Best Practices - Zettelkasten

Patterns

Species of Slip

There are different “species” of slips in the Zettelkasten, and this varies person to person. For example, Luhmann had hubs which served as a sort of “table of contents” — it lists links to relevant ideas/slips.

We could easily imagine, for a truly huge Zettelkasten, the usefulness of hubs, and hubs of hubs. Quite a bit of hubbub may be avoided in this manner.

Math Specific Slip Species

My Zettelkasten is mostly mathematics and physics (and other hard sciences). Consequently, there are several “mathematical registers” which one may expect to find in a math text:

The label of a slip includes this (e.g., “Defn: Lie Group”, “Ex: SU(3) [Lie Group]”, “Thm. Closed Subsets of Lie Group are Lie”, etc.). Proofs are just “Pf: [claim to be proven]”.

There is another type of slip I’ve found useful: a “Link” slip. I’ve used this when I need to review the salient parts of a concept, germane to the present discussion, but don’t want to get bogged down in the irrelevant details. Or I have the definition elsewhere, discussed in much greater detail, and I don’t want to repeat it all, but there are some aspects worth emphasizing again.

For example, Clifford algebras are necessary for constructing spin representations of Lie algebras. But I have a thorough discussion of Clifford algebras elsewhere. So I have a slip “Link: Clifford Algebras” which reviews the salient aspects of Clifford algebras for spinor representations, with links to the full discussion elsewhere.

Or, another example, I have a rather healthy Zettelkasten, littered with examples of mathematical gadgets. When I define a new concept, and I want to use previously constructed examples, I have a link back to the existing gadget. In some instances, this turns out to be a “hub”, just a sequence of links to existing gadgets.

Defer writing IDs while working through a text

I often have used a binder clip to keep in one spot the permanent notes I’ve written while reading an article (or book chapter). During this period, I do not write an ID number on these slips.

Once I’m done with the article/chapter, I see if I can reorganize the permanent notes in an intuitive manner.

Sometimes (e.g., when taking notes on untyped lambda-calculus), I defer this process until I have finished reading several sources (e.g., three chapters from Barendregt’s book, a chapter from Pierce’s TAPL, a couple chapters from Nederpelt and Geuver’s Type Theory and Formal Proof).

Write as if the Zettelkasten were an intelligent collaborator

It helps to have an audience defined when writing, and when writing permanent notes for the Zettelkasten, treat the kasten as if it were an “intelligent but completely ignorant” collaborator or colleague. You need to define some background knowledge (e.g., a high school graduate-level understanding of stuff), otherwise you end up in an infinite regress (which is bad).

Thread of Examples for a definition

I’ve noticed, for math notes, I tend to make a definition part of a thread; e.g., 5.2/1 Def. Category is the definition of a category. I tend to make a branch for a sequence of examples, e.g., 5.2/1a1 Set, 5.2/1a2 FinSet, 5.2/1a3 Vect, etc.

Structured Proofs as a Branch off of a theorem

Similarly, theorems are part of a thread, e.g., 5.1.1/7 Fundamental Theorem of Algebra. Its proof is then written like a structured proof (in the sense of Lamport):

If I think/find a second proof, I place it in a second branch 5.1.1/7b, etc. (Seldom are there 26+ alternate proofs for a proposition.)

Anti-Patterns

“Worst practices” to avoid.

Using the Zettelkasten (or Bibliography Apparatus) as a Database

Don’t just collect slips. The goal is to make connections (form links) between disparate topics.

Collecting Reading Notes without writing Permanent Notes

I’ve found that about 75% of reading notes are used to produce final permanent notes, but sometimes I’m in such a rush I don’t write final notes for around 25% of reading notes. This is a symptom of failing to adhere to the method.

Treating Blank Reading Notes as “To Read” list

This clutters up the bibliography box. Instead of storing a “reading list” using blank reading notes, store them in a computer file or separate notebook or something.

At worst, if your reading list grows exponentially, you’ll never find anything in your bibliography apparatus.

Forgetting to write notes while reading

The whole point is to digest what you’re reading, to re-formulate it in your own terms, to re-describe what has been published. These should be /condensed/ reformulations of the material. (Sometimes this is difficult to do, e.g., in math; we need to copy the definition of unfamiliar terms.)

Then, later, examine how it relates to what exists in the Zettelkasten.

But skipping the “reading notes” is like trying to make coffee without grounds (or tea without leaves): you literal lack the raw material to make the finished product.

This is undesirable for several reasons: