On the Jokerzettel: An Apocalyptic Interpretation of Luhmann’s note ZKII 9/8j

Niklas Luhmann’s Jokerzettel 9/8j

Many have asked about the meaning of Niklas Luhmann’s so-called jokerzettel over the past several years.

9/8j Im Zettelkasten ist ein Zettel, der das
Argument enthält, das die Behauptungen
auf allen anderen Zetteln widerlegt.

Aber dieser Zettel verschwindet, sobald man
den Zettelkasten aufzieht.
D.h. er nimmt eine andere Nummer an,
verstellt sich und ist dann nicht zu finden.

Ein Joker.

—Niklas Luhmann, ZK II: Zettel 9/8j

Translation:

9/8j In the slip box is a slip containing the argument that refutes the claims on all the other slips. But this slip disappears as soon as you open the slip box. That is, he assumes a different number, disguises himself and then cannot be found. A joker.

An Apocalyptic Interpretation

Here’s my slightly extended interpretation, based on my own practice with several thousands of cards, about what Luhmann meant:

Imagine you’ve spent your life making and collecting notes and ideas and placing them lovingly on index cards. You’ve made tens of thousands and they’re a major part of your daily workflow and support your life’s work. They define you and how you think. You agree with Friedrich Nietzsche’s concession to Heinrich Köselitz that “You are right — our writing tools take part in the forming of our thoughts.” Your time is alive with McLuhan’s idea that “The medium is the message.” or his friend John Culkin‘s aphorism, “We shape our tools and thereafter they shape us.”

Eventually you’re going to worry about accidentally throwing your cards away, people stealing or copying them, fires (oh! the fires), floods, or other natural disasters. You don’t have the ability to do digital back ups yet. You may ask yourself, can I truly trust my spouse not to destroy them? What about accidents like dropping them all over the floor and needing to reorganize them or worse, what if the ghost in the machine should rear its head?

You’ll fear the worst, but the worst only grows logarithmically in proportion to your collection.

Eventually you pass on opportunities elsewhere because you’re worried about moving your ever-growing collection. What if the war should obliterate your work? Maybe you should take them into the war with you, because you can’t bear to be apart?

If you grow up at a time when Schrödinger’s cat is in the zeitgeist, you’re definitely going to have nightmares that what’s written on your cards could horrifyingly change every time you look at them. Worse, knowing about the Heisenberg Uncertainly Principle, you’re deathly afraid that there might be cards, like electrons, which are always changing position in ways you’ll never be able to know or predict.

As a systems theorist, you view your own note taking system as a input/output machine. Then you see Claude Shannon’s “useless machine” (based on an idea of Marvin Minsky) whose only function is to switch itself off. You become horrified with the idea that the knowledge machine you’ve painstakingly built and have documented the ways it acts as an independent thought partner may somehow become self-aware and shut itself off!?!

And worst of all, on top of all this, all your hard work, effort, and untold hours of sweat creating thousands of cards will be wiped away by a potential unknowable single bit of information on a lone, malicious card; your only recourse is suicide, the unfortunate victim of dataism.

Of course, if you somehow manage to overcome the hurdle of suicidal thoughts, and your collection keeps growing without bound, then you’re sure to die in a torrential whirlwind avalanche of information and cards, literally done in by information overload.

But, not wishing to admit any of this, much less all of this, you imagine a simple trickster, a joker, something silly. You write it down on yet another card and you file it away into the box, linked only to the card in front of it, the end of a short line of cards with nothing following it, because what could follow it? Put it out of your mind and hope your fears disappear away with it, lost in your box like the jokerzettel you imagined. You do this with a self-assured confidence that this way of making sense of the world works well for you, and you settle back into the methodical work of reading and writing, intent on making your next thousands of cards.

