jhm - jhm labs

On Voronoi’s Projective Model of Hyperbolic Geometry

Voronoi rushed into the room exclaiming, It’s linear, It’s all linear!

Idea On Steklov-Selberg Trace Formula for Arithmetic Spaces

We have idea about the Steklov spectrum versus the Laplace spectrum on noncompact arithmetic spaces. This suggests a Steklov Selberg trace formula on rational bordifications. Thus we bypass all complications related to continuous versus discrete spectra of Laplacian on noncompact spaces, and immediately obtain discrete spectrum.

Tao-Szemeredi, Significant Bits, and Under-Over Fitting

We introduce an idea about Tao-Szemeredi and it’s application to understanding under and over fitting in the training of neural nets. Basically there is a certain entropy dimension which supports the most significant coarse bits. These significant coarse bits are the proper goal of training, whereas the backpropagation gradient step tends to approach then blow past these significant coarse bits during optimization. Under- and over- fitting occurs according to our hypothesis depending on whether the neural net is supported below or above the dimension of the most significant bits. This allows, in our estimate, a priori estimates about the effectiveness of retraining and transferability of neural nets.

Physics is a Calling

The basic premise at JHMLabs is that Wilhelm Weber’s and Ralph Sansbury’s work synthesizes into a completely unified Classical Physics 2.0 which demonstrates that Bohr’s quantum hypothesis is disposable, and the stability of the atom can be resolved according to classical principles. We wish we only had the opportunity to make our case to Einstein, Rutherford, Planck, Ampere, Weber, Gauss, the masters themselves.

Boole vs Hegel vs Wittgenstein. Triviality of Logic and Contingency of the World.

Quid est veritas?

A Critique of Godel’s Incompleteness Theorem

We discuss our critique of Godel’s incompleteness theorem and especially the claim that Godel’s proposition \(G\) has Godel number \(g\) as claimed.

Update: Announcing a New Spine for Teichmueller Space of Closed Hyperbolic Surfaces

We announce a new spine for Teichmueller space of closed hyperbolic surfaces. We claim the new spine consists of hyperbolic surfaces whose shortest essential nonseparating curves are homologically filling. The spine is distinct from Thurston’s original proposal. Here we post a preprint.

On Northern Aurora As a Source of Ionic and Electrodynamic Energy for Northern Communities: Asking the Question.

Ampere Faraday and Benjamin Franklin walk into the north pole. What happens? Today JHMLabs begins a series of posts on NRC Challenge Program with an idea on the northern aurora as potential electrodynamic power source for northern communities. This would involve tapping in and interacting with the plasma currents just above the ionosphere. This requires further study on Langmuir sheath structure of Earth, i.e. directly understanding the formation of the ionosphere as directly caused by the polar Birkeland currents in the Earth-Sun circuit, and beyond…Is there a way to direct and interact with the huge ionic and electrodynamic currents that are beyond the double layer? Is it possible to capture lightning in a bottle?

What is Proper Time in Special Relativity?

Sequel to our post on What is Time? Here we briefly discuss proper time as defined in special relativity. We argue that proper time (tau) evidently does not have units of time as typically understood, since Lorentz lengths \(ds'\) (defined as squareroot of difference of squared lengths) do not have units equal to the units of Riemannian length (defined as squareroot of sum of squared lengths). This might seem pedantic at first glance, but it’s absolutely necessary to observe. The Riemannian length is the Pythagorean sum of squares, and there are always right angled triangles to construct and represent all the Riemannian lengths. But the Lorentz length is actually anti- Pythagoras, and looks to misrepresent differences of squares as if they were sums of squares. This leads to reverse triangle inequalities, which by definition are anti-Riemannian. The point is we prefer Classical Physics 2.0 where time is defined after Mach as matter in motion, and we avoid the Lorentz formalism.

2025 Year of World Magnetic Model

World Magnetic Model 2025. We begin with surprising review of Gauss’ 1836 memoir on General Theory of Terrestrial Magnetism which is amazing for it’s references to Amperes molecular current hypothesis and the aurora. Conclusion is that Gauss is correct assuming his classical magnetic fluid hypothesis, but Ampere’s electrodynamic cylinder and Poisson’s magnetic dipole surfaces are not complete. We identify our starting point for an Amperian Birkeland update to the standard Gauss spherical harmonic model, and this is subject of further work.

