How did the Borg come to know about Earth?

Question

When the Enterprise-E destroyed a Borg cube in the 24th century, a small part of it travelled back in time (2063) to stop first contact of Humans with Vulcans. During the fight with Picard, two Borg crash-landed on Earth in Arctic ice.

They became active in the 22nd century and sent spatial co-ordinates of Earth to their home world.

Well, I have answered myself, but not really...

Isn't it a paradox? Borg crash-land on Earth because they already knew the co-ordinates of Earth. And, the Borg (race) got the co-ordinates because of these crash-landed Borg. How did the Borg come to know about Earth in the first place?

Answer 1

You did answer yourself in the question. This is commonly known as a Stable Time Loop (Warning: TVTropes), and is not the only one in Star Trek!*

The message sent during ENT to Borg space arrived before Q sent the TNG-era Enterprise to encounter the one Borg cube, by around a decade if we can trust T'Pol's estimate of 200 years, and that it didn't take longer. That is how it was already on its way to Earth when it was encountered in Q Who.

"First Contact" with the Borg could technically be considered to be any of:

• The NX-01 Enterprise's encounter. However, the name "Borg" is unknown at this time.
• When the message arrived, somewhere around a decade before Q showed the Cube to the NCC-1701 D Enterprise. The Borg now know about the Federation, but not vice-versa.
• TNG 2x16 Q Who, where Q shows the Borg Cube to the NCC-1701 D. I don't fully recall the episode, but according to the quotes on Memory Alpha, the Borg did not identify themselves as such - Guinan identified them.
• TNG 3x26 The Best of Both Worlds, where the Borg finally arrive in Federation space.

*The other stable time loop is from VOY 3x08 - 3x09, the two parts to "Future's End". Without the technological advancements made by Chronowerx Industries, humans could not have joined the galactic scene as early as they did, and the Federation would likely not have formed. But all of Chronowerx's inventions were based off of 29th century Starfleet technology.

*The TVTropes page even points out several other Star Trek stable time loops from TNG and DS9 I'd forgotten about, under the "Live Action TV" section.

Answer 2

This is called the bootstrap paradox, and is a fairly common occurrence in the sci-fi world. There is no cause and effect, just a cycle. In this case, one might argue that through his desire to save Humans from the Borg, Q inadvertently caused the danger from which he was trying to save them.

Answer 3

We have Q to thank for the Federation's first contact with the Borg. This would be the contact that would ultimately precipitate their time travel into the past and eventually send a message with the location of Earth. When Q sends the Enterprise to meet the Borg, the Borg were already on their way to Earth. Q considered himself helping the Federation by revealing the new threat.

This might appear as a paradox except the events occur with the 24th century Enterprise D meeting the Borg, engaging in combat, losing, meeting the Borg again at Wolf 359. Eventually traveling back in time, leaving two Borg behind, who later in the 22nd century send a message which is delayed likely due to a reduced quality subspace signal or even worse, a signal sent at the speed of light... which eventually reaching the Borg. The Borg begin a trip to the Alpha Quadrant which Q interrupts by sending the Enterprise to meet them in the 24th century; temporal loop closed or bootstrap paradox created.

Wikipedia entry on the supposed first contact with the Borg:

The Borg first appear in the Star Trek: The Next Generation episode "Q Who?", when the omnipotent life-form Q transports the Enterprise-D across the galaxy to challenge Jean-Luc Picard's assertion that his crew is ready to face the unexplored galaxy's unknown dangers and mysteries. The Enterprise crew is quickly overwhelmed by the relentless Borg, and Picard eventually asks for and receives Q's help in returning the ship to its previous coordinates in the Alpha Quadrant. At the episode's conclusion, Picard suggests to Guinan that Q did "the right thing for the wrong reason" (a T. S. Eliot quotation) by showing the dangers they will eventually face. It is suggested that the Borg may have been responsible for the destruction of Federation and Romulan colonies in the final episode of season one, "The Neutral Zone".

I am certain the Federation's temporal dynamics agency is certainly displeased with how this event took place, but since it was precipitated by Q, it isn't as if they could punish him, and as terrible as the events at Wolf 359 were, the entire Federation might have been assimilated by a single Borg cube without the experiences of the Enterprise crew at their first contact with the Borg.