Weinacht’s Binary Theory

Weinacht’s Binary Theory supplies the mathematical premise for Rong Jinzhen’s ambitious graduation thesis and, through it, a way to frame the limits of artificial intelligence. The theory concerns the binary nature of certain constants. Rong Jinzhen attempts to develop that premise into a pure-mathematical argument about human intelligence: if intelligence is itself an irrational, unending constant, then its element of indefinable confusion cannot be completely reproduced by artificial means. The thesis is daring, but its force depends on a foundation the book presents as unproved.

Mathematical premise and political context

In the academic year when Rong Jinzhen’s classmates began their graduation work, he chose to write about Georg Weinacht’s theory and to construct a mathematical proof from it. The choice was far beyond the work he had encountered in class and was more like an advanced graduate research topic. It also carried political risk. Georg Weinacht was known for his anti-communist position and, during the Korean War, had publicly encouraged the American Army to cross the Yalu River. In a number of communist countries led by the Soviet Union, his theories were not accepted or even discussed except in criticism. The theory’s reception was therefore shaped not only by its mathematics but by its author’s politics.

Other professors in the department feared the thesis would be impossible to supervise and asked Young Lillie to persuade Rong Jinzhen to choose another subject. Young Lillie instead took on the supervision himself and consistently encouraged him to continue. His support placed him against the prevailing caution: the thesis could be read as a defense of a theory associated with an intensely anti-communist figure. The episode shows how an abstract mathematical proposition could acquire political consequences without changing its mathematical form.

From theory to thesis

Rong Jinzhen’s thesis, titled The Constant π as a Definable yet Irrational Number, grew from his reading beyond the university curriculum. Young Lillie had earlier opened a storeroom in the attic and shown him two cases of books left by Liseiwicz, inviting him to read them. The thesis’s subject and level reflected that independent intellectual range: rather than working within familiar course material, Rong Jinzhen built his argument around a difficult question concerning π and Weinacht’s theory.

Young Lillie was struck by the first draft’s incisive, logical reasoning, though he thought some proofs unnecessarily complicated. In revision, he sought to simplify their presentation and remove elements he considered superfluous. Developing the underlying proofs nevertheless required sophisticated methods and understanding beyond mathematics alone. The first draft ran to 20,000 characters; after several revisions, the final version was just over 10,000. It was later published in Popular Mathematics and made a considerable impression in Chinese mathematical circles. Yet the improvement brought suspicion as well as acclaim: readers found the finished work so accomplished that many doubted an undergraduate could have written it independently, particularly given Young Lillie’s role in revising it.

The argument about intelligence

The thesis’s central move is to extend the discussion from a mathematical constant to human intelligence. Rong Jinzhen proposes that intelligence should be regarded as a mathematical constant and an irrational number that never comes to an end. On this account, intelligence includes confusion: something indefinable, not fully knowable and therefore not fully replicable. Artificial intelligence might approach human intelligence, but under existing conditions it could achieve only an approximation, not a complete reproduction.

This conclusion is not presented as wholly unprecedented. The narrator notes that many mathematicians, including contemporary ones, agree with Rong Jinzhen’s position on the limits of reproducing intelligence. What makes his work distinctive is the attempt to derive that position from the daring hypothesis about π’s binary nature, using pure mathematics. The ambition is not merely to state that human intelligence resists replication; it is to make that resistance follow from a formal argument. If the premise holds, the proof gives the reader the impression of grasping something ordinarily invisible. If it does not, the construction has no secure ground.

Unproved foundations and consequences

The decisive weakness is that the proofs treat π as a constant, while the book describes that status as not conclusively proved. Many mathematicians believe π is constant, but belief does not substitute for proof; until the premise is established, the argument rests on an assumption. The thesis therefore has two sharply opposed readings. If π is not accepted as a constant, the work’s reasoning collapses. If it is accepted, Rong Jinzhen’s achievement appears striking, and the proposed extension to artificial intelligence becomes consequential. The theory’s power is conditional on the very foundation it needs to secure.

The narrator accordingly distinguishes between the shared plausibility of the conclusion and the originality of Rong Jinzhen’s effort to prove it from a speculative premise. Strictly considered, the unresolved foundation leaves the thesis without established academic value; its demonstrable success is the intelligence and daring it displays. It does not change Rong Jinzhen’s life, but it does affect the final years of Young Lillie’s. The theory thus becomes more than a mathematical framework: it is the point at which an audacious argument, political suspicion, questions of authorship, and the limits of proof converge.