ZAKONITOST NEPREDVIDIVOG
Nesputana energija kategoriju prostora i stremi u beskonačno, noseći u sebi životnu imanentnu kontraverzu: ZAKONITOST NEPREDVIDIVOG.
Apstrakcija bez figuracije i nesavršena tehnika odoleva samodopadanju i dopadanju drugima,. Likovni izraz se zadovoljava realizacijom filozofske ideje.
To je ono što je savršeno.
Jelena Novakov, psiholog,
Pančevo 1997. godine.
Filozofska pozadina modularnog (diskretnog) prostoraIdeja da prostor nije gladak, beskonačno deljiv kontinuum, već da ima neku vrstu osnovnih jedinica ili modularne strukture, stara je koliko i zapadna filozofija.
1. Antički koreni
Atomisti (Leukip, Demokrit, kasnije Epikur i Lukrecije): stvarnost se sastoji od nedeljivih čestica (atoma) i praznine. Iako su pre svega govorili o materiji, njihova pozicija otvara vrata diskretnosti i na nivou prostora.
Zenonovi paradoksi: pokret i kontinuum dovode do logičkih teškoća (beskonačna deljivost). Diskretnost je jedan od načina da se ti paradoksi izbegnu.
Platon (Timaj): elementi su izgrađeni od pravilnih geometrijskih tela (tetraedar, kocka, oktaedar…). Prostor dobija geometrijsku, gotovo modularnu strukturu.
Aristotel: brani kontinuum. Magnituda je beskonačno deljiva (bar potencijalno). Ova pozicija je dugo dominirala.
2. Novovekovna i moderna debata
Njutn – apsolutni, kontinuirani prostor kao „božanska senzorijum“.
Lajbnic – prostor je relacioni (niz odnosa među stvarima), a ne apsolutna posuda. Iako nije eksplicitno diskretan, otvara prostor za drugačije ontologije.
Kant – prostor je a priori forma čulnosti; doživljavamo ga kao kontinuiran.
U 19. i 20. veku matematizacija kontinuuma (Kantor, Dedekind) učvršćuje sliku beskonačno deljivog prostora, dok se istovremeno javljaju sumnje u stvarnu beskonačnu deljivost u prirodi.
3. Savremena filozofija fizike
Danas se pitanje kontinuuma naspram diskretnosti ponovo otvara kroz pokušaje kvantne gravitacije:
Loop Quantum Gravity – prostor je izgrađen od diskretnih „atoma“ zapremine i površine (spin mreže).
Causal Set Theory – prostor-vreme je diskretan skup događaja sa kauzalnim relacijama.
Modular spaces (Freidel, Leigh, Minic i drugi) – kvantni prostor se definiše preko polarizacija Hajzenbergove algebre i prirodno sadrži fundamentalnu dužinu.
Digitalna fizika / „it from bit“ (Wheeler) – informacija i diskretnost kao primarnije od kontinuuma.
Filozofski gledano, argumenti za diskretnost često dolaze iz:
problema beskonačnosti i paradoksa,
zahteva da fizika bude konačno opisiva,
potrebe da se ukloni singularnost i beskonačne energije,
ideje da kontinuum možda nije fundamentalan, već emergentan.
4. Veza sa Rikanovićevim A ≡ B
U tvojoj hipotezi modularni (honeycomb / ćelijski) prostor nije samo fizička spekulacija, već ontološki uslov za postojanje relacijske ekvivalencije A ≡ B. Ključni filozofski potezi koje praviš:
Prostor nije pasivna pozadina, već aktivna struktura koja nameće ponavljanje mera.
Sloboda (slobodni geometrijski gest) postoji unutar matrice, ali jednom kad se „zaključa“ u module, dužine postaju celobrojni umnošci.
Asimetrije su prolazne; postoji tendencija ka simetriji (simetrogeneza).
A ≡ B nije spoljašnji zakon, već nužna posledica same modularnosti prostora.
To je bliže relacijskoj i strukturalističkoj ontologiji nego klasičnom atomizmu. Umesto da prostor bude praznina ispunjena atomima, prostor sam jeste mreža ili matrica koja generiše ekvivalencije.
