This is an OC summary of how the world of Work In Progress works. It was gradually refined over the course of the game.
The world of Work In Progress is composed of 3 planes: the Mundane, the Dreamscape(s), and the Transcendental. The Mundane and Transcendental are simpler, being entirely one thing or the other, while Dream is connected to both, and is sort of a hybrid.
The Mundane works almost entirely like real life, where objects are precisely the sum of their parts. The only difference is its connection to the other planes. Except in the case of strange things happening with pits, the only connection is that of Dreamscapes inspiring the creativity of the people they're connected to.
The Transcendental is akin to the world of Platonic forms. For every possible concept, there is a corresponding Concept in the Transcendental. Each Concept is something like a statement or property something could have. Concepts can describe things in the Mundane, for example The Bottle is related to each Mundane bottle, but the Concept and its Mundane instances exist entirely independently of each other. It is only a description, not a part of how bottles work.
As consequences of this, each Concept is unique. As Concepts are properties, if they had the same properties they would simply be the same. Also, the Transcendental is timeless, because time is irrelevant to what concepts theoretically exist.
The vast majority of Concepts are incomprehensible nonsense that doesn't actually correspond to anything in Dream or the Mundane, but the parts closest to Dream are those that exist in the mind of the human it's connected to, which is why the Muses who visited it were able to understand (mostly) the Concepts they met.
The view Muses got of the Transcendental is very different from how it works internally. When you talked to The Revolutionary for example, The Revolutionary was unchanged, but the Concept contained implications, in that it describes a sort of person, which implies behaviours conditional on the input they got. When Muses arrived there, the appropriate response was some sort of greeting, so within the context of that interaction the Muses perceived them as saying some particular greeting.
The way that Concepts work is fundamentally non-reductionistic. They have (or are) high-level properties without having any specific parts that would be able to cause that. This is why sometimes Concepts in the Transcendental looked confusingly generic.
Dreamscapes are connected both to the Mundane, via the mind of a particular person, and the Transcendental, via the Concepts available to that mind. The things within it are all made of a mixture of Tropes and Juice.
Juice is the essence of the Mundane in Dream, related to the attention and creative effort of the human, and within Dream related to reductionism and mutability. It is the power that allows Muses and other things to drive change within Dream, and its ability to inspire change and mechanistic nature both make it very useful for engineering, hence Juicetronics.
Tropes are the essence of the Transcendental in Dream, each being connected to a particular Concept. Tropiness exists both in concentrated purified form as Trope Cards when Muses extract it from the environment in a useful form, and as an active part of the composition of nearly everything in Dream. Most objects have little bits of various Tropes relating to aspects of their nature. The influence of many Concepts allows the objects to be morefully defined as specific objects, rather than abstract like the Concepts themselves. As things tend to be made of the Concepts most available to the mind connected to the Dreamscape, they mostly follow physical rules that seem realistic so long as you don't look too closely, or otherwise Narrative logic. Impressions are just this, but containing Tropes of personhood.
Jo's Dreamscape was unusual in several ways. As the society of Muses within each Dreamscape is built up entirely without communication with any other Dreams, there is a wide variation in what they end up like, and Jo's rather extreme version had some strange concequences.
Due to highly intensive Trope mining, Jo's Dreamscape drifted closer than usual to the Transcendental, allowing some Concepts to start breaking through. One of the first of these was The Sage, who went on to try to hide the Transcendental and prevent more Concepts getting through. They were quite successful for a long time, but by the start of the game, the Transcendental connection was growing again.
The stronger connection to Concepts made it more difficult to modify things from their existing strongly-defined natures, causing the Great Fade and Jo's writer's block.
The portal to the Mundane was simply caused by the pit machine, which compressed a huge amount of Juice to a very high density, therefore strengthening the local connection to the Mundane to the point of it being a physical portal. Because the Magnum Opus was mirroring the events of Spindle and was particularly prominent in Jo's thoughts, the actual portal manifested there as the whirlpool, and the Pit was just a Transition to the whirlpool.
Portals between Dreamscapes and either the Mundane or the Transcendental have existed many times before. What was most unusual (unique in modern times at least) was the existence of both at the same time. The unusually high amount of Tropiness in Jo's Dream caused by the Transcendental Cracks spilled through into the Mundane, altering its nature locally around Jo towards being more like Dream, with a mixture of Tropey things and normal Mundane matter.