On The Interdisciplinarity of Zettelkasten: Card Numbering, Topical Headings, and Indices

As humans we’re terrifically spectacular at separating things based on perceived categories. The Dewey Decimal System systematically separates mathematics and history into disparate and distinct locations, but your zettelkasten shouldn’t force this by overthinking categories. Perhaps the overlap of math and history is exactly the interdisciplinary topic you’re working toward? If this is the case, just put cards into the slip box closest to their nearest related intellectual neighbor—and by this I mean nearest related to your way of thinking, not to Melvil Dewey’s or anyone else. Over time, through growth and branching, ideas will fill in the interstitial spaces and neighboring ideas will slowly percolate and intermix. Your interests will slowly emerge into various bunches of cards in your box. Things you may have intially thought were important can separate away and end up on sparse branches while other areas flourish. If you make the (false) choice to separate math and history into different “sections” it will be much harder for them to grow and intertwine in an organic and truly interdisciplinary way. Universities have done this sort of separation for hundreds of years and as a result, their engineering faculty can be buildings or even entire campuses away from their medical faculty who now want to work together in new and exciting interdisciplinary ways. This creates a physical barrier to more efficient and productive innovation and creativity. It’s your zettelkasten, so put those ideas right next to each other from the start so they can do the work of serendipity and surprise for you. Do not artificially separate your favorite ideas. Let them mix and mingle and see what comes out of them.

If you feel the need to categorize and separate them in such a surgical fashion, then let your index be the place where this happens. This is what indices are for! Put the locations into the index to create the semantic separation. Math related material gets indexed under “M” and history under “H”. Now those ideas can be mixed up in your box, but they’re still findable. DO NOT USE OR CONSIDER YOUR NUMBERS AS TOPICAL HEADINGS!!! Don’t make the fatal mistake of thinking this. The numbers are just that, numbers. They are there solely for you to be able to easily find the geographic location of individual cards quickly or perhaps recreate an order if you remove and mix a bunch for fun or (heaven forfend) accidentally tip your box out onto the floor. Each part has of the system has its job: the numbers allow you to find things where you expect them to be and the index does the work of tracking and separating topics if you need that.

The broader zettelkasten, tools for thought, and creativity community does a terrible job of explaining the “why” portion of what is going on here with respect to Luhmann’s set up. Your zettelkasten is a crucible of ideas placed in juxtaposition with each other. Traversing through them and allowing them to collide in interesting and random ways is part of what will create a pre-programmed serendipity, surprise, and combinatorial creativity for your ideas. They help you to become more fruitful, inventive, and creative.

Broadly the same thing is happening with respect to the structure of commonplace books. There one needs to do more work of randomly reading through and revisiting portions to cause the work or serendipity and admixture, but the end results are roughly the same. With a Luhmann-esque zettelkasten, it’s a bit easier for your favorite ideas to accumulate into one place (or neighborhood) for easier growth because you can move them around and juxtapose them as you add them rather than traversing from page 57 in one notebook to page 532 in another.

If you use your numbers as topical or category headings you’ll artificially create dreadful neighborhoods for your ideas to live in. You want a diversity of ideas mixing together to create new ideas. To get a sense of this visually, play the game Parable of the Polygons in which one categorizes and separates (or doesn’t) triangles and squares. The game created by Vi Hart and Nicky Case based on the research of Thomas Schelling (Dynamic Models of Segregation, 1971) provides a solid and visual example of the sort of statistical mechanics going on with ideas in your zettelkasten when they’re categorized rigidly. If you rigidly categorize ideas and separate them, you’ll drastically minimize the chance of creating the sort of useful serendipity of intermixed and innovative ideas. A zettelkasten isn’t simply the aggregation repository many use it for—it’s a rumination device, a serendipity engine, a creativity accelerator. To get the best and most of this effect, one must carefully help to structure their card index to generate it.

It’s much harder to know what happens when you mix anthropology with complexity theory if they’re in separate parts of your mental library, but if those are the things that get you going, then definitely put them right next to each other in your slip box. See what happens. If they’re interesting and useful and they’ve got explicit numerical locators and are cross referenced in your index, they are unlikely to get lost. Be experimental occasionally. Don’t put that card on Henry David Thoreau in the section on writers, nature, or Concord, Massachusetts—especially if those aren’t interesting to you. Besides, everyone has already worn down those associative trails, paved them, and re-paved them. Instead put him next to your work on innovation and pencils because it’s much easier to become a writer, philosopher, and intellectual when your family’s successful pencil manufacturing business can pay for you to attend Harvard and your house was always full of writing instruments from a young age. Now you’ve got something interesting and creative. (And if you really must, you can always link the card numerically to the other transcendentalists across the way.)

