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Measuring Primitive Accumulation: An Information-Theoretic Approach to Capitalist Enclosure in PIK2, Indonesia
Sandy Hardian Susanto Herho, Alfita Puspa Handayani, Karina Aprilia Sujatmiko, Faruq Khadami, Iwan Pramesti Anwar, Rusmawan Suwarman, Dasapta Erwin Irawan, Deny Juanda Puradimaja
TL;DR
Quantifying the velocity, topology, and irreversibility of contested mega-development remains difficult. This paper applies information-geometric, Markov-chain, and percolation analyses to PIK2, identifying a 2019–2020 construction pulse and planned connectivity at unusually low occupation probabilities.
Problem
Urban-growth models are seldom integrated with political-economy categories to quantify the velocity, topology, and irreversibility of contested spatial enclosure.
Method
The study combines Fisher–Rao geometry, absorbing Markov chains, and site percolation to measure landscape transformation, conversion horizons, connectivity, and frontier morphology.
Results
At p ≈ 0.10–0.16, a giant component contains over 89% of built pixels, while 2019–2020 records the highest reduced-simplex velocity of 0.405 rad/yr.
Takeaways & Limitations
The framework provides a statistical-mechanical diagnostic of the kinematic, stochastic, and topological signatures of spatial enclosure in georeferenced LULC time series.
Takeaways & Limitations
Expected absorption times assume a stationary transition matrix, although the G-test decisively rejects stationarity.
Abstract
from arXiv · showhide
Large-scale land enclosure for speculative mega-development constitutes a non-equilibrium spatial process whose velocity, topology, and irreversibility remain poorly quantified. We study the Pantai Indah Kapuk 2 (PIK2) coastal mega-development north of Jakarta, Indonesia, using eight years (2017--2024) of Sentinel-2 land-use/land-cover (LULC) data at 10-meter resolution. The landscape is projected onto a Marxian probability simplex partitioning terrestrial pixels into Commons, Agrarian, and Capital fractions. Fisher-Rao (FR) geodesic distances on this simplex identify a transformation pulse of $0.405$~rad/yr during 2019--2020, coinciding with major construction activity. Absorbing Markov chain analysis yields expected absorption times into the built environment of $46.0$~years for cropland and $38.1$~years for tree cover, with a pooled built-area self-retention rate of $96.4\%$. Percolation analysis reveals that a giant connected component containing $89$--$95\%$ of all built pixels persists at occupation probabilities $p \in [0.096, 0.162]$, far below the random percolation threshold $p_c \approx 0.593$, indicating planned rather than stochastic spatial growth. The box-counting fractal dimension of the urban boundary increases from $d_f = 1.316$ to $1.397$, consistent with increasingly irregular frontier expansion. These results suggest that information-geometric and statistical-mechanical tools can characterize the kinematic and topological signatures of capitalist spatial accumulation with quantitative precision.
1 Introduction
The paper frames PIK2’s expansion as an externally driven, irreversible spatial transformation in which commons and agrarian land are enclosed and commodified. It develops an information-geometric, Markov-chain, and percolation framework to quantify the rate, directionality, and topology of this process.
- Motivation: PIK2’s urban expansion is modeled as a non-equilibrium lattice process driven by capital investment, state regulation, and infrastructure planning.The process converts agricultural and natural sites into built, commodified space.
- Motivation: Primitive accumulation describes the recurring enclosure of commons and peasant agriculture into commodified real estate.The introduction presents primitive accumulation as an ongoing structural mechanism rather than a historical relic.
- Research framework: The study applies information geometry, Markov chain theory, and percolation theory to measure enclosure rate, directionality, and spatial topology at PIK2.PIK2 is a mega-development on Jakarta’s northern coast, where the framework is applied to satellite land-use data.
- Study area: PIK2 represents a rapid spatial transformation of reclaimed and expropriated coastal land developed by private consortia northwest of central Jakarta.The project replaced a landscape containing fish ponds, mangrove remnants, and smallholder agriculture with residential, commercial, and road infrastructure.
- Political economy: In early 2024, PIK2 received National Strategic Project status, granting developers accelerated land acquisition powers after aggressive land clearance was visible in satellite records.The designation was followed by agrarian conflicts and public scrutiny.
