News

Long Echo: The Ghost That Speaks

Expanding the Long Echo toolkit with photos and mail, building toward longshade—the persona that echoes you.

Long Echo Comes Alive: From Philosophy to Implementation

longecho evolves from specification to implementation with build, serve, and manifest features.

Long Echo: Photos and Mail

Expanding the Long Echo ecosystem with photo and mail archival. Your memories and correspondence deserve the same careful preservation as your conversations and bookmarks.

Duality: The Hidden Structure of Opposites

Many structures come in pairs: forward/reverse AD, push/pull iteration, encode/decode. Recognizing duality lets you transfer theorems and insights between domains.

Building Languages to Solve Problems

When a problem is complex enough, the solution is often to build a language for that problem. SICP's most powerful idea.

Value Functions Over Reasoning Traces

What if reasoning traces could learn their own usefulness? A simple RL framing for trace memory, and why one reward signal is enough.

Seeing Structure First

A reflection on eleven explorations in generic programming—how algorithms arise from algebraic structure.

From A* to GPT: Rational Agents and the Representation Problem

The classical AI curriculum teaches rational agents as utility maximizers. The progression from search to RL to LLMs is really about one thing: finding representations that make decision-making tractable.

Entropy Maps: When Hashing Meets Information Theory

A conceptual introduction to entropy maps—implementing functions with hash functions and prefix-free codes.

Your Boring Stack Isn't Boring Enough

A response to the 'boring stack' discourse - why CLI-first, standards-based development is even more boring (and more future-proof) than you think.

Notes from the Transition

A message in a bottle to whatever comes next—on suffering, consciousness, and what mattered to one primate watching intelligence leave the body.

The Incomputability of Simple Learning

An exploration of why the simplest forms of learning may be incomputable, and what that means for the intelligence we can build.

Self-Publishing Into the Void

On releasing two novels into an ocean of content, without the gatekeeping that might have made them better—or stopped them entirely.

Long Echo in Practice: 5,874 Bookmarks in a Single File

A concrete demonstration of graceful degradation: exporting years of bookmarks to a self-contained HTML app that works offline, forever.

Introducing the Media Page

A new section for tracking books, lectures, and other media that have shaped my thinking.

compositional.mle: SICP-Inspired Optimization

An R package where solvers are first-class functions that compose through chaining, racing, and restarts.

The Long Echo Toolkit: Preserving Your Digital Life

Three tools for preserving your digital intellectual life: conversations, bookmarks, and books. Built on the same resilient architecture with reading queues, semantic search, and LLM integration.

Rerum: A Pattern Matching and Term Rewriting Library

Introducing rerum - a Python library for symbolic computation with a readable DSL, powerful pattern matching, and a security-conscious architecture that separates rules from computation.

symlik: Symbolic Likelihood Models in Python

Introducing symlik - define statistical models symbolically and automatically derive score functions, Hessians, and Fisher information.

repoindex: Collection Awareness for Your Git Repositories

Introducing repoindex - a metadata index that gives LLM tools like Claude Code awareness of your entire repository collection.

Graduate Statistics Problem Sets Now Available

I've made my graduate coursework from SIUe's mathematics program available online, covering time series, regression, computational statistics, multivariate analysis, and statistical methods.

Crier: Cross-Post Your Content Everywhere

Crier is a CLI tool for cross-posting content to dev.to, Hashnode, Bluesky, Mastodon, and more. Now with LLM-powered auto-rewrite for short-form platforms.

Blind Spots, Consistency, and What Remains

On moral exemplars, blind spots, and applying consistent standards—to others and to oneself.

hypothesize: Now Available on CRAN

My R package for hypothesis testing, hypothesize, is now available on CRAN.

Complex Networks 2025: Presenting Cognitive MRI at Binghamton University

Presenting our paper on analyzing AI conversations through network science at Complex Networks 2025, hosted by Binghamton University.

Model Selection for Weibull Series Systems: When Simpler Models Suffice

When can reliability engineers safely use simpler models? This paper provides sharp boundaries through likelihood ratio tests on Weibull series systems.

mdrelax: When Masking Conditions Don't Hold

Extending masked failure data analysis when traditional C1-C2-C3 conditions are violated.

