Concept Contrast Fable

Chain of thought and scratchpad

Conclusion first:The chain of thought is the homework notebook you hand in—organizing the reasoning process into a clear path that others can review. The scratch area is the calculation paper in the desk drawer—filled with crossed-out attempts, arrows doubling back, and intermediate results meant only for oneself. Both are called “reasoning processes,” but the goal of the homework notebook is reviewability, while the goal of the scratch paper is trial and error. If you demand that scratch paper meet the standard of a homework notebook, you will cut off the model's most valuable exploratory steps; if you submit homework by the standard of scratch paper, the reviewer will not understand it at all.

The chain of thought is the homework notebook you hand in—organizing the reasoning process into a clear path that others can review. The scratch area is the calculation paper in the desk drawer—filled with crossed-out attempts, arrows doubling back, and intermediate results meant only for oneself. Both are called “reasoning processes,” but the goal of the homework notebook is reviewability, while the goal of the scratch paper is trial and error. If you demand that scratch paper meet the standard of a homework notebook, you will cut off the model's most valuable exploratory steps; if you submit homework by the standard of scratch paper, the reviewer will not understand it at all.

Fable

Scratch paper and exercise books

There was a rule at the academy: arithmetic exams required not only the answer but also the work. When grading, the teacher looked at the work first, then the answer. A correct answer with skipped steps would be questioned; a wrong answer with a clear path could still reveal where understanding went astray. This submitted work was for others to review.

Another thing was hidden in the students' desks: scratch paper. On it were casually listed numbers, half-drawn and crossed-out diagrams, and arrows looping from the third line back to the first. It did not need to be handed in, nor did it need to be clean; it was just a place where students temporarily put their thoughts while solving problems.

Xiao Qi thought there was no difference between the two, since both involved calculation. The next day the teacher set a problem: find the shortest route from the academy to the city gate, sketch freely on scratch paper, but leave only one route in the workbook that others can understand.

Xiao Qi tried four paths on paper, crossed out dead ends, and bypassed the market, and finally got the right answer. But when copying it into the notebook, he did not know which step to start from. The scratch paper helped him find the path, but it did not automatically become an auditable explanation.

The teacher said that scratch paper is the working surface for yourself, while the homework notebook is the trail for others to see. Scratch paper can be dirty, repeated, and hide detours; the submitted process must be clear, stable, and allow others to judge whether it works.

Later Xiao Qi observed his classmates and found that their workbooks often showed only the straightest line, while the real trial and error was hidden in their desks. When learning, detours are valuable; when grading, if detours are not organized, they will lead the reviewer astray.

In the end, the teacher wrote the rule on the wall: when explanation and review are needed, look at the submitted reasoning; when carrying temporary attempts, use your own scratch paper. Both are called process, yet they serve different people, different stages, and different responsibilities. At the year-end exam, the teacher allowed everyone to keep their scratch paper but graded only by the workbooks. The students finally understood: one sheet of paper absorbs chaos, the other bears explanation; merge the two into one, and you can neither learn well nor audit clearly. Later, the academy revised its rules: scratch paper can aid exploration, but workbooks must withstand re-examination.

Chain of Thought

A prompting technique that lets a model show step-by-step reasoning before outputting the final answer. The reasoning steps are oriented toward human readability and reviewability, with the goal of improving answer accuracy and explainability.

Draft area

A temporary workspace used internally by the model to store intermediate computation results, try different reasoning paths, and backtrack and correct. It is not exposed externally, and its purpose is to expand the model's effective thinking capacity.

Story Mapping

Workbook (chain of thought): a clear reasoning path for reviewers, with every step readable and verifiable
Scratchpad (draft area): the model's internal temporary workspace, allowing edits, backtracking, and trial and error
Shortest-path problem: requiring the scribbled draft to be organized into a clean trajectory
Four attempts to find the right path: the draft area carries the trial-and-error process; the workbook shows only the final correct path
Exams look at the homework notebook, learning relies on scratch paper: CoT is for evaluation and explanation, Scratchpad is for exploration and computation

Applying it to Andy Ren Xu's project

When designing an Agent's reasoning flow, explicitly separate the chain of thought from the scratchpad. The chain of thought is the reasoning path shown to users and debuggers—it should be concise, logical, and every step traceable. The scratchpad is the Agent's internal workspace—it may jot freely, revise repeatedly, take detours, and come back. Do not show the scratchpad's contents directly to users, and do not constrain the scratchpad's free exploration with the chain-of-thought format. Each space has its own boundaries, and only then can the Agent find balance between being explainable and being able to think.

Chain of Thought Draft area