kram1032

@[email protected]
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kram1032Dec 4, 2024

@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

Assumptions of Physics - Overview

Show threadkram1032Jul 3, 2023
@codinghorror Meta-Attention is All you Need?
kram1032Feb 14, 2023
@andrejbauer thanks, can confirm the link works now 😄
kram1032Feb 13, 2023
@andrejbauer hey just wanted to say the link on your blogpost https://math.andrej.com/2023/02/13/formalizing-invisible-mathematics/ behind "slides with speaker notes" currently leads to a 404 Page Not Found.
Also my browser claims your comments form is "insecure".
Mathematics and Computation | Formalizing invisible mathematics

Show threadkram1032Feb 10, 2023
@troy_s @nihal_rahman
I suspect as an artistic choice it could be particularly interesting whenever you go for something like a comic book -esque or painterly feel
Show threadkram1032Feb 10, 2023

@troy_s @nihal_rahman

also, wouldn't there be a state where, like, subtractive and additive "cancel out" or "are in balance"? Like, if you rotate by 180°, you're definitely gonna swap additive and subtractive notions. But what happens around the 90° mark?

Show threadkram1032Feb 10, 2023

@troy_s @nihal_rahman

Yeah you could shift three different angles, so exploring the entire parameter space in a smooth way is gonna be tricky. You could definitely find paths thruogh that space inspired by space filling curves or the like though.
Or in a different approach, you rotate them by different frequencies, say, based on sqrt(2), sqrt(3), and sqrt(5), so they drift out of sync and slowly explore the entire space. Would take many more frames tho.

However, even just a lockstep rotation (all primaries by the same amount in the same direction) would be a good starting point as a first visualization. You'd just have to pick an arbitrary initial phase and then go from there.

Show threadkram1032Feb 9, 2023

@troy_s @nihal_rahman

could be fun to do a movie of how this choice affects the end result, simply sweeping through all choices of angles across like, say, 24 frames or so (so each frame would uniformly rotate the primaries by an additional 15° - more frames would allow for a finer sweep of course)

Show threadkram1032Feb 9, 2023

@troy_s @nihal_rahman

what, this?
https://blenderartists.org/t/feedback-development-filmic-baby-step-to-a-v2/1361663/1829

that's just three numbers.

Presumably meant to be angles to rotate the primaries by for an adjusted color space? - You kinda dropped those numbers in there without any explanation or context what so ever. Didn't even share the results you showed here over there, so probably a lot of people in that thread haven't even seen what you did here.

But ok, that makes sense, so you are saying all that needs to be done for this is to try to do really extreme rotations of the primaries before applying the sigmoid. I can see how that would effectively flip the relationship of black and white with respect to color mixing. The high end gets soft-clamped towards the opposite of the primary, and the low end gets soft-clamped towards the primary, so if you sufficiently rotate the primary, those things will switch roles.
And then, after the sigmoid, stuff gets inverted.

It's neat, that that still results in reasonable images.

Feedback / Development: Filmic, Baby Step to a V2?

-pr 55.0 70.0 40.0

Blender Artists Community
Show threadkram1032Feb 8, 2023

@troy_s @nihal_rahman

can you link to the specific post that talks about this particular idea? I might have missed that