Ettore Majorana and application of physics to study social and economic processes — I

Author’s Note: This manuscript represents a collaborative effort between artificial intelligence tools and original authorial input. It is an iterative work currently at Version 1.1, reflecting ongoing revisions and enhancements. The updated version will be available on my blog at Soul of Matter.

The famed Italian physicist Ettore Majorana was probably the first to apply in a dedicated manner the principles of a fundamental branch of physics — statistical physics — to the study of social and economic problems. In his tenth article, “ Il valore delle leggi statistiche nella fisica e nelle scienze sociali” (“ The Value of Statistical Laws in Physics and Social Sciences “) [1], Majorana explored the intrinsic probabilistic nature of quantum mechanics and established a formal analogy with the statistical laws governing social sciences. This pioneering work highlighted the potential of using statistical physics to understand and model complex social and economic systems, laying the groundwork for the later development of the interdisciplinary field of econophysics.

The Majorana theory on social sciences pertains to his innovative work on the statistical laws in physics and their application to social sciences. Majorana is renowned for his contributions to theoretical physics, including his pioneering work on quantum mechanics and the concept of Majorana particles, which are fermions that are their own antiparticles. However, a lesser-known aspect of his work, as highlighted in the text, involves his contemplation of the statistical nature of physical laws and the parallels he drew between these laws and those governing social sciences.

Fig. 1 — AI-generated image of Ettore Majorana crossing the channel where he mysteriously disappeared forever on March 25, 1938.

In his article, Majorana suggested that the intrinsic statistical character of fundamental physical laws, as revealed by quantum mechanics, indicates a profound analogy between physics and social sciences. He argued that just as quantum mechanics has shown that events at the atomic level must be understood statistically, with outcomes that are probabilistically determined rather than strictly deterministic, similar statistical approaches could be valuable in understanding economic and social phenomena. This perspective was quite forward-thinking, considering that in the early 20th century, the dominant view in physics was still largely deterministic, following the Newtonian paradigm.

Majorana’s insight proposed a shift in how we understand the predictability and determinism of both natural phenomena and human societal dynamics. He recognized that the uncertainty and statistical nature inherent to quantum events could provide a methodological framework for social sciences, where many events are also not deterministic but can be probabilistically modeled.

Majorana’s multidisciplinary approach demonstrates not just his depth and breadth as a physicist, but also his original thinking about applying physics concepts to larger fields of investigation. His work offers a unified view on the rules that control both the physical world and human civilisation, emphasising the importance of statistical laws across several scientific fields. Ettore Majorana’s ideas, particularly his investigation of statistical principles in physics and social sciences, provide a unique viewpoint that may be used to better comprehend societal processes. His pioneering work emphasises the importance of statistical principles in understanding the behaviours of complex systems, such as atomic particles or human civilisations.

Fig.2 — Using Quantum Mechanics Tools to Analyze Society: This image represents the polarization of citizens, highlighting the potential of quantum-inspired models to provide insights into social dynamics and collective behavior

Key Points from Majorana’s Ideas for Understanding Society:

Ettore Majorana’s pioneering principles in statistical physics provide an interesting framework for examining the complexities of social systems. His findings suggest that societal actions and outcomes may be innately probabilistic, similar to the principles that govern particles in quantum science. This approach contends that, while deterministic principles may provide a framework for anticipating physical events, understanding society may need acknowledging the inherent ambiguity and variability in human conduct (see also Ref. [2]).

1. Probabilistic Nature of Laws: Majorana’s study implies that, much as quantum physics accepts the essential probabilistic character of physical rules regulating particles, society behaviours and results may be intrinsically probabilistic. This suggests that, while deterministic principles might give a framework for forecasting physical occurrences, comprehending society may need admitting the inherent ambiguity and variety in human behaviour. Illustrative Scenario: Consider a government planning its annual economic policy amid global economic uncertainties. What steps should it take?

