How do you define humanity?
How do you ensure it includes every human?
How do you ensure it doesn’t include every non-human?
I’m not even asking about computation or algorithms. I straight up don’t think you can make a definition that isn’t a tautology or an approximation. Both of which are useful, but neither of which can fit a _proof_.
You're not wrong, but something can work well enough to still be useful despite falling short of the idea of a proof or any formal definition.
Let's say that 95% of individual humans can pass it and only 2% of bots. For someone maintaining a website, who has to decide between using this system and shutting down their site because of the increased costs, that may very well be good enough
Every place on earth has some legal definition of who is human. The system I’m thinking of isn’t a technical/captcha one, it’s a human curated list of humans. Just an electronic ID. Those already exist but the challenge is making them (acceptably) privacy-preserving.
I want to take my existing national digital ID and use it online basically. BUT I don’t want the websites to know it’s me. Just that I’m human (or perhaps over a certain age). And I don’t want the ID issuer to know what site/service asked whether I’m a human or I’m 18 etc.