@andrejbauer

Hi, I have a maybe weird question about your paper on "Countable Reals"

Gabriele Carcassi is working on a project of Reverse Physics (in analogy to Reverse Mathematics) https://assumptionsofphysics.org/overview.html

And in that process, he formulated several open questions. One of these concerns the Continuum Hypothesis:

https://github.com/assumptionsofphysics/assumptionsofphysics.github.io/blob/master/_problems/006-ContinuumHypothesis.md

Basically, the question is whether the choice of the continuum hypothesis (there are or aren't sets larger than the natural numbers (which are countable) but smaller than the reals (which are uncountable)) could ever matter in any physical theory.

But that reminded me of your paper The Countable Reals https://arxiv.org/abs/2404.01256

I unfortunately don't really have the necessary background to know this for sure or to fully grasp your paper, but I suggested to him that maybe this question could be completely side-stepped if it turns out that it suffices to use these countable Dedekind Reals. If everything that needs to be done to "do physics" can already be done in a countable fashion, that should imply that, no, the continuum hypothesis really does not matter for this project.

Do you have an opinion or any insights or pointers on this? It would be much appreciated

@paula
Hi, ich kenn mich mit Mastodon noch nicht wirklich aus. Wollte nur wissen:
Diese Instanz ist auf v3.5.3
Die neueste Version dürfte v4.0.2 sein
Aber ich hab keinen Changelog gefunden, der klar aussagt, was sich in der Zeit geändert hat.

- Wie kompliziert ist ein Upgrade?
- Ist eines geplant?
- Was würde sich ändern?

@rohansawhney
@keenancrane

Just had an odd idea for an application of Monte Carlo geometry processing and am wondering whether it makes any sense at all:

There is this rendering technique called Gradient-Domain Path Tracing (and various extensions thereof)

https://onlinelibrary.wiley.com/doi/abs/10.1111/cgf.13652

This method basically tries to find similar paths on nearby pixels to estimate the local gradient of the image and adaptively sample where there is a large gradient, thereby hopefully using samples more where they actually are needed.

You then take those gradients to reconstruct the actual image.

This, as I understand it, relies on a usually discrete pixel-space shift-operator.

It occurred to me, that images are basically like discretized geometry. It's highly regular of course, but still: It's inherently discrete and scale-dependent.

Now I wonder whether it would be possible to do this same sort of sampling but in an unbiased, continuous manner using the methods you worked on