i've been toying with this theory that all discrete things have feedback loops inside of them. some examples:
microphone and speaker: the simplest one; if the feedback is above the threshold, it becomes as loud as the speaker supports. if the gain isn't above a threshold, it tends to zero. it's either one or zero.
languages: languages are memes with human culture as vehicles. languages are useful and so they spread, and they loop because they are evolving memes that evolve with themselves. in other words, languages evolve when conversing with other people of your own language. it's like how species (see below) become discrete by not breeding with other species. of course, languages aren't fully discrete; there exist spanglish and singlish and i'm sure many other language hybrids i haven't heard of. but they look a lot like species.
species, sexes: covered by Dawkins in Selfish Gene. genes prevent themselves from interbreeding with other species such that they propagate their own existence. sexes are explained by a feedback loop in the size of the sex cell; sperm is rewarded by getting smaller and eggs are rewarded by getting bigger.
country borders: generally the state is discrete. there is the United States and Mexico and not sorta-Mexico-sorta-US. why? usually because we have a state government and limited land, and there is a "grabbing" of the land that happens, and then you make it your land; you farm on it. and you get support from the government and they make sure that nobody is going to Steal Your Chickens or take your land and so then there's an ownership, which is a loop, by you (this is My Farm Land not yours) but also the government that provided you with basic protection.
life and death: death is inherently a dissolution of boundaries. when something dies, its boundary no longer exists; it is one with its environment. a dead body is now a part of nature, and our language treats it as such. much like state borders above. so in this sense, life is discrete because of its ability to maintain a border. the metaphors in our language reflect this as well [credit to my friend Sarv]
but you can come up with more philosophical examples too:
consciousness: things either seem to be conscious or not; we don't see much in between. explained by Hofstadter in GEB/I am a Strange Loop; tbh i don't fully understand this yet, and i am not convinced that there's not an in-between.
what is a spoon?: well, i don't think that a spoon is actually discrete. i mean, we have sporks! but what is this spoon, the one i am holding? it's one that's had a feedback loop through its process of being manufactured. it used to be raw metal, but now it's been molded or punched and bent into this shape by machines that say "no, don't try to be something else, you will be this spoon." and it's sold by people who say "this is a spoon." and in fact, if it ever doesn't take its spoon form, it will be discarded, so i wouldn't have seen it. so in this very spoon lies a feedback loop, but also in the symbol the spoon i use to eat this soup lies another feedback loop.
of course, this theory is itself introducing discreteness; i can't think of what metaloop lies in it but maybe i will later :)