What is a "theta-prime dimensional fractal topology"?

Question

In a story I read, a conceptual entity(it was an idea with sentiency, but thats besides the point) was described as a "theta-prime dimensional fractal topology". Is this gobbledygook or is there any math behind it?

I saw this in the book "There is no Antimemetic Division" by QNTM.

Answer 1

The "theta-prime" is a reference to SCP-033:

Description: SCP-033 appears as a field of complex mathematical symbols ranging from simple layman-identifiable representations to those only interpretable by highly-trained mathematicians. The "sum" of the symbols is equal to a previously unknown integer (designated Theta Prime [emphasis mine] by Prof. Hutchinson) of intermediate value between █ and █.

The reference to fractals, in combination with the reference to dimensions, could be thought of as a reference to Hausdorff dimension, which is a way to assign non-integer dimensions to fractals. However, it's worth clarifying that Hausdorff dimension is not a topological concept, the way mathematicians use that word; it relies crucially on metric structure, meaning the ability to measure distances.

"$d$-dimensional fractal geometry" could be meaningfully interpreted in terms of Hausdorff dimension. Non-mathematicians frequently use "topology" or "topological" in a different and looser sense than the meaning that term has in mathematics, which is quite specific.

Of course $\theta'$ does not exist. (But I would say that, wouldn't I...)