Unlock Systematic Problem Solving with the FeiShi (Flying Arrow) Analysis Method

During the Spring Festival holiday I focused on polishing my problem‑solving thinking chain.

Polish my problem‑solving thinking chain

My core question is how to conduct systematic comprehensive analysis (clear view), scientific effective decision‑making (good planning), and precise execution (do it right) . This article presents the analysis part of my original method—the FeiShi (Flying Arrow) analysis method—while other parts will be updated later.

Origin of the FeiShi Method: Nine‑Screen Thinking

The Nine‑Screen Thinking method is an innovative technique that expands thinking beyond the immediate object by considering both time dimensions (past, future) and space dimensions (supersystem, subsystem).

For example, my current focus is the marketing of the new book “Effective Use of ChatGPT for Mathematical Modeling,” which I treat as the current system.

If I only think about how to market the book, I might consider channels, sales, budget, etc., which can be overwhelming for someone not versed in marketing. To achieve a systematic and comprehensive approach, the Nine‑Screen method urges us to consider both time and space dimensions.

Time‑Dimension Thinking

First, examine the past and future of the current system. Looking back at my previous two books:

First book (2023) was promoted only via a WeChat Moments post and a preface on the public account.

Second book (2024) added expert endorsements, extensive gifting to friends and fans, in addition to the previous channels.

From this review I learned:

Book marketing requires careful planning.

The launch period is the sales golden window.

Appreciating friends who help promote is essential.

Looking ahead, I consider what results I want—mediocre sales, poor performance, or exceeding expectations—and which factors and actions will influence those outcomes.

Space‑Dimension Thinking

Next, consider the system dimension, which includes:

Supersystem – the larger system that contains the current object.

Subsystem – the components that make up the current object.

“Book marketing” is one stage of a book’s lifecycle; other stages include idea generation, writing, publishing, proofreading, errata, re‑printing, digitization, etc. All parts are interrelated, and placing the object within a system clarifies its position.

The marketing subsystem follows the 4P theory (product, price, place, promotion). For channels:

Online channels : e‑commerce platforms (JD, Taobao) and media platforms (WeChat public account, Douyin, Xiaohongshu).

Offline channels : bookstores, university collaborations, etc.

Finally, we examine the past and future of both the supersystem and the subsystems.

Case Study and Limitations of the Nine‑Screen Method

The method’s advantage is its systematic thinking, but in practice finding the supersystem and subsystems can be difficult because many options exist. For example, “book marketing” can be seen as a part of the broader concept of “marketing.” Subsystems can be defined as instances (specific marketing plans), attributes (economics, practicality, coverage), or composition (different parts of marketing).

Core Concepts of the FeiShi Method

Horizontal arrows represent time; the diagram shows seven such arrows. The relationships among supersystem, subsystem, and current system include instance, attribute, and composition.

Examples of subsystems:

Composition subsystem : the different parts or stages of book marketing.

Instance subsystem : specific book‑marketing cases.

Attribute subsystem : important attributes such as economic efficiency, reach, etc.

The diagram looks like multiple arrows fired together, hence the name “FeiShi (Flying Arrow) analysis method.”

Aside: Thinking Chains and Artificial Intelligence

The “thinking chain” concept has recently gained attention due to large language models (especially DeepSeek). When I design problem‑solving frameworks, I find a regular, traceable thinking chain crucial—clear analysis, good planning, and actionable execution.

During the holiday I applied this thinking chain (the analysis part described here; decision‑making and execution parts will follow) to various problems, continuously solidifying and improving it, much like reinforcement learning in large language models.

While I welcome AI’s progress, I aim to become better myself by building a scientific, effective problem‑solving thinking chain, integrating practice and optimization, and showcasing my unique value in the new era.

Readers interested in this topic are welcome to discuss in the comments.

Below is a recommendation for my new book “Mathematics for Deep Learning – Using Python” , which is suitable for friends interested in the mathematics behind large language models and neural networks.