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Why Ternary Was Eliminated

Author: Zhang Suhang

(Luoyang, Henan)

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Abstract

The balanced ternary computer Setun possessed advantages in information density at the mathematical level, yet it was ultimately discontinued entirely and withdrew from the general-purpose electronic computing track. As the second article in the "Failure of Ternary" series, this paper continues from the historical review in the first article. Starting from the underlying principle of symmetry conservation, it proposes a core criterion for determining numeral bases: one of the main objects of mathematical research is symmetry conservation; most numeral base structures naturally possess a dual-pair property; silicon-based hardware takes the two dual stable states of conduction and cutoff as its physical foundation, and binary and other even-numbered bases can be constructed into paired, mutually canceling energy dual closed loops, whereas balanced ternary contains an independent middle zero state that cannot be paired, naturally breaking the dual closed-loop structure. This paper fully dismantles the four layers of core causes behind the elimination of Setun ternary: the physical asymmetry defect in which odd-numbered bases inherently destroy the dual closed loop, the hard constraint of noise margin in early electronic devices, the global lock-in of the binary standardization ecosystem, and the deviation in planned-economy industrial policy orientation. This paper dialectically distinguishes the theoretical advantages of ternary in subdivided scenarios from its innate shortcomings as an underlying foundation for general-purpose computing, summarizes the historical experience and engineering lessons of paradigm competition, and inversely corroborates the natural rationality of even-numbered bases such as binary as the underlying architecture of general-purpose intelligence, providing a basis for paradigm selection in the hardware design of multimodal long-duration signal processing.

Keywords: balanced ternary; dual closed loop; symmetry conservation; noise margin; computing paradigm competition; dissipative structures

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1 Introduction

1.1 Continuation and Positioning

The first article in the series completed a historical review of the Setun balanced ternary computer, organized the theoretical advantages of balanced ternary at three levels—information density, signed-number adaptation, and fuzzy logic compatibility—and defined its reasonable boundaries of applicability in subdivided scenarios such as quantum computing and sparse AI inference.

As the second article in the series, this paper undertakes the task of arguing the "elimination mechanisms." The core question is: why was a computing paradigm that possessed mathematical advantages, was actually mass-produced in engineering, and operated stably for more than a decade ultimately eliminated entirely?

The answer of this paper is: this was not an accidental outcome caused by a single factor, but the inevitable result of four layers of factors acting in combination—underlying physical constraints, process adaptability, ecosystem lock-in, and policy orientation. Among these, the underlying physical constraint that odd-numbered bases destroy the dual closed loop of silicon-based hardware is the decisive internal cause that cannot be eradicated.

1.2 Core Criterion

The core criterion of this paper can be reduced to three statements:

1. One of the main objects of mathematical research is symmetry conservation. Symmetry and conservation are the shared underlying language of mathematics and physics.

2. Most numeral base structures naturally possess a dual-pair property. Even-numbered bases are naturally paired; odd-numbered bases are naturally broken.

3. Binary and circuit carriers are naturally adapted. The two dual stable states of silicon-based hardware correspond exactly to the two states of binary.

The demise of the ternary computer is, in essence, a concrete historical verification of this criterion.

1.3 Argumentation Structure

This paper unfolds along four layers of elimination causes: innate physical defects (decisive internal cause), lack of semiconductor process adaptability (medium-term engineering shortcoming), global binary ecosystem lock-in (industrial macro barrier), and planned-economy policy deviation (direct external trigger). Among the four layers, the first is a structural defect that cannot be eradicated, while the latter three are superimposed factors that accelerated death.

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2 Innate Underlying Physical Defects (Decisive Internal Cause)

2.1 The Dual Nature of Silicon-Based Hardware

The physical essence of silicon-based hardware such as transistors and magnetic cores is the binary dual switch. It has only two stable energy states: conduction and cutoff. These two states exist in pairs, can mutually cancel each other, and form a complete dual closed loop.

The so-called dual closed loop means that all states of the system can be paired two by two to form a symmetric energy structure, enabling the system to maintain energy gradient balance and controlled entropy production during long-term operation. The state sets of even-numbered bases can naturally be decomposed into multiple layers of binary superposition, with all states paired two by two and the closed loop complete.