• Probabilistic Approach: Economists use probabilistic models to forecast economic growth, employment rates, and inflation under different scenarios, considering factors like global market trends, domestic policy changes, and consumer behavior.
• Insights Gained: The models indicate a range of possible outcomes, showing high probabilities for moderate growth but also accounting for scenarios with lower growth due to potential external shocks (e.g., geopolitical tensions or natural disasters).
• Accelerate investment in infrastructure projects to create jobs and stimulate economic activity. Focus on projects that improve long-term productivity, such as transportation networks, renewable energy installations, and digital infrastructure; 8) R&D Incentives: Increase funding and tax breaks for research and development to stimulate innovation and future growth. 9) Social Safety Nets: Improve social safety net services, such as healthcare, housing aid, and food security, to help disadvantaged people during economic downturns. Invest in job training and reskilling programs to help employees adapt to shifting economic conditions and burgeoning sectors. 9) Data-driven decision-making: Create a system for real-time monitoring of economic data in order to make educated decisions swiftly. Use big data and analytics to forecast trends and evaluate the effectiveness of policy interventions. Collaborate with private-sector organisations to harness their data and insights, ensuring that policies are founded on comprehensive and up-to-date facts. Applications: Based on these probabilistic forecasts, policymakers design flexible economic policies that include contingency plans for different scenarios. For instance, they might prepare additional stimulus measures that can be quickly deployed if growth falls below expectations or create regulatory frameworks that can be adjusted based on real-time economic data. Among others, here are some concrete measures the government should take: Adaptive Fiscal Policies: 1) Stimulus Packages: Prepare additional fiscal stimulus measures that can be deployed quickly if economic growth falls below expectations. This could include direct cash transfers to citizens, increased unemployment benefits, or targeted subsidies for struggling industries; 2) Tax Adjustments: Implement temporary tax relief measures for individuals and businesses during economic downturns. This can help maintain consumer spending and business operations; 3) Interest Rate Adjustments: The central bank should be ready to lower interest rates to encourage borrowing and investment if economic indicators show signs of slowing growth; 4) Quantitative Easing: Be prepared to engage in or increase quantitative easing measures to inject liquidity into the financial system if necessary; 5) Dynamic Regulatory Frameworks, i.e., Regulatory Easing: Temporarily ease certain regulations on businesses to reduce their operational burdens during economic stress. For example, relax reporting requirements or extend compliance deadlines; 6) Sector-Specific Support: Provide tailored support to sectors disproportionately affected by economic downturns, such as tourism or manufacturing. This could include grants, loans, or tax incentives; 7) Investment in Infrastructure and Innovation:

1. Considering the probabilistic character of economic and social systems allows policymakers and economists to devise more robust methods to uncertainty and volatility. The above outlined approach, which is influenced by Majorana’s findings on the probabilistic character of laws, emphasises the significance of flexible, adaptive planning in the face of inherent social and economic uncertainty.
2. Statistical Laws as Descriptive Tools: Majorana’s comparison of statistical principles in physics and those that may apply in social sciences highlights the importance of statistical methods as powerful tools for capturing the collective behaviour of people within a society. This method can help identify patterns and trends that govern social interactions and dynamics, even when individual behaviours are unanticipated. Illustrative scenario: Consider a town that is experiencing a contagious illness epidemic. What is the more appropriate approach? Using statistical approaches to analyze the collective behaviour of individuals in the community, public health professionals may create and implement effective interventions to reduce disease transmission. This method is influenced by Majorana’s parallel between statistical physics and social sciences. It demonstrates the power of statistical laws as descriptive tools for capturing and influencing collective behavior in society.
3. Statistical Models: Public health authorities use statistical models to analyze data on infection rates, contact patterns, and recovery rates. They use the SIR model to forecast illness transmission and pinpoint possible areas for intervention. Insights gained: Statistical study shows that specific regions of the community have greater infection rates due to intensive social contacts. Officials also identify super-spreaders, who contribute greatly to the disease’s spread. Applications: Using these information, public health actions such as targeted vaccination programs and social distancing measures in high-risk regions are implemented. Additionally, specialised public health messaging is created to address specific problems and enhance adherence to health recommendations.
4. Complex Systems: Majorana’s physics research focused on complicated systems that are sensitive to initial conditions and whose outcomes are best explained statistically. Applying this approach to society, we may see societal structures as complex systems in which minor changes or acts by individuals can have far-reaching consequences, making statistical analysis critical for understanding societal trends and behaviours. Illustrative Scenario: Consider a city experiencing rapid population growth, leading to increased pressure on its transportation and housing systems. what should be done? By treating urban environments as complex systems, city planners can make data-driven decisions that consider the intricate interdependencies within the system. This approach, inspired by Majorana’s work on complex systems, allows for more effective management of urban challenges, ensuring sustainable and resilient city development. City planners use complex systems theory to model the interactions between different components of the urban environment. They apply network theory to analyze the public transportation system and identify key nodes that, if improved, could significantly enhance overall network efficiency. Statistical analysis reveals that certain intersections and transit hubs are critical for maintaining smooth traffic flow and efficient public transport. Planners also identify potential phase transitions in the housing market, indicating areas at risk of gentrification if current trends continue. Based on these insights, the city implements targeted improvements to the transportation network, such as adding new bus routes and upgrading key transit hubs. Housing policies are introduced to ensure affordable housing in vulnerable areas, preventing displacement and promoting balanced urban growth.
5. Formal Analogies for Cross-Disciplinary Insights:Majorana’s utilisation of formal parallelism between disciplines encourages cross-disciplinary approaches to solve complex problems. Using statistical and probabilistic models from physics, we may get insights into social phenomena such as information diffusion, social effect, and network dynamics.Illustration Scenario:Consider a public health agency whose goal is to understand and limit the spread of an infectious disease in a city. The public health department may use cross-disciplinary insights from physics to design more effective and focused disease management and control techniques, demonstrating how Majorana’s formal analogies can be realistically utilised to tackle complex social concerns. They may mimic illness propagation using an epidemiological model influenced by the Ising model, similar to how physics works. In this approach, people canThe probability of an individual getting infected depends on their interactions with infected neighbors. By applying this model, the department identifies that certain neighborhoods (highly connected clusters) are critical for the disease’s spread. Targeting these areas with interventions (e.g., vaccinations, awareness campaigns) can significantly reduce the overall infection rate. Additionally, by using percolation theory, the department assesses the network’s resilience. They determine the minimum number of critical nodes (individuals) whose vaccination would prevent the disease from percolating through the entire network, thus controlling the outbreak more efficiently.
6. Uncertainty and Decision Making: The probabilistic character of societal rules, as derived from Majorana’s concepts, can have far-reaching consequences for policymaking and social planning. They emphasises the importance of flexible and robust strategies in the face of social system uncertainty. As an Illustrative Scenario let us consider this: Consider a coastal city prone to hurricanes. Traditional planning might focus on the most likely hurricane path and intensity based on historical data. However, using Majorana-inspired probabilistic models, the city can prepare for a spectrum of hurricane scenarios, from minor storms to catastrophic hurricanes. This involves: Designing evacuation routes that can be adjusted based on the storm’s actual path and intensity, ensuring effective evacuation even if the hurricane deviates from the expected course. Establishing shelters that can accommodate a varying number of evacuees, with supplies and facilities that can be scaled up or down as needed; Training emergency services to respond to different levels of disaster severity, with protocols that can be quickly adapted based on real-time updates.
7. Ethics and Responsibility: While Majorana’s work was largely concerned with the natural sciences, the application of his concepts to society raises significant ethical concerns concerning determinism, free choice, and the role of individuals and institutions in creating social outcomes. To grasp better his ideas, which at first sight can be elusive, consider this Illustrative Scenario: Consider a parole board that employs an AI algorithm to determine the chance of reoffending for those eligible for parole. To generate a risk score, the AI system considers a number of characteristics, including age, criminal history, and socioeconomic status. Ethical Issue 1: Determinism vs. Free Choice. The AI system assesses an individual who has made considerable rehabilitation efforts and has a strong support network. Despite these positive elements, the algorithm calculates a high-risk score based on previous data, resulting in the refusal of parole. This decision may be regarded as disrespecting the individual’s ability to change and weakening their free will. Ethical Issue 2 — Bias and Fairness: The AI system’s risk assessment model is discovered to disproportionately give higher risk ratings to people of specific racial or ethnic origins, mirroring previous prejudices in the criminal justice system. As a result, these persons are wrongly denied parole at greater rates than others;
   Ethical Issue 3: The Role of Institutions The parole board implements precautions to address the possibility for prejudice and the ethical concerns of deterministic models. These include frequent audits of the AI system, openness regarding decision-making processes, and the ability for individuals to appeal parole decisions. The board also invests in teaching members to grasp the limitations and ethical implications of employing AI in decision-making.

