An Unneccesary Abomination - The Theory of The Idea and Manure

The Virology of Memetics: Biological Growth Models and the Spread of Cultural Replicators

Author: Rhombus Ticks
Affiliation: Tom of Salem, MA

Abstract

This study investigates the applicability of classical biological population growth models to memetics, the quantitative study of idea transmission and cultural replication. Through systematic analysis, we demonstrate direct parallels between exponential and logistic population dynamics and the propagation of memes within finite attention ecologies. Our findings establish the viability of virological frameworks as analytical and predictive tools for understanding memetic behavior. We present extended models incorporating mutation, suppression, and ecological interactions, positioning meme evolution as analogous to infectious agent dynamics in biological host systems. These mathematical frameworks provide quantitative foundations for analyzing cultural phenomena ranging from political ideologies to internet virality trends.

Keywords: memetics, cultural evolution, population dynamics, viral transmission, mathematical modeling

1. Introduction

The conceptualization of the "meme" as a cultural replicator, first articulated by Dawkins (1976) in The Selfish Gene, established foundational parallels between genetic and cultural transmission mechanisms. This theoretical framework has gained increasing relevance as the velocity and scale of idea propagation have intensified in digital environments, necessitating rigorous quantitative methodologies for analysis and prediction.

The exponential proliferation of ideas, rituals, symbols, and internet phenomena demands systematic investigation through established mathematical frameworks. Biological population growth models, originally developed to characterize organism population dynamics, present a mathematically robust foundation for memetic analysis. This paper demonstrates the direct applicability of these models to cultural replicator systems and proposes extensions to accommodate the complexity of memetic ecosystems.

2. Theoretical Framework: Biological Growth Models

2.1 Exponential Growth Model

The fundamental exponential growth model describes unrestricted population expansion:

$$\frac{dN}{dt} = rN$$

where:

• $N$ represents population size
• $r$ denotes the intrinsic growth rate
• The model assumes unlimited resources and spatial constraints

2.2 Logistic Growth Model

The logistic model incorporates environmental limitations through carrying capacity:

$$\frac{dN}{dt} = rN \left(1 - \frac{N}{K}\right)$$

where:

• $K$ represents the carrying capacity
• Population growth self-regulates as $N$ approaches $K$

These mathematical formulations derive from seminal ecological research, including Verhulst's (1838) demographic studies and Pearl and Reed's (1920) population analysis, establishing foundational principles for modeling bacterial, human, and other organismal growth patterns.

3. Memetic Applications and Analogies

3.1 Basic Memetic Growth Model

By substituting cultural replicators for biological organisms, we define memetic population $M(t)$ governed by:

$$\frac{dM}{dt} = rM \left(1 - \frac{M}{K} \right)$$

where:

• $r$ represents the virality coefficient, quantifying transmissibility
• $K$ denotes memetic carrying capacity, reflecting cognitive bandwidth and cultural saturation limits

This formulation captures characteristic memetic lifecycles: initial viral propagation, market saturation, and subsequent decline phases.

3.2 Validation Through Cultural Phenomena

This model framework accurately describes observable patterns in various cultural transmission contexts, from the rapid spread and eventual decline of internet memes to the adoption curves of political ideologies and social movements.

4. Extended Mathematical Models

4.1 Mutation and Evolutionary Dynamics

To incorporate memetic variation and drift, we introduce mutation rate $\mu$ and variant populations $M_i$:

$$\frac{dM_i}{dt} = r_i M_i \left(1 - \frac{\sum_j M_j}{K} \right) + \mu \sum_{j \neq i} M_j P_{ji}$$

where $P_{ji}$ represents transition probabilities between memetic variants.

4.2 Competitive Dynamics

Coexisting and antagonistic meme interactions follow Lotka-Volterra competitive dynamics:

$$\begin{cases} \frac{dM_1}{dt} = r_1 M_1 - \alpha M_1 M_2 \ \frac{dM_2}{dt} = -r_2 M_2 + \beta M_1 M_2 \end{cases}$$

where $\alpha$ and $\beta$ quantify competitive interaction strengths.

4.3 Cultural Immune Response Model

Cultural resistance mechanisms can be modeled through suppression terms:

$$\frac{dM}{dt} = rM \left(1 - \frac{M}{K} \right) - \gamma I(t) M$$

where $\gamma$ quantifies cultural suppression effectiveness, encompassing fact-checking, censorship, and audience fatigue responses, and $I(t)$ represents the intensity of immune response over time.

5. Applications and Computational Analysis

These mathematical frameworks enable quantitative modeling of diverse phenomena:

• Political ideology propagation: Analysis of belief system spread patterns (e.g., conspiracy theories, political movements)
• Digital virality dynamics: Predictive modeling of social media content propagation
• Cultural resistance mechanisms: Quantification of debunking networks, fact-checking effectiveness, and cultural immune responses

The models provide analytical tools for applications in narrative influence analysis, public health communication optimization, and propaganda effectiveness assessment.

6. Discussion and Implications

The successful application of biological growth models to memetic systems demonstrates the fundamental similarities between biological and cultural evolutionary processes. These mathematical frameworks offer several advantages:

1. Predictive capability: Quantitative forecasting of idea propagation patterns
2. Parameter estimation: Measurement of virality coefficients and carrying capacities
3. Intervention modeling: Analysis of suppression and promotion strategies
4. Cross-system comparison: Standardized metrics for comparing different memetic phenomena

The models' flexibility allows for adaptation to specific cultural contexts while maintaining mathematical rigor and predictive power.

7. Conclusions

Biological population growth models provide a mathematically robust and empirically validated framework for memetic analysis. Through systematic adaptation of these models to incorporate cultural complexity factors—including mutation, competition, and immune responses—we establish powerful analytical tools for the emerging science of idea propagation.

Future research directions include refinement of parameter estimation techniques, expansion to multi-dimensional memetic spaces, and integration with network-based transmission models. These developments will enhance our quantitative understanding of cultural evolution and provide increasingly sophisticated tools for analyzing information dynamics in complex societies.

Acknowledgments

The author acknowledges the foundational contributions of researchers in both biological population dynamics and cultural evolution theory whose work enabled this interdisciplinary synthesis.

References

Blackmore, S. (1999). The Meme Machine. Oxford University Press.

Brodie, R. (1996). Virus of the Mind: The New Science of the Meme. Integral Press.

Dawkins, R. (1976). The Selfish Gene. Oxford University Press.

Pearl, R., & Reed, L. J. (1920). On the rate of growth of the population of the United States since 1790 and its mathematical representation. Proceedings of the National Academy of Sciences, 6(6), 275-288.

Shifman, L. (2014). Memes in Digital Culture. MIT Press.

Verhulst, P.-F. (1838). Notice sur la loi que la population suit dans son accroissement. Correspondance Mathématique et Physique, 10, 113-121.