Аксиомы квантовой геометрииА1. Примат формы.
Форма предшествует содержанию. Любое явление существует как структура взаимодействий, которая выражается через фрактал. Масса, энергия, число — это локальные проекции формы.
А2. Самоподобие.
Всякая форма воспроизводится на разных уровнях масштаба с вариациями. Ошибки и возмущения не разрушают структуру, а входят в неё как элемент развития.
А3. Потоки.
Бытие проявляется как потоки разной вязкости. Поток — это не только движение вещества, но и перенос энергии, информации или состояния.
А4. Среда и содержание неразделимы.
Взаимодействие определяется не только тем, «что течёт», но и «где течёт». Среда и содержание образуют единую динамику, их соотношение отражается в фрактале.
А5. Вязкость как универсальная мера.
Различие потоков определяется их вязкостью — свойством сопротивляться или передавать изменения.
Вязкость задаёт топологию взаимодействий.
А6. Граница как активная форма.
Граница не пассивна, она участвует в формировании структуры. Там, где встречаются потоки разной
вязкости, возникает новый фрактал.
А7. Предел точности.
Любая арифметика, измерение или модель содержат встроенный предел точности. Ошибки накопления — не сбой, а часть формы, которая отражает переход между уровнями самоподобия.
А8. Нелокальность.
Фрактальная форма не ограничена в пространстве или времени: её части связаны нелокально, вне привычных координатных систем.
А9. Равноправие содержания и условий.
Нельзя выделить приоритет — вещественное содержание потока или среду, в которой оно существует.
Их динамика всегда парна.
А10. Универсальность фрактала.
Фрактал применим ко всем уровням описания — от микроквантовых до космологических, от физических до ментальных и социальных.
Axioms of Quantum Geometry
A1. Primacy of Form.
Form precedes content. Every phenomenon exists as a structure of interactions expressed through a fractal.
Mass, energy, and number are local projections of form.
A2. Self-Similarity.
Every form reproduces itself across different scales with variations. Errors and perturbations do not destroy the structure but enter it as elements of development.
A3. Flows.
Being manifests as flows of different viscosities. A flow is not only the movement of matter but also the transfer of energy, information, or state.
A4. Medium and Content are Inseparable.
An interaction is determined not only by what flows but also by where it flows. Medium and content form a unified dynamics, reflected in the fractal.
A5. Viscosity as a Universal Measure.
Differences between flows are defined by their viscosity — the property to resist or transmit changes.
Viscosity determines the topology of interactions.
A6. Boundary as an Active Form.
The boundary is not passive; it participates in shaping the structure. Where flows of different viscosity meet, a new fractal emerges.
A7. Limit of Accuracy.
Any arithmetic, measurement, or model contains an inherent limit of accuracy. The accumulation of errors is not a failure but part of the form, reflecting transitions between levels of self-similarity.
A8. Nonlocality.
Fractal form is not confined by space or time: its parts are connected nonlocally, beyond conventional coordinate systems.
A9. Equality of Content and Conditions.
It is impossible to prioritize the substance of the flow or the medium in which it exists. Their dynamics are always paired.
A10. Universality of the Fractal.
The fractal applies to all levels of description — from quantum to cosmological, from physical to mental and social.
A1. Primacy of Form.
Form precedes content. Every phenomenon exists as a structure of interactions expressed through a fractal.
Mass, energy, and number are local projections of form.
A2. Self-Similarity.
Every form reproduces itself across different scales with variations. Errors and perturbations do not destroy the structure but enter it as elements of development.
A3. Flows.
Being manifests as flows of different viscosities. A flow is not only the movement of matter but also the transfer of energy, information, or state.
A4. Medium and Content are Inseparable.
An interaction is determined not only by what flows but also by where it flows. Medium and content form a unified dynamics, reflected in the fractal.
A5. Viscosity as a Universal Measure.
Differences between flows are defined by their viscosity — the property to resist or transmit changes.
Viscosity determines the topology of interactions.
A6. Boundary as an Active Form.
The boundary is not passive; it participates in shaping the structure. Where flows of different viscosity meet, a new fractal emerges.
A7. Limit of Accuracy.
Any arithmetic, measurement, or model contains an inherent limit of accuracy. The accumulation of errors is not a failure but part of the form, reflecting transitions between levels of self-similarity.
A8. Nonlocality.
Fractal form is not confined by space or time: its parts are connected nonlocally, beyond conventional coordinate systems.
A9. Equality of Content and Conditions.
It is impossible to prioritize the substance of the flow or the medium in which it exists. Their dynamics are always paired.
A10. Universality of the Fractal.