2 Study area and data
The study examines the PIK2 coastal mega-development and surrounding hinterland across a 173.4 km^2 domain, using eight annual Sentinel-2 LULC composites from 2017–2024. The analysis maps terrestrial land-cover classes onto Commons, Agrarian, and Capital categories to study land enclosure.
- Study domain: 173.4 km^2: The domain spans PIK2 and its coastal and agrarian hinterland north of Jakarta, with approximately 70% shallow ocean.The marine portion contains 126,223 pixels, with mean depth −6.68 m and maximum depth −22.32 m.
- Data: 8 annual composites: Sentinel-2 LULC data cover 2017–2024 at 10 m spatial resolution on a uniform WGS-84 grid.The rasters are reprojected and compiled into a compressed analysis dataset.
- Data: 1,734,054 pixels: The spatial lattice contains 1,113 rows × 1,558 columns, with zero no-data and cloud-contaminated pixels.The classification retains K = 7 substantive classes: Water, Trees, Flooded Vegetation, Crops, Built Area, Bare Ground, and Rangeland.
- Macrostructural classification: 3 macrostructural categories: After excluding marine Water, terrestrial classes are aggregated into Commons, Agrarian, and Capital.Commons groups Trees, Flooded Vegetation, and Rangeland; Agrarian corresponds to Crops; Capital groups Built Area and Bare Ground.
- Macrostructural classification: Bare Ground is assigned to Capital because exposed soil in coastal reclamation and mega-development contexts typically indicates recently cleared or graded land awaiting construction.This assignment is treated as an empirical assumption examined through Markov transition analysis.
3 Methods
The methods represent the landscape as spatial LULC states and aggregate them onto a Marxian probability simplex, then quantify temporal transformation, land-conversion horizons, and built-environment connectivity. Information-geometric, Markov-chain, and percolation-based analyses are applied to the resulting pixel and class distributions.
- Landscape representation: 10×10 m² pixels are modeled as sites in a discrete random field with K = 7 LULC classes.The landscape state maps each spatial site and time to a class label.
- Landscape representation: The reduced Marxian state q(t) = [qcom(t), qagr(t), qcap(t)]⊤ lies on the 2-simplex after summing land-only class probabilities and excluding Water.The fine-grained distribution p(t) resides on the standard (K−1)-dimensional probability simplex.
- Information geometry: Four information-theoretic quantities use the full K=7 distribution, while Mann-Kendall testing evaluates entropy-series monotonicity through Kendall rank correlation τ and its associated p-value.The framework includes Shannon and Rényi entropies, Kullback-Leibler divergence, and Fisher-Rao distance.
- Information geometry: Transformation pulses are defined as FR transitions exceeding the sample mean plus standard deviation of the |T|−1 = 7 consecutive FR distances.Reduced-simplex FR distances, cumulative arc length L(t), direct displacement D, and sinuosity σ characterize trajectory non-linearity.
- Markov dynamics: Built Area is designated the sole absorbing state in a pooled discrete-time Markov chain, with KT = K −1 = 6 transient states and absorption times derived from the fundamental matrix.Transition matrices are constructed from consecutive-year pixel counts, pooled across seven periods, and row-normalized.
- Spatial connectivity: Built pixels are analyzed as 4-connected occupied sites, with connectivity measured by the largest-cluster fraction and boundary complexity quantified by box-counting fractal dimension df.The method also compares df with compact-growth, Eden-model, and Diffusion-Limited Aggregation reference universality classes.
4 Results
PIK2 underwent rapid, nonlinear conversion toward Capital, with Built Area showing strong retention and a giant connected component far exceeding random-percolation expectations. Information-geometric, Markov, and spatial analyses identify the strongest transformation during 2019–2020 and increasingly irregular frontier expansion.
- Land-use composition: Capital rose from 39.70% to 53.80% between 2017 and 2024, while Agrarian declined to 29.31%, indicating a 13.2-pp cropland-to-Capital transfer.The Capital increase was +14.1 pp and +36% relative; Commons declined from 17.83% to 16.89%.
- Information geometry: 1.251 rad cumulative FR arc length versus 0.303 rad direct displacement produced sinuosity σ = 4.12, with peak velocity of 0.405 rad/yr in 2019–2020.The trajectory zigzagged through seasonal and construction-related fluctuations while drifting toward the Capital vertex.
