Comment on We've got it all worked out
JustAPenguin@lemmy.world 10 hours agoI disagree in part with this logic.
Gödel’s incompleteness theorem says that a system typically cannot prove all truths that come from axioms.of the system, like you said.
Where I disagree is how this is applied to theoretical physics. Depending on where you draw the line of “everything”, the limits of proof comes down to two things: observation and the language we use to describe it.
As it stands, for example, gravity is difficult to fit into the standard model. It may be impossible to do so within that system. However, it may work well in an alternate description of the universe. In this case, the core mathematics is the same, but the theories differ. It may be likely that our understanding of the universe is filled with logical holes and fallacy, but that does not mean that the incompleteness theorem says anything regarding the ability to unify physics.
Mathematically, physics is nothing more than descriptions of observation and expectations. It could very well be that our perception of the universe is fundamentally flawed and, in essence, we can only perceive certain truths that appear correct in our perspective. As such, it isn’t necessarily impossible to formulate a correct theory; it’s just that we are unable to succinctly describe reality.
More simply, math is just the thing we use to describe the universe. So, it’s likely we can keep “adding new math” as we discover new physics. The hard part is understanding the physical nature of the universe, first.
Or perhaps the universe truly cannot be described all at one, such that everything is related. As a mathematician, I like to believe that we simply lack the ability to perceive the full reality of, well, “reality”. And as such, we are missing important information that would tie all the loose ends together.
SmokeyDope@piefed.social 6 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:
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.