A First-Principles Thought Experiment
Sir Isaac Newton was deeply influenced by hermetic traditions. Tragically, this was not really known until a lot of his works, kept unpublished due to English heresy laws, became available. (A lot of the initial cataloguing of these works was done by John Maynard Keynes, who later described him as the ‘last of the magicians’).
Using those same traditions; we are asking whether it is possible to derive mathematics and, ultimately, physics from a single underlying first principle.
We want to ask whether the structures we normally take as our starting point could themselves be consequences of something even simpler.
Most mathematical systems begin by assuming certain things already exist: numbers, logic, sets or axioms, and then explore everything that follows from them. We want to see if we can take it one more step backwards.
Instead of, “What follows from mathematics?” We ask, “What has to be true before mathematics can exist at all?”
If mathematics is genuinely describing reality, then what is the explanation behind the foundations?
This begins with an attempt to imagine nothing, where not even a vacuum or the laws or physics exist. If that could really exist, then there would be nothing to describe, and nothing to compare.
The first step is simply existence, exists, and that there is not nothing. If this existence was perfectly uniform, with nothing identifiable about it, you wouldn’t be able to distinguish a particular part from another.
Nothing countable, measurable, or distinguishable. Before the math we use to measure these can exist there has to be something distinguishable.
A one whole that has distinguishable positions. Smithian Fold Theory calls this first distinction a fold.
A method of picturing this, is taking a sheet of paper and observing that the surface is one continuous surface. If you then fold it in half, it’s still one sheet of paper, but you’ve created a relationship within it. Different parts of the same whole are distinguishable without it ceasing to be a part of the original object. This is, in its simplest form, the Fold.
If a fold can exist in 1 of 2 distinguishable states, then 1 fold gives 2 possibilities, A or B. When another fold is introduced, all previous possibilities branch into 2 more:
AA
AB
BA
BB
From here another fold would create 8 possibilities, then 16, 32, and so on. Every additional fold doubles the number of possible structures.
The pattern 2^n, emerges naturally from repeatedly introducing new distinctions into the same underlying whole.
Using this principle, Smithian Fold Theory attempts to derive counting, comparison, ratios, order, geometry, information, computation, and eventually the mathematics used to describe quantum mathematics and gravitation.
We go into a lot more detail about this in posts and links on my profile, and I’m slowly working on making more explanations of the work on our GitHub and website.
This post is only a simplified introduction to Smithian Fold Theory.
We began by focusing on the mathematical structure first. We’ve then applied this to reconstructing arithmetic, ratios, geometry, information computation, and then the mathematical structures underlying quantum mechanics and gravitation from the same relational foundation, as opposed to them being independent axioms.
One of the initial blind validations of the mathematical framework, was to apply it to protein structure prediction without access to the target structures, achieving median Cα RMSD95 ≈ 0.78 Å and median TM-score ≈ 0.93 across the benchmark. That’s not, by itself, a validation of the theory as a theory of physics, but it is evidence that the underlying mathematics can make quantitative predictions in a genuinely blind setting.
If you’re interested in the formal mathematics, derivations, proofs, and technical papers, links can be found on my profile. There’s also a website, which has links to our Zenodo publications, GitHub repositories, and supporting research.
We’ve also incorporated Lean 4 into the framework by expressing the generated mathematical structures as machine-checkable proofs. Instead of replacing the derivation itself, we used Lean to independently verify that each logical step follows from the preceding one without hidden assumptions. The complete verification pipeline, together with the tools needed to reproduce the process yourself, is on our GitHub.