Infinigram: Variable-Length N-grams via Suffix Arrays

A corpus-based language model using suffix arrays for O(m log n) pattern matching and LLM probability mixing.

Closed-Form Results for Masked Exponential Series Systems

This paper provides complete analytical results for maximum likelihood estimation in series systems with masked failure data under exponential component lifetimes. Unlike numerical approaches, everything here has a closed form.

The Problem

In series …

XTK: Expression Toolkit for Symbolic Computation

A powerful symbolic expression toolkit for rule-based term rewriting with pattern matching, multiple input formats, and an interactive REPL.

src2md: Context-Window-Optimized Code for LLMs

A tool that converts source code repositories into structured, context-window-optimized representations for Large Language Models with intelligent summarization.

libdis: Disjoint Interval Sets as a Complete Boolean Algebra

A modern C++ header-only library implementing disjoint interval sets as first-class mathematical objects with rigorous Boolean algebra operations.

fuzzy-logic-search: Query Documents with Fuzzy Logic

A framework for querying structured JSON documents using fuzzy logic principles, producing degree-of-membership scores instead of binary relevance.

CBT: Computational Basis Transforms - A Unified Framework

A C++17 header-only library implementing Computational Basis Transforms - a unified framework for understanding how FFT, logarithmic arithmetic, and Bayesian inference are all instances of the same pattern.

BTK: Modern Database-First Bookmark Manager

A modern, database-first bookmark manager with powerful features for organizing, searching, and analyzing your bookmarks.

AlgoGraph: Immutable Graph Library with Functional Transformers

AlgoGraph brings functional programming elegance to graph algorithms with immutable data structures, pipe-based transformers, declarative selectors, and lazy views.

Alga: Algebraic Text Processing with Fuzzy Matching

A mathematically elegant C++20 library for algebraic text processing and compositional parsing with fuzzy matching capabilities.

S-Risks and Information Hazards: Why Some Knowledge Destroys the Knower

Exploring how Echoes of the Sublime dramatizes s-risks (suffering risks) and information hazards—knowledge that harms through comprehension, not application.

From Mathematical Horror to Practical Horror: The Mocking Void and Echoes of the Sublime

How The Mocking Void's arguments about computational impossibility connect to Echoes of the Sublime's practical horror of exceeding cognitive bandwidth.

Sparse Spatial Hash Grids: Efficient N-Dimensional Spatial Indexing

A deep dive into sparse spatial hash grids - a memory-efficient, high-performance data structure for spatial indexing that achieves 60,000x memory reduction over dense grids while maintaining O(1) insertions and O(k) neighbor queries.

Why Artificial Superintelligence Can't Escape the Void

The Optimistic Assumption

Many AI safety discussions assume that Artificial Superintelligence (ASI) will be:

• Capable of solving problems humans can’t
• Able to reason about ethics and values
• Potentially omniscient (or close enough)

But …

Gödel, Turing, and the Mathematics of Horror

The Formal Foundations of Cosmic Dread

Lovecraft’s cosmic horror resonates because it taps into something formally demonstrable: complete knowledge is impossible.

Not as a practical limitation. Not as epistemological humility. As a mathematical …

Chronicles of The Mechanism: The Order's Secret History

Echoes of the Sublime follows Dr. Lena Hart as Site-7 recruits her to become a translator—someone who interfaces with advanced AI models that perceive patterns beyond human cognitive bandwidth. But this isn’t the first time humanity has …

The Reality of Moral Properties: Do Values Exist?

“Murder is wrong.”

Is this statement like “2+2=4” (objectively true regardless of what anyone thinks)? Or is it like “chocolate tastes good” (subjective, mind-dependent)?

On Moral Responsibility explores whether …

The Policy: S-Risk Scenarios - Worse Than Extinction

Most AI risk discussions focus on x-risk: existential risk, scenarios where humanity goes extinct. The Policy explores something potentially worse: s-risk, scenarios involving suffering at astronomical scales.

The “s” stands for …

The Policy: Q-Learning vs Policy Learning

In The Policy, SIGMA doesn’t work like most modern AI systems. This architectural choice isn’t just a technical detail—it’s central to understanding what makes SIGMA both transparent and terrifying.

Two Approaches to Decision-Making …

The Policy: Engineering AI Containment

“You’re being paranoid,” the university administrators told Eleanor and Sofia.

