$ cd /home/sethuiyer/presentations && ls -la

Mathematical Explorations

Where abstract mathematics meets computational reality—exploring the deep connections between spectral logic, topological optimization, and the fundamental structures that govern both proofs and algorithms.

Blog Posts

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Mathematics with a Pulse

Episode 30 of SpaceTime Cafe introduces spectral logic—a revolutionary framework treating mathematical proofs as thermodynamic journeys with measurable energy costs.

  • Prime-weighted axiom costs and proof partition functions
  • Arithmetic acoustics: numbers as vibrating strings
  • Wave-particle duality for integers
  • Quadratic reciprocity as sympathetic resonance
  • Arithmetic uncertainty principle
play_arrow Explore Spectral Logic
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Topology of Planning

TopoGRPO extends policy optimization through topological decomposition, discovering that complex RL problems possess intrinsic geometric structure exploitable for efficient learning.

  • Cohomological obstructions in partially observable environments
  • Chart discovery via DBSCAN clustering
  • Localized advantage computation within topological regions
  • Prime-number hashing for scalable topological sketching
  • Dixmier-Douady loss functions with gerbe-theoretic guarantees
explore Dive into TopoGRPO
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How Prime Numbers Shape Geometry

Episode 16 of SpaceTime Cafe explores the profound tension between arithmetic identity and geometric proximity, revealing how primes sculpt fractal objects with counterintuitive properties.

  • Dynamic Prime Cantor Set: zero length, full dimension one
  • Fat Dynamic Prime Cantor Set with positive measure 6/π²
  • Prime Ghost Line: infinite holes, complete geometric integrity
  • Prime-driven curvature and "prime gravity" analogies
  • The paradox of arithmetically distinct but geometrically close points
play_circle Watch Prime Geometry
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The Mathematical Tug of War between Identity and Proximity

⚠️ Audio-focused episode • Best listened to rather than watched • Production issues with visuals

Episode 18 of SpaceTime Cafe introduces the universal functional P(ψ) + λI(ψ) that governs balance across machine learning, quantum gravity, and consciousness. Features insights from "Primal Privacy: A Computational Metaphysics."

  • Universal trade-off functional between proximity and identity forces
  • Euler-Lagrange equations governing equilibrium states
  • Lagrangian submanifolds in symplectic geometry
  • Applications from machine learning to quantum extremal surfaces
  • Computational metaphysics and the nature of optimization
headphones Listen to Deep Dive
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Primal Privacy: A Computational Metaphysics — A Treatise

Version 1.0 (2025) — A comprehensive treatise exploring extremization as the universal archetype. Introduces the Fundamental Tradeoff Functional ℒ(ψ) = P[ψ] + λI[ψ] governing reality from quantum gravity to consciousness.

  • Euclidean Proximity vs Hyperbolic Identity dynamics
  • Prime-driven fractals and computational metaphysics
  • Quantum extremal surfaces and spacetime emergence
  • Machine learning, differential privacy, and neural dynamics
  • Universal variational principle underlying complex systems
auto_stories Read the Treatise
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Category Theory in Deep Learning

Medium Deep Dive — A new lens for abstraction, composition, and the nature of intelligence. Exploring how categorical structures provide fundamental insights into neural architectures and learning dynamics.

  • Functorial neural network architectures
  • Compositional learning and abstraction layers
  • Natural transformations in deep representations
  • Category-theoretic foundations of intelligence
  • Morphisms, objects, and learning as functor optimization
article Read on Medium
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The Unreasonable Effectiveness of Hyperbolic Geometry

Geometric Insights — Exploring how hyperbolic spaces naturally represent hierarchical structures with exponential precision. From Poincaré embeddings to tree-like data in continuous curved manifolds.

  • Poincaré ball models for hierarchy representation
  • Exponential capacity in finite-dimensional spaces
  • Tree structures and hyperbolic distance metrics
  • Applications in NLP and knowledge graphs
  • Curvature as a natural measure of hierarchy depth
article Read on Medium
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Understanding Generalization

Medium Deep Dive — Journey through complexity and simplicity. Exploring the fundamental mechanisms by which machine learning models transcend their training data to make meaningful predictions on unseen examples.