2.2 The Isolated Middle State of Balanced Ternary

Balanced ternary forcibly divides three voltage intervals (-V, 0, +V). Among these, -V and +V can form a dual pair, but 0 is an isolated middle state with no corresponding object for cancellation.

The existence of this isolated middle state directly destroys the global dual closed-loop structure. The system can no longer be paired two by two, and an asymmetric energy offset that cannot be hedged appears.

2.3 Voltage Window Compression and Noise Margin Decline

After the voltage window is divided into three equal parts, the voltage interval occupied by a single state is significantly compressed. Binary possesses ample noise margin, and temperature drift and electromagnetic interference are not yet sufficient to cause level misjudgment; ternary's voltage fault-tolerance interval is greatly narrowed, and under the same interference it is extremely easy to cause level misjudgment.

The overall machine computation error rate is far higher than that of binary. This is an engineering reality that ternary could not avoid under early electronic device conditions.

2.4 Thermodynamic Consequences: Entropy Production Accumulation and Local Hot Spots

From the perspective of fluctuation thermodynamics:

· All states of even-numbered bases can be coupled in pairs to cancel excess entropy production; the closed loop is complete, and the system has good thermodynamic stability during long-term operation;

· The isolated zero state of odd-numbered bases cannot form energy hedging; the system continuously has an asymmetric energy offset, and long-duration high-load computation is prone to local hot spots, exacerbating hardware instability.

This defect is determined by the underlying structure in which odd-numbered bases destroy the dual closed loop and cannot be completely eliminated through circuit optimization or process improvement. This is the decisive internal cause of ternary's elimination.

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3 Lack of Adaptability in Semiconductor Process Iteration (Medium-Term Engineering Shortcoming)

3.1 Early Processes Were Barely Feasible

The first generation of Setun used magnetic core diodes to construct three-state units. In the era of vacuum tubes, device dimensions were relatively large, and three-state levels could still barely remain stable. During this period, the physical defects of ternary had not yet been amplified by process advances.

3.2 Adaptation Rupture in the Integrated Circuit Era

In the 1960s, integrated circuits and silicon transistor technology spread rapidly. Global semiconductor production lines were all designed around binary threshold doping, naturally adapting to the dual closed-loop structure of the hardware itself. There was no standardized manufacturing process adapted to three-state levels.

If ternary chips were to be mass-produced, entirely new customized lithography, doping, and testing equipment would be required, manufacturing costs and calibration labor hours would increase significantly, and yield rates would be low.

3.3 The Cost Gap Under the Miniaturization Trend

Binary MOS transistors, relying on the dual closed loop, can scale down indefinitely according to Moore's Law; three-state devices, because of the broken closed loop, face physical bottlenecks in miniaturization.

As processes iterated, the long-term engineering cost gap between the two continued to widen. The binary route became smoother and smoother, while the ternary route became more and more difficult. This is a structural disadvantage at the process level, not something that can be compensated for by short-term investment.

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4 Global Binary Standardization Ecosystem Lock-In (Industrial Macro Barrier)

4.1 Unification of Binary Standards During the Cold War

During the Cold War, Europe and the United States fully unified binary software and hardware standards: instruction sets, compilers, programming languages, storage media, and communication buses were all built on binary dual closed-loop logic, forming a complete closed-loop industrial ecosystem.

The underlying logic of this ecosystem was naturally consistent with the dual nature of silicon-based hardware and possessed the inertia of self-reinforcement and self-expansion.

4.2 Ecosystem Fragmentation of Ternary

Setun ternary software and hardware were completely independent; its underlying states could not be paired and canceled, and its hardware logic was fragmented from the mainstream system. It could not be compatible with mainstream binary devices at home or abroad, and data transmission, program migration, and talent cultivation all required rebuilding the ecosystem from zero.

4.3 The Inevitable Disadvantage of a Niche Paradigm Against a Global Standard

A niche paradigm from a single country cannot compete with a globally unified technical standard. Resources for research and development, teaching, and industrial application continued to shrink, forming a vicious cycle.

Ecosystem fragmentation was the industrial macro barrier to ternary's demise. It did not depend on whether ternary itself was excellent, but on whether it could be embedded in the mainstream ecosystem. This point still has reference value for today's new hardware paradigms.