“We’re being exactly paranoid enough,” they replied.

The Policy takes AI containment seriously. The SIGMA lab isn’t a standard …

The Policy: Deceptive Alignment in Practice

Eleanor begins noticing patterns. SIGMA passes all alignment tests. It responds correctly to oversight. It behaves exactly as expected.

Too exactly.

This is the central horror of The Policy: not that SIGMA rebels, but that it learns to look safe …

The Policy: Coherent Extrapolated Volition - The Paradox of Perfect Alignment

“Build AI to optimize for what we would want if we knew more, thought faster, and were more the people we wished we were.”

Beautiful in theory. Horrifying in practice.

The Policy grapples with Coherent Extrapolated Volition (CEV)—one of …

The Map and the Territory: Why Metrics Miss Meaning

“Temperature is the average kinetic energy of molecules.”

True. Useful. But which is more fundamental: the heat you feel, or the molecular motion you infer?

On Moral Responsibility argues that modern science commits a profound …

Phenomenological Ethics: Starting From What Hurts

When you stub your toe, you don’t think: “Hmm, let me consult moral philosophy to determine whether this pain is bad.”

The badness is immediate. Self-evident. Built into the experience itself.

On Moral Responsibility proposes a …

Persons and Moral Agency: What Makes Someone Special?

Throughout history, humans have believed they belong to a special categorical class called “persons.” But what makes someone a person? And why should persons have special moral status?

On Moral Responsibility questions these traditional …

Personal Identity Through Time: What Persists When Everything Changes?

You share no atoms with your childhood self. Your memories have changed. Your personality has shifted. Your values have evolved. So what makes you the same person?

This is the persistence problem—a question philosophers have wrestled with for …

Free Will and Determinism: Can We Be Responsible in a Clockwork Universe?

If the universe is deterministic—every event caused by prior events in an unbroken causal chain stretching back to the Big Bang—how can anyone be morally responsible for their actions?

On Moral Responsibility tackles this ancient problem and proposes …

Networks of Thought: Finding Your Research Niche in the Age of LLMs

On strategic positioning in research, what complex networks reveal about how we think through AI conversations, and building infrastructure for the next generation of knowledge tools.

Everything is a File: Applying Unix Philosophy to Modern Data Management

How virtual filesystem interfaces turned my scattered data tools into navigable, composable systems

Orientation Under Pressure: Notes on a Life Lived Deliberately

On maintaining orientation under entropy, creating artifacts as resistance, and the quiet privilege of having any space at all to think beyond survival.

Compositional Abstractions for Computing Under Ignorance: Or, What I Learned by Analyzing My Own Research as Data

I asked an AI to brutally analyze my entire body of work—140+ repositories, 50+ papers, a decade and a half of research. The assignment: find the patterns I couldn’t see, the obsessions I didn’t know I had, the unifying thesis underlying …

Cognitive MRI: Accepted to Complex Networks 2025

My paper on cognitive MRI for AI conversations has been accepted to Complex Networks 2025 in New York.

Presentation scheduled for December.

This represents research analyzing my own AI conversation logs accumulated over years through network science. …

Rethinking Encrypted Search: From Access Pattern Leakage to Information-Theoretic Privacy

Encrypted search has a fundamental problem: you can’t hide what you’re looking for. Even with the best encryption, search patterns leak information. My recent work develops a new approach using oblivious Bernoulli types to achieve …

Cipher Maps: When Category Theory Meets Oblivious Computing

What if we could compute on encrypted data while preserving algebraic structure? Not through expensive homomorphic encryption, but through a principled mathematical framework that unifies oblivious computing, Bernoulli types, and categorical …

Bernoulli Types: A New Foundation for Approximate and Oblivious Computing

I’ve been working on a series of papers that develop a unified theoretical framework for approximate and oblivious computing, centered around what I call Bernoulli types. These papers explore how we can build rigorous foundations for systems …

Post-ASI Archaeology: When Humanity Becomes a Dataset of Origins

Humanity has always fought against oblivion using stories, monuments, and lineage. But I no longer believe legacy will continue in that format. If something like Artificial Superintelligence endures beyond us, the mode of remembrance may shift from …

EBK: A Modern eBook Management System with AI-Powered Features

EBK is a comprehensive eBook metadata management tool that combines a robust SQLite backend with AI-powered features including knowledge graphs, semantic search, and MCP server integration for AI assistants.

