Oct 29, 2026, 6:28 AM@sophieschmieg Wait okay there ARE other ultrafinitists!
Do you have, like, names or links to people explaining (a) their ultrafinitism and what it means to them and (b) how it impacts how they do/interact with mathematics?
Like, I listened through a bunch of Wildberger's videos, which... do give HIS answer to those, but he is, like, a full-on conspiracy theorist and so I don't necessarily expect him to represent the non-conspiracy-theorist ultrafinistist positions.
@gaditb I would consider myself somewhere between a formalist and ultrafinitist. To me the main thing about ultrafinitism is that at a certain size, numbers stop making sense, as a "quantity is a quality of its own" thing. It also jells well with the type of Wittgenstein inspired philosophy of reality being best understood through socially influenced models that can only ever approximate, but never reach a true, independent reality, to the point of denying the existence of such a reality as being more real in the first place.
Oct 29, 2026, 6:04 PM@sophieschmieg Does it influence how you, like, /do/ mathematics practically, or just (I assume this at least) how you approach mathematics emotionally/philosophically?
Like, constructivism has a practical impact on what moves are legitimate in mathematical proof and discovery.
And Wildberger's take on Ultrafinitism drove him away from using real or even algebraic numbers at all, building up his own parallel, differently-behaving, constructions of geometry and functions (e.g. his concept of "circles" and "lines", he will say that a line with a point inside a circle and a point outside a circle will intersect the circle at 2, 1, or 0 pointa) -- but, his is a conspiratorial take on it, so maybe a /non-/conspiratorial take wouldn't require any changes to practice.
Oct 29, 2026, 6:05 PM@sophieschmieg (e.g. "if we reach some object and describe some properties with a proof, then THAT object has a formal existence in THAT respect, sure, but any concrete consequences like "has a digit there" or "allows this computation" require their own arguments about reachability as concrete outcomes, and don't come inherently through implication from the more-abstract level."
Which I don't... /think/ would make doing-the-math-itself (which is.. always a concrete act in its own right? right?) still work the same, and it's just the reaction/outlook on that math that changes? But also I don't actually know anything this is just guesses.)
@gaditb no it doesn't really change anything about how I do mathematics, which is why I call myself at least partially formalist. I do prefer explicit constructions, and certainly when it comes to algorithms, don't quite see the point of algorithms that only exist by contradiction, or require impossibly large numbers.
The most complicated situation is almost feasible algorithms, which are a risk factor for cryptography, but don't quite work without further optimization.