It is clear that Majorana’s pioneering ideas, though rooted in physics, offer a valuable framework for exploring the complexities of social systems. Majorana realized what Francis Bacon, one of the founders of the scientific attitude, suggested as the foundation for a new science: “Philosophers should diligently investigate the new force of the influence of customs, exercises, friendships, education, censure, exhortation, reputation, laws, books, studies, etc., because they are the things that imperate on human morals; the spirit is formed and disciplined by those factors” (see De Augmentis Scientiarum, IX). They highlight the importance of embracing uncertainty, the utility of statistical and probabilistic models, and the potential of interdisciplinary approaches in understanding and addressing societal challenges. Social model based on Ettore Majorana’s ideas, particularly his insights into the application of statistical laws from physics to social sciences, offers a framework where the inherent unpredictability and probability found in quantum mechanics are used as metaphors or direct influences on understanding social dynamics and human behavior. And this vision and methodology can become a significant contribution to the progress of our societies.

Core Principles of the Social Majorana Model:

The core model in the Majorana paper on social sciences is based on these main ideas.

1. Probability and Unpredictability: Just as particles in quantum mechanics have probabilities of being in certain states, individuals’ behaviors and decisions could be seen as having probabilities influenced by various factors, both internal and external. This model would account for the inherent unpredictability in human actions, acknowledging that behavior can only be predicted to a certain extent.
2. Interconnectedness: Drawing from quantum entanglement, where particles remain connected such that the state of one (no matter the distance) can affect the state of another, this social model would emphasize the deep interconnectedness of individuals within a society. Actions and events are not isolated but have ripple effects across the social fabric.
3. Observation Effect: In quantum mechanics, the observer effect postulates that the mere observation of a phenomenon inevitably changes that phenomenon. Applied socially, this could suggest that our understanding of social dynamics is shaped and potentially altered by the ways we study and interpret them. This principle encourages reflexivity in social research and policy-making.
4. Complex Systems Behavior: This model would view society as a complex system that exhibits behaviors not predictable from the properties of its individual parts. Similar to how complex quantum systems are studied, the focus would be on understanding the emergent properties of social groups.

Implementation of the Majorana Model in Society:

Incorporating Majorana’s ideas into practical applications can transform various sectors by embracing the probabilistic and interconnected nature of social systems. Here are some specific areas where these principles can be implemented:

• Policymaking: Policies could be designed with flexibility and adaptability, acknowledging the probabilistic nature of their outcomes. Pilot programs and A/B testing become standard, with continuous monitoring and adjustment based on observed results.
• Education: An emphasis on critical thinking and adaptability, preparing individuals to navigate an inherently unpredictable social landscape. Education systems would foster awareness of interconnectedness and the societal impact of individual actions.
• Social Planning and Urban Development: Urban planning that adapts to the emergent needs of communities, incorporating feedback loops that allow for continuous modification based on the changing dynamics of the population and environment.
• Economic Models: Economic systems that are more resilient to unpredictability, incorporating mechanisms to deal with shocks and stresses in a manner analogous to quantum systems’ ability to exist in multiple states.

This model, inspired by Majorana’s ideas, would not seek to predict social outcomes with certainty but rather to understand and manage the probabilities of different outcomes, fostering a society that is resilient, adaptable, and deeply aware of the interconnectedness of its members.