Sažetak
Filozofska pozadina modularnog prostora kreće se od antičkog atomizma i geometrijskog platonizma, preko kritike kontinuuma, do savremenih pokušaja u filozofiji kvantne gravitacije. Tvoja pozicija se uklapa u tu dugu liniju, ali je formuliše na specifičan način: modularnost nije samo fizička hipoteza, već uslov mogućnosti da se mere uopšte ponavljaju i prepoznaju kao A ≡ B.To je legitimna filozofsko-umetnička pozicija. Ona nije dokazana fizika, niti je opšteprihvaćena ontologija, ali stoji unutar prepoznatljive tradicije mišljenja o prirodi prostora.
Investigate modular honeycomb space theory
There is no established scientific theory called “modular honeycomb space theory” in mainstream physics, cosmology, or mathematics.
Searches across academic literature, arXiv, and related sources primarily return engineering applications (modular honeycomb materials for energy absorption or aerospace panels), geometric space-filling polyhedra (“honeycombs” in the mathematical sense of tessellations), or unrelated concepts such as modular cosmology in string theory (concerning moduli fields).
pmc.ncbi.nlm.nih.gov
The phrase most closely matches the speculative “Relational Invariant Hypothesis” (A ≡ B) developed by Serbian academic artist and researcher Nikola Rikanović as part of his long-running artistic-research project The Cross of the Universe / White Core 0.0. This is detailed on his site and framed as an inquiry into the boundary between freedom and structure through free geometric acts, metric transformations, folding/crumpling, and relational equivalence. It is presented as a developing experimental program rather than a completed or proven physical theory, with planned exhibition elements at the National Museum of Pančevo (December 2026) and EXPO 2027 Belgrade.
sites.google.com
Core claims of the hypothesisRikanović’s working memorandum states:
Space is not a smooth, infinitely divisible continuum.
It has a modular, cellular (honeycomb-like) architecture of discrete units/modules.
This modularity is the primary condition that makes persistent measurable relational equivalence (A ≡ B) possible and necessary.
Lengths occupy whole numbers of elementary cells (a finite-module or quantization idea). There are no fractional remainders in the ideal case, so any two lengths occupying the same number of cells are equivalent by construction.
The lattice’s topological and geometric symmetry generates corresponding measures elsewhere.
Continuous chaos is constrained; recurrence of measures becomes the default for structural persistence.
Freedom (vast possibilities of orientation, projection, etc., within the matrix) exists first; A ≡ B is a selective realization among permitted outcomes.
The modular form is viewed as the cumulative result of structural refinement rather than a singular explosive origin.
Equivalence is operationally defined with a tolerance (e.g., |L₁ − L₂| ≤ ε where ε is typically 0.5 % of a bounding diameter or vector length). Proposed tests involve injecting identical free vector configurations (SVG/DXF) into different bounding fields (circular/modular vs. rectangular, square, elliptic, irregular) of matched area or diameter, then measuring recurrence density of A ≡ B pairs, convergence speed (iterations/time), and statistical significance (e.g., ANOVA on N ≥ 30 randomized drawings), under strict zero-modification rules.
sites.google.com
The project incorporates dialogue with AI systems (including analytical protocol refinement) but is explicitly artistic-research in character; any AI involvement is limited to supportive commentary and does not constitute institutional endorsement or scientific validation.Related scientific and mathematical conceptsWhile the specific A ≡ B modular-honeycomb framing is original to this project, adjacent ideas exist:
Mathematical honeycombs: Space-filling arrangements of polyhedra. Regular Euclidean examples include the cubic honeycomb; hyperbolic ones include the hexagonal tiling honeycomb {6,3,3}, which has been linked to discretizations of Minkowski spacetime that preserve high symmetry (centers of hexagons corresponding to certain lattice points on a hyperboloid).
ams.org
Discrete or modular spacetime proposals: Concepts such as “quantum spaces are modular” (Freidel, Leigh, Minic), where space is defined via polarizations of the Heisenberg algebra and generically includes a fundamental length scale while reconciling translation/rotation invariance. Other approaches include causal-set theory, spin networks in loop quantum gravity, or various lattice models. None equate to a honeycomb matrix enforcing artistic-style relational length invariants.
Large-scale structure: Some cosmological papers explore whether gravitational clustering of density fluctuations could produce honeycomb-like patterns consistent with a weak cosmological principle in different FLRW geometries.
