by Jan Malakhovski, version 2.0.0, updated , published , created
My university classmate once joked that “[classical] topologists only recognize obvious and false statements.”1 Personally, I prefer to acknowledge that I have some intermediate states, one of which is the state where I understand the definitions but almost nothing else. However, once a set of ideas steps over that mark, usually, it quickly moves towards the “obvious” states with a bit more effort. If not immediately, then after a good night of sleep. In other words, from my point of view, all knowledge acquisitions follow the following path: “it’s completely unknown to me” → “I’ve heard about it” → “I understand its definitions” → “it’s obviously true” or “it’s obviously false”.
Now, if you think about it, most people actually prefer documents that consist of series of almost obvious statements. After all, “Ah, I get it!” feeling is much more pleasant than “What?! I don’t see how this follows from the previous paragraph!” In fact, to reach the flow state while reading/watching a document essentially requires that document to be structured in such a way that almost every new statement is almost obvious. In other words, most statements in a well-made teaching material should be almost obvious and you shouldn’t be embarrassed to admit that you like consuming the almost obvious content. Moreover, reading some almost completely obvious things about the things you already know is a good way to find different perspectives and small sweet details, thus deepening your understanding.
However, counter-intuitively, it’s pretty hard to actually make a document made of almost obvious statements:
Firstly, obviously, there’s the issue of understanding something deeply enough so that you actually can write down a series of true statements that reach the target state from your chosen base state, Hilbert-style.
But, secondly, personally, I also usually feel like that I don’t have a lot of new things to say, and so I shouldn’t bother anyone with my thoughts on any chosen subject.
Thus, I find writing about the almost obvious to be especially hard. The good thing is, I feel much better writing about the almost obvious than writing about the absurd.
Which is why I’m going to work on writing some things here.
blog.oxij.org to oxij.org/note.By which he obviously meant that all true statements in topology are obvious.↩︎