When people talk about "the algorithm" in a vernacular sense (i.e. not the technical definition), they mean the thing that chooses what they see in their social feed. All mainstream social media select content for you, promote stuff you never asked for, while not necessarily even showing you all the messages from the sources that you specifically subscribed to. That's "the algorithm".

The clients that I use in Nostr don't do any of that. They just show me the notes of people I subscribed to, end of.

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This isn't accurate. All of the relays do some filtering, so the algorithm is just a level lower. You don't know what was sorted out before it got to you, even if it was a bot or spam from one of the npubs you follow. The relays would eventually collapse under notes, if they didn't curate, at least a bit.

That is a simple attack vector: just flood them with nonsense notes saying "Happy Birthday!" or containing kiddie-porn, or whatever, and shut down the server.

Indeed, you can't prevent filtering, although you can improve the chances by subscribing to multiple relays, especially relays that you have in common with your follows.

But is there a nostr client that mixes in crap you didn't ask for? I think that's the main problem with "the algorithm". I'm amazed at how much outrage p*rn gets shoved down your throat in Twitter/X, Youtube, etc.

The closest we have to that is Primal, but you can get around their regarded Highlights feed, so it's not a real barrier.

And your example helps me illustrate:

How does your client know who you subscribed to?

1) You wrote a list "follows" or "favorites" or "people who know about Formula-1 racing" and posted an event containing the list, and the client lets you select that list.

2) Your client lets you select someone else's "Cool Nostriches" list.

3) You client assumes you subscribed to everyone not on your "mute" list.

4) You paid to be let onto a relay, that you know lots of interesting people write to, and the client allows you to add that relay and see the notes in your feed.

5) You plugged into a DVM, that suggests interesting notes to you in your DMs, and your client doesn't block those DMs.

6) You downloaded the source for a client (like oddbeans) and changed the filter code, to show you what you want to see.

Etc. There are many different algorithms for showing you the notes you want to see.