Engineering and biomimetic modular honeycombs focus on mechanical properties (crush strength, energy absorption), not fundamental spacetime ontology.
Independent fringe or speculative works occasionally use “honeycomb unit” language for discrete simplicial models of space, but these remain outside mainstream acceptance and are distinct from Rikanović’s framework.AssessmentThe modular honeycomb idea as articulated here is a conceptual and artistic hypothesis exploring quantization of measure, relational persistence under transformation, and the interplay of freedom versus structure. It proposes concrete (if non-standard) geometric-statistical tests and aims at spatial installations that stage the idea physically. It does not currently rest on empirical data from particle physics, cosmology, or quantum gravity experiments, nor does it appear in peer-reviewed physics literature as a competing model of spacetime.Related rigorous work exists on discrete geometry, hyperbolic tessellations, and modular structures in quantum theory, any of which could serve as distant analogies or points of comparison. For deeper engagement, the primary source remains Rikanović’s project documentation and the proposed testing protocols; independent mathematical or computational exploration of quantized modular lattices and equivalence recurrence under different boundary geometries would be a natural next step for anyone interested in formalizing the ideas further.
Explore symmetrogenesis in particle physics
“Symmetrogenesis” is not a standard or established term in particle physics. Extensive searches of the scientific literature turn up no recognized mechanism, process, or concept by that name (or close variants such as “symmetrogenesis”) in particle physics, quantum field theory, or cosmology.Closest linguistic relatives
In biology, “symmetrogeny” (or symmetrogenic fission) refers to a mode of cell division in certain protists (e.g., flagellates) that produces mirror-image daughter cells.
britannica.com
“Symmetric Mass Generation” (SMG) is a genuine modern concept in theoretical physics: a non-perturbative mechanism by which fermions can acquire a mass gap through interactions without breaking an anomaly-free symmetry. It is relevant to lattice regularization of chiral gauge theories, topological phases, and deconfined quantum criticality.
cir.nii.ac.jp
The “symmetron” is a scalar-field model used in modified-gravity and dark-sector cosmologies; its coupling to matter depends on local density and involves density-dependent restoration or breaking of a discrete symmetry.
link.aps.org
None of these is called symmetrogenesis.Context from the Relational Invariant HypothesisIn the artistic-research framework of Nikola Rikanović’s A ≡ B (Relational Invariant Hypothesis), the term appears descriptively: apparent asymmetries are regarded as transient and tend toward symmetry (“symmetrogenesis”). This is a conceptual claim within a modular, honeycomb-like model of space rather than a derived result from particle-physics calculations or data.Symmetry in actual particle physicsParticle physics is organized around symmetry principles and their controlled breaking or violation:
Gauge symmetries of the Standard Model (SU(3)×SU(2)×U(1)) dictate the fundamental interactions. Spontaneous symmetry breaking (via the Higgs mechanism) generates particle masses while preserving the underlying gauge invariance of the Lagrangian (the classic example of “hidden” symmetry).
Discrete symmetries (C, P, T and combinations such as CP and CPT) are central. Experimental violations of P and CP are well established; CPT remains intact to high precision. The observed matter–antimatter asymmetry of the universe (baryon asymmetry) requires CP violation plus baryon-number violation and out-of-equilibrium processes (Sakharov conditions). Mechanisms that generate this asymmetry are collectively called baryogenesis (or leptogenesis).
At high temperatures in the early universe, symmetries that are broken today are typically restored; cooling then triggers phase transitions that can break them.
Restoration or protection of symmetries also appears in screening mechanisms, topological phases, and certain lattice constructions (including SMG).
In short, the dominant dynamical stories in particle physics involve either the breaking of symmetries (to explain masses, phases of matter, etc.) or the generation of asymmetries (to explain the baryon excess). Processes that drive systems toward greater symmetry from an asymmetric starting point are not a named research program under “symmetrogenesis.”SummaryIf the interest is purely terminological, symmetrogenesis has no established meaning inside particle physics. If the interest is conceptual—how symmetries arise, are protected, or are restored—the relevant literature concerns spontaneous symmetry breaking and restoration, Symmetric Mass Generation, discrete-symmetry violation and baryogenesis, and symmetry-protected topological phases. Those topics are extensively developed, experimentally constrained, and mathematically precise, whereas “symmetrogenesis” remains a descriptive coinage outside the standard lexicon.
