Aaaand how many beacons we need if we know time when signal received?
( As I understand it, beacons transmits signals (*2) , but we want to receive a signal on at least 3 receivers that is very far from each other )
We can only know the time when we receive the signal on each position. So you mean you get identical signals but with different timestamps on each position, that we know has the same origin based on how the signal looks like ( *1) . Then we only need 3 to know that the signal is from one of two possible locations.
However, if the distance to said signal is extremely far off, the gravitational field in the universe would have distorted the signal so much that we can not tell anymore if it is of the same origin and would also get a slight variation in time, which makes location very unsure. Then we start talking about the location as a sphere of interest, rather a specific location.
In this situation, I think FD has the location in the range 0 - 100000 ly, which means it will be fairly accurate. Also, if one of the two possible locations is way outside of our galaxy, and the other one is inside, we would assume that the inside one is of more interest to start with.
So the answer is 3 if we know the time difference between the timestamps of when the signal was received at those three positions. We need to assume that the three positions, as described as named Systems, have not moved at all since the original transcript/message, which we deduced from the ancient artefacts, was made ( complex sentence, I know... sorry ).
Since the three systems actually are moving around over time, we need the time when the message was constructed, or the time it meant where the triangulation is supposed to take place. Timing is everything.
I assume FD made it simple, and just ignored the time factor. Meaning we can assume that the three positions, or the source we seek, have not changed in position relative each other.
And that assumes that we are supposed to do this kind of approach at all.
Assumption is the mother of all f-ups. ( - = uck )
-
So, I propose that since everything is moving around in the universe over time, we are not looking for a mathematical solution for a location, but instead, several hidden clues to the position, that does not change much over millions of years. The time aspect is important here. Exactly how ancient are the ruins? Hours..... Thousands of days ... millions of months... or BILLION sol-years old?
The lack of atmosphere at the ruin site does not necessarily mean it was always without one. A geologist should be able to figure out if there was artificial violence, weathering or just micrometeorites that did the obvious "ancient" look to the site.
All these factor in to deduce how old the ruins really are. If we know that the ruins tells us the positions of actual named systems, we can deduce by approximation how far back that unique stellar pattern did align. But, I do not believe that FD actually provide time mechanics for the entire galaxy on stellar level ( but I have been surprised before ).
We could also ask ourselves: What exactly are we supposed to be looking for? An interstellar source? Who said anything about that? Maybe we are just puzzling a grocery list for all I know.
What are we doing here?
Speculation:
It is more likely that the ruins are a lock mechanism, which when operated correctly reveal more information. The cryptic stuff we are finding have a purpose. We just need to take a step back and ask ourselves: What would FD have done for us here? ( And not what actual aliens would have done, because it is a very different thing indeed. ). This is just a game, not reality ( ... 2.3 maybe
)
*1 - What signal? Did we find a signal or a signal description anywhere?
*2 - E.T. phone home? Do we activate the phone?
