Upon watching Part 5 and 6 of the 'Mysteries of the Universe' videos, some information about the Dharma symbol has been "unearthed". It's easily watched so I won't go into it all here but the Dharma logo "is a Bagua symbol... that dates back to the Ancient Orient" (not sure if this was common knowledge or not since the intro of the DI in Season 2 but nevertheless). It represents protection and that when one stands in the centre, they are protected on all sides by the outside forces (represented by the 8 sides of the Octagon, ie. 8 opponents). This is all coming straight from the video itself. Now, does that sound like anything? The Temple! I'm happy to be proven wrong but I would hazard a guess that the wall we see surrounding the Temple in 'This Place Is Death' and 'Dead Is Dead' is shaped like an Octagon, and the DI based their symbol off of the shape of the Temple. Or if not based on the Temple, they must be about the same ideologies that the Ancient Ba gua symbol represents, ie. protection from the outside.
The arrangement of the lines is also spoken about, and if I recall correctly, someone on here had mentioned the specific lines in the Dharma symbol representing something. While I don't necessarily think the Temple has these lines, it's at least confirmed that the lines in the symbol itself represent something - "astronomy, astrology, geography, anatomy and more" - which are (at best) vaguely what the Dharma Initiative was studying on the Island. The "and more" could refer to zoology, electromagnetism, parapsychology etc, which we know from the Swan Orientation video were other aspects of the DI's work.
I also have to say that I am eager for the information about Hanso, Valenzetti and the Equation to finally make an appearance in the show rather than be a B story in the background, especially now that we have an understanding of what the DI was about, and an apparent connection between the Temple (an ancient Others' structure) and the DI.
My final thought concerns another comment made in the video. Seeing as it's the final video and the end of this particular "episode" of 'Mysteries of the Universe', it sounds like a preview of what's to come. The narrator says "The exact answers are perhaps known only by the cultures of the past". This makes me think that Jack, Kate, Sawyer etc. in 1977 will once again time travel after Jughead's explosion, but this time, to much further into the past, back when the Others first got to the Island, or when the Black Rock did. Maybe the Others were the first ever humans and therefore the first culture on Earth, or, at the very least, on the Island. But of course, the Others from 1950 to 2007 don't look like any relations to an Ancient Chinese culture so something isn't syncing up there. But I still think this comments is a preview given to us to say that those ancient cultures are either the ancient Others, the current Others, or some other group of people that the survivors from 1977 will soon be visiting.