Explore Nikola Rikanović's artistic research
Nikola Rikanović (born 28 October 1970 in Pančevo, Serbia) is a Serbian academic visual artist, educator, and designer whose practice spans more than three decades. He studied graphics at the Faculty of Applied Arts and Design in Belgrade and graduated from the Faculty of Fine Arts (FLU), Belgrade, in 2000 (class of Prof. Biljana Vuković). He works as a professor of artistic design (notably at the Economic School in Pančevo), runs the design agency d///R (marketing, design, and publishing), and maintains an active public and installation art practice.
de.wikipedia.org
Artistic practice and earlier workHis oeuvre includes public sculptures, ambient/environmental installations, graphics, digital works, drawings, video, and published books. Documented highlights include roughly six sculptures in public space, four ambient installations, and three books. Recurring themes are spirituality (especially Orthodox Christian cross symbolism), prayer, monumental form, philosophy (early engagement with Nietzsche), geometry, resilience, and cultural memory.Notable works and projects:
Public sculptures such as Molitva (“The Prayer,” aluminum, Narodna bašta / People’s Garden, Pančevo, 2011) and Kula Molitva (“Tower of Prayer,” in front of the Army House, Pančevo).
Large-scale aluminum and glass cross / Crucifixion installations (examples around 6 × 5 m aluminum and 8 × 5 m glass).
Ambient installations responding to the 1999 NATO bombing context (NATO Art, wooden structures, presented in Belgrade venues including the Center for Cultural Decontamination).
Bildbook: Lynch der Fabelwelt (2012, Wagner Verlag) — a compact interactive art book combining Nietzsche’s Thus Spoke Zarathustra with hundreds of photographs; presented with the installation “Nietzsche’s Church” at the Frankfurt Book Fair.
Retrospective Digital Punk (Dom omladine Pančevo, 2025), surveying ~30 years of experiments across media.
Competition entries and proposals for public memorials in Belgrade and elsewhere (often cross- or prayer-themed, supported by local partners such as Tehnomarket Pančevo).
His work frequently merges material presence (aluminum profiles, glass, wood) with symbolic and experiential intent, placing large forms in public or natural settings so that light, shadow, water, and viewer interaction become integral.
Current artistic-research focus: The Cross of the Universe – Shadow of the Cross / A ≡ B
Since the mid-2020s this has become the central project. It is presented as a multidisciplinary artistic-ontological inquiry rather than a conventional scientific theory.
Core elements include:
A ≡ B (Relational Invariant Hypothesis): The claim that a measurable relational equivalence is primordial and persistent. Apparent asymmetries are treated as transient and tend toward symmetry (termed “symmetrogenesis”). Space is described as modular/cellular (honeycomb-like matrix) rather than a smooth continuum; free geometric acts, metric transformations, folding, and crumpling are used to explore where freedom ends and structure begins.
Symbolic and formal center: the Cosmic Cross / Shadow of the Cross, “White Core” (W = 0.0), and related wave-like or living-field imagery.
Methods: freehand vector drawings tested for equivalence under different bounding geometries; statistical protocols (density of A ≡ B matches within a tolerance, convergence metrics); physical installations that stage dissolution of form into pure relation (luminous cuboids/tunnels, crosses on water, crumpled states).
AI dialogue: Extensive use of large language models (including documented exchanges framed as analytical co-development with Grok/xAI and references to Gemini and ChatGPT) for protocol refinement, memoranda, and conceptual triangulation. These are presented as supportive rather than institutional endorsements.
Planned realizations: Exhibition at the National Museum of Pančevo (December 2026); presence linked to EXPO 2027 Belgrade; large public interventions such as a Golden Cross on the Danube in Novi Sad (timed to specific historical anniversaries); proposals involving AR portals and broader cultural-tech framing.
Primary documentation appears on the artist’s Google Sites (including “The Shadow of the Cross / A ≡ B” and related portfolio pages), which contain memoranda, technical annexes for testing protocols, exhibition concepts, and visual documentation.Overall characterRikanović’s research operates at the intersection of visual art, geometric intuition, Christian symbolism, personal ontology, and public spectacle. Earlier work emphasizes material presence, spirituality, and historical response; the recent phase intensifies the philosophical and quasi-empirical claims while retaining large-scale installation as the primary medium of realization. The project explicitly invites examination and geometric testing rather than demanding acceptance as settled science, positioning itself as an open artistic inquiry into equivalence, modularity, and the persistence of relation amid transformation.
