treppenverstand @treppenverstand@types.pl

Driven out of Cantor's paradise and thrown into setoid hell.

I do math because it means I need to do less annoying garbage than when programming. I do Proof Theory because I'm still an annoying garbage doer at heart.

Here's the quote justifying my weird username. It's from Dedekind's "Was sind und was sollen die Zahlen" ("What are numbers and what are they good for?").

"But I know that, in the shadowy forms which I bring before him, many a reader will scarcely recognize his numbers which all his life long have accompanied him as faithful and familiar friends; he will be frightened by the long series of simple inferences corresponding to our step-by-step understanding [ger. Treppenverstand], by the matter-of-fact dissection of the chains of reasoning on which the laws of numbers depend [...]"

The term thus characterizes our capability of reasoning to be restricted to discrete steps and is meant to contrast the rather informal, intuition-based proofs that were the norm back in 1888 when the paper was written.

It is also a very funny sounding word.

But just spelling this out already makes it clear that that's *way* too good to be true. At least it's nice to know that all the recursive ordinals I need to care about are path's through Kleene's O...

Sadly, the proof is not effective. It would slap if I could just pass decidable well-ordering to some function and it would compute me a Kleene ordinal coding of the order type.

Always super cool when a surprising fact has a simple proof. Today: Every recursive ordinal has a code in Kleene's O.

When a paper is so old it needs to explain what "recursive" (in the sense of mu-recursive) means.

Neoliberalism strikes again, I guess :/

All spaces/content around/for PhD students are full of negativity (stress, impostor syndrome, depression, loneliness). Kinda fucked up that it is so hard to enjoy this. At least from what I have gleamed from historical stuff, it wasn't always like that.

Maybe I should start collecting nice quotes? Could be cool to have handy.

There seems to be a fascinating connection between mathematics and environmental activism. There ought to be some writing on this...

I have been convinced to give the presentation. I just hope they won't be mean to my face about it!

I've been offered to present something at a workshop in a few weeks. But it is organized by the person who gave our last paper such a scathing review. So now I'm sort of scared...

This *has* to be illegal!

Ordinal notation systems are hard.