Meta model, the model of model

01-30

This article is first posted in my WeChat public account: GeekArtT.

In theory, the math is no limit and only requires to obey its internal logic. But that』s also one trap here. But the generality, freedom of math is not used to create branches in any arbitrary directions. It』s a powerful tool used to constrain our unknown thing.

No matter the theory of probability, or the geometry, there』re always some very basic questions which can be answered by us: like what』s the meaning of probability? What does the length mean? Those meta problems are like the question in physics: why an object can be keep static or do the uniform linear motion when no external force existing? Why the motion of object are governed by Newtonian?

In fact, we just don』t know these meta problems』 answers. And, science is not intent to answer those questions directly. Instead, science and math use another indirect way, a more pragmatic way to research them: admit the unknown things first, and give/create/build the definitions of those unknown things directly. The definitions should be kept as simple, obvious as possible. This plan is as we can』t answer it, we just give our own common understanding as their definitions. Equivalently, it』s the process of modeling. The whole theory is a big model, the meta model. Those prior given definitions are the model』s model. Then, use those definitions as tools to explore the nature, the world.

In the exploration stage, once we meet conflict we』ll modify our model, or even the meta model to improve its performance. We don』t expect to answer those final question at once. We』d like to accept the unknown thing, and package them into one definition, a constraint realm. This process can help us control the degree of unknown, reducing them into one clear part/package. Then, the following explorations or explanation can be very clear with rigorous logic, without further vague ignorance. Now, except the definitions contains vague mess, all the remaining parts can be expressed with definitions without any blur details.

From this viewpoint, you should NOT use the math arbitrary. Your definition building should be based on the abstract of experience, phenomena in world, the modeling of life, instead of non-guided arbitrary direction.

This kind of thinking/technique is very powerful and can be used in our daily life. Instead of knowing all the thing, like manage one medium account or build one product, we can do some prototype first, which is the process of packaging our unknown into one concrete prototype. Then, based on this no perfect prototype, we can further exploring more details, give them more improvement based on the feedback of this prototype. We can』t conquer one big problem at once. In many situations, the worse part is we even can』t propose the right question. Thus, we need some prototype as the bridge, as one experiment to get more information back. At this step, no matter this prototype is getting closer to the answer or not, this bridge testing is valuable. Because even the negative result can give us the information that there』s one method is invalid for the problem, which gives us the boundary of this problem. And this boundary can help us shape more efficient tools to conquer the problem.

This is the thinking of science or math. Admit our unknown and package them into one constrain prototype, and use the rigorous logic to discuss the remaining parts.

This perspective also warns us that: don』t propose fake problem. For lots of mathematicians, the pursue of researching one field is coming from the superiority of their high IQ. The harder the question is, the more they want to go into. But math, science, and life are not running as that way. It』s like a misunderstanding that your focus is based on the complexity of one problem instead of the impact of one problem. But you do need to solve the important problem instead of the hard problem. That』s different. As you don』t know what the importance of one problem, you can』t understand why one problem is existing, why it deserves your commitment. You may just jump into one field based on the hot fever of others, instead of your own desire. They』re never your really problems that make you take the pain. This is what I call your fake problem. In my opinion, you shouldn』t enter one field unless you do have, understand why this field is existing, how pain the problem the field tries to solve impacts you. And once you know your desire, your purpose, and your pain, you won』t be trapped by those technique details. You』d know the big picture that how it models the reality and your real painful problem into the concepts of this field. You』d know every part concretely instead of treating them as magic.

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