This became considerably worse once the Rank ? Archetype The Trickster was played directly above the Pit, opening a crack there. This allowed The Trickster to draw Juice directly from the Mundane into itself in the Transcendental in a positive feedback loop of increasing power that, had it not been stopped, would have eventually connected The Trickster directly to the Mundane and allowed so much Tropiness into the Mundane that it would permanently change its nature to become much like Dream, with an overlap of Conceptual and natively Mundane elements.
As it actually happened, though, this process was cut off from both ends at once, as The Trickster was defeated and the Pit was closed, preventing the Tower ending.
There ended up being a lot of different types of people in Work In Progress who worked in fundamentally different ways. There are a few other unusual examples like Dr. Tangle, which were usually some sort of mixture. The most common types are listed.
The only sentient species native to the Mundane (at least on Earth, but aliens were outside the scope of the game), humans work almost the same way as they do in real life. Their intelligence is based mostly on the detailed arrangement of neurons, with a little influence from the Dreamscape they're connected to.
Not fundamentally different from non-sentient Concepts, but embodying a concept that contains the idea of sentience. They are only intelligent to the extent that their concept implies thoughts and actions conditional on their circumstances. In their usual state in the Transcendental, they don't actively progress through thoughts, but every possible sequence of thoughts is part of their existence. When they are exposed to Juice or manifest in other planes, they become more coherent and experience time, borrowed from the other plane, in a more ordinary way.
Although they don't need Juice to survive, with it they are more able to alter other things that are themselves Juicy (and therefore mutable). In the Dreamscape, this is manifested as powers metaphorically and thematically related to the Concept.
Impressions can be related to either Vignettes or Far Dream. They are made almost entirely of Tropes, and have intelligence in a way similar to how Concepts do, by containing bits of Tropes that imply intelligence, and behaving in ways consistent with those Tropes. They naturally contain a small amount of Juice, derived from the Vignette they are attached to (or Far Dream, as appropriate), which allows them to participate normally in the flow of time, but isn't enough to give them much power to effect change, and isn't a very fundamental part of them.
Muses work a bit like a hybrid of Impressions, humans and Concepts. They contain a Persona made of Tropes, like an Impression, that contains much of the information about how they interact with the world. Part of them is made of Juice, though, and works like a human by complicated bottom-up organisation that mechanically acheives things, rather than those high-level properties simply being present as Tropes. Their intelligence is made partially of intelligence-themed Tropes, and partially of Juicetronic neurons, which is why they develop at a rate intermediate between Impressions and humans.
The Ideal is a Concept that is particularly strongly linked to the Muse, which gives them powers similar to the powers of Concepts in Dream themed around the Ideal.
They naturally arise from liquid Juice when an Ideal becomes strongly enough present in it that it gains Skills and is able to apply those to making itself more coherent, building up the basis of its Persona, at which point it becomes solid and sentient and emerges from the Juice.
Strong interactions with Concepts distort the Persona, causing the Touched by Transcendental quirks. Even stronger interactions could give additional Ideals.
They have a particular affiliation to creativity and narratives because the nature of Dream biases them in that direction at their creation, possibly because humans evolved to have Dreamscapes that would be useful to them.
These are made almost entirely of Juice, working like Mundane creatures but existing in Dream. They are poorly organised, having not had time to evolve, with the initial organisation imparted by an interaction with the Concept of life (as in actual life, not the Ideal). They are physically reasonably strong because of the large content of concentrated Juice, but lack Concept/Muse like powers entirely.
Their creation is similar to that of Muses, but environments of extremely high Juice concentration bias the process towards creating Juicier creatures, and enables more advanced Juicy structures, allowing them to become coherent and emerge without developing complex Tropey components like normal Muses have.
Creatures created by playing Trope cards on Mutants, thereby giving them a Persona like a Muse has. They are effectively the same as Muses, except they lack an Ideal, and aren't inherently related to creativity. They are therefore stronger than Impressions, but don't have Skills like Muses and don't have the same knack for narrative. The same method used by Muses to gain additional Ideals could turn a Semimuse into a Muse.
They are also capable of Fading like Muses (though slower, as they lack Skills to spend their Juice on), but would have a harder time replenishing their Juice as they don't have the same relation to creativity that true Muses do. As they're organised a little differently, perhaps they could survive by drinking Juice.
Only three examples came up in the game, the Rabid Animal, the Haunting Fairy and the Orc, Scarf, who were all created to help with the fight at the Pit just before it opened.