ID Schemes - Zettelkasten

by Alex Nelson, 1 December 2021

There are many different ways to assign ID numbers to slips in one’s Zettelkasten. This seems to be the subject of Folgezettel, but I don’t know German well, so I cannot adequately say.

My Scheme

An ID in my scheme consists of two components: the category part, and the thread part. They are separated by a /. There is at most one slash in an ID number in my scheme.

The formal grammar looks like:

<ID> ::= <category id>
      | <category id> "/" <thread id>

<category id> ::= <number>
               | <number> "." <category id>

<thread id> ::= <number>
             | <number> <lowercase letter> <thread id>

Categories

Some slips, like 5.6 Lie Group, just start a category or subcategory. These are quick summaries of the subject for myself.

Addendum . After much thought, I realize I am misusing the word "category" here for sections. I have written my thoughts about Categories, Sections, and Tags elsewhere.

Later I include links to other places where results are generalized or related (e.g., later I have a discussion of finite groups in 5.3.4 Finite Group Theory which includes extensive discussions of groups of Lie type 5.3.4.4 Finite Lie groups — then I make a note of this on 5.6 Lie Group to the effect of “This discusses Lie groups over Fields of characteristic 0, for finite fields see (5.3.4.4)”; and on 5.3.4.4 I note something like “Lie groups (5.6) specialized to finite fields”).

My top-level categories and sub-categories are:

  1. Zettelkasten
  2. System and Method
  3. Computer Science
  4. Symbolic Math
    1. Elementary Algebra
    2. Differential Calculus in Single Variable
    3. Integral Calculus
    4. Series
    5. Vectors
    6. Multivariable Calculus
    7. Vector Calculus
  5. Abstract Algebra
    1. Linear Algebra
      1. Elementary Linear Algebra (start with systems of equations, then matrices, discusses a lot of matrix algebra, then vector spaces)
      2. Intermediate Linear Algebra (start with field axioms and the abstract definition of a vector space, then linear transformations & operators, etc.)
      3. Advanced Linear Algebra (modules over rings, etc.)
    2. Number Theory
    3. Group Theory
    4. Category Theory
    5. Rings and Fields
    6. Lie groups
  6. Analysis
    1. Real Analysis
    2. Complex Analysis
    3. Numerical Analysis
    4. Fourier Analysis
    5. Partial Differential Equations
  7. Geometry and Topology
    1. Point-set topology
    2. Differential topology
  8. Foundations of Math
    1. Naive Set Theory
    2. First-order logic
    3. Axiomatic Set theory
    4. Type theory
    5. Higher-Order logic
  9. Theorem provers
    1. Automath
    2. LCF
    3. Coq

Threads

Like most mathematicians, my notes on mathematics may be viewed as a thread of concepts (definitions). Any results about a concept are a branch off the concept.

What did Luhmann do?

Curiously, Luhmann seems to have a rather different approach to ID numbers. It’s worth looking at the subtree rooted at 9/8 in his Zettelkasten.

Luhmann seems to develop a train of thought: 9/8, 9/8a, 9/8b, 9/8c, …, 9/8j. This should be understood as something analogous to a “Twitter thread”, Luhmann wanted to say a number of things which didn’t fit on one card, so he wrote one thought per slip.

There is also some addendum to 9/8 as a subsequent, independent, train of thought numbered 9/8.1, 9/8.2, 9/8.3. What is the reason for this different ID numbering scheme of <period> <number> suffix? It is unclear to me. In footnote 30 of Johan Schmidt’s “Niklas Luhmann’s Card Index: Thinking Tool, Communication Partner, Publication Machine”, Schmidt writes (p.301):

For reasons of clarity, the principle of numbering that Luhmann applied will be illustrated in simplified fashion. In addition to the sequence outlined below, there are also cards that are numbered using two consecutive numbers or letters (e.g., 1/1aa or 1/2,1). This pattern is a consequence of applying the described method of adding cards and inserting a card in an already existing sequence at a later point in time.

But there is also a “branch” off 9/8a as 9/8a1, 9/8a2.

Luhmann’s numbering scheme made a little more explicit

More abstractly, Luhmann numbering scheme seems to be simplified to something like:

This is a simplified toy model from Johan Schmidt’s “Niklas Luhmann’s Card Index: Thinking Tool, Communication Partner, Publication Machine” (p.301).

Did Luhmann always work this way? No. For example, there are two cards 9/9 or 9/9 which deal with either Systems Theory or Women’s studies. Card 9/7 discusses Heraclitus. There doesn’t seem to be any obvious “continuation” of Heraclitus into 9/8, nor any obvious continuation of Zettelkasten 9/8 into either Women’s Studies 9/9 or Systems Theory 9/9.

The important thing is that this alternation between letters and numbers offered Luhmann a branching mechanism, which allowed him to discuss related topics. However, as we observed with 9/8.1 as a branch off 9/8, it was insufficient as the only branching mechanism. (Schmidt reports there are branches like 1/2aa, too.)

There are some days I think Luhmann’s scheme is superior, because it forces you to think carefully about what you’re writing. Sometimes giving the user too much power is a bad thing, giving the user too many ways to “branch” off can be bad (it leads to “analysis paralysis”).

References