Akritai were locals who were to be used as the defenders of the borders instead of deploying regular Army or mercenaries. For this reason they were given land (so as to have skin in the game) and tax breaks. When the tax breaks stopped the Akritai rapidly vanished. These are also mentioned in Wikipedia pages.
So, in terms of a security project an Akritas would be you running an EDR agent on a machine that you own, not some of the signatory companies who basically do not own anything on the edge (end user equipment).
To be fair, the Akritai was the Byzantine Empire's effort to use the local population to defend the land, instead of having to deploy regular Army or mercenaries. It happened to be Muslim states that was the border. It bears no anti-muslim connotations as a word in Greek. In fact the epic of Digenes Akritas, speaks of Basil, an Akritas of a Greek mother and an Arab father (hence the name Digenes, of two descents).
This is a very simplified and uninformed view of what the Akritai were. The name choice is so wrong, it cannot even be called out as cultural appropriation, because it is far worse than that. LF just stick with languages you understand.
I wrote the blog post just to expand a bit on the reply I gave on twitter because of the excerpt from "The Roots of Lisp". I never really expected to see on the HackerNews first page.
The width of the question makes it a tough one. I am lucky enough to have a mathematics professor one phone call away. You will find spending hours in your University's library rewarding. Start with a good book on discrete mathematics and move on from there. A good book is the one for which you can have someone explain your questions (meaning the one that your professor proposes).
But even the fact that you have to decide on the buffer size is a matter of understanding the theory. Choosing to multiply by 5 too. Why is it 5 and 12? Why the buffer size is not the half or double the size that it has? How can you prove that you have chosen the correct values if not by theory?
The low level API calls that you make, make use of the OS scheduling. But you may claim that you can be agnostic to this fact. On the other hand optimizing your code to run efficiently can be done either using your gut feeling, or by understanding the complexity of your code, to make it run faster, with fewer calls, and optimal buffer usage. Would that suffice as an answer to your question?
So, in terms of a security project an Akritas would be you running an EDR agent on a machine that you own, not some of the signatory companies who basically do not own anything on the edge (end user equipment).