Steve Jobs emphasized design because humanity deserves better. It's a noble attitude, but paradoxically humanity often ignores design when people run corporations. The main argument is that design provides marginal advantage in the market at best. While empirical studies are not very solid, it's noticeable that many corporations view design as cosmetics. Explaining simplicity isn't necessarily minimalism to corporations often doesn't make profit. In short, few believes humanity deserves better. Before convincing corporations the importance of design, perhaps designers should establish it as a strategy. People often judge products by their quality and don't necessarily buy the cheapest product. If design can become a critical factor of quality, it may justify the premium. The market for design is pretty harsh. Despite Apple's success, most corporations pay lip service to its approach. Endless number of executives cut design budget and expect business success. The

The Value of Empiricism

Many rationalists, especially those from the mathematics department, tend to assume the superiority of human thought. They often cite the success of mathematics in sciences as evidence. Oh. Apart from the fact that most people aren't Maxwell or Einstein, it's mistaking the word Moon for the real Moon. Ask a mathematician to deduce what's on the Moon without evidentiary investigation. It's easy to see the fallacy of rationalism. Mathematics as a language is important, but it's not the ultimate validation of scientific theories. This is the value of empiricism. It's well known that Maxwell's achievement in electromagnetism is the mathematical formulation of previous electromagnetic experiments. Yes, experiments. Rationalists see the mathematics of Maxwell equations, and forget the most important substance these equations describe. Absurd. The same thing happens to the digital revolution. Rationalists have little to offer other than claiming superiority, while

Ribbon Concordance on 3-Manifolds

This post is a guess. Ribbon concordance on 3-manifolds can be separated into partial order systems associated with each element of the fundamental group of the 3-manifold. For each element of the fundamental group, a partial order system can be associated. The reason behind the guess is that if the knotty part can shrink to very small and the remaining part is largely isotopic to a representative element of the fundamental group, then it's likely that the structure obtained in 3-sphere case is applicable to each element of the fundamental group. It's a interesting research topic.

PDF on the Cloud

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

Beyond Ribbon Concordance

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.

Screen Time

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