Some beautiful geometry for optimal working class and interracial interactions...

And how my work relates to theories by Karl Marx, Michal Kalecki, John von Neumann, Rosa Luxemburg, and Richard Goodwin

This paper explores how to build neighborhoods that bring people from different races and income levels together instead of keeping them apart. Inspired by earlier work from economist Glenn Loury, the study uses math and computer models to show how the shape and layout of a neighborhood can help or hurt people’s chances of meeting and learning from one another.

Key Contributions:

1. New Shape Ideas for Neighborhoods:
   Instead of keeping low-income and minority residents in one corner and high-income, mostly white residents in another, the paper shows that neighborhoods with wavy or checkerboard patterns help people from different groups interact more often.

2. Proofs:
   The paper uses new equations and simulations to prove that these mixed-up layouts lead to better results for everyone: more trust, stronger communities, and more fairness.

3. Simulations:
   The author created 3D models to compare traditional, segregated neighborhoods with new, integrated ones. The visual models show that interaction increases when housing boundaries are creatively designed.

Policy Implications:

1. Better Public Transportation:
   Making buses and trains cheaper and more connected can help people live where they want and still get to work or school easily, breaking down invisible walls between rich and poor areas.

2. Mixed-Income Housing Rules:
   Cities should build housing that mixes different income levels and racial backgrounds, especially near parks, libraries, and schools where people naturally gather.

3. Redesigning Public Spaces:
   Parks, recreation centers, and public buildings should be placed along the lines where different groups live so they become shared spaces where real community can happen.

4. Government Funding Based on Fairness:
   Federal money should go to places that are actively working to mix groups fairly and reduce separation, not just to those with the most land or wealth.

5. Measuring and Fixing Inequality:
   Cities should regularly measure stress, food access, and education gaps in different neighborhoods. Then, they should adjust rules or money flows to fix unfair patterns before they get worse.

Big Picture:
This research shows that segregation doesn’t just happen by accident, and it’s built into the way we design cities. But with the right planning and policies, we can build communities where everyone has a fair shot, feels connected, and grows together.

I posted the other day about why Marx matters and economists look quite absurd saying we don’t need to engage with his theories. The integration of Marxian work benefits from developments in Bayesian inference, nonlinear optimization, topology, set theory, neuroscience, behavioral economics, and moral-political theory, yielding extensions and re-articulations of foundational Marxian ideas using modern tools.

Below I’ve explained the relationship between my research and theories of Marx, Richard Goodwin, Michal Kalecki, Abram Harris, and Rosa Luxemburg:

Karl Marx – Surplus, Inequality, and Beliefs

Marx believed that profits come from paying workers less than the value they produce. I extend these ideas but update them using modern math and psychology. It shows that people’s beliefs, especially shaped by being left out or treated unfairly, can affect how much they work, trust the system, or even take care of themselves. My work shows that inequality doesn't just hurt wallets and can change minds.

Marxian Foundations and Structural Set-Valued Dynamics

Marx’s surplus-value theory can be modernized via set-valued mappings and convex cone analysis from von Neumann growth frameworks:

\(Y = A x, \quad x \in \mathbb{R}_+^n, \quad \text{with } Y - w \cdot L = s \cdot Y \Rightarrow \pi = s(Y - wL)\)

where s is the surplus rate and pi is the profit share. My work modifies this in a Bayesian Riemannian manifold:

\(U_i = f(x_i, \theta_i), \quad \theta_i \sim \mathcal{B}(\lambda_i), \quad \lambda_i = g(H_i, D_i)\)

with endogenous belief formation based on historical exclusion and material deprivation (this is connected to insights from Chichilnisky). The surplus extraction now occurs over a manifold with curvature bounds, reflecting constraint-induced moral drift.

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Rosa Luxemburg – Global Trade and Fairness

Luxemburg thought that rich countries needed poor ones to sell their extra goods, which kept inequality going. Some of my work takes that idea and shows how global trade could work differently. Instead of trade being about profits, it could be about reducing suffering, letting every country get what it needs, not just what it can afford. This would mean changing how we think about what trade is for.

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Michał Kalecki – Jobs, Profits, and Public Spending

Kalecki explained how profits depend on how much businesses invest, spend, and how little workers save. This paper builds on that and adds a twist: it shows how government jobs, especially ones aimed at helping people in need, can help the whole economy. The government can choose who to help based on how unfairly they’ve been treated, using smart data and moral decision-making.

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Richard Goodwin – Job Cycles and Moral Momentum

Goodwin showed how jobs and wages go in cycles, like nature. This paper adds a moral layer: it says that how fair or unfair society feels also affects these cycles. If people feel exploited, or communities feel stressed and disrespected, the whole economy can wobble. The paper suggests we can stabilize things by making policy more caring and aware of people’s struggles.

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Abram Harris – Race, Status, and Economic Beliefs

Harris said that racism and inequality block the market from working fairly. My research extends that by showing how people’s sense of status and the messages they get from society can change how they act. It models how unfair treatment and disrespect interfere with people's mental health and decision-making. Fixing the economy means fixing how people are seen and treated, not just giving them money.

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Synthesis – Connecting the Dots in a Fair Economy

All five thinkers were trying to understand how power and unfairness shape the economy. Some of my research pulls their ideas together using modern tools like geometry and AI-style learning. It imagines a better system where governments plan in a way that respects human dignity, reduces suffering, and learns from people's real experiences.