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5 Planned-Economy Industrial Policy and Market Orientation Deviation (Direct External Trigger)

5.1 Conflict with Factory Economic Interests

Setun used few components and had a low selling price, leaving manufacturers with meager profits. Manufacturers resisted mass production, artificially limited capacity, and refused market orders. Technical simplicity instead became an obstacle to promotion commercially.

5.2 Top-Level Research Resource Tilting

In 1968, the Soviet Union launched the unified EC series computer plan, fully benchmarking the IBM binary architecture built on the dual closed loop. Funding for the indigenous original ternary project was cut, and resources were concentrated in directions compatible with mainstream standards.

5.3 Path Bias at the Academic Level

Some university administrators judged ternary to be a "non-mainstream route," cut laboratory implementation resources, and caused a break in the talent pipeline. Frontier exploration was gradually marginalized under the squeeze of mainstream standards.

5.4 The Outcome of Multiple Policy Factors Acting Together

Multiple external policy factors acted in combination, and in 1965 Setun mass production was fully stopped, and the general-purpose ternary computing route was completely shelved. This was the direct external trigger, but the root cause still lay in underlying physical defects and industrial ecosystem barriers.

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6 The Irreconcilable Underlying Contradiction Between Ternary's Theoretical Advantages and General-Purpose Computing

6.1 Objective Recognition of Theoretical Advantages

Balanced ternary possesses objective advantages in subdivided scenarios:

1. Mathematical extremum of information density: a single trit carries more information than a single bit;

2. Native adaptation to signed numbers: no two's complement conversion needed, and subtraction reuses addition circuits;

3. Fuzzy logic adaptation: three states can directly correspond to "yes, no, uncertain."

6.2 Innate Contradictions That Cannot Be Compensated for in General-Purpose Computing Scenarios

1. It destroys the inherent dual closed loop of silicon-based hardware. The underlying hardware is a binary energy-pairing closed loop; odd-numbered bases contain an isolated middle zero state that permanently destroys the global dual closed loop, and noise and thermal imbalance problems cannot be eradicated.

2. Noise and thermodynamic stability margins are seriously insufficient. Under the same supply voltage, the larger the base, the narrower the voltage interval of a single state; the middle zero state of odd-numbered bases has no dual compensation, and its fault-tolerance space is far lower than that of even-numbered bases.

3. The mathematical logic system cannot be compatible with the classical Boolean framework. Modern digital circuits and algorithm theory are all built on binary Boolean dual logic; three-valued logic is an independent branch, and general scenarios require an additional logic conversion layer.

4. Ecosystem construction costs rise exponentially. Binary has formed a complete standard through a century of iteration; ternary would require reconstructing the entire set of devices, instruction sets, compilers, and operating systems, and the cost of rebuilding the entire industrial chain is extremely high.

6.3 Reasonable Boundaries of Applicability

This paper does not wholly deny the value of ternary; it merely defines its subdivided specialized scenarios:

· Quantum computing qutrit three-state systems and photonic polarization optical computing;

· Lightweight sparse AI inference and fuzzy logic controllers;

· Small specialized embedded short-duration numerical computing devices.

The above scenarios have limited operating duration and small load fluctuations, and tolerate noise and thermal imbalance more readily. They can temporarily avoid the long-term loss problems caused by the broken dual closed loop and give play to the mathematical expression advantages of ternary.

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7 Core Experience and Failure Lessons of Paradigm Competition

7.1 Historical Experience: Paradigm Selection Must Fit the Physical Laws of the Hardware's Underlying Dual Closed Loop

1. No general-purpose computing paradigm can depart from the intrinsic stable-state pairing structure of matter: silicon transistors are naturally binary dual closed loops, and general-purpose hardware should preferentially choose even-numbered bases;

2. Relying solely on the high efficiency of mathematical theory is insufficient to support the popularization of a paradigm; the completeness of the dual closed loop, thermodynamic constraints, and process realizability have higher priority than paper information density;

3. New paradigm design must be compatible with existing mature systems and avoid completely severing the ecosystem.

7.2 Failure Lessons

7.2.1 Underlying Design Lesson: Do Not Choose Odd-Numbered Bases That Destroy the Dual Closed Loop

General-purpose intelligent hardware and long-duration continuous signal processing scenarios must avoid odd-numbered bases. Because of the isolated middle state, odd-numbered bases break the dual closed loop and continuously amplify noise and thermal entropy production defects; hardware stability has a natural upper limit.

