3 ms·
There's an interesting misunderstanding in this article. The argument for O(n) is well formed here. O(n^2) is not, the core argument is that these grow faster
by fooker 1y ago
There's an interesting misunderstanding in this article.
The argument for O(n) is well formed here.
O(n^2) is not, the core argument is that these grow faster because of compounding. Compounding is fundamentally an exponential process, far larger asymptotically than a quadratic.
- nine_k 1y agoTrue exponential growth is possible, but I suspect is rare, because the expenses can also compound, so a polynomial growth may be an acceptable approximation. It's also important to remember that "every exponential growth curve is a sigmoid in real life" (can't remember the source of the quotation).
- jxjnskkzxxhx 1y ago> True exponential growth is possible, but I suspect is rare, because the expenses can also compound If you have an exponential (revenues) and another exponential of smaller rate (expenses; assume you have profit) then the difference is still an exponential.
- fooker 1y agoThis is in fact the most interesting exponential! Plot the graph of 2^x - 1.99^x to see what I mean. It stays close to the axis for a while and then suddenly shoots up. Follows the trajectory of quite a few companies now that I think of it.
- robocat 1y agoThe article clearly isn't meant to be mathematically correct: you are being over-rigorous in your criticism. From the article: Businesses generally grow following a few patterns. They generally have some TAM to saturate and saturate the TAM at some rate. This rate can be vaguely linear, what I call O(n), or vaguely superlinear, what I call O(n²). 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 n² 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. Article would be better using something like O(linear) and O(≫linear). The big O notation is a useful and memorable metaphor, but the n squared is really confusing. The article also doesn't use Unicode for the notation - which fucks usability (e.g. I used screenshot OCR and reedited).
- ocean_moist 1y agoAddressed in the footnotes: > [2] Perhaps choosing a better two functions could more closely explain the growth dynamics of network effects, which could be more exponential. I think the analogy diminishes in value if you try to directly numerically match it to some growth metric.