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Now, size, when using terms like "big" or "small" is a bit relativistic. Obviously what's large to a bug might be small to us, but I don't think it's accurate to say that all things related to bugs are necessarily small from the human's perspective. Take the termite mound that's 3-9 meters tall. Not tiny by any man's perspective. And I likewise imagine the world of Hallownest to be not small by any stretch of the imagination.
Back on topic, you'll probably need some kind of softward to do the pixel count for you. It's an interesting question, but additional tools are needed.
lol, while I like the idea of this, we can set limits if we assume arthropod anatomy. Even with highly oxygen rich environment, there's only so much oxygen these organisms can utilize. This is why you have 70 cm dragonflies (still large), but never 5 or 6 meters. And in fact all terrestrial animals have a hard limit in how tall they can grow, so we can say if bugs were living in a 100% oxygen rich environment, this is how large Hallownest would be and it cannot be larger than this due to the laws of physics preventing further growth on land.
In addition, while we do have a lot of greenery to explore, there is also a lot of industrial-level technology in concurrent existance. Mines, mining carts, lasers, saws... A lot of the technology that came bundled with these tools also came with a heavy oxygen requirement along with equal CO2 output, making modern measurement assumptions safer to make.
In the end, sure it's a fictional world, you may have 2 meter tall bugs, and you can't say for certain exactly what the dimensions for this world are, but rather than closing the book on an unanswerable question, we can make suppositions based on the world we live in today and make rough guesstimates. It's still an interesting question if we start off with assumed conditions, even if they're not true. Let's say that the dung defender is as large as a regular dung beetle. Then how big would the world of Hallownest be? It'd still be interesting to know.
On top of this, I still don't think it really works to compare the in-game insects to irl insects, as there is nothing clarifying that they are the same.
Also single-celled organisms vary massively in size so we can't use that.
I do like the idea of using the rain in the City of Tears, however. Maybe not from the speed of the falling drops as we can't assume Hallownest is on Earth, but the size of the raindrops could give us some clues.
If you're going with the "we can't assume anything because our animals don't look like or behave like animals in hallownest" approach, then asking the question about the size of hollownest to begin becomes impossible. You're not even okay with using rain since we dont' know if the rain is actually water or if it's liquified hydrogen or molten iron from a different planet where bugs can survive such harsh environments. It's ok to start off with a few assumptions to set the foundations towards an answer of sorts. No answer is truly going to be satisfactory because none of our insects behave in humanoid ways or look anything like the characters of this fictional universe, nor are the relativistic sizes in comparison to each other accurate to the proportions presented on our planet.
Just take one character or set of characters that are consistent in size and change the question from, "what is literally the size of hollownest on our planet?" to "If Dung defender was 2.4 inches, the largest size of known dung beetles on our planet, what would be the size of Hollownest?" Assume life on this planet requires the same conditions as life on ours, so yes, that rain is water, on a planet with gravity smiilar to our own. Don't be so hypercritical of every hair-splitting nuance. Start with a set of conditions that are easy to work with, find an acceptable answer based on those conditions. I think it'd still make for an interesting project one way or another. Lol, you guys are too invested in what would make the project null and void. It's just a fun question, no need to make it an impossible endeavor.
You must be thinking fundamentally differently to me then. The reason I asked this question in the first place wasn't because I wanted any answer. To me, an answer that assumes anything that isn't necessarily true isn't complete. The reason I asked originally was because I was interested to see if there was any possible comparison between the bug world and our world, that we could use to find a difinitive answer. This isn't to say that your ideas about finding a potential answer are invalid, if you want to find an answer that assumes that, say, the size of the Dung Defender is 2.4 inches precisely, go wild, and I agree it would be a fun project. That simply wasn't what I was asking.
Also, fortunately we do have clarification that the substance in the Blue Lake is water, as Quirrel says so: https://steamcommunity.com/profiles/76561198117704794/screenshot/939447588391818279. And if we're gonna need anything more specific than that I agree, it would be impossible.
I'm no physicist, but I think water underground follows the same physical principles as water on the surface, and we know all of it is coming from the Blue Lake.