SmokeyDope
@SmokeyDope@piefed.social
- Comment on We've got it all worked out 2 hours ago:
Thank you for your thoughtful response! I did my best to cook up a good reply, sorry if its a bit long.
Your point that we can simply “add new math” to describe new physics is intuitively appealing. However, it rests on a key assumption: that mathematical structures are ontologically separate from physical reality, serving as mere labels we apply to an independent substrate.
This assumption may be flawed. A compelling body of evidence suggests the universe doesn’t just follow mathematical laws, it appears to instantiate them directly. Quantum mechanics isn’t merely “described by” Hilbert spaces; quantum states are vectors in a Hilbert space. Gauge symmetries aren’t just helpful analogies; they are the actual mechanism by which forces operate. Complex numbers aren’t computational tricks; they are necessary for the probability amplitudes that determine outcomes.
If mathematical structures are the very medium in which physics operates, and not just our descriptions of it, then limits on formal mathematics become direct limits on what we can know about physics. The escape hatch of “we’ll just use different math” closes, because all sufficiently powerful formal systems hit the same Gödelian wall.
You suggest that if gravity doesn’t fit the Standard Model, we can find an alternate description. But this misses the deeper issue: symbolic subsystem representation itself has fundamental, inescapable costs. Let’s consider what “adding new math” actually entails:
- Discovery: Finding a new formal structure may require finding the right specific complex logical deduction path of proof making which is an often expensive, rare, and unpredictable process. If the required concept has no clear paths from existing truth knowledge it may even require non-algorithmic insight/oracle calls to create new knowledge structure connective paths.
- Verification: Proving the new system’s internal consistency may itself be an undecidable problem.
- Tractability: Even with the correct equations, they may be computationally unsolvable in practice.
- Cognition: The necessary abstractions may exceed the representational capacity of human brains.
Each layer of abstraction builds on the next (like from circles to spheres to manifolds) also carries an exponential cognitive and computational cost. There is no guarantee that a Theory of Everything resides within the representational capacity of human neurons, or even galaxy-sized quantum computers. The problem isn’t just that we haven’t found the right description; it’s that the right description might be fundamentally inaccessible to finite systems like us.
You correctly note that our perception may be flawed, allowing us to perceive only certain truths. But this isn’t something we can patch up with better math. it’s a fundamental feature of being an embedded subsystem. Observation, measurement, and description are all information-processing operations that map a high-dimensional reality onto a lower-dimensional representational substrate. You cannot solve a representational capacity problem by switching representations. It’s like trying to fit an encyclopedia into a tweet by changing the font. Its the difference between being and representing, the later will always have serious overhead limitations trying to model the former
This brings us to the crux of the misunderstanding about Gödel. His theorem doesn’t claim our theories are wrong or fallacious. It states something more profound: within any sufficiently powerful formal system, there are statements that are true but unprovable within its own axioms.
For physics, this means: even if we discovered the correct unified theory, there would still be true facts about the universe that could not be derived from it. We would need new axioms, creating a new, yet still incomplete, system. This incompleteness isn’t a sign of a broken theory; it’s an intrinsic property of formal knowledge itself.
An even more formidable barrier is computational irreducibility. Some systems cannot be predicted except by simulating them step-by-step. There is no shortcut. If the universe is computationally irreducible in key aspects, then a practical “Theory of Everything” becomes a phantom. The only way to know the outcome would be to run a universe-scale simulation at universe-speed which is to say, you’ve just rebuilt the universe, not understood it.
The optimism about perpetually adding new mathematics relies on several unproven assumptions:
* That every physical phenomenon has a corresponding mathematical structure at a human-accessible level of abstraction.
* That humans will continue to produce the rare, non-algorithmic insights needed to discover them.
* That the computational cost of these structures remains tractable.
* That the resulting framework wouldn’t collapse under its own complexity, ceasing to be “unified” in any meaningful sense.I am not arguing that a ToE is impossible or that the pursuit is futile. We can, and should, develop better approximations and unify more phenomena. But the dream of a final, complete, and provable set of equations that explains everything, requires no further input, and contains no unprovable truths, runs headlong into a fundamental barrier.
- Comment on 7 hours ago:
You are close! though its not quite that simple. According to penrose spacetime diagrams the roles of space and time get reversed in a black hole which causes all sorts of wierdness from an interior perspective. Just like the universe has no center, it also has no singularity pulling everything in unlike a black hole.
Now heres where it gets interesting. Our observable universe has a hard limit boundary known as the cosmological horizon due to finite speed of light and finite universe lifespan. Its impossible to ever know whats beyond this horizon boundary. similarly,black hole event horizons share this property of not being able to know about the future state of objects that fall inside. A cosmologist would say they are different phenomenon but from an information-theoretic perspective these are fundamentally indistinguishable Riemann manifolds that share a very unique property.
