A book by Kenneth A. Mendoza · Popular physics / popular mathematics · Manuscript shoppable for literary representation
A working scientist watches his own cross-domain framework — built from Koopman operators, von Neumann's Hilbert lift, and minimum description length — classify three-body orbits, predict material failure, and survive a brutal falsification test, told in present tense as it happens.
On the night of May 9, 2026, the framework at the center of this book failed its own most demanding test. I was at my desk. The result was unambiguous: the prediction was wrong; the falsification was clean; the standard discipline was to stop. I did not stop. I worked through what the failure actually meant, what survived the falsification, and what the survival implied for the next experiment. The book is the record of that night and the methodology that produced it — a working scientist's portrait of cross-domain thinking under fire, told as it happens, with the receipts.
The manuscript is at the stage where a literary agent can evaluate it from the proposal, two polished sample chapters (Chapter 1 — The Flash on the Lemniscate, and a later chapter — The Long Hunch — covering the author's research arc from UCLA microbiology through Cornell philosophy of science, the Erdős Atlas, and the merged DeepMind formal-conjectures PR), and a one-pager. Full draft available on request.
Primary audience: adult readers of popular physics and popular mathematics. The reader who buys Rovelli, Carroll, Strogatz, Becker, and Gleick already has the appetite this book serves. Secondary audience: working scientists, graduate students, and informed generalists who want a methodology book disguised as a memoir.
Twelve chapters in four parts, plus a Counter-History Interlude, five methodological appendices, and an Afterword.
The book opens with a working scientist watching a mathematical animation and noticing something the animation was not meant to show.
It did not begin with an equation. It began with a motion.
I was watching Dan Pike's lemniscate animations on Mathstodon — the kind of mathematical animation most people treat as a beautiful toy. A curve breathes. A level set folds. A polynomial field becomes visible for a second, then hides again behind the smooth authority of the screen.
But something in the animation did not feel decorative. There was a flash on the level set. Not a glitch exactly. Not random jitter. It was the kind of motion a careful eye sees before the mind has language for it: the system started to misbehave, then snapped back into order. A local instability appeared, like the orbit was about to leave the lawful track, and then the geometry seemed to correct it. The curve did not merely trace a path. It acted as if some deeper program had reached in and re-positioned the orbit back into normal behavior.
That was the first clue.
Most people would have watched the animation as a picture. I watched it as instrumentation. That distinction matters. A picture is a surface. An instrument is a thing that lets reality push back. The moment the lemniscate pushed back, it stopped being visual ornament. It became a probe.
The question changed from What does this curve look like? to What computation is the curve performing?
The answer did not arrive whole. It came as a collision of separate intuitions that had been building for years. The first was an old beat from earlier work: a system near transition does not simply move from one state to another. It hesitates. It dwells. It flickers. The warning is not in the final state; it is in the rhythm of almost changing. You do not catch the transition by staring at a static photograph. You catch it by listening to the timing.
The second was a different animation entirely — quadratic motion, drawn plainly enough that the hidden idea could be seen. What looks linear in one plane can become elliptical in another. A line, under the right lift, becomes an orbit. A simple rule, moved into the right space, becomes curvature. That was enough.
I had already been living with the tension between Euclidean space and Hilbert space. Euclidean space is where the eye lives — points, distances, curves, bodies, orbits. Hilbert space is where the program lives — projections, modes, coefficients, inner products, squared error. Euclidean geometry shows you the object. Hilbert geometry shows you the computation that makes the object identifiable.
The lemniscate flash suggested that these were not two worlds. They were two views of the same event.
Continue reading Sample Chapter 1: The Flash on the Lemniscate (PDF)
Or read Sample Chapter 2: The Long Hunch — the author's research arc (PDF)
I am an independent researcher operating through MendozaLab and Oregon Coast AI LLC. I work across pure mathematics, materials science, dynamical systems, and information theory, with a public artifact track that includes a merged pull request to Google DeepMind's formal-conjectures Lean 4 repository on Erdős Problem 505 (Borsuk's conjecture, PR #3746), a Zenodo-deposited preprint on the Erdős–Herzog–Piranian problem with concept DOI 10.5281/zenodo.19184467, and a multi-domain patent portfolio in hysteresis-based stability control and information-theoretic methods.
My ORCID iD is 0009-0000-9475-5938. I post working notes at Bluesky, on LinkedIn, and at mendozalab.io. I live on the Oregon coast.
Transdimensional Painter is my first trade book. I am writing it because the framework it describes — and the discipline of cross-domain work under live falsification pressure — has not been laid out for a general audience anywhere, and the audience that reads Rovelli, Strogatz, and Carroll is the audience that already has the appetite for it.
The author's outward presence is concentrated on platforms where mathematicians, physicists, and informed readers congregate. The platform is curated rather than mass-market; each anchor below is verifiable and active.
If you represent trade-nonfiction authors in the popular-physics / popular-mathematics space and the project resonates, the author would welcome a conversation. The form below reaches the author directly. Email is also fine: [email protected].