Digital Revolution

There are two primary models for working with PDF files on the cloud with Apple devices. One is to store PDF files in iCloud Drive and use apps like Preview to access the PDF. Another is to store PDF files in Apple Books and read it directly. Supposedly, the former is more flexible, while the latter is more focused. However, due to implementation issues, both models work awkwardly. First the iCloud Drive model, it's really flexible to use iCloud Drive to store whatever PDF at wherever organization finds suitable. With Preview on the Mac, reading PDF files is really tidy. For example, consider bunch of research papers and books in various folders on iCloud Drive. Classification can be added with Finder. Annotation can be added with Preview. The problem is that Apple didn't ship Preview on the iPad. Viewing PDF files in the Files app on the iPad just sucks. Then the Apple Books model, due to limited organization functionalities, it's best used to store only important PDF file...

Ribbon concordance has been proved to be a partial order system on knots and forms a complexity hierarchy. However, in this case, the knots are assumed to be in the three dimensional sphere. A natural question to ask is whether similar relations may be defined in 3-manifolds other than the three sphere. Since in general the fundamental group of 3-manifolds does not vanish, significant complexity different from the case of the three sphere is expected. It's a interesting research topic.

In D8, Steve Jobs boldly predicted a iPad revolution, that tablets would replace PCs just like cars replaced trucks. Years later, we can pretty safely say that this kind of dramatic revolution didn't and wouldn't occur. Primarily, in offices, PCs are still the productive powerhouse tablets can not replace. However, another kind of quiet revolution has happened. For many people, the screen time on tablets is much longer than that on PCs. Tablets have become the primary source for casual computing. For daily tasks like reading books and news, browsing the web, organizing calendars, and managing todos, etc., the iPad has become paramount in that it's much more convenient and accessible than Macs. The ergonomics of the iPad makes it super easy to use, and the large screen is very capable of usual computing tasks. True, for office tasks, PCs are still more productive, but the primary computer at home is more and more likely a iPad. After Steve Jobs passed away, Apple began to eq...

Complementing his marvelous Thoughts on Flash, Steve Jobs described tech cycles to justify Apple's position in D8. Essentially, tech cycles means that technology grows from infancy to maturity to the grave. While, in the case of Flash, it's certainly correct, the mantra has widespread influences so that tech blogs began to apply it across all technologies. However, email is clearly a counterexample in that it never enters the grave. There are pieces of technologies that are close to eternal. The most conspicuous implication of the widespread mantra is that technological revolution occurs everywhere, rather than in specific fields. As a instance of the mantra, tech blogs claimed that smartphones are going to be replaced by other sorts of technologies, ruling out the possibility that smartphones in certain form may be close to eternal. These tech blogs were not far from Jack Ma's view. We believe, however, that these tech blogs are misguided and misinterpreted the famous Stev...

Everyone knows bugs can plague software, but buggy software from Apple still makes big money. There is a unsatisfactory response to the situation: regular backups. For Macs, Time Machine seems quite reliable. For iPhones, iPads, and Apple Watches, the reliance on iCloud for backup is quite dangerous, because iCloud reliability isn't very impressive. Yet, people often store critical information on mobile devices. There are cases like losing all Apple Books upon update. It's a horrible experience. The reason Apple can get away with this is that there is little regulatory and legal pressure for fixing bugs. As noted before, consumers have little power and often can not make Apple pay for damages. It seems that this is a much more important issue than crude antitrust against Apple.

Intermediate Value Theorem is a basic theorem in calculus. Usually, there is nothing more to say about the theorem. But with the rigorous bounds obtained in numerical algorithms that we discussed before, much can be done through the basic theorem. In mathematical research, existence is often very hard to establish. Part of the reason is most existences afford no constructive description. Here we are left with indirect methods like the Intermediate Value Theorem. Traditionally, numerical algorithms offered insights but were not applicable in rigorous proof. With rigorous bounds proven, numerical algorithms can be utilized to provide rigorous estimates of simulated values. Together with the likes of Intermediate Value Theorem, existence of objects can be established rigorously. Providing rigorous bounds for numerical algorithms is a game changer.

To many people who do not like fitness, Apple Watch has been a redundancy. The case is about to change with the introduction of Apple Watch Ultra. Although Apple Watch Ultra has been marketed as a sports watch, its life-saving features beyond fitness can really help, like for people who climb mountains. Fitness was controversial primarily due to misunderstanding. Since completing fitness circles can not guarantee actual fitness, it's been described as a flaw. However, life-saving features could really matter in case of emergency. Although the coverage of Apple Watch Ultra in tech blogs has been quite mundane, containing additional marketing material for Apple, Inc., its subtle expansion of scope in apps is really pleasing. Because the watch can be taken to harsh environments, it offers possibilities for apps like real-time care. The main drawback is still the somewhat usable but unsatisfactory battery life. Many tech bloggers speculate Apple Watch Ultra indicates the future replace...