[nis251413]

Big-O notation is about asymptotics. You have to approach something, and typically there is some infinity involved because if it is not, then you can just compute things instead of giving asymptotic approximations, or else you have 10^10*n and 0.001*n^2-10^20*n and the big-O asymptotics at infinity are useless for smaller numbers. I understand what OP tries to say but that's not really a good framing point for many reasons. If you want to talk about a finite period of time, use a regression model, not asymptotics. But that's probably also a more personal preference around using mathematics colloquially but also in a manner that is not a good metaphor and does not correspond with what the mathematical theory is referring to. And I am not sure at all whether it is very well understood "what part of the graph we're talking about", in the sense that the modern organization of economy is far from acknowledging the fact that resources on earth are actually finite. Talking about O(n) and O(n^2) or O(exp(n)) as if growth can be indefinite comes with a specific kind of mindset, and the frame used reflects this type of mindset.

[godelski]

  > Big-O notation is about asymptotics.

Excuse me, but what made you believe I do not understand this? I'm not sure what comment you're responding to, but it sure isn't mine.

  >> I took the author's use of O(n) vs O(n^2) as a framing point rather than a literal model.

Honestly, the reason I said this is because from the article

  | The reason I borrow the asymptotic notation is because it implies the growth rate is an upper bound (best case scenario) and generalizes away specific constant factors and sums. The analogy breaks down when you force n or n^2 imply something numerically specific about your growth rate, or introduce functions with different growth rates like logs or exponentials. For now we will (somewhat unprincipledly) stick with two sole classes: O(n) and O(n^2).

Along with their emphasis on "vaguely". I can forgive the author for bad verbage. It is a personal blog where they're not trying to sell anyone on a fully fledged out idea and appear to be trying to spur conversations. Especially considering it looks like they are an undergrad. Frankly, I can understand them despite the wrong words. Given this, it would require me to operate in bad faith by rejecting the main thing they are attempting to communicate by focusing on the details that ultimately don't matter to their claim.

  > If you want to talk about a finite period of time, use a regression model, not asymptotics

They did. They said "startup". The whole time they bound the conversation to early businesses. I even directly stated this

  >> Considering startup as context I think we know what part of the graph we're talking about...

Maybe you're referring to the preceding line

  >> Besides, we can approximate sigmoids with linear or quadratic functions when windowing them. 

Which again, same thing.

My point is: you're derailing the conversation

You are technically right, but you're derailing the conversation in an effort to prove your intellectual capabilities to a person who were not questioning them in the first place. You're flexing to the wrong group. You just responded to something my comment was never about.

  >  I understand what OP tries to say but that's not really a good framing point for many reasons.

So address what the OP tries to say, *and while doing so* you can add additional technical correctness. *This does not derail the conversation.* It continues the conversation and enhances it! You can do both! But as your comment stands (and bee_rider's), you just are moving the conversation away from what OP wanted to discuss and instead hyper-fixating on what they themselves said is not the best language.