Final Boss of "The Twinning" Hunting for lore (Spoilers)

[Iscah]

What I mean is that once you can observe Omega and discern what it's doing, you can recreate its functions as a means of traversing the rift. It's a logical hierarchy.

I think there might be some confusion going on with terminology.

The phrase "Wings of Time" is specifically invoked when calling Alexander to move through time.

The mathematical ability to calculate possible futures is separate, and seems to be referred to as "Alexander's dream".

Quotes:

BIGGS AND WEDGE'S EXCELLENT ADVENTURE
https://www.garlandtools.org/db/#quest/67872

ROUNDROX
Pssshkoh... Yes... Much swirlybright... Timewings...can spread... Travel to overtimes... Make bad things...good again...
[...]
Uplanders...hold on to braincases. Timewings...spread!

JUDGEMENT DAY
https://www.garlandtools.org/db/#quest/67874

QUICKTHINX ALLTHOUGHTS
O, Alexander! Lord of steel and whirlycogs! Outspread wings of time─let ignorant and unworthy feel divine judgment!

Y'SHTOLA
The codex responds... He means to return to the past!

DAYAN
Oh, if you could see the worlds we have seen! A world in which the Illuminati rule history with an iron fist, every nation brought under their yoke. A world in which Alexander spread wide the wings of time and swept the lesser moon from the heavens, averting the Calamity...

DAYAN
Were the wings of time to fall into the hands of the Illuminati, the repercussions would be dire indeed. History would be rewritten over and over again, each time bleeding the land of aether. And in the end, the colossus would usher in another calamity.

And on "Alexander's dream"...

DAYAN
How best to put it? We stand inside a mathematical simulation, calculated and projected by the device at the heart of the colossus. One might equally say it is the dream that Alexander dreams...
[...]
Alexander dreamed all the realities imaginable─all the realities mathematically computable [...]

So saying they could use the "wings of time" to observe Omega is dependent on them being able to open a real window through time and space to observe it without being detectable. Using the "dream" (supercomputer) to calculate its abilities is different.

But by the way the phrase is used in Alexander, the Future Ironworks team haven't actually used the wings of time until that one moment where they "throw the switch and pray".

"Rise" is about the Illuminati rising up to use Alexander's power to solve all of their problems and dominate the world. Thematically, it's more Quickthinx's theme than Alexander's. Kind of a subtle hint that Alexander wasn't really the villain of the story at all.

I did read the lyrics and think that, but the thought didn't make it into my post.

'Locus' is definitely more generic (by chance or design?) but 'Rise' is specifically linked to the events of Alexander.

[Anonymoose]

The phrase "Wings of Time" is specifically invoked when calling Alexander to move through time.

The mathematical ability to calculate possible futures is separate, and seems to be referred to as "Alexander's dream".

That works. I was going by this, but that distinction fits here, too.

Dayan
How best to put it? We stand inside a mathematical simulation, calculated and projected by the device at the heart of the colossus. One might equally say it is the dream that Alexander dreams...

Mide
And what of our companions? Are they...?

Dayan
...Their fate was not mine to change, Mide. All that came to pass did so for a reason. History is as it was─as it should be─free of the paradoxes that spelled its undoing.

From this place─unfettered by the mortal construct of time─Alexander looks out upon past, present, and future, seeing infinite possibilities. I see what it sees, and feel what it feels─this perfect machine, born from yearnings for an ideal world.

Oh, if you could see the worlds we have seen! A world in which the Illuminati rule history with an iron fist, every nation brought under their yoke. A world in which Alexander spread wide the wings of time and swept the lesser moon from the heavens, averting the Calamity...

Alexander dreamed all the realities imaginable─all the realities mathematically computable─and in the end, reached a single, logical conclusion. It would change nothing, and erase itself from existence.

Mide
But...why?

Dayan
Alexander possesses the power to travel through time and space, and reshape history for the better─but such power comes at great cost. The sheer quantity of aether consumed in the process means that Alexander itself would─mayhap not immediately, but inevitably─bring ruin to this world. This perfect machine, this supreme manifestation of logic and science, deemed its own existence a threat.

And so it chose to do nothing. To leave history untouched, and the future in the hands of man, with all his imperfections. Such was Alexander's divine judgment.

A time will come when the fate of this world is placed in the hands of one warrior. For reasons hidden to me, the future from that day forth remains shrouded in mystery─beyond even the colossus's ability to calculate. And yet Alexander chose to believe in that [person], and the light within [them].

Though it does raise some questions about the completely different category of time shenanigans we're dealing with in 5.0