Digital Revolution

Simulation algorithms for dynamical systems rely on the shadowing lemma to establish the proximity of a pseudo-orbit and a true orbit. The power of the shadowing lemma is tremendous in that it takes all sorts of errors in a computer simulation into account. Numerical analysis, on the other hand, is not that fortunate. There is no systematic error analysis that encompasses all possibilities. Finite element method's error equation, for example, only deals with discretization error, but ignores computational round-off error, and can not provide a good estimate of the proximity of the real solution based on mesh properties. Here we briefly discuss the error estimate in a numerical simulation of contraction mapping. The fixed point and iterated epsilon-pseudo-orbit can be estimated to be within epsilon/(1-C) plus a arbitrarily small number, where C is the contraction constant. That is, if the contraction constant is close to 1, much smaller round-off and general computational errors ar...

Knuth isn't a huge fan of parallel computing. He acknowledged several fields where parallel computing speeds things up, like computer graphics, but remains unsatisfied with its daily-life impact. On the other hand, Tim Mattson, a proponent of OpenMP, embraces parallel computing for its power saving capability. Here, a computational complexity perspective is provided to reconcile various contentious issues regarding parallel computing, like its longevity. Computational complexity measures the growth of logical depth with respect to growing inputs. If the number of parallel machines is of O(1), it can be shown that parallel speedup doesn't change the order of computational complexity, but only affects the constant factor. From traditional point of view, the order of computational complexity is of prime importance, for the presumption that data sets may grow astronomically, while the constant factor is of little interest. However, we wish to emphasize that in many practical and ...

It's hard not to think of Russian invasion of Ukraine. While it has little to do with the digital revolution, we feel that the rest of the world must accommodate huge volume of refugees, if civilization is to be preserved. Those in political circle, often cynical, dishonest, and hypocritical, will use the war to justify whatever political view they have, but if civilization can make these dirty political people do some good, it's worth a try. That said, here are some observations of the war. First, Putin played into the West's hands. Before the invasion, the West was divided and lacked a common purpose. Russian invasion of Ukraine united the West. In some way, Western politicians are content with sacrificing Ukraine to fulfill the revival of the Western block. A new Cold War is almost certainly called for. The worst possible hawks now have their voice crushing any peaceful imagination of future world order. Russians made the same mistake Chinese Communist Party made, that t...

Automatic updates for operating systems are very problematic. Modern operating systems and drivers are really buggy. For business applications, unreliability due to automatic OS updates can cripple entire company. ERP, for example, may not work in new OS releases, and there are IT stories that complain how painful restoring a host of computers is. Usually, IT should test updates against business operations and distribute updates afterwards. But few OS vendors support flexible update mechanisms. Thus, computers are often left vulnerable without security updates or unreliable with unscrupulous automatic updates. Consider how to disable automatic updates in Windows. It's clear that the troublesome steps indicate Microsoft's intention to force automatic updates upon most people. Apple is nicer, but updates are usually a permanent act without reversal. If new releases are buggy, one is stuck with it until bug fixes. To be fair, building large software is hard. But it seems there ar...

Apple launched Mac Studio, and as we speculated before, it employs architectural optimization, UltraFusion, to boost performance. While the advertisement is for studio use, it's clear the performance can easily cover vast areas of pro uses. It's reasonable to envisage, say, graphics departments within corporations will happily adopt Mac Studio to improve productivity. Mac Studio fills the gap between entry-level Macs and future Mac Pro. In some way, Mac Studio reminds people of the notorious Mac Pro 2013, but the lack of configurability may be justifiable given extended connectivity for peripherals. The outstanding hardware, however, can not succeed alone without quality software. It's well-known that recent macOS releases are very buggy, which may significantly impact pro workflows. As every serious Apple user knows, Apple can not be trusted with critical data, because software unreliability may wipe out all previous efforts. Lack of well-written developer documentation...