies using carbon paper, we're left with the question of where Luhmann pulled his particular non-topical ordering as well as his numbering scheme.

While it's highly likely that Luhmann would have been familiar with the German practice of Aktenzeichen ("file numbers") and may have gotten some interesting ideas about organization from the closing sections of the "Die Kartei" section 1.2 of the book, which discusses library organization and the Dewey Decimal system, we're still left with the bigger question of organization.

It's obvious that Luhmann didn't follow the heavy use of subject headings nor the advice about multiple copies of cards in various portions of an alphabetical index.

While the Dewey Decimal System set up described is indicative of some of the numbering practices, it doesn't get us the entirety of his numbering system and practice.

One need only take a look at the Inhalt (table of contents) of Heyde's book! The outline portion of the contents displays a very traditional branching tree structure of ideas. Further, the outline is very specifically and similarly numbered to that of Luhmann's zettelkasten. This structure and numbering system is highly suggestive of branching ideas where each branch builds on the ideas immediately above it or on the ideas at the next section above that level.

Just as one can add an infinite number of books into the Dewey Decimal system in a way that similar ideas are relatively close together to provide serendipity for both search and idea development, one can continue adding ideas to this branching structure so they're near their colleagues.

Thus it's highly possible that the confluence of descriptions with the book and the outline of the table of contents itself suggested a better method of note keeping to Luhmann. Doing this solves the issue of needing to create multiple copies of note cards as well as trying to find cards in various places throughout the overall collection, not to mention slimming down the collection immensely. Searching for and finding a place to put new cards ensures not only that one places one's ideas into a growing logical structure, but it also ensures that one doesn't duplicate information that may already exist within one's over-arching outline. From an indexing perspective, it also solves the problem of cross referencing information along the axes of the source author, source title, and a large variety of potential subject headings.

And of course if we add even a soupcon of domain expertise in systems theory to the mix...

While thinking about Aktenzeichen, keep in mind that it was used in German public administration since at least 1934, only a few years following Heyde's first edition, but would have been more heavily used by the late 1940's when Luhmann would have begun his law studies.

https://hypothes.is/a/CqGhGvchEey6heekrEJ9WA

When thinking about taking notes for creating output, one can follow one thought with another logically both within one's card index not only to write an actual paper, but the collection and development happens the same way one is filling in an invisible outline which builds itself over time.

Linking different ideas to other ideas separate from one chain of thought also provides the ability to create multiple of these invisible, but organically growing outlines.