李毅伟
杂感 | 应用数学遭遇:任务、过程和结局
2021-2-23 17:33
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[按:下文是群邮件的内容,标题是新拟的。主旨是通过思想模型和简单图示,说明真正的应用数学注定是一场遭遇。]

This is coming to you from Yiwei LI (PhD, Applied math), Taiyuan University of Science and Technology  (TYUST) Taiyuan, China

Scratch time is a topic under the column of Theory of Mathematics (TOM), an attempted framework to understand invented and un-invented mathematics from the core.

It appears necessary to address some typical situations that one would meet in (genuine) applied math.

---- By "genuine", I refer to the situations occurring in a foreign field where mathematical problems arise.

---- You know what ? I feel difficult to continue.

---- Well, it's 4 o'clock and I'm watching a movie (Saving Mr. Banks), yet a dull one...

.

So, I decide to share a thought model concerning genuine applied math.

---- In a way that everyone could understand, or that everyone might think they really understand.

---- Before one moves on, I declare no profession implication.

---- It's just a simple thought model on the abstract level.

.

---- The problem can be illustrated like ——

                 

                 

                 

---- This is from the objective perspective.

.

---- To the problem holder, it looks like ——

                 

                 

                 

Note: the green parts are assumed solved; the dark part is the assumed problem.

.

---- So comes the assignment ——

                 

                 

                

Note: The gray parts are typically not visible to the one assumed to solve the problem.

.

---- So comes the first step of the process of applied math (应用数学过程) ——

                 

                 

                

---- The assignment appears accomplished, from the perspective of the one assumed to solve the problem.

.

However, to the problem holder, it looks like ——

                 

                 

                

---- The solution might be a foreign matter to the problem holder.

.

---- So, after a long or not short while, comes the second stage of the process of applied math (应用数学过程) ——

                 

                 

                

.

                 

                 

                

.

                 

                 

                

.

.

                 

                 

                

---- So all the modules are eventually identified, each of them is a a foreign matter to the one assumed to solve the problem.

---- As the other modules are so familiar to the problem holder that it may become a source of difficulties, contrary to the usual intuition.

---- And, all these efforts are very likely thought not necessary, in the view of the problem holder.

---- Actually, such efforts are either invisible to or not valued by the problem holder.

.

---- So comes the dilemma ——

---- Should these other modules be implemented for the second time ?

---- Very likely one needs to solve them one by one.

---- The original architecture might not be compatible to the solution of the original assignment.

---- Actually, one has already sunk in by the cost.

.

So comes the third stage of the process of applied math (应用数学过程) ——

                 

                 

                

.

                 

                 

                

.

                 

                 

                

.

.

                 

                 

                

---- This appears the final station of the process to the one assumed to solve the problem.

.

To the problem holder, it looks like ——

                 

                 

                

.

(to be continued).

 

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