Understanding theory means only understanding part of the reality

It is somewhat surprising to hear from an optics physicist that after two thousand years of inquiry, the fundamental question "what is light" still remains. Classical theory describes light as electromagnetic waves, whereas quantum mechanics describes light as particles. The result is what physicists called the duality of light. But obviously not all physicists are satisfied with this duality explanation because of its inherent ambiguity.

The evolution of the understanding of light demonstrates the idea that understanding a theory means only understanding part of the reality, the part of reality that the theory can accurately predict observations.

Image source: xkcd.com

Maths and Music

In an interview on the ethical legacy of Einstein, a theoretical physicist made a very nice analogy between physics and music. He said maths to physicists is as musical scores to musicians. When looking at musical scores, musicians plays the music in their heads. Similar things happen to physicists: when they look at equations, they see the physical images of what those quantities in the equations represent.

Image source: amazon.com

Critical self-assessment 3 -- Projects

Too many things I want to do, but too little time of actually doing them. As a result, I have a long list of projects I have started and a long list of things I want to start: website construction, modeling, type-watching, When Pigs fly, martial art, public speaking, travel, traditional Chinese medicine, humor study, running, soccer, conversation, writing, and recently added to the list, existentialism study, skate, ski.

Solution? The rational approach is to prioritize the projects and to do them in the order of their importances, and of course with proper time management. But this approach doesn't apply to these hobby projects.

Sometimes another approach works better: take whatever I feel like doing at the moment, "Just do it" and enjoy doing it.

Critical Self-assessment 3 -- Research

Slow, always slow. I am in a non-competitive environment that it seems that there is no urge of being the first in doing anything. But whenever this idea comes to my mind, this idea of being slow frightens me, energizes me, and drives me. Perhaps, I need competitors, good competitors.

Critical self-assessment 3 -- relationship

Whenever I travel, I enjoy a lot the freedom of going wherever I want to go and doing whatever I want to do. That's exactly the reason why I prefer not to travel with a group. And then I get this frightening idea that if I were to travel with a girl, I have to compromise my choices. Then even more frightening is that life is like travel. Am I not ready for a relationship yet?

Critical Self-assessment 3 -- Health

The last thing one would do in a trip is to get sick, that's what I did during my trip to Banff. The day after I got Lake Louise Hostel, I went ice-skating on Lake Louise, and then I got sick. While I was lying on my bed, I got this crazy idea of linking the rate of metabolism with what traditional Chinese medicine call the small furnace in human body. The more vigorously your small furnace burns, the faster the rate of metabolism, and hence the more heat the body generates, and the less susceptible to cold the body is.

This idea of linking metabolism with small furnace in the body, though may not be justifiable scientifically, explains quite a few things happened to me. In cold weather, metabolism slows down, and the small furnace is slowed down too. As a result, my digestions slows down; my body doesn't generate or preserve enough heat, and I get sore knees, sore head. The most annoying symptom is that I cannot do anything but rest after I have food.

This linkage provides me with a solution too. To increase the rate of metabolism in cold weather, the body has to get used to cold weather so that it functions as if it is in normal weather. Early morning running in winter and cold water shower are too possible options. Besides, food with the character of hotness like ginger and cinnamon tea will help me cope with cold weather too.

I am on my way back.

Image source: www-old.cs.st-andrews.ac.uk

The Effect of the Hierarchical Structure of Knowledge on Learning

This post is my first attempt to rationalize my understanding of the structure of knowledge. This understanding will provide guidance on what to know, how to know, and why to know a particular subject, especially in self-studying, for I have a tendency to indulge myself in studying whatever I get.

Two observations form the basis of my understanding. First, the volume of knowledge is too huge for any one person to know it all. Second, this vast volume of knowledge is stored in a hierarchical structure. To illustrate the second point, take a look at the table of contents of wikipedia, or simply the disposition of faculties in any comprehensive university, and you will find these three basic divisions: natural science and technology, social science, and arts. And all three major divisions are subdivided into many categories and then subdivided again and again. These divisions and sub-divisions exemplify the hierarchical structure of knowledge.

My first conclusion is that one does NOT NEED to know everything. By everything, I mean every detail of every subject existing on earth. The hierarchical structure of knowledge suggests that a group of details is related to another group of details in the same way. To make an analogy of this point, consider the statement that your uncle's child is your cousin. Whether your cousin is a girl or a boy is an unnecessary detail to determine his/her relationship with you, as long as his/her father is your mother's or father's brother. Knowing more details will give you deeper understanding of a subject. Let us generally state that knowing different levels of details corresponds to different levels of understanding of a particular subject.

Then, in a particular subject, the question what to know becomes the question to which level of details one knows? This question is closely intertwined with the question why to know, which serves as a criterion to eliminate unnecessary details. For example, for general interest, one would take a helicopter view of the subject first to understand its principles before going depth in any of its branches. On the other hand, for the purpose of solving any real-world problem, one needs to identify what is relevant to the problem and must know every possible detail of relevant knowledge.

The process of determining to which level of detail one needs to know is also closely related to the question how to know. Existing knowledge can be obtained through books, journals (both paper and electronic) and direct communication with people who knows, none which is infallible. A good mentor is invaluable for beginners and often largely determined the student’s area of study. However for beginners, it is very hard to judge who is a good mentor and who is not, as it is often the case of judging the quality of a book by only reading the introductory chapter of the book. Peer opinions will give some insights on these matters, but best solution is still hard to find.

The foregoing analysis enables me to address the most practical concern, how to learn things fast. It seems to me that the speed of learning, particularly in self-study, is largely determined by the amount of details one needs to know. Obviously the fewer the details, the faster the learning process. A fair judgment of what levels of detail one needs to know will save you enormous amount of time. (The choice of books, journals and mentors is also critical.)

Therefore, don’t indulge yourself in any seemingly significant details.

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