Collection

PhD Qualification Musings

In August 2025 I sat for my doctoral qualifying examination in computational neuroscience at Yale. The format was unusual: three open-ended questions from my committee, answered in essay form over several weeks, followed by an oral defense. No closed-book exam. No problem sets. Just three questions and enough rope to hang yourself with, or to build something.

The three questions asked me to think about developmental programming in neural circuits, about the computational architecture of cortical oscillation, and about network-level self-organization in synaptic systems. They were chosen independently by different committee members. They were not designed to connect.

Writing the responses, I kept finding the same structures—the same mathematical moves, the same conceptual tensions, the same implicit assumptions about what kind of thing the brain is—recurring across all three. The fourth essay, Through-Lines, is an attempt to make those invariant structures explicit. It was written after the qualifying process, not for the committee, but for myself—to understand what I actually believe, and why, and what the three questions were really asking all along.

Read the three responses in any order. Read Through-Lines last.

The Essays

Response 1

Computational NeuroscienceDynamical Systems

Born to Fly: Developmental Programming and Neural Machine Code

How evolution programs neural circuits before birth—exploring the computational demands of precocial species and what they reveal about developmental 'machine code' in the brain.

On the developmental programming of neural circuits—how evolution encodes behavior before birth, and what precocial species reveal about the computational demands of embodied cognition.

Response 2

Computational NeuroscienceDynamical Systems

The Analog Brain: Harmonic Analyzers and Neural Computation

What mechanical tide predictors reveal about the computational differences between cortical and subcortical structures—and the shared oscillatory language of neural information flow.

On the harmonic structure of neural computation—what mechanical tide predictors share with cortical oscillators, and why the brain might be better understood as an analog frequency analyzer than a digital processor.

Response 3

Computational NeuroscienceNetwork Science

The Rich Get Richer: Preferential Attachment in Neural Networks

From party dynamics to power laws—how the mathematics of 'rich-get-richer' networks connects to Hebbian plasticity and the self-organization of synaptic weights.

On preferential attachment and Hebbian plasticity—how the mathematics of power-law networks connects to the self-organization of synaptic structure and the emergence of representational hierarchy.

Synthesis

Computational NeurosciencePhilosophy

Through-Lines: Insights from my Qualification Process & The Eigenvectors of Thought

Reflections on my doctoral qualifying examination—how forty-eight papers, four mentors, and three essays revealed the invariant structures underlying my approach to neuroscience, physics, and computation.

The synthesis essay. Written after the three qualifying responses, tracing the eigenvectors of thought that run through all of them—the invariant structures underlying how I think about neuroscience, physics, and computation.