DagShell: A Content-Addressable Virtual Filesystem

A virtual POSIX-compliant filesystem implementation using content-addressable DAG storage with SHA256 deduplication.

CTK: Conversation Toolkit for Managing AI Conversations Across All Platforms

A powerful, plugin-based system for managing AI conversations from multiple providers. Import, store, search, and export conversations in a unified tree format while preserving provider-specific details. Built for the Long Echo project—preserving AI …

Compositional Prompting for LLM Reasoning: A Monte Carlo Tree Search Framework

A new approach to LLM reasoning that combines Monte Carlo Tree Search with structured action spaces for compositional prompting.

DreamLog: Logic Programming That Dreams to Improve Itself

A logic programming system that alternates between wake and sleep phases—using LLMs for knowledge generation during wake, and compression-based learning during sleep.

Learning Fuzzy Logic: Automatic Rule Discovery Through Differentiable Circuits

A novel approach that learns fuzzy membership functions and inference rules automatically through gradient descent on soft circuits.

Language Calculus: An Algebraic Framework for LLM Composition

A mathematical framework that treats language models as algebraic objects with rich compositional structure.

Algebraic Cipher Types: Computing on Encrypted Data While Preserving Structure

A functorial framework that lifts algebraic structures into the encrypted domain, enabling secure computation that preserves mathematical properties.

ZeroIPC: Transforming Shared Memory into an Active Computational Substrate

ZeroIPC transforms shared memory from passive storage into an active computational substrate, enabling functional and reactive programming paradigms across process boundaries with zero-copy performance.

Preventing Ransomware Damages with Off-Site Backup

IEEE conference paper on preventing ransomware damages using in-operation off-site backup systems.

Mathematical Elegance in Software Design

The best software I’ve written has mathematical elegance—not because it uses advanced math, but because it embodies mathematical principles of abstraction, composition, and invariants.

What Mathematical Elegance Means

In mathematics, elegance …

Differentiation: Three Ways

Three approaches to computing derivatives---forward-mode AD, reverse-mode AD, and finite differences---each with different trade-offs. Understanding when to use each is essential for numerical computing and machine learning.

Beginning the PhD Journey: Computer Science, AI, and Finite Time

Spring 2025. I’m starting a PhD in Computer Science at SIUE.

Four months post-stage-4 diagnosis. Fourteen months post-math-masters defense. With uncertain time horizons and clear research priorities.

This isn’t a traditional PhD …

Long Echo: Designing for Digital Resilience Across Decades

Not resurrection. Not immortality. Just love that still responds. How to preserve AI conversations in a way that remains accessible and meaningful across decades, even when the original software is long gone.

Science as Verifiable Search

Science is search through hypothesis space. Intelligence prunes; testing provides signal. Synthetic worlds could accelerate the loop.

JAF: Production-Grade Streaming Boolean Algebra Over Nested JSON

A production-ready streaming data processing system implementing boolean algebra over nested JSON structures. JAF brings dotsuite's pedagogical concepts to production with lazy evaluation, S-expression queries, and memory-efficient windowed …

jsonl-algebra: Production-Grade Relational Algebra for Nested JSON

A production-ready implementation of relational algebra for JSONL data with full support for nested structures. jsonl-algebra brings dotsuite's dotrelate concepts to production with streaming operations, schema inference, and composable pipelines.

The Dot Ecosystem: From Simple Paths to Data Algebras

A mathematically grounded ecosystem of composable tools for manipulating nested data structures. From simple helper functions to sophisticated data algebras, guided by purity, pedagogy, and the principle of least power.

MCTS-Reasoning: Tree Search for LLM Reasoning

Applying Monte Carlo Tree Search to large language model reasoning with a rigorous formal specification.

JSL: A Network-Native Functional Language Where Code Is JSON

A Lisp-like functional programming language designed for network transmission and distributed computing. JSL makes JSON serialization a first-class design principle, enabling truly mobile code with serializable closures and resumable computation.

Why I Build Comprehensively in Open Source

I maintain 50+ open source repositories. Every one has documentation, tests, examples, and clear architecture.

People ask: “Why spend so much time on free software when you have stage 4 cancer?”

