I’m currently learning to build a PKM for notes and knowledge related to my studies (STEM) with the following objectives

- It should be an evergreen library that I can easily access whenever I’m studying something new that depends on things I’ve already studied
- It should allow me to explore my knowledge and gain new insight as I’m researching or working on tasks
- It has a well-defined set of objective rules and structure (that I actually keep written as a note)

To achieve this, I’ve looked at the Zettelkasten method and the Evergreen Notes method, and I really ended up liking the idea of interconnected notes.

As I am writing notes and actively applying the core principles, I’m left with a couple of doubts about atomic notes and linking best practices.

Core questions I’ve been trying to answer myself before linking:

- “Am I linking this note just because I’m saying its name, or does this link actually add a good amount of meaning?”
- “Will this be useful to my future self?”/“Will my future self need this link to expand or understand better?”

**After writing this, I’m also starting to feel afraid of “thinking too much about graph view/backlinks rather than knowledge itself”, so please point me out of this is the case.**

## Problem 1: How atomic is too atomic

As an example, consider the notes “Matrices” and “Addition operator for matrices”.

If “Addition operator for matrices” appears only in the “Matrices” note (see “Implied links” problem), wouldn’t it be right to merge those two notes as one note even if they express two different ideas and concepts?

### Discussion on problem 1 (How atomic is too atomic)

- Creating only one note would make reading easier and would keep my vault less cluttered
- Avoids, for some part, the “Implied links” problem
- The notes can be split when I talk about something very specific about addition
- All notes linked to “Matrices” need to be reviewed (see “Implied links”)
- I can still embed the addition note into matrices for ease of reading

**This violates the core principle of atomic notes. I am mixing different ideas together** and creating extra work for linking and reviewing (whenever I will want to link only the specific note or split them).

## Problem 2: Implied links

As an example, consider the notes “Matrices”, “Determinant of a matrix” (determinant is something that I defined exclusively for matrices) and “Addition operator for matrices”.

When it comes to writing, it usually goes something like this:

- “Consider the [[Determinant of a matrix|determinant]] of the [[Matrices|matrix]] $A$ …”
- “Let $A$ be a [[Matrices|matrix]] that has a non-zero [[Determinant of a matrix|determinant]] …”
- “[[Addition operator for matrices|Add]] the [[Matrices|matrix]] $A$ to …”

Would it be right to assume that if the related context is obvious, links can (should) be avoided (as they add no extra information or value)?

- If I am talking about the determinant of a matrix, then I am obviously talking about matrices
- If I’m also discussing or making use of something very specific to “matrices” and unrelated to “determinant” this, of course, does not apply
- “Consider the [[Determinant of a matrix|determinant of the matrix]] $A$ …”
- “Let $A$ be a matrix that has a non-zero [[Determinant of a matrix|determinant]] …”

- The fact that “matrices can be added” is one of the fundamental things I would talk about in the matrices note, so I assume it’s obvious that if I talk about matrices, then I must know how to add them.
- “Add the [[Matrix|matrix]] $A$ to …”

### Discussion on problem 2 (Implied links)

Linking, without the assumption for context, seems too redundant and not meaningful: it does not add (that much) extra value.

It also mixes notes in a way that actually ends up mixing useful data with unrelated data:

- Both local and global graph view start to get those “MOC like” shapes where data about “manipulating matrices” is mixed with “usage of matrices”, if you get my point
- If I am looking at the “Matrices” note, it’s very likely that I am more interested in manipulation or notes strictly related to matrices than the usage of matrices themselves

**This violates the core principle of densely linked notes:**

**The context (thought to be “obvious”) can be forgotten/lost****I am creating distance between my notes**, which can be easily felt by going through links in the text rather than graph view or backlinks.- As an example (from “Yet another example for implied links”), consider writing a note only linking to “Vector subspace” but it turns out what’s actually needed/what I’m looking for is something linked to the note “Vectors”
- A big part of my studies is “learning to apply what I already know to new things” (and it’s mostly done by generalizing ideas for bigger contexts). I am afraid this can get in the way

**I also have no way to objectively define “obvious”.**

### Yet another example for implied links

Consider the notes “Vectors”, “Base of a vector subspace” (it’s composed by vector), “Vector subspace” (you need a base to make one).

I start writing a note about the R2 space as follows:

- “Let the [[Vector subspace|vector subspace]] generated by the [[Vectors|vectors]] (…) that form a [[Base of a vector subspace|base]] (…)”

Since I defined a base to be composed by vectors, then I would rewrite it as: - “Let the [[Vector subspace|vector subspace]] generated by the [[Base of a vector subspace|base]] (…)”

Since I stated that a vector subspace is generated by a base, the base is a core component of the vector subspace. Then, I would rewrite as: - “Let the [[Vector subspace|vector subspace]] generated by the base (…)”

## Problem 3: Merge notes

As an example, consider the notes “Matrices”, “Property A of matrices” and “Property B of matrices”.

I’m very interested in matrices that follow both property A and B and I create 20 notes that begin with something along the lines of:

- “Let $A$ be a [[Matrices|matrix]] that follows both [[Property A of matrices|property A]] and [[Property B of matrices|property B]]”

Wouldn’t it be right to create a note a “merging note” called [[Matrices that follow A and B]] to group that context? - “Let $A$ be a [[Matrices that follow A and B|matrix that follows both property A and property B]]”

### Discussion on problem 3 (Merge notes)

Without a merging note, I feel like I have the following issues:

- Backlinks and graph don’t always seem appropriate or relevant
- Increases (in my opinion) the work required to move, merge, split and sort linked notes

**This violates the core principle of fine-grained associations**, and it creates the same “distance” issues as the “Implied links” problem.

I also am afraid of filling my vault with notes that provide no value or knowledge to the system itself.