In case they didn’t hear it in the back, I’ll shout it again:

ACTIVELY WORK AGAINST YOUR NATURAL URGE TO USE YOUR ZETTELKASTEN NUMBERS AS TOPICAL HEADINGS! MIX IT UP INSTEAD.

Featured image by Michael Treu from Pixabay

S.D. Goitein’s Card Index (or Zettelkasten)

Abstract

Scholar and historian S.D. Goitein built and maintained a significant collection of over 27,000 notes in the form of a card index (or zettelkasten1) which he used to fuel his research and academic writing output in the mid to late twentieth century. The collection was arranged broadly by topical categories and followed in the commonplace book tradition though it was maintained on index cards. Uncommon to the space, his card index file was used by subsequent scholars for their own research and was ultimately digitized by the Princeton Geniza Project.

Introduction to S.D. Goitein and his work

Shelomo Dov Goitein (1900-1985) was a German-Jewish historian, ethnographer, educator, linguist, Orientalist, and Arabist who is best known for his research and work on the documents and fragments from the Cairo Geniza, a fragmented collection of some 400,000 manuscript fragments written between the 6th and 19th centuries.

Born in Burgkunstadt, Germany in 1900 to a line of rabbis, he received both a secular and a Talmudic education. At the University of Frankfurt he studied both Arabic and Islam from 1918-1923 under Josef Horovitz and ultimately produced a dissertation on prayer in Islam. An early Zionist activist, he immigrated to Palestine where he spent 34 years lecturing and teaching in what is now Israel. In order to focus his work on the Cairo Geniza, he moved to Philadelphia in 1957 where he lived until he died on February 6, 1985.

After becoming aware of the Cairo Geniza’s contents, S.D. Goitein ultimately devoted the last part of his life to its study. The Geniza, or storeroom, at the Ben Ezra Synagogue was discovered to hold manuscript fragments made of vellum, paper, papyrus, and cloth and written in Hebrew, Arabic, and Aramaic covering a wide period of Middle Eastern, North African, and Andalusian Jewish history. One of the most diverse collections of medieval manuscripts in the world, we now know it provides a spectacular picture of cultural, legal, and economic life in the Mediterranean particularly between the 10th and the 13th centuries. Ultimately the collection was removed from the Synagogue and large portions are now held by a handful of major research universities and academic institutes as well as some in private hands. It was the richness and diversity of the collection which drew Goitein to study it for over three decades.

Research Areas

Goitein’s early work was in Arabic and Islamic studies and he did a fair amount of work with respect to the Yemeni Jews before focusing on the Geniza.

As a classically trained German historian, he assuredly would have been aware of the extant and growing popularity of the historical method and historiography delineated by the influential works of Ernst Bernheim (1899) and Charles Victor Langlois and Charles Seignobos (1898) which had heavily permeated the areas of history, sociology, anthropology, and the humanities by the late teens and early 1920s when Goitein was at university.

Perhaps as all young writers must, in the 1920s Goitein published his one and only play Pulcellina about a Jewish woman who was burned at the stake in France in 1171. [@NationalLibraryofIsrael2021] # It is unknown if he may have used a card index method to compose it in the way that Vladimir Nabokov wrote his fiction.

Following his move to America, Goitein’s Mediterranean Society project spanned from 1967-1988 with the last volume published three years after his death. The entirety of the project was undertaken at the University of Pennsylvania and the Institute for Advanced Study to which he was attached. # As an indicator for its influence on the area of Geniza studies, historian Oded Zinger clearly states in his primer on research material for the field:

The first place to start any search for Geniza documents is A Mediterranean Society by S. D. Goitein. [@Zinger2019] #

Further gilding his influence as a historian is a quote from one of his students:

You know very well the verse on Tabari that says: ‘You wrote history with such zeal that you have become history yourself.’ Although in your modesty you would deny it, we suggest that his couplet applies to yourself as well.”
—Norman Stillman to S.D. Goitein in letter dated 1977-07-20 [@NationalLibraryofIsrael2021] #

