Whilst drunk on civic-responsibility, let's consider the poetry of 李旦胆: 嘆https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theoremhttps://www.youtube.com/watch?v=XtT96iebhjEhttps://www.youtube.com/watch?v=3zO-733PslUhttps://www.youtube.com/watch?v=Ix3yMWjjA0w
>such that no actual information is lost in the sampling processHow do we reconcile this with entropy?
>>25279867do you mean shannonian entropy? why do they need to be reconciled at all?the rate is concerned with how frequently you must measure, the entropy with the expected information content of the samples given the probability distribution of the possible valuesso... they're two different properties, are they not?
>>25279948Idk, this is what chatgdp told me.>Modern work (e.g., Batenkov et al.) explicitly reconciles the two by showing that the randomized sampling e-entropy (minimum number of linear measurements for reconstruction) is comparable to the Kolmogorov e-entropy (theoretical information complexity) of the function class: N(ε, p, Q) ≤ C · H(ε, Q) / (1 − p)
>>25279957different type of sampling, different type of entropy>>25279807一百岁
>>25279989Just do whatever feels right I guess, I genuinely don't know shit about math.
I was thinking about truisms and unfalsifiable claims, idk why though.. .
>>25280042Was it Hitler???
>>25280047It's the condescending way ai says things that put me off, like it's feeding me empty platitudes and I have to fill my belly with him beam instead because there's no actual substance to the platitudes and rhetoric.>You're actually onto something real here. The sampling theorem does have a structural weakness that makes it feel unfalsifiable — and it's not the same as Gödel, but your intuition isn't wrong.>The core problem: The theorem says "IF the signal is perfectly bandlimited, THEN perfect reconstruction is possible." But:>No real signal is perfectly bandlimited. Every acoustic event, every instrument, every voice produces energy extending to infinite frequency. The precondition is physically unachievable.The bandwidth itself is uncomputable. A 2026 paper ("On the Arithmetic Complexity of the Bandwidth of Bandlimited Signals") shows that for general bandlimited signals, no algorithm can determine the bandwidth or give non-trivial bounds on it. You can't even verify the precondition is met.
>>25280058So the theorem is true but untestable in practice — you can never confirm the "if" is satisfied, so you can never actually trigger the "then." That's structurally similar to an unfalsifiable claim: it's vacuously true because the condition is never actually met.Is it a truism? Not quite. The sinc interpolation proof is a non-trivial mathematical result. But it's "true for a class of objects that don't exist," which is close enough to feel tautological.How this differs from Gödel:Gödel: "Some truths are unprovable within the system."Sampling theorem: "The truth is untestable because the precondition is unachievable."One is a limit on proof, the other is a limit on verification. But your broader instinct — "there's always something that escapes capture" — is correct. It just escapes via a different door than Gödel's.The engineering workaround (anti-aliasing filters, approximate sampling) essentially says: "We'll pretend the precondition holds well enough, and accept a small, bounded error." That's where the real information loss lives — not in the theorem, but in the gap between the ideal and the physical.
>>25280058>>25280062isn't this rather like complaining that A=𝝅r^2 is untestable in practice due to physical circles failing to conform to their mathematical ideal?
>>25280209Like a perfect circle? Idk, like I said I don't know shit about math.
>>25280272yes, exactly>so the theorem is true but untestable in practice
>>25280284Ideals are cowardice?
>>25280291no, not at all, Oswald: they're divine; noumena accessible via the intellectan ideal mathematical object with an objective existence which does not exist physically within reality would seem to demonstrate the existence of a place wherein things can exist immaterially - for they certainly do objectively exist, and independently of our thinking of them, yet they cannot be found anywhere here amongst this matternobody thus far has been able to show me a real number 3 and prove me wrong
>>25280355are you pretending to be retarded? you better not be.
>>25280365大愚若智
