subagents! subagents?

welcome to october.

In Social Studies, beloved (ex?-)blogger mercury says:

We could also explain the observed behavior by claiming that the mind contains subagents or some hogwash like that. The subagent that is in control of leaving an argument enjoys arguing, and the subagent that is in control of reporting if a good time was had does not enjoy arguing. I have no idea what to do about that so I hope it is not true. It sounds scary.

It is now October. That means it is time to discuss the scary. Let us begin.

Category Theory, butchered by April

my mind wanders...
to the life i poured into it all
working in a frenzy, managing a community
disrupting [agent foundations]
building upon it, something new and greater
and then it fell in upon itself
jiano saw it first; i was foolish
it couldn’t be unified; all the categories are arbitrary

—Narcissa Wright, All the Categories are Arbitrary

As we all know,¹¹ Citation needed sub has a very specific²² I assert despite the fact that the definition seems to maybe be a little inconsistent from category to category. But like, they’re all morally the same. Sort of. meaning as a prefix as mathematical terminology³³ It is also used in some other cases as a more general prefix meaning “under”, such as in “subterranean” and “submissive”. Though actually now that I think about it I’m totally going to add submissive to my vocabulary as a word meaning “a (not necessarily proper) portion of a letter”.

English needs a short prefix that means “not necessarily”, that is a critical prefix for discussing mathematics.

Shhh don’t remind people about the word “subadditive.”. An object X is a subobject of an object Y when you have defined some specific embedding map—that is, a structure-preserving⁴⁴ That is to say, it’s a morphism. What’s a morphism? Well, it depends. injective⁵⁵ You can’t make me think about whatever they say I’m supposed to replace “injective” with to do category theory properly. You can’t. You cannot. I refuse. function⁶⁶ Maybe I’m only supposed to use ι for “inclusion mappings”, which are technically slightly different from embeddings. But I’m pretty sure the whole point of category theory is to not care about this. Structuralism baybeeeeee

A common choice of structure-preserving injective function is the identity morphism⁷⁷ Quickly realizes that she really shouldn’t make the claim that the category of agents is a concrete category and switches to the term “morphism” instead of saying “identity function”. on X, given by

Since the human mind is an agent,⁸⁸ Citation needed and the category of agents⁹⁹ Which I arbitrarily assert to exist has identity morphisms by virtue of being a category, we can establish that the mind indeed contains subagents, just as mercury fears. Now, perhaps a more interesting question is whether a mind has proper subagents. A proper subobject requires a proper embedding, which strengthens the injectivity requirement by also requiring nonsurjectivity.

Breaking News: Cartesian Frames

Breaking news, everyone. It’s time to shitpost slightly less. I just figured out that Scott Garrabrant is way ahead of us. Like, way the hell ahead of us. For example, now I know that there is a distinction between additive subagents and multiplicative subagents. This is very exciting. Let’s take a quick tour which probably at most suffices to convince you that Garrabrant has done some interesting mathematics.

Garrabrant says:

A Cartesian frame C over a set W is a triple (A, E, ⋅), where A and E are sets and ⋅ : A × E → W.

Counterintuitively—at least to me right now, I can see this terminology making more sense to me after I get used to it—A is called an agent and the elements of A are called possible agents. Like, okay, sure, agents are sets of possible agents, I guess. I sort of feel like I am one specific thing? Like, okay, my ego, my sense of self, these are weird and nebulous. But as like, as a whole human person? I feel like there is one specific human person that I am in one specific world, and I’m just uncertain about which. I don’t feel like I am a set of possible mes.

Anyways. E is an environment, and contains possible environments, and W is a world, and contains possible worlds.

So. A set of possible agents. A set of possible environments for that agent. This makes sense. Now, the definition of subagent:

Let C and D be Cartesian frames over W. We say that C’s agent is a subagent of D’s agent, written C◃D, if for every morphism ϕ : C → ⊥ there exists a pair of morphisms ϕ₀ : C → D and ϕ₁ : D → ⊥ such that ϕ = ϕ₁ ∘ ϕ₀.

I could explain what ⊥ is—if you’ve ever looked into linear logic, yes it’s basically the ⊥ from linear logic—but I think it’s funnier to say that ⊥ is God and refuse to elaborate. You can check my work if you want. In the context of Cartesian frames, a morphism seems to be a device which determines the actions¹⁰¹⁰ Or like, which possible agent D’s agent chooses to be. Garrabrant distinguishes this from actions. of D’s agent as a function of the actions of C’s agent. So C is a subagent of D if any way God could make a decision based on C’s action is secretly also the combination of a way that God could make a decision based on D’s action and a way that D could make a decision based on C’s action.

Folk Subpsychology

Well, okay. We’re all subagents of ourselves, and of God, and also the number one is a subagent of all of us. And also, like, I’m a subagent of the system consisting of me and my water bottle, and my left arm is a subagent of me. And this can all be described with something called Chu spaces. Truly enlightening stuff.

Anyways, how did we start this article?

The subagent that is in control of leaving an argument enjoys arguing, and the subagent that is in control of reporting if a good time was had does not enjoy arguing.

Right. Okay, so this is maybe a more specific concern than “do subagents exist?” I think my main comment on this is… what, exactly, is an “enjoy”? Obviously we can only conclude that the subagent in control of leaving arguments doesn’t choose to do so. Who says there’s any enjoyment going on at all? I think people who fail to leave arguments usually don’t report that they can peer inside themselves and see some part of them who loved it¹¹¹¹ I think in arguments that I report having disliked, I might say there’s a part of me that was averse to leaving the argument moreso than I would say there was a part of me that enjoyed it..

So, on the one hand, that just makes it worse. No subagent is even enjoying it! On the other hand, hey, maybe if you figure out how to avoid arguments you aren’t especially screwing over any part of yourself?

Well, yeah, maybe. I would advise a little caution though. Sometimes you feel averse to a thing for a good reason, and trying to force it can be bad for you! Broadly I think it’s not great whenever you end up viewing yourself as like, fighting another part of yourself, or something. That’s usually a bad sign. Your subagents should generally be working with each other, not against each other.

Come back another day for my post on quotient agents.