In the early days of his Mediterranean Society project, he was funded by the great French Historian Fernand Braudel (1902-1985) who also specialized on the Mediterranean. Braudel had created a center in Paris which was often referred to as a laboratoire de recherches historiques. Goitein adopted this “lab” concept for his own work in American, and it ultimately spawned what is now called the Princeton Geniza Lab. [@PrincetonGenizaLab] #

The Card Index

Basics

In addition to the primary fragment sources he used from the Geniza, Goitein’s primary work tool was his card index in which he ultimately accumulated more than 27,000 index cards in his research work over the span of 35 years. [@Rustow2022] # Goitein’s zettelkasten ultimately consisted of twenty-six drawers of material, which is now housed at the National Library of Israel. [@Zinger2019] #.

Goitein’s card index can broadly be broken up into two broad collections based on both their contents and card sizes:

  1. Approximately 20,000 3 x 5 inch index cards2 are notes covering individual topics generally making of the form of a commonplace book using index cards rather than books or notebooks.
  2. Over 7,000 5 x 8 inch index cards which contain descriptions of a fragment from the Cairo Geniza. [@Marina2022] [@Zinger2019] #

The smaller second section was broadly related to what is commonly referred to as the “India Book” # which became a collaboration between Goitein and M.A. Friedman which ultimately resulted in the (posthumous) book India Traders of the Middle Ages: Documents from the Cairo Geniza “India Book” (2007).

The cards were all written in a variety of Hebrew, English, and Arabic based on the needs of the notes and the original languages for the documents with which they deal.

In addition to writing on cards, Goitein also wrote notes on pieces of paper that he happened to have lying around. [@Zinger2019] # Zinger provides an example of this practice and quotes a particular card which also shows some of Goitein’s organizational practice:

 In some cases, not unlike his Geniza subjects, Goitein wrote his notes on pieces of paper that were lying around. To give but one example, a small note records the location of the index cards for “India Book: Names of Persons” from ‘ayn to tav: “in red \ or Gray \ box of geographical names etc. second (from above) drawer to the left of my desk 1980 in the left right steel cabinet in the small room 1972” is written on the back of a December 17, 1971, note thanking Goitein for a box of chocolate (roll 11, slide 503, drawer13 [2.1.1], 1191v). 

This note provides some indication of some of his arrangements for note taking and how he kept his boxes. They weren’t always necessarily in one location within his office and moved around as indicated by the strikethrough, according to his needs and interests. It also provides some evidence that he revisited and updated his notes over time.

In Zinger’s overview of the documents for the Cairo Geniza, he also provides a two page chart breakdown overview of the smaller portion of Goitein’s 7,000 cards relating to his study of the Geniza with a list of the subjects, subdivisions, microfilm rolls and slide numbers, and the actual card drawer numbers and card numbers. These cards were in drawers 1-15, 17, and 20-22. [@Zinger2019] #

Method

Zinger considers the collection of 27,000 cards “even more impressive when one realizes that both sides of many of the cards have been written on.” [@Zinger2019] Goitein obviously broke the frequent admonishment of many note takers (in both index card and notebook traditions) to “write only on one side” of his cards, slips, or papers. # This admonishment is seen frequently in the literature as part of the overall process of note taking for writing includes the ability to lay cards or slips out on a surface and rearrange them into logical orderings before copying them out into a finished work. One of the earliest versions of this advice can be seen in Konrad Gessner’s Pandectarum Sive Partitionum Universalium (1548).

Zinger doesn’t mention how many of his 27,000 index cards are double-sided, but one might presume that it is a large proportion. # Given that historian Keith Thomas mentions that without knowing the advice he evolved his own practice to only writing on one side [@Thomas2010], it might be interesting to see if Goitein evolved the same practice over his 35 year span of work. #

The double sided nature of many cards indicates that they could have certainly been a much larger collection if broken up into smaller pieces. In general, they don’t have the shorter atomicity of content suggested by some note takers. Goitein seems to have used his cards in a database-like fashion, similar to that expressed by Beatrice Webb [@Webb1926], though in his case his database method doesn’t appear to be as simplified or as atomic as hers. #

Card Index Output

As the ultimate goal of many note taking processes is to create some sort of output, as was certainly the case for Goitein’s work, let’s take a quick look at the result of his academic research career.

S.D. Goitein’s academic output stands at 737 titles based on a revised bibliography compiled by Robert Attal in 2000, which spans 93 pages. [@Attal2000] # # A compiled academia.edu profile of Goitein lists 800 articles and reviews, 68 books, and 3 Festschriften which tracks with Robert Atta’s bibliography. #. Goitein’s biographer Hanan Harif also indicates a total bibliography of around 800 publications. [@NationalLibraryofIsrael2021] #. The careful observer will see that Attal’s list from 2000 doesn’t include the results of S.D. Goitein’s India book work which weren’t published in book form until 2007.

Perhaps foremost within his massive bibliography is his influential and magisterial six volume A Mediterranean Society: The Jewish communities of the Arab World as Portrayed in the Documents of the Cairo Geniza (1967–1993), a six volume series about aspects of Jewish life in the Middle Ages which is comprised of 2,388 pages. # When studying his card collection, one will notice that a large number of cards in the topically arranged or commonplace book-like portion were used in the production of this magnum opus. # Zinger says that they served as the skeleton of the series and indicates as an example:

 …in roll 26 we have the index cards for Mediterranean Society, chap. 3, B, 1, “Friendship” and “Informal Cooperation” (slides 375–99, drawer 24 [7D], 431–51), B, 2, “Partnership and Commenda” (slides 400–451, cards 452–83), and so forth. #

Given the rising popularity of the idea of using a zettelkasten (aka slip box or card index) as a personal knowledge management tool, some will certainly want to compare the size of Goitein’s output with that of his rough contemporary German sociologist Niklas Luhmann (1927-1990). Luhmann used his 90,000 slip zettelkasten collection to amass a prolific 550 articles and 50 books. [@Schmidt2016]. Given the disparity in the overall density of cards with respect to physical output between the two researchers one might suspect that a larger proportion of Goitein’s writing was not necessarily to be found within his card index, but the idiosyncrasies of each’s process will certainly be at play. More research on the direct correlation between their index cards and their writing output may reveal more detail about their direct research and writing processes.

Digital Archive

Following his death in February 1985, S.D. Goitein’s papers and materials, including his twenty-six drawer zettelkasten, were donated by his family to the Jewish National and University Library (now the National Library of Israel) in Jerusalem where they can still be accessed. [@Zinger2019] #

In an attempt to continue the work of Goitein’s Geniza lab, Mark R. Cohen and A. L. Udovitch made arrangements for copies of S.D. Goitein’s card index, transcriptions, and photocopies of fragments to be made and kept at Princeton before the originals were sent. This repository then became the kernel of the modern Princeton Geniza Lab. [@PrincetonGenizaLaba] # #

Continuing use as an active database and research resource

The original Princeton collection was compacted down to thirty rolls of microfilm from which digital copies in .pdf format have since been circulating among scholars of the documentary Geniza. [@Zinger2019] #

Goitein’s index cards provided a database not only for his own work, but for those who studied documentary Geniza after him. [@Zinger2019] # S.D. Goitein’s index cards have since been imaged and transcribed and added to the Princeton Geniza Lab as of May 2018. [@Zinger2019] Digital search and an index are also now available as a resource to researchers from anywhere in the word. #

Historically it has generally been the case that repositories of index cards like this have been left behind as “scrap heaps” which have meant little to researchers other than their originator. In Goitein’s case his repository has remained as a beating heart of the humanities-based lab he left behind after his death.

In Geniza studies the general rule of thumb has become to always consult the original of a document when referencing work by other scholars as new translations, understandings, context, history, and conditions regarding the original work of the scholar may have changed or have become better understood.[@Zinger2019] # In the case of the huge swaths of the Geniza that Goitein touched, one can not only reference the original fragments, but they can directly see Goitein’s notes, translations, and his published papers when attempting to rebuild the context and evolve translations.

