Imagine you have a message written on a piece of paper. You intentionally show this message to two people, Alice and Bob, and are fully aware that they have both read and can perfectly remember the entire contents of the message.

Now imagine that Alice thought about the message independently (not recalling it, but actually thinking new thoughts), and that Bob did not do this.

Are you claiming that Alice violated your privacy by thinking about something you showed her and asked her to remember? Or perhaps would it only be a violation of privacy if she then subsequently told you one of those thoughts?

I do not see any difference between these parts, no. If a human read my email I would expect them to be completely incapable of not working these things out, so I'm not really too concerned if a computer does it either.

> training a ML algorithm on it

Also not really. If it were a machine learning algorithm that was trying to write realistic emails there'd be a reasonable concern of it revealing things about the training data, but when it's just generating ad recommendations based on only your data that only you see, I'm not too sure there's a serious privacy concern there. I'm unaware of any allegations that you could uncover private details about someone else's life by looking at an advertisement you received on your own email inbox.

> and automatically propagating that to other google products?

I would definitely perceive this differently depending on the product, as Google products are usually distinct enough that you can functionally treat them as if they were different companies (and often they either used to be, or eventually become so). So in this case there are now four entities that know the contents of the email: the sender, the recipient, Gmail, and e.g., YouTube.

But again, I've not heard any claims that Google are using the contents of your emails to decide what YouTube videos to recommend you. It's certainly not outside the realms of plausibility, but that seems like the kind of thing people wouldn't ever shut up about, so I'm surprised that I haven't heard about it if it is in fact happening.

> you can sure as hell know that they build an extensive profile out of your private emails

Oh absolutely, but I don't see how that's a privacy violation when you gave them your private emails. How much thinking does someone have to do about a message you gave them before it becomes a privacy violation?

> and your ads are targeted based on that..

This is the main reason I'm okay with it. Google's entire business model relies on them preventing anyone else from seeing that data, so that they're the only ones who can target ads that effectively. If there was a significant risk of data leaks then I can absolutely see why people would be concerned, but Google has some absolutely gargantuan incentives to avoid that.