This article is surprisingly close in spirit to my latest article published just yesterday! We touch on some of the same ideas but from different angles so I guess that's a very happy coincidence. I also have a follow up coming up on some of the bizarre consequences of interpreting limiting results in theoretical CS as fundamental epistemic limits of physics. Can't wait to see what you guys come up with next! Keep up the good work.
Hello Alejandro! happy new year! I’m really really glad to hear you enjoyed the article, because that means a lot.
I’ve been genuinely inspired by your work, and it’s honestly a pleasure to keep reading your articles; they’re consistently excellent and thought-provoking.
The overlap in themes feels like one of those rare, happy coincidences that signal something interesting is in the air. I’m really looking forward to your follow-up on the epistemic limits angle, and to reading many more of your pieces.
Pls keep up with your great work. It’s really amazing !!!!!
The framing of computational complexity as a physical law rather than just an abstract mathematical concept is profoundly insightful. The observation that black holes scramble information at the theoretically maximum rate allowed by physics, and that Bekenstein-Hawking entropy limits scale with area not volume, shows that spacetime geometry itself enforces computational boundaries. What strikes me most is the nightmare scenario, that some physical questions are answerable not due to technological limits but because no physical process can compute the answer. Last year when working on simmilar problems involving quantum field dynamics we kept hitting walls that we attributed to computational resources, but this suggests some predictions might be intrinsicaly irreducible regardless of how much compute power we throw at them. The idea that undecidability isn't a mathematical quirk but woven into physical reality fundamentally reshapes what we can expect from a theory of everything.
That’s exactly what I think. Once computational complexity is treated as a physical constraint, many familiar frustrations in physics stop looking contingent and start looking fundamental.
Black holes probably make this unavoidable. They scramble information at the fastest rate allowed by causality and quantum mechanics, and their entropy scaling with area rather than volume shows that spacetime itself limits information storage and processing. Geometry is not passive. It enforces what can and cannot be computed.
From this angle, as you said, the walls you hit in quantum field dynamics may not have been about insufficient resources. Some quantum systems generate entanglement and complexity faster than any physically allowed process can track.
The state exists, the laws are known, yet detailed prediction is impossible in principle. And that’s both exciting and terrifying.
I genuinely thing that this reframes undecidability entirely. It is not a mathematical oddity leaking into physics. It is a whole property of the world. Certain questions are well defined but physically unanswerable, not because we are weak, but because no process allowed by the universe can compute the answer.
In my own view, then, a theory of everything, then, cannot be a theory of total prediction. It can specify the rules, but not guarantee compressibility of their consequences. The universe may be lawful, and still fundamentally opaque.
This article is surprisingly close in spirit to my latest article published just yesterday! We touch on some of the same ideas but from different angles so I guess that's a very happy coincidence. I also have a follow up coming up on some of the bizarre consequences of interpreting limiting results in theoretical CS as fundamental epistemic limits of physics. Can't wait to see what you guys come up with next! Keep up the good work.
Hello Alejandro! happy new year! I’m really really glad to hear you enjoyed the article, because that means a lot.
I’ve been genuinely inspired by your work, and it’s honestly a pleasure to keep reading your articles; they’re consistently excellent and thought-provoking.
The overlap in themes feels like one of those rare, happy coincidences that signal something interesting is in the air. I’m really looking forward to your follow-up on the epistemic limits angle, and to reading many more of your pieces.
Pls keep up with your great work. It’s really amazing !!!!!
Thanks! I'm genuinely honored. Nothing better than finding like minded writers over here. We should try a collab sometime ;)
I’d love to collaborate with you !! Can’t wait to see what we’ll be able to do
The framing of computational complexity as a physical law rather than just an abstract mathematical concept is profoundly insightful. The observation that black holes scramble information at the theoretically maximum rate allowed by physics, and that Bekenstein-Hawking entropy limits scale with area not volume, shows that spacetime geometry itself enforces computational boundaries. What strikes me most is the nightmare scenario, that some physical questions are answerable not due to technological limits but because no physical process can compute the answer. Last year when working on simmilar problems involving quantum field dynamics we kept hitting walls that we attributed to computational resources, but this suggests some predictions might be intrinsicaly irreducible regardless of how much compute power we throw at them. The idea that undecidability isn't a mathematical quirk but woven into physical reality fundamentally reshapes what we can expect from a theory of everything.
That’s exactly what I think. Once computational complexity is treated as a physical constraint, many familiar frustrations in physics stop looking contingent and start looking fundamental.
Black holes probably make this unavoidable. They scramble information at the fastest rate allowed by causality and quantum mechanics, and their entropy scaling with area rather than volume shows that spacetime itself limits information storage and processing. Geometry is not passive. It enforces what can and cannot be computed.
From this angle, as you said, the walls you hit in quantum field dynamics may not have been about insufficient resources. Some quantum systems generate entanglement and complexity faster than any physically allowed process can track.
The state exists, the laws are known, yet detailed prediction is impossible in principle. And that’s both exciting and terrifying.
I genuinely thing that this reframes undecidability entirely. It is not a mathematical oddity leaking into physics. It is a whole property of the world. Certain questions are well defined but physically unanswerable, not because we are weak, but because no process allowed by the universe can compute the answer.
In my own view, then, a theory of everything, then, cannot be a theory of total prediction. It can specify the rules, but not guarantee compressibility of their consequences. The universe may be lawful, and still fundamentally opaque.