If I have some specific problem to solve, I find technology that seems relevant, then I scan the Internet for some basic introduction, then some tutorial, then documentation.

My usual problem is that the issue I want to solve is usually not in the introduction nor the tutorial. I rarely find ready-to-use solution and unfortunately I tend to really dislike adjusting my idea to what you can easily achieve with tutorial-like solutions. That means I usually have to read large parts of the documentation just to find few little details hidden somewhere in the middle.

Even though it’s really the best way IMO, I believe that reading through whole documentation of some project can be too time consuming. Our world is accelerating and I believe that the ability to find a small subset of information to reach specific goal may soon be a necessity.

Knowledge basics

Let’s consider a basic example: learning hwo to calculate the area of a triangle.

First you may notice that there are few ways of calculating that area, there are easier and harder ones. Some methods simplify calculations based on some assumptions about triangles, others are totally universal.

Let’s use the basic formula known from the school:

$$ A = \frac{1}{2} bh $$

This formula may seem very simple - that’s because we already know all the smaller parts it consists of: we know how to multiply numbers, what a fraction is, we also know how to measure the length in 2D space. We know it because we’ve learnt it before. Even such basic things like the length of a line segment: you need to know what is a point, a line, metric unit.

What we can see even from this small example is that knowledge terms form a pretty well formed graph of dependencies:

%%{init: {'theme': 'forest', "flowchart" : { "curve" : "basis" } } }%% graph TD ta[Triangle area]; mult[Multiplication]; ll[Line segment length]; ls[Line segment]; l[Line]; p[Point]; f[Fractions]; d[Division]; n[Real numbers]; c[Circle]; ll --> ta; mult --> ta; ls --> ll; l --> ls; p --> ls; f --> ta; d --> f; n --> d; n --> mult; n --> f; n --> ll; p --> c; ls --> c;

In this example graph it’s pretty clear what you need to learn in order to know how to calculate the area of a triangle. There’s also an alternative term - Circle. It does share some of it’s dependencies with Triangle area. And it’s pretty clear that after mastering the Circle term, you don’t have to learn about Points and Line segments once again to master the Triangle area.

Graph theory

In more complex, real-world scenarios you’d see a huge cloud of terms and dependencies between them all over the place. Even though it would be gigantic, graphs have some really nice properties and we know efficient algorithms to extract information from them.

For each node in such graph we could easily calculate it’s complete dependency list and order it so that you start from the basics, go through more complex terms and finally get into the destination one. It’s also trivial to skip those paths which are irrelevant to the topic being mastered.

Some terms may also have alternative learning paths. If you learn a new programming language, it may be easier for you to start with a language you already know rather than learning everything from scratch. A nice algorithm could find the best way for you to master the new term, suggest alternative paths etc.

There are some nice opportunities in this area I’d like to explore. But that’s a topic for some future blog post.