The "Alita: Battle Angel" movie strayed from the original "graphic novel" in some interesting ways, but stayed true. The 3D was great, the CG was good, but not exceptional. The flaws in the medium of a CG main character actually added to the protagonist. The film had deeper threads, almost allegorical, than one would normally expect of a film like this. The action was well paced and placed appropriately throughout the film.

Also, THE WORLD-BUILDING. I love the world-building.

Now, to see if this conception of mine about the form and function of mathematics is correct. Now I need to study a category theory book to see what the theorems mathematicians in that field are creating and if they can serve as tools useful in many situations or as the basis for other mathematical fields, more specific/concrete fields.

The current hotness, I believe, is category theory, which is like a slightly more abstracted idea of set theory. Where set theory defines things as sets and subsets, category theory only defines things as how they relate to other things. It's so beautiful! A relation is like a single fact, it's so much like the theory of the mind that analytic philosophers invented in the past century or two.

So it becomes useful to study the truths which hold across all fields of mathematics. This requires defining a language in which you can re-define any and all other mathematical fields. I think this is what is called a "univalent foundations of mathematics". For a long time people thought set theory was that thing, but it's always felt like "a hack" to use the language of set theory as such a foundation, because it feels too concrete, too much based on counting.

However, there is also the pitfall - the power can only be wielded on problems which can be described in the language of that mathematical field. Here is where it's useful to have and understand multiple fields of mathematics - if you can't easily describe your problem in the language of one field, perhaps there is another field which has a language in which it is easier to describe your problem.

So, mathematics becomes interesting when you read a sentence written by someone else who speaks that language and you are surprised by something it entails in the specific cases to which you are applying these universal truths. Each statement spoken in this language can be trusted to be true, because logic. You can apply the language to any problem you encounter, so long as you can properly encode the problem in that language. Learn once, apply anywhere.

Each mathematics field defines a language, a set of terms each defined in terms of some basic truths (axioms) and a way of building sentences, often with adjunction of the language of logic. Any sentence you speak in this language is Always True, because logic often uses universal quantification. It's possible to make truths which hold in specific cases using the idea of existential quantification, but they are less interesting/celebrated because they are specific applications.

If I wasn't on anti-depressants I would be cowering in a cave and cancelling all my appointments.

I only have 3 hobby projects and I can't make consistent progress on any of them, which is setting me up for disappointing others involved in them. Problem is I spend my few hours after work recovering from the intense work day rather than my hobby projects, and as a result make no hobby progress.

I wonder if automata is an equivalent and more simple way to solve problems that people are using FRP for...

Implementing "Game of Life" sounds like it would be enlightening.

When I implemented Pong, I got pretty lost when figuring out how to keep states of the paddles and ball "encapsulated" from the program. I ended up just using one big state thing, which was easy, but surely wouldn't scale to bigger programs, so I was disappointed.

PureScript, Nintendo, keyboards, languages & types

Joined Apr 2018