And Keltham holds forth upon the Way.
Even when you truly expect and anticipate that something will happen to you, sometimes, something else happens to you instead. "Beliefs" are the name given to those things that control your anticipations; that which gives to you your actual experiences is termed "reality". Sufficiently young children have not yet developed the capability to appreciate that their beliefs, the beliefs of other people, and reality, are three distinct objects of thought; they are not capable of distinguishing between what they know themselves, and what other people know. Comprehending this marks a threshold in what is taught to dath ilani children. Keltham thinks everybody here probably understands that already, so he's going to skip over that threshold and the exercises leading up to it, but people should let him know if this starts being a sticking point.
Reality possesses both overt order and deeper order; surface appearances, and facts behind them. Deeper order can be obvious or nonobvious. When you observe that Jennith resembles her mother Merwen, you observe a surface seeming; when you say that daughters often resemble mothers in general, you are observing a deeper order. If you could peer at things that were arbitrarily small, like being able to look at a bug as though it were the size of a bird, and smaller yet; and you saw tiny twisting spirals inside Jennith, all carrying the same very long intricate pattern; and you saw that half of those tiny twisting spirals appeared also in Merwen, and the other half of Jennith's spirals had come from her father Eveth, you would have discovered a nonobvious deeper order, something with the promise of explaining the obvious deeper order. Baseline has a separate word by which to speak of the nonobvious deeper order, the hidden order. Behind a hidden order may lie another hidden order. Even when you are not told about a hidden order, even when nobody knows what the hidden order is, it may still exist and be the secret factor that has organized the seeming chaos of the experiences before you.
The understanding that reality is full of hidden order is the threshold that marks a mind's readiness to apprehend the Lawfulness of reality. Once a child becomes able to distinguish between what they know, and what others know, and what is, that child can soon after apprehend that what seems to them like madness, confusion, noise, or simply a collection of boring unconnected facts, is only the appearance of a collection of unconnected facts, the absence of knowledge of an explanation if one exists; these children are ready to understand that their own bewilderment is their map of the world; and that the territory itself is never feeling bewildered, and that it is often full of hidden orders.
(It is possible to believe that something is a hidden order, and be wrong about that; maps of hidden orders are not thereby part of the territory, they're just maps of a supposedly deeper part of the territory. Children are led through several exercises meant to help them appreciate this fact on a deep level: that you in your own mind are really impressed with a theory of hidden order is not the same fact as that hidden order actually being present in the territory and able to control your experiences. This has always seemed like a really obvious point to Keltham now that his brain is mature, so he's just going to press on without doing a lot of exercises there, but people should speak up if that's somehow torpedoing the rest of his lecture.)
It was the way of reality, in the universe that Keltham knew, that complicated things possessed the hidden-order of being made of simpler parts: and in dath ilan, knowledge of this fact was power. He's not quite sure that the same also holds true of Golarion, but Keltham did do some preliminary checks, and was told, for example, that snowflakes have hexagonal symmetry. Keltham knows the hidden order underlying snowflakes in dath ilan, the tiny pieces that nestled together in sixfold symmetry there; so he's guessing that snowflakes have the same hidden order in Golarion. And by extension, that Keltham's own body has the same hidden orders of the same kind rather than having been remade and rewritten on his arrival here. There are a lot of hidden orders invoked within a dath ilani body. It is a further guess, though not a certain one, that Golarion possesses all the same hidden orders of that kind - that the things here that Keltham recognizes, are ultimately made out of the same tiny parts that Keltham knows.
In Keltham's world, they don't have spells; some of the hidden-orders here must have been absent from Keltham's world. In Keltham's world, when you want to go from one place to another place very far away, you get into a huge metal structure with fixed wings and powerful engines that push out air behind it, thrusting that 'aeroplane' forwards to fly across oceans and continents. To build something like that, you have to understand the hidden orders of metal, in order to build sufficiently strong metal. You have to understand the hidden orders of fire, in order to find dense-enough fuels that burn hot enough for the fuel on board the aeroplane to last for flying across the continent. But these hidden orders are invariant within dath ilan; they work for everyone, not just spellcasters. They aren't truths about the people using the aeroplane, they're truths about metal and fire. For a quarter of a day's income, you can buy a ticket for an aeroplane trip across a pretty large ocean, going slightly less fast than the speed of sound in air, and get to the next continent in a quarter-day or half-day. Keltham is not sure how much it costs to teleport the same distance here, but he gets the impression it is more expensive than that. Artifacts that exploit dath-ilan-style hidden orders can be made without spellcasters. They are economically scalable. That is part of the change that Keltham hopes to bring to Golarion; and driving back the demons of the Worldwound will only be the bare beginning of its consequences.