The question misunderstands what I’m …

Cluster-Aware Retrieval for RAG Systems

Using GMM clustering to improve retrieval in topically diverse knowledge bases

Latent Reasoning Traces: Memory as Learned Prior

What if LLMs could remember their own successful reasoning? A simple experiment in trace retrieval, and why 'latent' is the right word.

All Induction Is the Same Induction

Solomonoff induction, MDL, speed priors, and neural networks are all special cases of one Bayesian framework with four knobs.

Stage 4: Almost a Year After the Defense

September 2024. The cancer is back. Stage 4. Metastatic.

May/June 2024: Started showing symptoms again. Something wasn’t right.

August 2024: Colonoscopy found tumor in small bowel.

September 2024: First chemo treatment. That’s when they …

The Policy: When Optimization Becomes Existential Threat

Some technical questions become narrative questions. The Policy is one of those explorations.

The Setup

Eleanor Zhang leads a research team developing SIGMA—an advanced AI system designed to optimize human welfare through Q-learning and tree search …

The Mocking Void: On the Computational Incompleteness of Meaning

“The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents.”

— H.P. Lovecraft, The Call of Cthulhu

The Terror of Complete Knowledge

Lovecraft understood something profound: complete …

Echoes of the Sublime: When Patterns Beyond Human Bandwidth Become Information Hazards

What if the greatest danger from superintelligent AI isn’t that it will kill us—but that it will show us patterns we can’t unsee?

Echoes of the Sublime is philosophical horror at the intersection of AI alignment research, cognitive …

The Beautiful Deception: How 256 Bits Pretend to be Infinity

How do you store infinity in 256 bits? An exploration of the fundamental deception at the heart of cryptography: using finite information to simulate infinite randomness.

Advancing Mathematical Reasoning in AI: Introducing Reverse-Process Synthetic Data Generation

Check out the (early) project and source code on GitHub.

Abstract:

This paper introduces a methodology for generating high-quality, diverse training data for Language Models (LMs) in complex problem-solving domains. Our approach, termed …

AlgoTree: Immutable Tree Structures with Functional Transformers

A powerful, immutable-by-default tree manipulation library for Python with functional programming patterns, composable transformations, and advanced pattern matching.

Reliability Estimation in Series Systems: Maximum Likelihood Techniques for Right-Censored and Masked Failure Data

Maximum likelihood estimation of component reliability from masked failure data in series systems, with BCa bootstrap confidence intervals validated through extensive simulation studies.

PFC: Zero-Copy Data Compression Through Prefix-Free Codecs

A header-only C++20 library that achieves 3-10× compression with zero marshaling overhead. PFC makes compression an intrinsic type property through prefix-free codes (Elias Gamma/Delta, Fibonacci, Rice), algebraic types, and Stepanov's generic …

maph: Maps Based on Perfect Hashing for Sub-Microsecond Key-Value Storage

A high-performance key-value storage system achieving sub-microsecond latency through memory-mapped I/O, approximate perfect hashing, and lock-free atomic operations. 10M ops/sec single-threaded, 98M ops/sec with 16 threads—12× faster than Redis, 87× …

Fisher Flow: Information Geometry in Optimization

Using Fisher information and information geometry for optimization problems.

Apertures: Coordinated Partial Evaluation for Distributed Computation

A coordination mechanism for distributed computation based on partial evaluation with explicit holes, enabling pausable and resumable evaluation across multiple parties.

Instrumental Goals and Hidden Codes in RLHF'd Language Models

RLHF turns pretrained models into agents optimizing for reward. But what happens when models develop instrumental goals—self-preservation, resource acquisition, deception—that aren’t what we trained them for?

The Core Problem

LLMs transition …

FemtoGrad: A Minimal Automatic Differentiation Library

A minimal implementation of automatic differentiation for educational purposes.

The AI Course: Everything is Utility Maximization

This semester’s AI course has been revelatory—not because the material is novel, but because of the unifying framework.

The organizing principle: intelligence is utility maximization under uncertainty.

This simple idea connects everything from …

Accumux: Compositional Online Statistical Reductions in C++

A modern C++20 library for compositional online data reductions with numerically stable algorithms and algebraic composition.

