I wasn't clear about the egg thing either until well in to my 20's. I even have an uncle who farms chickens (for meat, not eggs). Also my older brother works in a manufacturing factory for New Holland.
So hens lay eggs whether they have sex with roosters first or not. The eggs hens lay when they have not mated with a rooster are the ones sold in grocery stores. Meaning they are not fertilized and will never produce an actual baby chicken. Not unless the facility screwed up real bad and somehow let a fertilized egg through. There's some kind of test they do at some point to make sure this doesn't happen I think.
Great read! Fallen London didn't stick with me very well, but I was always interested in its narrative structure and appreciated exactly how much it left for the player to interpret and, well, create.
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