bucket foundation — inverse omegabucket.foundation

topology

models. First of all, in our models, things are discrete. So the idea that, for example, there is a transformation between one kind of topological structure of spacetime and another that has to be this strange discontinuous thing when you're dealing with traditional general relativity and manifolds and continuous structures. It isn't a discontinuous thing in our models because something that didn't have a hole, there isn't a notion of a distinct hole, so to speak.
Concept
topology
Cross-concepts
relativity
Score
4 · must · because
Status
candidate — not yet promoted to canon

Corpus evidence — top 10 passages

Most-relevant passages from the entire indexed corpus (67,286 paragraph chunks across YouTube transcripts, PubMed, arXiv, archive.org, Stanford Encyclopedia of Philosophy, OpenAlex, and more) ranked by semantic similarity (bge-small-en-v1.5).

  1. 01 · yt0.812

    You can collect evidence forever, any kind  of empirical evidence you could ever imagine. And   the idea of that not being enough to pin down  what the universe is like, that's something   that naturally pops up in theories of space and  time. So I don't think GR is special here. I think   you can prove a similar kind of theorem pretty  much in any space-time theory that's modeled on   a manifold with geometric structures on it.  So a Newtonian version of space-time physics,   you'd have similar results there. So I&nbsp

    yt/iGOGxaZZHwE-it-s-not-that-we-don-t-know-it-s-that-we-can-t/transcript.txt

  2. 02 · yt0.808

    And  so you can ask the question, is GR deterministic   relative to this collection of models,  relative to that one, relative to that one,   relative to that one? And you'll get different  answers depending on which one you're looking at. I think that's all interesting. And if  you want to go a step further and say,   but which is the real one? I just  want to say that's a little bit   misguided. We're never going to be in  a position to get at that question. Now, we'll never be in a position to get  to that question.

    yt/iGOGxaZZHwE-it-s-not-that-we-don-t-know-it-s-that-we-can-t/transcript.txt

  3. 03 · yt0.794

    You might   term it the cut-and-paste construction.  It's where you take models of space-time,   like relatively well-behaved models, like  something like a Minkowski space-time, and what   you're going to do is you're going to cut slits  here, and you're going to glue things together.   You're going to create wildly crazy topologies in  this way. They're going to be standard models of   GR. They're going to count as models of GR,  but they're going to be wildly unphysical. Now, those folks, Penrose, Geroch, others,&nbs

    yt/iGOGxaZZHwE-it-s-not-that-we-don-t-know-it-s-that-we-can-t/transcript.txt

  4. 04 · yt0.794

    They can become bigger.   And so physicists are going to want to say, hey,  that's not a physically reasonable space-time.   That's not a physically reasonable model of GR.  And you ask, well, what's your reason? Why not? And the original justifications given  by — it was originally Penrose, Geroch,   and a few others back in the 60s in the golden  era. You look at the justifications there,   and it's very much metaphysics. It's Leibnizian  metaphysics. It's the idea that, oh, well,   nature — why would nature stop when

    yt/iGOGxaZZHwE-it-s-not-that-we-don-t-know-it-s-that-we-can-t/transcript.txt

  5. 05 · blog0.791

    This line of work establishes that (some) global properties cannot be established observationally, and raises the question of whether there are alternative justifications. 2.3 Establishing FLRW Geometry? The case of global spacetime geometry is not a typical instance of underdetermination of theory by evidence, as discussed by philosophers, for two reasons (see Manchak 2009, Norton 2011, Butterfield 2014). First, this whole discussion assumes that classical GR holds; the question regards discriminating among models of a given theory, rather than a choice among competing theories. Second, these

    blog/plato-stanford-edu/philosophy-of-cosmology.md

  6. 06 · blog0.787

    What does \(J^-(p)\) reveal about the rest of spacetime? In classical GR, we would not expect the physical state on \(J^-(p)\) to determine that of other regions of spacetime—even the causal past of a point just to the future of \(p\). [ 19 ] There are some models in which \(J^-(p)\) does reveal more: “small universe” models are closed models with a finite maximum length in all directions that is smaller than the visual horizon (Ellis & Schreiber 1986). Observers in such a model would be able to “see around the universe” in all directions, and establish some global properties via direct observ

    blog/plato-stanford-edu/philosophy-of-cosmology.md

  7. 07 · archive0.786

    give rise to space-time, then different mathematical structures could correspond to different universes with different properties and laws. The ontological nature of this level lies in the assertion that these structures exist as a fundamental reality, regardless of whether we can derive or fully understand them through our epistemological frameworks.

    archive/ThesisTOEdll/00- Quantum Cosmology : An Epistemological and Ontological Perspective on Quantum Cosmology and Levels of the Multiverse (rev0)_djvu.txt

  8. 08 · yt0.785

    You have all these models around, and  a lot of them seem maybe a bit crazy.   Some of them might allow for time  travel. But things start getting   really crazy once you start looking  at these Heraclitus-type models. One can use science to show  that science has limits. This is unlike any conversation  I've had on this channel,   and I've had hundreds of conversations with  physicists, mathematicians, philosophers,   etc. Professor J.B. Manchak is the only  person that I know who connects general   relativit

    yt/iGOGxaZZHwE-it-s-not-that-we-don-t-know-it-s-that-we-can-t/transcript.txt

  9. 09 · yt0.783

    It's just the model. The point is, we are prepared for something that  hasn't happened yet, right? If somebody sees   matter that cannot have due to their behavior  a Lorentzian background but you would then,   phenomenologists would pretty quickly figure out  what may be the simplest background that could do   that, then the question comes up, but what's the  action for that background? It can't be Einstein,   right? Einstein is for a Lorentzian metric  or a metric in general. But then you would   try to solve our equa

    yt/Bnh-UNrxYZg-frederic-schuller-the-physicist-who-derived-gravity-from-ele/transcript.txt

  10. 10 · yt0.781

    I'll try and talk about all of those things. So let's talk about physics first of all. So there's been this question that sort of existed since antiquity which is is the universe discrete or continuous? Is it made of a bunch of discrete atoms or does everything sort of flow like water or something? And uh that was something people didn't know for a long time. End of the 19th century finally got discovered yes matter is made of discrete things made of atoms and molecules and so on. And then a little bit later it was clear that you know you could think of light as being made of photons and so on

    yt/OWyugUdBups-stephen-wolfram-computation-at-the-foundations-of-everything/transcript.txt

Curation checklist

  • ☐ Verify excerpt against source recording
  • ☐ Tag tier (axiom · law · principle · primary derivation · observation)
  • ☐ Cross-cite to ≥1 primary source (PubMed / arXiv / archive.org)
  • ☐ Promote to bucket-canon/01-mathematics/