Oh fuck, I just had an epiphany during my 4th playthrough!
INSIGHT = PHANTASMS !
YES! You know, that
madman's knowledge picture with the little bright worms flowing out of the skull? Those are not symbolic abstract representations of knowledge or something, those are actual invertebrates/worms/phantasms! The same ones seen on hunter tools as augur of ebrietas and empty phantasm shell. In fact, if you take a close look at Blacksky Eye, you will see there are vestiges of the little worm coming from inside the eye! Which means, they - the invertebrates/worms/phantasms - are the responsible for contacting the cosmos and the great old ones (and bringing forth a mini-star to throw at people in case of Blacksky Eye). Which means "Insight" in the game is an actual,
concrete thing - the presence or vestiges of these slimey worms inside one's skull! Now, sure, it seems you also gain insight as an abstract thing per se when you first meet some bosses and eldritch things, so it means the stat Insight may represent both your character knowledge of the cosmos AND the presence of these slimeys inside his skull, and maybe one lead to another and vice-versa.
That's fascinating because all this time I thought this were just some abstract/symbolic shit when it's in fact concrete ! And that's what "Eyes on the inside" means in the end, little cosmic inveterbrates inside one's skull!
Extrapolating from that, we can understand exactly what the Church experiments on the research hall are about: brain fluid is an attempt to replicate the slimey invertebrates. They fill patients heads with that shit so they can grow "eyes on the inside" and make contact with the cosmos. And they succeeded partially, as proved by Adeline. Also, take a look at the
blue alien beings/celestials seen on Forbidden forest, see how similar they are to the bloated head patients? It seems the Church attempted to replicate the celestials they found in the Isz labyrinth and the bloated head people was the result. Some bloated heads even got the powers of the celestials, as shown by the ones in the garden that attack you with laser beams from the hands. Remember, though, that the Hunter nightmare is a mirror of the distant past. In the present the Choir actually made the breakthrough and replicated the celestials perfectly, as can be seen by false Iosefka experiments in the clinic. (a shame that the night of the hunt hapenned just as she/the Choir was about to conclude the experiment ?)
Now some heavier speculation on my part:
If Master Willem is the one searching for "eyes on the inside", the one who led the students to contact the cosmos and achieve partial evolution, as seen on their mutated forms on Byrgenwerth and the lecture building... Laurence is the one who seeked the old blood, the easier path to evolution. Remember the note found on the lecture hall "Master Willem was right. Evolution without courage will be the downfall of our race". The blood path is the lazy one, the one for cowards. You just go to a clinic and infuse some blood and BAM! Youre cured, you live longer, you feel better, you're new. You don't need Insight, and in fact Lawrence skull in the Nightmare doesn't have any "insight" on it. And it was indeed the downfall of our race as the note said, as it brought the downfall of Yharnam. It's interesting how these two paths - Willem and Laurence's - seem opposite to each other, not only from a personal philosophy, but also from a cosmic point of view. This duality is formed on one side by the blood, the Beasts/Beasthood, and the "Paleblood" Great One/Moon Presence. On the other side by Insight, Arcane, Rom, the Celestials, Ebrietas. And perhaps humanity is in the middle, on a neutral point of the spectrum.
Going back to the duality Beasthood vs Insight, perhaps the Moon Presence is a Great One whose nature is all instinct, ferociness, hunting, and this puts it naturally against the other Great Ones whose nature is its polar opposite of arcane, discovery, cosmos. And maybe that's exactly what it's contract with Laurence and Gehrman is all about: they bring it the blood it craves, and it helps them with the side-effects of their experiments for evolving the human race. (That is, until Micolash/Mensis fucks it all by invoking a Great Old one and the whole city goes crazy)