Generally speaking I agree with you here. But we´re not talking about a mere similarity or resemblence from an obscure movie Roddenberry/Jefferies may or may not have seen. We´re talking about an exact number taken directly from the SF movie that Roddenberry drew his inspiration from.
Yes, and that's exactly why it's a coincidence -- because it looks to us like there's a connection. But the point is that there doesn't
have to be. The human brain is a pattern-recognition machine, so we expect to find meaning and connections everywhere we look. So we expect every similarity to be intentional. But many of them are not. Similarity alone does not
prove intent.
First off, this wasn't the
only movie Roddenberry was influenced by, just one of them. Second, Roddenberry didn't come up with the number, Jefferies did. The more people are involved and the more works they're referencing, the more the variables multiply and the more likely it becomes that coincidences will occur. You're drawing a pattern out of the data because you expect it to be there, and that's how we mislead ourselves into seeing meaning where it doesn't exist. That's why it's important to approach a hypothesis skeptically, to try to
disprove it and only give it credence if it withstands the attempt. Our brains are trying to trick us all the time, and so we have to examine our own assumptions and beliefs just as critically as we need to approach the claims that other people try to sell us.
What about the deceleration chamber in FP? Is it also just coincidence it looks almost exactly like the
Enterprise´s transporter?
Non sequitur. A specific argument and a general argument are two separate things. I'm not saying
nothing in Trek was an homage to FP; I'm saying there's no compelling proof that
this single specific thing was an homage. I've already granted that it's
possible that it could be an homage like certain other things were, but establishing that something is possible does not prove that it is true.
If you wanted to make a numerical homage to FP, why not choose the "1701"?
That's a meaningless question. Again, I'm not saying it's impossible, I'm saying it's not proven. Besides, it's circular reasoning to start with an "if" statement that includes the very thing you want to prove.