star trek - How did Picard send a binary message to Data in the future?

In the Star Trek TNG episode "Times Arrow", parts one and two, recall the following:

• Data's head was found in an excavation on Earth that dates from the 19th century (it actually is Data's head).


• Data, Picard, Crusher, Worf, and others go back in time to the 19th century to investigate.


• Guinan (her 500-year younger self) was living in San Francisco in the 19th century.


• This is where Guinan first meets Picard, but not where Picard first meets Guinan.


• It turns out that alien time travelers are sucking energy out of people on Earth from the 19th century.


• In the process, Data is caught in an altercation which essentially blows his head off.

Here's where things get especially interesting...

• In an effort to stop these aliens, all of the away team along with Samuel Clemens, except Picard and Guinan end up back in the future to try to destroy the aliens time travel site on their planet.


• Picard, still in the 19th century finds out from one of the aliens that if the Enterprise in the future fires upon the alien time travel site, the energy from the ship's phasers will only serve to increase the aliens' power.


• Commander LaForge manages to reassemble the 500 year old Data head, after removing a suspicious piece of metal lodged in one of Data's cranial ports. "How did that get in there?" LaForge asks.


• We are then taken back in time to see Picard is responsible for putting the metal piece in there. He also enters a binary message into Data's static memory warning the Enterprise not to fire on the alien site.


• Data (reassembled) receives this message, and the crew make a plan to destroy the alien site by making a tweak to the ship's weapons.


• Before destroying the site, Samuel Clemens goes back in time and allows Picard to return to the 24th century

Everybody wins! What an awesome episode!

But here's the rub

From Picard's perspective, he simply entered the binary message into Data's head, and then was immediately rescued. I should think that Picard would have had to have lived a lifetime in the 19th century, then died, and then 500 years later, Data's head would be found. At this point, the static memory in Data's head warning the Enterprise would be there legitimately and the episode could continue as normal.

So how does entering the binary message into Data's static memory seemingly transcend the space time continuum and make it to the future?

Answer

Welcome to the Grandfather Paradox. Start with the Wikipedia article.

There are at least four ways to handle this:

1. 
   

   Picard's actions form a self-determining loop. That is, the origins of his actions are contained entirely with the loop. The classic along these lines is Heinlein's All You Zombies.

   
   



2. 
   

   When Picard altered Data's memory, he created a parallel universe (timeline) in which the data exists/existed/will exist. When the team returned from the past, they entered this new timeline. In the old timeline, they never returned.

   
   


3. 
   

   When Picard altered Data's memory, he created a history which overwrote the original history which caused him to go back in time. The original history, in which Data's memory was not modified, ceases to "exist", as far as the word applies.

   
   


4. 
   

   There's no problem. The away team went back in time without having performed a detailed examination of Data's head. So it had always been modified, and Picard's actions had always occurred. Again, as far as the word "always" applies.

   
   

An excellent discussion of the peculiarities of time travel (from a purely speculative viewpoint, of course) is Larry Niven's The Theory and Practice of Time Travel