I'll admit that I didn't think terribly hard about who the audience is. This is another tricky thing of course - anyone can look at a YouTube video. I guess I

I'll admit that I didn't think terribly hard about who the audience is. This is another tricky thing of course - anyone can look at a YouTube video. I guess I tried to give an intuitive explanation of how a topologist thinks about hole-like things. One can only get so far before you have to start getting precise (and technical). This is where I give the names "homotopy group" and "homology groups", so that viewers at least have something to look up to learn more if they want to. I certainly didn't intend to give the impression that viewers were supposed to know what those terms are already. Maybe there is a video to be done on giving a better introduction to homotopy or homology groups, without requiring any background knowledge, but this wasn't that video. Incidentally, topologists don't use the word "hole" in a technical sense. So yes, we wouldn't claim to know what a hole should be better than anyone else. But in trying to make precise the intuitive ideas of what it means for something to have a hole, or a "loop" in it, we got to the kind of definitions we do work with. These ideas can, in principle, come back to be useful to analyze objects in the real world (persistent homology is trying to do this). Glad you liked some of my other videos!