Modelling an idea spreads through a network of individuals

!pip install numpy matplotlib networkx import numpy as np import matplotlib.pyplot as plt import networkx as nx # Create a social network with 100 individuals num_nodes = 100 social_network = nx.erdos_renyi_graph(n=num_nodes, p=0.1) # Visualize the network plt.figure(figsize=(8, 8)) nx.draw(social_network, node_size=50, with_labels=False) plt.show() # Initialize all nodes as not having adopted the idea for node in social_network.nodes(): social_network.nodes[node]['adopted'] = False # Randomly select a node to be the initial adopter initial_adopter = np.random.choice(social_network.nodes) social_network.nodes[initial_adopter]['adopted'] = True # Define the probability function def adoption_probability(num_adopted_neighbors, total_neighbors): """Higher number of adopted neighbors increases the probability of adoption.""" return num_adopted_neighbors / total_neighbors if total_neighbors > 0 else 0 # Simulation parameters num_iterations = 100 adoption_threshold = 0.25 # The threshold probability to adopt the idea 0.5 original value # Simulation loop for _ in range(num_iterations): for node in social_network.nodes(): if not social_network.nodes[node]['adopted']: neighbors = list(social_network.neighbors(node)) num_adopted_neighbors = sum([social_network.nodes[neighbor]['adopted'] for neighbor in neighbors]) if adoption_probability(num_adopted_neighbors, len(neighbors)) > adoption_threshold: social_network.nodes[node]['adopted'] = True # Count the number of adopters num_adopters = sum([social_network.nodes[node]['adopted'] for node in social_network.nodes()]) print(f"Number of adopters after {num_iterations} iterations: {num_adopters}") # Color nodes based on whether they've adopted the idea node_color = ['blue' if social_network.nodes[node]['adopted'] else 'red' for node in social_network.nodes()] plt.figure(figsize=(8, 8)) nx.draw(social_network, node_color=node_color, node_size=50, with_labels=False) plt.show()

In the final visualization of the Python notebook:

• Blue nodes represent individuals who have adopted the idea or technology. These are the nodes for which the simulation determined that the adoption threshold was met, based on the proportion of their neighbors who had already adopted the idea.
• Red nodes, the opposite color, represent individuals who have not adopted the idea by the end of the simulation. These are the nodes for which the adoption threshold was not met, indicating that either too few of their neighbors had adopted the idea for them to be influenced to adopt it themselves, or they simply never reached the point of consideration based on the simulation’s rules and thresholds.

This color-coding is used to visually differentiate between those who have been influenced by their social connections to adopt a new idea or behavior and those who have not, illustrating the spread of the idea through the network and highlighting the clusters or patterns of adoption that can emerge in social networks.

Conceptual Framework for an Advanced Model

Integrating quantum mechanics notions into social science models can lead to new insights into human behaviour and society processes. Key concepts include:

1. Quantum Superposition and Social Opinions: Borrowing the concept of superposition, individuals in a social system could be thought of as holding multiple potential opinions or behaviors simultaneously until an “observation” (a social event or decision point) collapses this superposition into a definite state. This could model how people’s public behavior or opinion might not be apparent until a specific context forces a decision.
2. Entanglement and Social Influence: Quantum entanglement could serve as a metaphor for the complex interdependencies and influences between individuals in a social network. Actions or changes in state for one individual could have non-local effects on others with whom they are “entangled” through social ties.
3. Tunneling and Social Change: Quantum tunneling, where particles pass through barriers they seemingly shouldn’t, could parallel sudden, unexpected shifts in social norms or behaviors, bypassing what might appear as insurmountable social barriers or gradual processes.

Sketch of a Model Incorporating Quantum Concepts

We will sketch up a Python model that includes these principles abstractly. Because actual quantum mechanical calculations will not apply directly to social phenomena, this model relies on metaphors from quantum mechanics to build a simulation of social dynamics.