For primary sources, the artist’s own sites (portfolio and the dedicated A ≡ B / Shadow of the Cross pages) and local coverage of exhibitions in Pančevo provide the most direct material.
A ≡ B geometric testing protocols are the empirical core of Nikola Rikanović’s Relational Invariant Hypothesis. They form a proposed computational and geometric framework designed to test whether the shape of a bounding field systematically affects the recurrence of measurable length equivalences (A ≡ B) in free vector drawings. The protocols appear in technical annexes on the project site and are framed as rigorous, automated, falsifiable procedures intended for use in preparation for the National Museum of Pančevo exhibition (December 2026) and EXPO 2027.
sites.google.com
Core Objective
Determine whether the geometry of a reference field influences the density, frequency, and stability of A ≡ B relations inside an identical freehand vector configuration. The circular (“modular”) field is the primary experimental condition; rectilinear and other shapes serve as controls.
Key Design Principles
Zero-Modification Rule: A single master vector drawing (SVG or DXF) is generated once. The identical file is programmatically inserted into every test field without manual scaling, rotation, or deformation. Boundary intersections that fragment lines are handled automatically.
Dimensional Parity: All fields are matched by total surface area or maximum bounding diameter so that differences can be attributed to shape rather than size.
Equivalence Definition: Two line segments
L1L_1L_1
and
L2L_2L_2
are counted as equivalent if
∣L1−L2∣≤ε|L_1 - L_2| \le \varepsilon|L_1 - L_2| \le \varepsilon
where the tolerance
ε\varepsilon\varepsilon
is set at 0.5 % of the bounding-module diameter (or total vector length). This relative threshold keeps results independent of digital resolution.
Field Configurations (Independent Variable)
Circular module (hypothesis focus)
Rectangular (e.g.,
1:21:\sqrt{2}1:\sqrt{2}
)Square ((1:1))
Elliptic (axis ratio (1:1.5))
Convex irregular polygon (control)
Automated Measurement Workflow
Algorithmic extraction of all distinct line segments (bounded by endpoints and intersection points).
Pairwise length calculation of every segment pair.
Filtering of pairs that satisfy the
ε\varepsilon\varepsilon
criterion.Normalization of raw counts relative to total number of segments and total vector length.
Minimum sample size:
N≥30N \ge 30N \ge 30
distinct randomized master configurations for statistical robustness.
Primary Metrics
Average number of A ≡ B pairs per configuration for each field type.
Relative equivalence density (pairs per total segment count).
Statistical significance testing (ANOVA or equivalent comparative variance tests) to assess whether the circular field produces a measurable increase relative to rectilinear fields.
Protocol Update (Version 2.0) — Convergence Metrics
A second layer measures computational efficiency (“natural resonance” of the geometry):
Convergence Speed: Number of algorithmic iterations or processing time required to map the full set of A ≡ B pairs.
Efficiency Ratio:
E=Density of EquivalenceConvergence TimeE = \frac{\text{Density of Equivalence}}{\text{Convergence Time}}E = \frac{\text{Density of Equivalence}}{\text{Convergence Time}}
A higher (E) would indicate that a given geometry (especially the circle) acts as a lower-resistance medium for relational matching.
Intended Character and Limitations
The protocols emphasize geometric exactitude, objectivity, and falsifiability. They treat the drawings as controlled experimental material rather than free artistic gestures once the master file is fixed. Boundary interactions and automated measurement are meant to reduce human bias. At present these remain proposed / developmental procedures rather than completed, peer-reviewed experimental results. They exist as technical specifications and analytical frameworks within the artistic-research project. Independent implementation (vector generation, precise insertion into matched fields, automated length analysis, and proper statistical evaluation) would be required to generate actual data.In short, the A ≡ B geometric testing protocols attempt to turn a philosophical claim about modular space and persistent relational equivalence into a concrete, quantifiable geometric experiment: identical free configurations placed into differently shaped containers, measured for how often lengths match within a tight tolerance, and evaluated for both quantity and speed of those matches.