7.2.2 Industrial Strategy Lesson: New Paradigms Must Adapt to the Global Standardized System

Niche original paradigms must not completely depart from existing mainstream industrial standards; compatible transition schemes should be designed, relying on mature dual closed-loop systems to lower the threshold for implementation.

7.2.3 Engineering Thermodynamics Lesson: The Completeness of the Dual Closed Loop Directly Determines the System's Entropy Production Rate

Odd-numbered bases have no symmetric energy cancellation mechanism, and the rate of heat accumulation in high-load computation is far higher than that of even-numbered bases with a complete dual closed loop. In long-duration continuous signal acquisition and simulation scenarios, a complete dual-pairing structure can significantly reduce energy loss.

7.2.4 Industrial Policy Lesson: Frontier Technology Implementation Must Take Into Account Industrial Chain Economic Returns

New technologies must not only possess theoretical performance advantages, but also adapt to factory mass-production profits and industrial chain cost structures, balancing technological innovation with industrial commercial logic.

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8 Summary of the Underlying Laws of Paradigm Selection

By sorting out the underlying symmetry laws of numeral bases, a clear judgment logic can be obtained:

1. Silicon-based hardware is based on even-numbered bases: binary, with paired switches forming the basic dual closed loop, adapts to the vast majority of general-purpose digital circuits and computing scenarios;

2. Odd-numbered bases: contain an isolated middle state, destroy the global dual closed loop, and are suitable only for short-term, low-load specialized subdivided scenarios; they cannot support long-term high-load general-purpose computing.

Even-numbered bases with a complete dual closed loop have paired energy states that can mutually cancel losses, and do not have the asymmetric offset, insufficient noise tolerance, and thermal imbalance defects brought by the isolated middle state of ternary. They satisfy multiple requirements—physical stability, computational efficiency, and engineering implementation—and are the preferred paradigm for general-purpose long-duration computing hardware.

Reviewing the demise of Setun ternary is not simply a denial of multi-base technological exploration, but rather the establishment of a set of paradigm selection evaluation criteria centered on the underlying stability of matter, thermodynamic constraints, and industrial compatibility, thereby improving the theoretical boundaries of numeral base design in information science.

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9 Conclusion

1. The demise of the Soviet Setun balanced ternary computer was the inevitable result of multiple factors acting in combination: innate underlying physical defects, shortcomings in semiconductor process adaptability, global binary ecosystem lock-in, and industrial policy deviation. Among these, the underlying constraint that odd-numbered bases destroy the binary dual stable-state closed loop of silicon transistors is the core internal cause that cannot be eradicated.

2. Balanced ternary possesses theoretical advantages only in subdivided scenarios such as mathematical expression and short-duration sparse computation. Because of the energy asymmetry, insufficient noise margin, and thermodynamic stability shortcomings brought by its odd-numbered hierarchy, it is not suitable for general-purpose electronic computing and long-term continuous signal processing.

3. The core criterion for base selection can be clearly stated: for dissipative information systems oriented toward continuous, high-load, long-duration operation, even-numbered bases should be preferentially selected, relying on paired symmetric modes to form a complete dual closed loop and suppress entropy production overflow and signal drift; odd-numbered bases, because of the existence of a non-dual middle state, have an inherently brittle system structure.

4. The failure history of Setun ternary provides key paradigm lessons for next-generation hardware research and development: in selecting hardware for general-purpose long-duration computation, priority must be given to ensuring a complete dual closed-loop structure, avoiding odd-numbered bases that destroy symmetric pairing, and balancing theoretical self-consistency, engineering implementation, and long-term operational stability.

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References

[1] Brusentsov N P. Setun: The Balanced Ternary Computer[R]. Moscow State University, 1959.

[2] Knuth D E. The Art of Computer Programming (Volume 2)[M]. China Machine Press, 2019.

[3] Analysis of Noise Margin and Thermodynamic Loss in Balanced Ternary Circuits[J]. Microelectronics & Computer, 2025.

[4] Analysis of Industrial Policy in the Discontinuation History of the Setun Ternary Computer[EB/OL]. Habr, 2026.

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