  • Bennett vs Simmons: The complexity debate in modern ML
  • Oxford's "grokking" phenomenon: from memorization to understanding
  • Why deep networks violate Occam's Razor yet still generalize
  • Category theory morphisms and universal properties in learning
  • Information theory and Kolmogorov complexity in neural pruning
article Read on Medium

Featured Novel

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Blossoming White Mirror

A Metaphysical Thriller

schedule 1h 52m audiobook headphones Full narration public Archive.org

When President Gojo breaks a fifty-six-year surveillance ritual, reality itself begins to unravel. A genre-cascading epic where political thriller meets quantum metaphysics, exploring the mathematical nature of consciousness and the price of perfect order.

play_circle Listen to Full Audiobook

Genre Evolution

gavel
Political Thriller
memory
Sci-Fi Mystery
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Quantum Metaphysics
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Social Transformation

Mathematical Philosophy in Fiction

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The Resonance Fork

Reality-tuning device embodying the universal functional P(ψ) + λI(ψ)

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Nada Lineage Harmonics

Ancient mantras connecting to arithmetic acoustics and spectral logic

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Surveillance vs Freedom

The proximity/identity tradeoff explored through political narrative

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Reality Optimization

Universe as active optimization process, "correcting" toward equilibrium

Core Themes

Death Prediction Systems
Computational Metaphysics
Reality Manipulation
Harmonic Consciousness
Timeline Correction
Social Optimization
Cosmic Mathematics
Free Will vs Determinism

BibTeX Index

📚 If you find these ideas useful, CONSIDER CITING this blog

This research represents original mathematical explorations at the intersection of spectral theory, topology, and computational methods. Academic attribution helps advance these interdisciplinary conversations.

Spectral Logic Framework

@misc{iyer2025spectral,
  title={Mathematics with a Pulse: Spectral Logic and Arithmetic Acoustics},
  author={Sethu Iyer},
  year={2025},
  url={https://sethuiyer.github.io/blog/mathematics-with-pulse/},
  note={SpaceTime Cafe Episode 30}
}

Topological Policy Optimization

@misc{iyer2025topo,
  title={TopoGRPO: Topological Group Relative Policy Optimization},
  author={Sethu Iyer},
  year={2025},
  url={https://sethuiyer.github.io/blog/topology-of-planning/},
  note={On the Topological Obstructions of Bellman Recursion}
}

Prime Fractals and Geometry

@misc{iyer2024primes,
  title={How Prime Numbers Shape Geometry},
  author={Sethu Iyer},
  year={2024},
  url={https://www.youtube.com/watch?v=ooT7DbpX4Lc},
  note={SpaceTime Cafe Episode 16: Prime Fractals and Geometric Paradoxes}
}

Identity vs Proximity Trade-offs

@misc{iyer2024identity,
  title={The Mathematical Tug of War between Identity and Proximity},
  author={Sethu Iyer},
  year={2024},
  url={https://www.youtube.com/watch?v=NHodSBlH50Y},
  note={SpaceTime Cafe Episode 18: Universal Optimization and Computational Metaphysics}
}

Computational Metaphysics Treatise

@book{iyer2025primal,
  title={Primal Privacy: A Computational Metaphysics},
  author={Sethu Iyer},
  year={2025},
  version={1.0},
  url={https://github.com/sethuiyer/project-delta/blob/main/BOOK.md},
  note={A Treatise on the Universal Fundamental Tradeoff Functional}
}

Category Theory & Deep Learning

@article{iyer2025category,
  title={Category Theory in Deep Learning: A New Lens for Abstraction, Composition, and the Nature of Intelligence},
  author={Sethu Iyer},
  year={2025},
  journal={Medium},
  url={https://medium.com/@sethuiyer/category-theory-in-deep-learning-a-new-lens-for-abstraction-composition-and-the-nature-of-2806963c677f},
  note={Functorial neural architectures and categorical foundations of intelligence}
}

Hyperbolic Geometry & Hierarchies

@article{iyer2024hyperbolic,
  title={The Unreasonable Effectiveness of Hyperbolic Geometry in Representing Hierarchies},
  author={Sethu Iyer},
  year={2024},
  journal={Medium},
  url={https://medium.com/@sethuiyer/the-unreasonable-effectiveness-of-hyperbolic-geometry-in-representing-hierarchies-aa3a6e8232f2},
  note={Poincaré embeddings and exponential hierarchy representation in curved manifolds}
}

Understanding Generalization

@article{iyer2024generalization,
  title={Understanding Generalization: Journey through complexity and simplicity},
  author={Sethu Iyer},
  year={2024},
  journal={Medium},
  url={https://medium.com/@sethuiyer/understanding-generalization-dbbec4f5985a},
  note={Bias-variance tradeoff and the mystery of deep learning generalization}
}