[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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