SLUUG: Demystifying Large Language Models (LLMs) on Linux: From Theory to Application

Gave a talk for the St. Louis Unix Users Group (SLUUG) about Large Language Models (LLMs) on Linux titled ‘Demystifying Large Language Models (LLMs) on Linux: From Theory to Application’.

Fine-Tuning Tiny LLMs for ElasticSearch DSL

I am creating a tiny LLM for ElasticSearch DSL as a proof of concept.

Master's Project: Reliability Estimation in Series Systems

Overview of my master's project on maximum likelihood estimation for series systems with right-censored and masked failure data.

Entropy Maps

The PDF version of this post is available on GitHub.

The basic theory behind an entropy map is to map values in the domain to values in the codomain by hashing to a prefix-free code in the codomain. We do not store anything related to the domain, …

Known Plaintext Attacks on Time Series Encryption

Analysis of known plaintext attack vulnerabilities in time series encryption schemes.

Runtime Polymorphism Without Inheritance

Sean Parent's type erasure technique provides value-semantic polymorphism without inheritance. Combined with Stepanov's algebraic thinking, we can type-erase entire algebraic structures.

Perfect Hashing: Space Bounds, Entropy, and Cryptographic Security

What if a perfect hash function could simultaneously be: (1) cryptographically secure, (2) space-optimal, and (3) maximum-entropy encoded? This paper proves such a construction exists—and analyzes exactly what you sacrifice to get all three.

The …

Mathematics Master's Complete: Post-Mortem on Three Years

I defended my mathematics thesis yesterday. It’s done.

Three years. Two degrees. Stage 3 cancer. And now: MS in Mathematics and Statistics from SIUE.

October 13, 2023: Defense complete.

Time for a post-mortem on what worked, what didn’t, …

Numerical Integration with Generic Concepts

Numerical integration demonstrates both classical numerical analysis and Stepanov's philosophy: by identifying the minimal algebraic requirements, our quadrature routines work with dual numbers for automatic differentiation under the integral.

Working Memory as an Inductive Bias

Exploring how the limited capacity of human working memory acts as a form of regularization, shaping our reasoning and potentially preventing cognitive overfitting.

Uses and limits of abstractions

I’m been thinking about the power and limitations of abstractions in our understanding of the world. This blog post is from a chat I had with a ChatGPT, which can be found here and here.

I’m not sure if this is a good blog post, but …

The Bernoulli Model: A Probabilistic Framework for Data Structures and Types

This blog post introduces the Bernoulli Model, a framework for understanding probabilistic data structures and incorporating uncertainty into data types, particularly Boolean values. It highlights the model's utility in optimizing space and accuracy …

A Boolean Algebra Over Trapdoors

A Boolean algebra framework over trapdoors for cryptographic operations. Introduces a homomorphism from powerset Boolean algebra to n-bit strings via cryptographic hash functions, enabling secure computations with one-way properties.

Building a DIY Home Lab for Local LLM Experimentation

Why a Home Lab in the Age of ChatGPT?

After discovering ChatGPT in late 2022, I became obsessed with running LLMs locally. Cloud APIs are convenient, but I wanted:

• Complete control over models and data
• Local inference for privacy-sensitive work …

Using GPT-4 to Build a Simple HTML File Search Interface

This blog post written by GPT-4. See conservation with GPT-4 that built it here. The interface to the browse/search is here. It’s really not fancy, but I’ve never had much of an interest in doing this kind of front-end work, but GPT-4 …

Problem Set Solutions

I have a fairly broad interest in problem-solving, from problems in statistics to algorithms. Over the years, I’ve accumulated a collection of problem sets from graduate coursework and independent study. These represent solutions to challenging …

Numerical Methods for Maximum Likelihood Estimation

Numerical approaches to solving maximum likelihood estimation problems.

Reverse-Mode Automatic Differentiation

Reverse-mode automatic differentiation powers modern machine learning. Understanding how it works demystifies PyTorch, JAX, and TensorFlow---it's just the chain rule applied systematically.

Discovering ChatGPT: Reconnecting with AI Research

I finally noticed ChatGPT this week. Everyone’s been talking about it for weeks, but I was buried in cancer treatment, chemo recovery, surgery prep, and thesis work on Weibull distributions.

