https://hackerpaper.kaipfister.de/p/1405.0324/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMThttps://news.ycombinator.com/item?id=23659812urn:hackerpapers:mention:1405.0324:23659812Sat, 27 Jun 2020 05:57:03 GMT<p>In many cases, Wikipedia actually lists the analogy for classical probability theory. For several theorems, the proof for Hilbert spaces can be directly brought to the classical world. The main difference to keep in mind is that we have amplitudes, not probabilities, and they can be negative or complex. We recover typical probability theory by taking norms/squares of amplitudes. The uncertainty principle follows via doing signal analysis on Fourier-transformed wavefunctions. A fun professional treatment from Baez et al. is [0], and 3blue1brown has an excellent two-video visual explanation…</p><p><a href="https://hackerpaper.kaipfister.de/p/1405.0324/">Paper and discussion history</a>. A mention is not an endorsement.</p>math.AThttps://news.ycombinator.com/item?id=16634550urn:hackerpapers:mention:1405.0324:16634550Wed, 21 Mar 2018 01:36:36 GMT<p>While it might seem arrogant of the author to take this stance, the Sampling Theorem generalizes extremely well and is considered an extremely stable result. My favorite generalized Sampling Theorem is https://arxiv.org/abs/1405.0324</p><p><a href="https://hackerpaper.kaipfister.de/p/1405.0324/">Paper and discussion history</a>. A mention is not an endorsement.</p>math.AT