- Markov dynamics: 96.4% Built Area self-retention accompanied expected absorption times of 46.0 years for Crops and 38.1 years for Trees.Period-specific P(B → B) ranged from 0.959 to 0.976, with leakage mainly reflecting Built Area–Bare Ground construction churn.
- Markov dynamics: G = 583,219 with df = 252 (p < 10^-10) rejected temporal homogeneity, while the Frobenius norm ranged from 0.41 to 0.92.The largest deviations occurred in 2017–2018 and around the 2019–2020 pre-PSN surge.
- Percolation structure: p increased from 0.096 to 0.162 while remaining below pc ≈ 0.593, yet Ω consistently exceeded 0.89 and peaked at 0.953 in 2023.A single giant connected component contained 89%–95% of all built pixels.
- Percolation structure: The number of connected clusters rose from 40 to 124 by 2022 before falling to 95 in 2024, while isolated single-pixel clusters increased from 22% to 43%.The later decline in cluster count suggests peripheral developments merged into the giant component; in 2024, Smax = 249,594 pixels versus 15,009 for the second-largest cluster.
5 Discussion
The analysis characterizes PIK2 as a pre-enclosure diversification phase marked by a dominant 2019–2020 transformation pulse, planned spatial growth, and substantial Agrarian-to-Capital transfer. These findings are tempered by non-stationary dynamics, regulatory contestation, and methodological limitations.
- Information-theoretic dynamics: 9.6% →16.2% Built Area growth increases entropy by redistributing probability mass from the Water-dominated baseline, reflecting transient fragmentation rather than ecological health.The landscape is interpreted as being in a pre-enclosure diversification phase.
- Transformation velocity: 0.405 rad/yr marks the highest reduced-simplex velocity during 2019–2020, aligning with the dominant full-simplex transformation pulse.The alignment of independently computed Fisher-Rao metrics supports identifying 2019–2020 as the primary construction-phase discontinuity.
- Enclosure horizon: 46.0 years is the expected Crops (Agrarian) absorption time under pooled dynamics, but stationarity is rejected and E[TCrops] falls to 10.9 yr in 2022–2023.The declining period-specific absorption times indicate that sustained construction acceleration could shorten the enclosure horizon.
- Spatial topology: Ω> 0.89 at p ≈0.10–0.16, roughly one-sixth of pc, indicates spatial organization consistent with planned infrastructure rather than uncorrelated site percolation.Road grids and utility corridors introduce long-range spatial correlations that produce observed supercriticality.
- Social and regulatory implications: −13.2 pp crops versus +14.1 pp capital quantifies near one-to-one Agrarian-to-Capital transfer, while 2024 Agrarian cover is 29.3% compared with 42.5% in 2017.In 2024, approximately 541,000 land pixels, or 54.1 km2, were classified, including approximately 15.9 km2 of Agrarian land.
- Social and regulatory implications: The framework links pre-PSN Bare Ground clearance, non-stationary transitions, and legal contestation to a legally contested pulse of primitive accumulation.The Sentinel-2 product, pixel-independent Markov model, and perfect Built Area irreversibility introduce stated methodological limitations.
6 Conclusion
The study presents a quantitative framework combining information geometry, absorbing Markov chains, and percolation theory to characterize land-enclosure dynamics in the PIK2 mega-development near Jakarta. Together, these tools identify construction pulses, quantify class-specific absorption times, and reveal planned connectivity with an increasingly irregular fractal frontier.
- Quantitative framework: The framework combines IG, absorbing Markov chains, and percolation theory to characterize spatial land-enclosure dynamics in PIK2.PIK2 is identified as a mega-development near Jakarta, Indonesia.
- Information geometry: FR geodesic distance isolates discrete construction pulses.
- Transition dynamics: Absorbing Markov chains quantify expected absorption times for each LULC class.
- Spatial topology: Percolation analysis reveals planned supercritical connectivity and an increasingly irregular fractal frontier.
Declaration of generative AI use
The authors used Claude 4.6 Sonnet and Gemini 3.1 Pro solely to improve the manuscript’s English and readability, while retaining full responsibility for the study’s substantive work.
- Declaration of generative AI use: Claude 4.6 Sonnet and Gemini 3.1 Pro were used solely for English grammar, vocabulary refinement, and manuscript readability.The authors retained responsibility for conceptualization, model development, computation, mathematical derivations, and social-theory integration and analysis.