rich1.0npub1re22dhneg8azw7z3979njqn2sp4gxzp4703g62tsrvmsvnj76heqj679nuhttps://nostr.ae/npub1re22dhneg8azw7z3979njqn2sp4gxzp4703g62tsrvmsvnj76heqj679nunjumphttps://nostr.ae📅 Original date posted:2016-03-09 📝 Original message:> On 9 Mar 2016, at 20:21, Bob McElrath <bob_bitcoin at mcelrath.org> wrote: > > Dave Hudson [dave at hashingit.com] wrote: >> A damping-based design would seem like the obvious choice (I can think of a >> few variations on a theme here, but most are found in the realms of control >> theory somewhere). The problem, though, is working working out a timeframe >> over which to run the derivative calculations. > > From a measurement theory perspective this is straightforward. Each block is a > measurement, and error propagation can be performed to derive an error on the > derivatives. Sure, but I think there are 2 problems: 1) My guess is that errors over anything but a long period are probably too large to be very useful. 2) We don't have a strong notion of time that is part of the consensus. Sure, blocks have timestamps but they're very loosely controlled (can't be more than 2 hours ahead of what any validating node thinks the time might be). Difficulty can't be calculated based on anything that's not part of the consensus data. > The statistical theory of Bitcoin's block timing is known as a Poisson Point > Process: https://en.wikipedia.org/wiki/Poisson_point_process or temporal point > process. If you google those plus "estimation" you'll find a metric shit-ton of > literature on how to handle this. Strictly it's a non-homogeneous Poisson Process, but I'm pretty familiar with the concept (Google threw one of my own blog posts back at me: http://hashingit.com/analysis/27-hash-rate-headaches, but I actually prefer this one: http://hashingit.com/analysis/30-finding-2016-blocks because most people seem to find it easier to visualize). >> The problem is the measurement of the hashrate, which is pretty inaccurate at >> best because even 2016 events isn't really enough (with a completely constant >> hash rate running indefinitely we'd see difficulty swings of up to +/- 5% even >> with the current algorithm). In order to meaningfully react to a major loss >> of hashing we'd still need to be considering a window of probably 2 weeks. > > You don't want to assume it's constant in order to get a better measurement. > The assumption is clearly false. But, errors can be calculated, and retargeting > can take errors into account, because no matter what we'll always be dealing > with a finite sample. Agreed, it's a thought experiment I ran in May 2014 (http://hashingit.com/analysis/28-reach-for-the-ear-defenders). I found that many people's intuition is that there would be little or no difficulty changes in such a scenario, but the intuition isn't reliable. Given a static hash rate the NHPP behaviour introduces a surprisingly large amount of noise (often much larger than any signal over a period of even weeks). Any measurements in the order of even a few days has so much noise that it's practically unusable. I just realized that unlike some of my other sims this one didn't make it to github; I'll fix that later this week. Cheers, Dave