Posthumous work

Similar to the pattern following Walter Benjamin’s death with The Arcades Project (1999) and Roland Barthes’ Mourning Diary (2010), Goitein’s card index and extant materials were rich enough for posthumous publications. Chief among these is India Traders of the Middle Ages: Documents from the Cairo Geniza “India Book.” (Brill, 2007) cowritten by Mordechai Friedman, who picked up the torch where Goitein left off. # # However, one must notice that the amount of additional work which was put into Goitein’s extant box of notes and the subsequent product was certainly done on a much grander scale than these two other efforts.

Notes per day comparison to other well-known practitioners

Given the idiosyncrasies of how individuals take their notes, the level of their atomicity, and a variety of other factors including areas of research, other technology available, slip size, handwriting size, etc. comparing people’s note taking output by cards per day can create false impressions and dramatically false equivalencies. This being said, the measure can be an interesting statistic when taken in combination with the totality of these other values. Sadly, the state of the art for these statistics on note taking corpora is woefully deficient, so a rough measure of notes per day will have to serve as an approximate temporary measure of what individuals’ historical practices looked like.

With these caveats firmly in mind, let’s take a look at Goitein’s output of roughly 27,000 cards over the span of a 35 year career: 27,000 cards / [35 years x 365 days/year] gives us a baseline of approximately 2.1 cards per day. #. Restructuring this baseline to single sided cards, as this has been the traditional advice and practice, if we presume that 3/4ths of his cards were double-sided we arrive at a new baseline of 3.7 cards per day.

Gotthard Deutch produced about 70,000 cards over the span of about 17 years giving him an output of about 11 cards per day. [@Lustig2019] #

Niklas Luhmann’s collection was approximately 90,000 cards kept over about 41 years giving him about 6 cards per day. [@Ahrens2017] #

Hans Blumenberg’s zettelkasten had 30,000 notes which he collected over 55 years averages out to 545 notes per year or roughly (presuming he worked every day) 1.5 notes per day. [@Kaube2013] #

Roland Barthes’ fichier boîte spanned about 37 years and at 12,250 cards means that he was producing on average 0.907 cards per day. [@Wilken2010] If we don’t include weekends, then he produced 1.27 cards per day on average. #

Finally, let’s recall again that it’s not how many thoughts one has, but their quality and even more importantly, what one does with them which matter in the long run. # Beyond this it’s interesting to see how influential they may be, how many they reach, and the impact they have on the world. There are so many variables hiding in this process that a fuller analysis of the statistical mechanics of thought with respect to note taking and its ultimate impact are beyond our present purpose.

Further Research

Based on a cursory search, no one seems to have picked up any deep research into Goitein’s card collection as a tool the way Johannes F.K. Schmidt has for Niklas Luhmann’s archive or the Jonathan Edwards Center at Yale has for Jonathan Edwards’ Miscellanies Index.

Goitein wrote My Life as a Scholar in 1970, which may have some methodological clues about his work and method with respect to his card index. He also left his diaries to the National Library of Israel as well and these may also have some additional clues. # Beyond this, it also stands to reason that the researchers who succeeded him, having seen the value of his card index, followed in his footsteps and created their own. What form and shape do those have? Did he specifically train researchers in his lab these same methods? Will Hanan Harif’s forthcoming comprehensive biography of Goitein have additional material and details about his research method which helped to make him so influential in the space of Geniza studies? Then there are hundreds of small details like how many of his cards were written on both sides? # Or how might we compare and contrast his note corpus to others of his time period? Did he, like Roland Barthes or Gotthard Deutch, use his card index for teaching in his earlier years or was it only begun later in his career?

Other potential directions might include the influence of Braudel’s lab and their research materials and methods on Goitein’s own. Surely Braudel would have had a zettelkasten or fichier boîte practice himself?

References

Footnotes

  1. In my preliminary literature search here, I have not found any direct references to indicate that Goitein specifically called his note collection a “Zettekasten”. References to it have remained restricted to English generally as a collection of index cards or a card index.↩︎
  2. While not directly confirmed (yet), due to the seeming correspondence of the number of cards and their corpus descriptions with respect to the sizes, it’s likely that the 20,000 3 x 5″ cards were his notes covering individual topics while the 7,000 5 x 8″ cards were his notes and descriptions of a single fragment from the Cairo Geniza. #↩︎

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