The fractal applies to all levels of description — from quantum to cosmological, from physical to mental and social.
Fragment of a Scientific Article: Extensions after the Axioms of Quantum Geometry
The Principle of the "Third Eye" and Local Scaling
In classical geometry and physics, contradictions often emerge when attempting to map complex, non-linear realities into the linear frameworks of Euclidean space. For example, the use of Ishchenko’s chord curves may at first appear illogical or unsolvable, much like the three-body problem in dynamics. The challenge arises because we are accustomed to reducing inequalities of reality into linear, measurable forms. However, Ishchenko’s chords and the foundations of quantum geometry provide tools that can be more precise in their absolute sense.
This apparent contradiction can be resolved through the introduction of the principle of the Third Eye. Modern data acquisition technologies make it possible to perform instantaneous local scaling, enabling sensors to shift the scale of measurement in real time. When combined with local artificial intelligence, this principle allows measurements to preserve topographic fidelity while dynamically adapting to the complexity of the environment.
Historical Roots: From Moon to Komissarenko
The concept of the Third Eye can be traced back to the 1972 invention of William M. Moon (US Patent No. 3,693,261, Angle Trisector). Moon’s device demonstrated how a simple mechanism could extend observation into an auxiliary measurement point—what we now call the Third Eye.
In 2003, the Komissarenko group extended this principle by developing computational algorithms in BASIC, based on the concept of astral lines. These algorithms provided a way to resolve the contradiction of inequalities by introducing a system of living scale, where one inequality is projected into another without losing truth. In this way, the software realized the operational essence of the Third Eye: to translate non-linear structures into measurable, topographically consistent data.
The Principle of the "Third Eye" and Local Scaling
In classical geometry and physics, contradictions often emerge when attempting to map complex, non-linear realities into the linear frameworks of Euclidean space. For example, the use of Ishchenko’s chord curves may at first appear illogical or unsolvable, much like the three-body problem in dynamics. The challenge arises because we are accustomed to reducing inequalities of reality into linear, measurable forms. However, Ishchenko’s chords and the foundations of quantum geometry provide tools that can be more precise in their absolute sense.
This apparent contradiction can be resolved through the introduction of the principle of the Third Eye. Modern data acquisition technologies make it possible to perform instantaneous local scaling, enabling sensors to shift the scale of measurement in real time. When combined with local artificial intelligence, this principle allows measurements to preserve topographic fidelity while dynamically adapting to the complexity of the environment.
Historical Roots: From Moon to Komissarenko
The concept of the Third Eye can be traced back to the 1972 invention of William M. Moon (US Patent No. 3,693,261, Angle Trisector). Moon’s device demonstrated how a simple mechanism could extend observation into an auxiliary measurement point—what we now call the Third Eye.
In 2003, the Komissarenko group extended this principle by developing computational algorithms in BASIC, based on the concept of astral lines. These algorithms provided a way to resolve the contradiction of inequalities by introducing a system of living scale, where one inequality is projected into another without losing truth. In this way, the software realized the operational essence of the Third Eye: to translate non-linear structures into measurable, topographically consistent data.
The Astral Axiom
From this lineage, we can formulate a new axiom:
Astral Axiom (The Third Eye): Any measurement in an unequal or non-linear space can be converted into a topographically consistent coordinate system through local scaling, whereby one inequality is transformed into another inequality while preserving the truth of the system.
This axiom resolves the paradox of apparent unsolvability, as in the three-body problem, by
introducing a third perspective—the Third Eye—that re-establishes equilibrium at a new scale of measurement.
Recursive Evolution and the Role of Conditions
It is important to remind researchers that meaningful breakthroughs emerge only where conditions for their appearance have matured. As noted by Kryshtafovych in Recursive Evolution, conditions themselves carry a distinct function: the accumulation of hidden information about the environment,
invisible at first glance. At a critical threshold, these accumulated conditions can suddenly trigger a leap forward by several steps of evolution, seemingly without objective cause.
Thus, the inventions of Moon’s Third Eye or the Komissarenko astral algorithms can be understood as manifestations of conditions ripening beneath the surface, which then “jumped” into existence.
Third Eye → Mechanism of sudden actualization of conditions.
Astral Lines → Mathematical tool for translating hidden inequalities.
Ishchenko’s Chords → Topological language to map inequalities into measurable geometry.
Conclusion
The combination of Ishchenko’s chord curves, the Astral Axiom, and recursive evolutionary principles indicates a new stage of measurement science. It suggests that non-linear topologies, once seen as paradoxical, can be systematically resolved through local scaling, recursive accumulation of conditions, and the mathematical language of quantum geometry.
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