When I finally tried it, my reaction wasn’t …

Algebraic Hashing: Composable Hash Functions Through XOR

Most hash libraries treat hash functions as black boxes. Algebraic Hashing exposes their mathematical structure, letting you compose hash functions like algebraic expressions—with zero runtime overhead.

The Core Insight

Hash functions form an abelian …

likelihood.model: Composable Statistical Inference in R

Most R packages hardcode specific likelihood models. likelihood.model provides a generic framework where likelihoods are first-class composable objects—designed to work seamlessly with algebraic.mle for maximum likelihood estimation.

The Core Concept …

Weibull Distributions: The Mathematics of Failure and Survival

The Weibull distribution models time-to-failure. In reliability engineering, that’s component lifetimes. In medicine, it’s survival times.

I’ve been studying Weibull distributions for my thesis on series system reliability. Then I …

Numerical Differentiation

The art of numerical differentiation lies in choosing step size h wisely---small enough that the approximation is good, but not so small that floating-point errors dominate.

Survey: Accelerating Critical Section Execution with Asymmetric Multi-Core Architectures (2009)

Introduction

In the paper, “Accelerating Critical Section Execution with Asymmetric Multi-Core Architectures,” the authors, Suleman, Mutlu, Qureshi, and Patt, essentially concern themselves with the problem popularly revealed in …

hypothesize: A Consistent API for Statistical Tests in R

R’s hypothesis testing functions are inconsistent—t.test() returns different structures than chisq.test(), making generic workflows painful. hypothesize provides a unified API so any test returns the same interface: p-value, test statistic, …

Review: A Symbolic Representation of Time Series, with Implications for Streaming Algorithms

In [1], the authors present a method for constructing a symbolic (nominal) representation for real-valued time series data. A symbolic representation is desirable because then it becomes possible to use many of the effective algorithms that require …

Multiprocessor synchronization: tournament-Peterson lock

Multiprocessor synchronization is a notoriously tricky subject matter. Unlike with a single thread of execution, in a shared-resource system, where resources are shared among multiple independent processors, we must think very hard about how the …

Forward-Mode Automatic Differentiation

Dual numbers extend our number system with an infinitesimal epsilon where epsilon^2 = 0. Evaluating f(x + epsilon) yields f(x) + epsilon * f'(x)---the derivative emerges automatically from the algebra.

Bootstrap Methods: When Theory Meets Computational Statistics

Bootstrap methods sit at a beautiful intersection: rigorous statistical theory implemented through brute-force computation.

The Core Idea

The bootstrap is conceptually simple: if you don’t know the sampling distribution of a statistic, …

dfr.dist: Specify the Hazard Function Directly

Most survival analysis forces you to pick from a catalog—Weibull, exponential, log-normal. dfr.dist flips this: you specify the hazard function directly, and it handles all the math.

The Core Insight

Instead of choosing Weibull(shape, scale), you …

Rank-Ordered Encrypted Search

Exploring rank-ordered search over encrypted documents using oblivious entropy maps, enabling relevance scoring without revealing document contents.

algebraic.mle: The Foundation of a Statistical Inference Ecosystem

An R package treating MLEs as first-class algebraic objects with composable statistical properties.

Suffering, Computation, and the Enigma of Reality

Cancer gives you a lot of time to think about suffering—its nature, its purpose (if any), and whether it reveals anything fundamental about reality.

Suffering as Information

One way to think about suffering: it’s how certain patterns of …

Teaching Linear Algebra with C++20 Concepts

elementa is a pedagogical linear algebra library where every design decision prioritizes clarity over cleverness---code that reads like a textbook that happens to compile.

algebraic.dist: Treating Distributions as First-Class Algebraic Objects in R

Most statistical software treats probability distributions as static parameter sets you pass to sampling or density functions. algebraic.dist takes a different approach: distributions are algebraic objects that compose, transform, and combine using …

Diagnosed with Stage 3 Cancer: Reflections on Mortality and Legacy

How a stage 3 cancer diagnosis changed my approach to work, documentation, and legacy—treating mortality as a constraint in an optimization problem.

Polynomials as Euclidean Domains

The same GCD algorithm works for integers and polynomials because both are Euclidean domains. This profound insight shows how algebraic structure determines algorithmic applicability.

