https://youtu.be/GVmepy9UdzU
Learn about mathematical induction, the difference between mutual and common knowledge, and the blue-eyed islanders puzzle in this Star Trek-themed logic cha...
“At least one of you is red”
They will all assume that they are the red one because they see no other red ones, but since that assumption is wrong, they will not shut down. They will discover that this is a lie and just assume that the intruder is a liar.
yes, some lie might work, to undo the original message. But to say that one is red poses the risk of all of them shutting down in a second. How can they know that they are not red?
They will believe the they are red, but since they are not, they won’t shut down because they don’t actually know their own colour, they just think they do.
I see what you are saying. I think it depends on the understanding of their rules. And whether they have the agency to shutdown themselves (which is my understanding), or whether the whole omniscient system is responsible for the shutdown (which I believe is your understanding).
I think it HAS to be the system, because otherwise prior to this, they would have come to a belief about their colour and shut down anyways.
More than that, shutting down when you know your own colour does not offer them any sort of natural advantage or purpose, it’s a system thing and not an individual thing.
it is open to interpretation. the idea was that shutting down keeps the harmony in the society (because only once they know their own color they have some sort of incentive for discrimination against other colors).
and yes, there is a question on trust and belief versus knowledge. but assuming Vulcans are trustworthy, I think the synths conclusions can be seen as knowledge (i.e. not just belief).
Offer to take several random synths as ambassadors. The collective does not know how many, or of which color, but understands that not only will their common knowledge of other beings grow, their own will be saved.
The death spiral presumes that every synth knows that every other synth correctly heard the external statement about color. It would not be logical for a synth to make such an assumptIon, and they cannot query each other about the content of the statement or propogate that knowledge, because they cannot talk about color.