I was talking to someone just now about the Numbers. Enzo Valenzetti was a mathematician that worked to calculate the probability that the human race would kill itself, and when he confirmed that we would, the Dharma Initiative was formed to change the main variables in his equation. They were: 4, 8, 15, 16, 23, and 42
What does this answer? A few things, if you look at it. I think S5 would have been stronger to touch on this, considering they joined Dharma and all. It would have strengthened the ultimate themes of destiny and whatnot, I think. Hell, Valenzetti could have actually appeared on the show. Lots of stuff they could've done, and I think the show would've been bettered, not cheapened, to do this.
Just the same, a common question is "why is the button 'the Numbers'? Why isn't it just a button?"
Well, think of the complex mindgames it would allow the technician to play if the hatch was overtaken by the Others (if you don't let me go and leave, we all die, and I do mean we all die). He or she would hold all the cards. So that's a good reason for there to be a password in the first place.
Why the Numbers? Well, gee. If you were part of a scientific team trying to change the equation that predicted the end of the world, what would be easier to remember than the Numbers themselves? The original technician (Radzinsky) definitely knew what was at stake, because he wasn't just some flunkie mopping the floors. He was one of the big Dharma guys, and designed the Swan station itself.
Furthermore, when you consider that Jacob assigned a number to each Candidate (many of which were not one of the Numbers, of course), things take on an interesting context. Who were the last six Candidates? Why bother with their names, how about I tell you their numbers: 4, 8, 15, 16, 23 and 42.
I used to think that these numbers were attached to them because of the variables in the VE and blah blah... but if you think about it, doesn't it make sense if these people were the variables themselves?
This list, after all, contains the company of Jack, Locke, Sawyer, and others from the final stretch. These were all flawed, Island-bound people who had the potential to release Smokey, either by siding with him or being tricked by him. In fact, each of them did one of these things by the time all was said and done.
Each one of them was not only a Candidate to replace Jacob, but one of the variables that could have released Smokey. Only one variable, presumably, needed to change. That variable was Jack.