"Adventures in the Universe of Sets"

[Ripheus23]

I'm not sure whether to try to present my model of transfinite arithmetic as a strict essay, or something more like Flatland (or GEB or the surreal-numbers essay set on a magical island, or what!). If I go with the latter, it'll go something like this:

[Ixthos]

The problem with what you are trying to do - and it is a good idea, don't get me wrong - is that you are presenting this in a highly esoteric manner along with a confusing one.

 

Putting aside my issues with your use of Biblical names, there are two parts to the problem. The first is that you are making the entire story and subtle details depend entirely on mathematical injokes and jargon without giving context to them, or explaining them for those who don't get them. For example, I get the reference to Pi walking in circles, being a certain distance from 3, and the significance of mentioning Cantor, but what is the significance of sqrt(2), 2, and 4 being involved, other than them being a sequence where each is followed by its square, and why is sqrt(2) running faster? Why are the primes being broken into fractions, and why is that a bad thing? Why are they surprised that adding Aleph null doesn't change the cardinality, as Aleph null has the same cardinality as the sum of an infinite series (Aleph null) of Aleph null. Things like that. I am fairly more aware of these concepts than most of the people that I know, and I know a few others who are more familiar with this topic than I am, but this feels a lot like a large in-joke which doesn't let anyone in on it unless they are already aware of the concepts. Unlike, for example, the Vsauce video on counting past infinity, which was educational and amusing, or as you cited Flatland, which I haven't read but from what I understand was also used to explain the details as well, rather than just assuming those who read it understood the ideas. Maybe I am being a little too hasty, but it seems like you need to establish these ideas more clearly as part of the narrative, rather than as a "see what I did there?" type approach.

The second issue is the CYOA style "jump to" points. I like choose your own adventure books, but how is someone supposed to navigate to that page if it isn't in a clearly layed out order? And the integers are a useful system that is highly mathematical - indeed they are the indexes for Aleph numbers, so why not use them instead? Actually ... why not use the integers, and have a few bonus or hidden pages in between, like a PI and e page, and a few bonuses like an omega, omega+1, omega*2, omega^omega, at the end - pages that only those who, with a better grasp of the ideas, can then take the appropriate choices to navigate to? So mainly integers, maybe a few negatives, everyone should start at page zero, but a few hidden bonus pages in a logical and well understood layout.

 

Sorry if this is a little too harsh. This looks like a good idea but those issues bug me.

Edited November 6, 2019 by Ixthos

[Ripheus23]

There's supposed to be a scene where √2 gives 4 the √ so 4 can disguise themselves as 2. Anyway, the point about adding aleph-zero but not getting anywhere, is supposed to be part of an actual explanation of the topic, like π asks why adding aleph-zero doesn't do anything, and so on.

The section numbers would be well-ordered in the complete document and the choice idea is a nod to Cohen's pluralism: the choices you make take you to ZFC, or ZFC+, or constructivist or intuitionistic or whatever set theory, and then there would be explanations of those subjects, and so on.

As for Apollyon, well that IS what the antiset is. In modal logic, the antiset function would define possibility from antipossibility, giving us a perverted modal order. This would form the image of a negative eternity, but then inside actual people, the disproof of the Axiom of Destruction is part of the metaproof of the axioms of transconstruction. So eventually the story would discuss the concept of transfinality, which is the subject of the fourth axiom of my system and the one required for the functional preimage of the deontic apex of transfinality, which has the power to "defeat" Apollyon by invoking absolute infinity in Cantor's religious sense (he also had a mistaken, I think, alternative absolute model that comes down to the antiset image, so the moral of the story is that we have to be careful about our concept of infinity in general, since the divine nature expresses this form of reality, but so does the ultimate enemy...).

EDIT: not all of the numbers who are characters will be totally important for "numerical" reasons. Instead, some just illustrate Brouwer's notion of freely chosen digitalization.

EDIT 2: and btw you're right, there are supposed to be bonus sections 

4: also I needed a number with √ so they can use it as a bow when they shoot Knuth arrows. I swear the actual notation will be explained too  like they're on top of the mountain and they are running out of time so they fire the arrow at 2 that makes the formula for the Continuum, so they teleport to the Temple of the Continuum.

Edited November 6, 2019 by Ripheus23

[Ixthos]

@Ripheus23 Fair enough :-) I definitely think this has a lot of possibilities and can be a fun read :-) I look forwards to seeing when it is done, and would enjoy giving a read. Take care!

[Ripheus23]

Some more visual prototypes...

[1st of Lunch]

Wait...what?

Nah, this is just math disguised as reading. That's messed up up man...I'm out!