They are geometric physically realized instances of godelian incompleteness and turing undecidability within the universes computational phase space. The universe is a finite computational system with finite state system representation capacity of about 10^122 microstates according to beckenstein bounds and planck constant. If an area of spacetime exceeds this amount of potential microstates to represent it gets quarentined in an inverse pocket universe so the whole system doesnt freeze up trying to compute the uncomputable.
The problem is that the universe can’t just throw away all that energy and information due to conservation laws, instead it utilizes something called ‘holographic principle’ to safely conserve information even if it cant compute with it. Information isn’t lost when a thing enters a black hole instead it gets encoded into the topological event horizon boundary itself. in a sense the information is ‘pulled’ into a higher fractal dimension for efficent encoding. Over time the universe slowly works on safely bleeding out all that energy through hawking radiation.
So say you buy into this logic, assume that the cosmological horizon isn’t just some observational limit artifact but an actual topological Riemann manifold made of the same ‘stuff’ sharing properties with an event horizon, like an inverted black hole where the universe is a kind of anti-singularity which distributes matter everywhere dense as it expands instead of concentrating matter into a single point. what could that mean?
So this holographic principle thing is all about how information in high dimensional topological spaces can be projected down into lower dimensional space. This concept is insanely powerful and is at the forefront of advanced computer modeling of high dimensional spaces. For example, neural networks organize information in high dimensional spaces called activation atlases that have billions and trillions of ‘feature dimensions’ each representing a kind of relation between two unique states of information.
So, what if our physical universe is a lower dimensional holographic projection of the cosmological horizons manifold? What if the undecidable bubble around our universe is the universe in its native high dimensional space and our 3D+1T universe is a projection?
- Comment on We've got it all worked out 9 hours ago:
What in particular do you want to know?
- Comment on We've got it all worked out 9 hours ago:
Are you kidding? Gödel proved that decades ago for all of mathematics including theoretical physics. The incompleteness theorem in a nutshell says no axiomatic system can prove everything about itself. There will always be truths of reality that can never be proven or reconciled with fancy maths, or detected with sensors, or discovered by smashing particles into base component fields. Really its a miracle we can know anything at all with mathematical proofs and logical deduction and experiment measurement.
But something you need to understand is that physicist types do not believe math is real. Even if its mathatically proven we cant know everything in formal axiomatic systems, theoretical physicist will go “but thats just about math, your confusing it with actual physical reality!” . They use math as a convinent tool for modeling and description, but absolutely tantrum at the idea that the description tools themselves are ‘real’ objects .
To people who work with particles, the idea that abstract concepts like complex numbers or Gödel’s incompleteness theorems are just as “real” as a lepton when it comes to the machinery and operation mechanics of the universe is heresy. It implies nonphysical layers of reality where nonphysical abstractions actually exist, which is the concept scientific determinist hate most. The only real things to a scientific determinist is what can be observed and measured, the rest is invisible unicorns.
So yes its possible that there is no ToE or GUT because of incompleteness and undecidability, but theres something alluring about the persuit.
- Comment on 10 hours ago:
- Rotation is meaningless without an external reference frame to compare against. Consider that right now the planet were on is rotating at ~1000km/h but to us it feels stationary. We only know the planet rotates because we observe the sun,moon,stars rotate around us (which ancient peoples misunderstood as earth-centerism thinking everything rotates around us)
- Rotation requires a center axis to rotate around. There is no true center to our observable universe, only subjective perspective reference frames. wherever you are is the center from your perspective. There is no definitive geometric center axis of our universe to rotate around.
- Comment on Don't like the 'left liberal bias' of cited and sourced Wikipedia articles? Not a problem, our lord and savior Elon is introducing Grokipedia. 17 hours ago:
“Yeah, I mean who even does that, right?” *nervously side eyes Garrett from the Thief Series with his occasional cool ass one-liners
- Comment on [AI] Oreo 17 hours ago:
Okay but what the fuck is up with the first highlighted part of that paragraph? It reads like the person was intentionally trying to mess with the output for the meme.
- Comment on Don't like the 'left liberal bias' of cited and sourced Wikipedia articles? Not a problem, our lord and savior Elon is introducing Grokipedia. 20 hours ago:
Your thirst is mine, my water is yours! … Oh shit, wrong sci-fi world I think my bad
- Comment on Don't like the 'left liberal bias' of cited and sourced Wikipedia articles? Not a problem, our lord and savior Elon is introducing Grokipedia. 20 hours ago:
… I really hoped that this wasn’t a thing, but im not surprised in the least.
Its just fucking painful, man.
- Comment on Don't like the 'left liberal bias' of cited and sourced Wikipedia articles? Not a problem, our lord and savior Elon is introducing Grokipedia. 23 hours ago:
- Don't like the 'left liberal bias' of cited and sourced Wikipedia articles? Not a problem, our lord and savior Elon is introducing Grokipedia.media.piefed.social ↗Submitted 23 hours ago to mildlyinfuriating@lemmy.world | 32 comments