import numpy as np import matplotlib.pyplot as plt import networkx as nx # Initialize a social network num_individuals = 100 social_network = nx.erdos_renyi_graph(n=num_individuals, p=0.1) initial_states = np.random.choice(['A', 'B'], size=num_individuals) nx.set_node_attributes(social_network, {i: {'state': state} for i, state in enumerate(initial_states)}) # Simulate superposition by allowing individuals to "hold" multiple opinions with different probabilities opinion_superposition = {i: {'A': 0.5, 'B': 0.5} for i in range(num_individuals)} # Function to simulate observation/event leading to opinion collapse def observe_opinions(network, opinion_superposition): for node in network: opinions = opinion_superposition[node] network.nodes[node]['state'] = np.random.choice(['A', 'B'], p=[opinions['A'], opinions['B']]) return network # Function to simulate entanglement effects - a change in one individual might affect connected individuals def simulate_entanglement(network): for node in network: neighbors = list(network.neighbors(node)) if neighbors: # If the node has neighbors entangled_node = np.random.choice(neighbors) network.nodes[entangled_node]['state'] = network.nodes[node]['state'] return network # Function to simulate tunneling - a sudden shift in opinion against the odds def simulate_tunneling(network, threshold=0.7): for node in network: if np.random.rand() < threshold: current_state = network.nodes[node]['state'] network.nodes[node]['state'] = 'A' if current_state == 'B' else 'B' return network # Run the simulation time_steps = 10 for _ in range(time_steps): social_network = observe_opinions(social_network, opinion_superposition) social_network = simulate_entanglement(social_network) social_network = simulate_tunneling(social_network, threshold=0.1) # Visualization of the final states in the social network final_states = [social_network.nodes[node]['state'] for node in social_network] plt.hist(final_states) plt.title('Distribution of Opinions in Social Network') plt.xlabel('Opinion') plt.ylabel('Number of Individuals') plt.show()

The histogram shows the number of individuals holding each of two opinions, labeled ‘A’ and ‘B’, at the end of the simulation. The x-axis represents the two opinions, while the y-axis represents the number of individuals. The bars indicate the final count of individuals who have settled on each opinion.

In the provided plot:

• The bar for opinion ‘A’ shows a higher count, with approximately 55 individuals holding this opinion.
• The bar for opinion ‘B’ shows a slightly lower count, with around 45 individuals holding this opinion.

Additional Context and Interpretation

The simulation incorporates several quantum-inspired mechanisms:

1. Observation: This mechanism allows individuals to “collapse” their probabilistic states into a definite opinion based on assigned probabilities.
2. Entanglement: This simulates the influence of social connections, where a change in one individual’s opinion can affect their neighbors, leading to clusters of similar opinions.
3. Tunneling: This mechanism introduces the possibility of sudden shifts in opinion, even against the odds, representing unexpected changes in individual beliefs.

Insights from the Simulation

Opinion Dominance: Opinion ‘A’ is more prevalent, suggesting that the network dynamics, influenced by the simulated quantum mechanisms, led to a slight dominance of this opinion. This could be due to stronger initial probabilities, more influential individuals adopting opinion ‘A’, or random chance.

1. Cluster Formation: The entanglement mechanism likely contributed to clusters of similar opinions forming within the network. Individuals connected to influential nodes may have adopted the same opinion, reinforcing the majority view.
2. Impact of Randomness: The tunneling mechanism ensures that there is always a degree of unpredictability in the system, preventing it from becoming entirely deterministic. This randomness reflects the inherent uncertainty and variability in human behavior.

Conclusion

Ettore Majorana’s pioneering insights, initially applied to physics, provide a new viewpoint on the social sciences. By embracing quantum physics’ probabilistic and statistical methods, we can get significant insights into social dynamics. This model, based on Majorana’s concepts, shows how quantum-inspired mechanisms may assist mimic opinion formation and comprehend how individual acts and societal factors interact to shape collective behaviour. It emphasises the significance of taking into account both deterministic frameworks and inherent uncertainties when analysing complex social systems, opening the way for more adaptive and robust approaches to social planning and governance.

REFERENCES:

[1] Majorana, E., Mantegna, R.N. (2006). The value of statistical laws in physics and social sciences. In: Bassani, G.F. (eds) Ettore Majorana Scientific Papers. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48095-2_11

[2] Statistical physics of social dynamics, Claudio Castellano, Santo Fortunato, and Vittorio Loreto, Rev. Mod. Phys. 81, 591 — Published 11 May 2009

Originally published at http://soulofmatter.wordpress.com on July 26, 2024.