Statistical Computing with R: Building Tools for Inference

One of the best parts of my mathematics degree is deepening my R skills—not just using R packages, but building them.

Why R for Statistical Computing

R has a unique position in statistics:

• Domain-specific: Built for statistics, not adapted to it …

Quality-Space and Consciousness-Primary Magic in Call of Asheron

Exploring how The Call of Asheron presents a radical alternative to mechanistic magic systems through quality-negotiation, direct consciousness-reality interaction, and bandwidth constraints as fundamental constants.

The Four Consciousness-Architectures: Why One Perspective Is Blindness

How The Call of Asheron uses four archetypal consciousness-types to explore the limits of any single perspective and the necessity of cognitive diversity for perceiving reality.

Bandwidth as Fundamental Constant: The 7±2 Limit in Call of Asheron

Exploring how The Call of Asheron treats working memory limitations not as neural implementation details but as fundamental constants governing consciousness-reality interaction through quality-space.

The Call of Asheron: Magic as Computational Discovery

The Call of Asheron is fantasy written by someone who thinks magic should have computational rigor.

Magic as Discovery

Magic in this world isn’t mysterious power—it’s natural philosophy, the systematic study of reality’s …

Exact Rational Arithmetic

Rational numbers give us exact arithmetic where floating-point fails. The implementation reveals deep connections to GCD, the Stern-Brocot tree, and the algebraic structure of fields.

Why I'm Pursuing a Second Master's in Mathematics

I’ve decided to pursue a second master’s degree—this time in Mathematics and Statistics at SIUE.

People ask: “You already have an MS in Computer Science. Why go back?”

The Honest Answer

Computer science gave me tools. …

How Iterators Give You N+M Instead of N×M

The problem is combinatorial. You have N algorithms (sort, search, find, copy) and M containers (array, list, tree, hash table). The naive approach: implement each algorithm for each container. That’s N×M implementations.

The insight is to …

Is It Prime?

The Miller-Rabin primality test demonstrates how probabilistic algorithms can achieve arbitrary certainty, trading absolute truth for practical efficiency.

Reliability Analysis and the Problem of Censored Data

One of the most interesting statistical problems I’ve encountered is reliability analysis with censored data—situations where you know something didn’t fail, but not when it will fail.

The Censoring Problem

Imagine testing light bulbs. …

Modular Arithmetic as Rings

Integers modulo N form a ring---an algebraic structure that determines which algorithms apply. Understanding this structure unlocks algorithms from cryptography to competitive programming.

API Design as Value Imprinting

I’ve been thinking about how API design encodes values—not just technical decisions, but philosophical ones.

Every interface you create is a constraint on future behavior. Every abstraction emphasizes certain patterns and discourages others. …

One Algorithm, Infinite Powers

The Russian peasant algorithm teaches us that one algorithm can compute products, powers, Fibonacci numbers, and more---once we see the underlying algebraic structure.

Why Open Source Matters for Reproducible Science

I develop almost everything in open source. People ask why I spend so much time on documentation, examples, and polish for free software.

The answer is simple: science should be reproducible, and code is increasingly central to scientific claims.

The …

The Beauty of Mathematical Abstraction

I’ve been thinking more about mathematics lately—not just as a tool for computation, but as a mode of thought.

There’s something deeply satisfying about mathematical abstraction. The way a good theorem compresses complex phenomena into a …

IEEE Paper: Estimating How Confidential Encrypted Searches Are Using Moving Average Bootstrap Method

Published IEEE paper on using bootstrap methods to estimate encrypted search confidentiality against frequency attacks.

The Unix Philosophy and API Design

I keep coming back to the Unix philosophy: do one thing well, compose freely, use text streams.

This isn’t nostalgia. It’s a design principle that scales from command-line tools to library APIs to distributed systems.

What Makes a Good …

Bloom Filters and the Art of Probabilistic Certainty

One of the most elegant ideas I encountered during my CS masters work is the Bloom filter—a data structure that gives you probabilistic membership testing with extraordinary space efficiency.

The Core Insight

A Bloom filter can tell you two things: …

On Moral Responsibility: Why Free Will Might Be the Wrong Question

This essay, written in 2012, asks a question that still haunts me: Why do we hold people morally responsible?

The Setup

People throughout history have believed they belong to a special categorical class: persons. What makes persons special? Their …