Sixteen years on:

where the First Science Project now stands

In January 2010 I set everything else aside to work full time on what I now call the First Science Project. It began as a book, “First Science,” written as an exploratory and clarifying exercise, a way of setting the ideas down and finding out whether they held together. The concentrated research came afterwards, and in essence it has been the long labour of turning those early sketches into the rigorous corpus I have today. (The book, “The First Science and the Generic Code,” is here: https://www.goodreads.com/book/show/15861518-the-first-science-and-the-generic-code) Sixteen years on, the work has reached a threshold I want to mark: five of the project’s papers are now under peer review at the same time, with a sixth in final preparation. What follows is a short account of what the work is, and of how those papers form parts of a single whole.

The guiding idea is easy to state, even if its consequences are not. For some three centuries the sciences have advanced on the strength of the quantitative calculus, the mathematics of number, measurement, and rate of change. Its success has been extraordinary. But it is not the only kind of rigorous mathematics one might have. The First Science Project develops a complementary qualitative calculus: a mathematics not of quantity but of organisation, disposition, and relation. It grows from a single principle I call First-Classness, the requirement that nothing in a system be intrinsically privileged, with no preferred origin, no special container, and no external vantage point. Taken seriously, that one constraint turns out to generate structure.

The formal core of the whole project is set out in “A Qualitative Calculus for Generative Form: Reconstructing Leibniz’s Analysis Situs,” now under review:
https://doi.org/10.5281/zenodo.18091611
The closest historical analogy I can offer is Oliver Heaviside, who turned the solving of differential equations into an operational calculus, a system in which one computes directly with operations. This paper attempts something of that spirit, but far wider in scope: not an operational method for differential equations alone, but an operational alternative to the quantitative mathematical world as a whole. In doing so it brings into working form Leibniz’s unfinished ambition of an Analysis Situs, a geometry of position and relation that has no need of number.

A companion paper carries the same principle to its deepest root. “Monads as Calculus: Formalising Leibniz’s Monadology,” also under review, asks what can survive when First-Classness is imposed on a single entity of wholly undetermined character, before number, order, or any distinguished element has been admitted. What emerges is not arithmetic but a qualitative opposition, between having and being, and out of that opposition a finite community of perspectives, each expressing the same whole from its own standpoint and none privileged above the rest. This is Leibniz’s monadology given explicit formal structure, together with its first mathematical yield: four elementary dyadic types, a single geometric product that combines them, and a scalar that appears as a derived role rather than as an assumed starting point. Where the Analysis Situs paper reconstructs Leibniz’s geometry of position, this one reconstructs his metaphysics of perspective; the two stand together at the foundation of the project:
https://doi.org/10.5281/zenodo.18910740

The remaining papers are not separate undertakings. Each is the same instrument turned upon a different field.

In biology, “First-Classness yields the redundancy architecture of the universal genetic code,” under review, shows that the familiar redundancy of the genetic code, the reason some amino acids are spelled many ways and others only once, follows from First-Classness alone, with no biological assumption introduced by hand:
https://doi.org/10.5281/zenodo.19301558
Its empirical companion, “Genomic codon usage is structurally consistent with First-Classness across the tree of life,” under review, then tests that derived structure against actual codon usage across tens of thousands of species:
https://doi.org/10.5281/zenodo.18102019

In computing, “Dispositional Typing: Eliminating Unsafe Annotations through First-Class Role Algebra,” under review, applies the very same small algebra to a wholly practical problem, that of certifying automatically that a program’s use of memory is safe, without the programmer having to mark up the code by hand:
https://doi.org/10.5281/zenodo.15632320

And in physics, “Logic-Driven Physics: An Operational Companion to the Standard Model for Reconstructing Particle Structure” reconstructs much of the observed inventory of fundamental particles from a codon-based geometric algebra, offered not as a rival to the Standard Model but as an operational companion to it:
https://doi.org/10.5281/zenodo.18102476
This sixth paper is being refined for publication. I intend to submit it only once one or two of the five papers now under review have been accepted, sequencing it deliberately so that it arrives on established ground.

Beneath these six papers lies a larger body of work. The foundations are laid out in a series of Euclid-style Supplementary Material books, which build the system up step by careful step in the manner of a classical treatise: a book of methodology and first principles, then the monadology, the dyadology, and the colour geometry on which the applications draw. The whole corpus, the papers, these supplementary books, and the applications alike, is catalogued in a single living Corpus Index that serves as a gateway to all of it and carries its own permanent identifier:
https://doi.org/10.5281/zenodo.18058102

Two commitments run through all of it. The first is rigour: the results are derived at the level of theorems and then demonstrated computationally, with reproducible verification packages accompanying the papers, so that a reader can check the claims rather than take them on trust. The second is a particular lineage of thought. Leibniz is present throughout; the project is in large part an attempt to carry forward what he began. So too, more quietly, are the Stoics, whose manner of reasoning, testing a candidate structure against its ground rather than building outward from bare axioms, is the method I have followed. The Stoic dimension is made explicit in Appendix B of the Qualitative Calculus paper, but it is at work in the background of the whole.

That, in brief, is where sixteen years have brought the project: a qualitative calculus, formally grounded and computationally checked, now meeting the scrutiny of peer review across philosophy, biology, and computing at once. I offer it here in that spirit, as serious work at a crucial stage, put forward for examination by anyone willing to entertain the thought that the quantitative calculus, for all its triumphs, may have a complement.