The Computational Limits of Universal Prediction
Just the other day I was listening to another podcast where they were saying that to travel through time and space at the speed of light, we'd need to know the state of every atom and be capable of calculating everything, because every atom and their state affects the output. The counter argument here is that since we can't know more about the universe than the universe knows about itself, we hit what Stephen Wolfram calls "computational irreducibility" – the universe is its own shortest program, and any simulation of it cannot be fundamentally more efficient than the universe running itself.
I was thinking about this for some time: whether we can know more than the universe, or at least the same amount as the universe. Let me clarify the first thing that comes to everyone's mind: we can model certain things and can sometimes predict more than what our limited data might suggest, but in complex systems "the whole is more than the sum of its parts" - emergent properties arise from interactions that cannot be predicted from knowing the individual components alone. Therefore it is thought to be implausible to predict the future via models without some major caveats, because of starting condition sensitivity and the fundamental quantum uncertainty principle, which places hard limits on simultaneous knowledge of complementary properties, plus the exponential growth of computational complexity as system size increases. That's where the reasoning about knowledge of everything becomes crucial. That's where the statement of "needing to know everything" argument emerges.
This requirement is arguably one of the fundamental limits we'd face with faster-than-light travel or time travel. I've been working with modern computers more often than ever and their calculation capability amazes me every time. If things can be simplified enough, very large numbers of calculations can be reached. But what is calculation to the universe anyway? Isn't math itself a compression? A simplification? So long story short, I was cautiously optimistic, believing perhaps we could find clever workarounds to such limits.
The Compression Paradox
Is math itself a compression of the universe? Perfect compression of a truly random or complex system approaches the size of the system itself. This is where information theory meets physics. The universe might be performing the most efficient computation of itself – any external simulation would require additional overhead for the simulation infrastructure itself.
Consider this: when we successfully predict or model natural phenomena, we're typically exploiting regularities, patterns, or symmetries that allow for compression. Weather patterns, planetary orbits, even quantum systems in certain states – they all have underlying structures that permit shortcuts in calculation. But a perfectly random system, or one at maximum entropy, offers no such shortcuts. Could this be our universe?
Overall, such problems boil down to: can something be more efficient than, or know more about, the thing it is trying to predict? When I read about Maxwell's demon and the whole dilemma with Szilard and Brillouin, I thought about how similar this problem is. In that case, they are again trying to overcome limits – specifically the second law of thermodynamics and the fundamental cost of information processing. The key insight is that erasing information (which any selective process requires) has an irreducible thermodynamic cost.
The parallel is striking: Maxwell's demon tries to violate entropy by selectively sorting molecules, but this requires measurement, memory, and eventually memory erasure – all of which have thermodynamic costs. I will go out on a limb and claim that it is trying to overcome the limits of what it is made of – this is not direct and is a gross oversimplification, but let's work with it for now. In the 1980s, Charles Bennett showed that such operations could theoretically be done without increasing entropy by using reversible computation. He demonstrated that the demon could sort molecules without violating thermodynamics by using a reversible memory that could be reset to its initial state, effectively making the information processing thermodynamically "free" – though this requires perfect reversibility, which itself may be an unattainable idealization.
That's where I see the parallel. Bennett's work doesn't eliminate the fundamental constraint – it just reveals how deeply information and physics are intertwined. The demon still can't violate the second law; it can only push the entropy cost around. Similarly, even with perfect reversible computation, a universal predictor would still be part of the very system it's trying to predict, creating an inescapable self-reference problem. Any measurement or computation changes the system, however slightly.
Perhaps these limits aren't meant to be overcome but understood. They might represent fundamental boundaries where information theory, thermodynamics, and computation converge – showing us not what we can't do, but revealing the deep structure of reality itself.