What is Time?

Question: What is time? Answer: Time is matter in motion. A brief post on a fundamental question.

Vintage Selling and Generative Matchmaking (Part 1)

We have an idea on generative matchmaking in vintage clothing. This means generating items and complete outfits with confidence to customers. Easier said than done. Here we present the hypothesis that colour pattern preferences are the dominant factor when buying clothes. This means that a person’s outfits consists of combinations of colour patterns. This is necessary before any so-called machine learning methods can be applied.

Remark on the Inherent Double Risk of Premature Quantum Adoption

We maintain that \(P\) is not equal to \(NP\) (following C.A. Feinstein) and that classical encryption is as secure as ever, quantum or no quantum computer. In this brief note we observe a compound risk inherent in premature quantum adoption. Quantum algorithms simultaneously claim to break the classical encryption protocols, while also claiming to offer quantum secure schemes. This double pressure is prompting authorities to a risky proposition. But why replace a system that remains secure with a replacement where everything is in beta stage.

Ampere, Weber, and Magnetism the Disposable Hypothesis

Magnetism interacts in every fundamental experiment in physics, yet magnetism is not so well understood. Here we review Andre Marie Ampere’s fundamantal principle of the equivalence of magneto and electrical forces, and it’s consequences. For example we recall Ampere’s observation that the trivial calculus identity \(div(curl)=0\) essentially implies the nonexistence of magnetic monopoles and one of Maxwell’s equations, namely \(div(B)=0\). This again is fundamental insight of Ampere.

Sansbury and Bohr. Who is More Energetically Probable?

Is Bohr’s planetary model of the hydrogen atom \([+1, -1]\) really more probable than Weber-Sansbury’s model of \([[+2, -1], [+1, -2]]\)? It’s a billion dollar question isn’t it?

Economics of Moving and Delivery.

How to save money on moving and delivery? Basically prepare and pack as much as possible into as many closed cardboard boxes as necessary, and order a large truck for transport. We also discuss the basic questions which are most useful for estimating the total cost of moving a household. This manages the client’s expectations, but also allows the moving manager to maximize their profit and schedule themselves accordingly

Computational Complexity of Fibonacci Sequences.

We review the complexity of Fibonacci’s sequence \(1, 1, 2, 3, 5, 8, 13,\) etc., and its relation to S. Wolfram’s informal definition of computational irreducibility. We consider whether topological irreducibility has analogy to computation, and this is somewhat speculative, as we are looking for strategies to prove that \(O(log_2~N)\) is the minimal complexity of computing the \(N\)th Fibonacci element \(f(N)\).

Weber Hamiltonian Gibbs Liouville Measure on State Space.

We examine the Hamilton equations for Weber’s potential in an isolated two-body system. We construct an invariant measure on the xv state space which is distinct from the conventional Gibbs Liouville measure. The invariant measure is necessary background measure from which we can define entropy of distributions.

On Yao’s Millionaire Problem. Part 1.

We begin the study of Yao’s Millionaire Problem, approaching via convex analysis. Two players have secret points, and the first player to guess an affine function separating the secrets wins. The question is whether the optimal strategy is uniform on the domain, or whether there is some variation in the density. This is elaborated below using both python and some elementary convex analysis

Bookstores and Image to ISBN Problem

People don’t buy what they don’t see. Take pictures of bookshelves, get an ordered index of ISBN numbers. Get books seen and sold.

Mathematics of Vintage Selling

This is our introductory pitch on math and vintage selling.

Mathematical Review of Faraday Cages. A Gap In the Literature.

Preliminary article. We review the basic properties of Faraday cages and a curious absence of any mathematical proof of their supposed properties from the Maxwell field equations. This leads to some basic questions.

Measuring Tapes and Physics

We present our preliminary thoughts on a new digital measuring tape. This is our answer to the question of dude would you hold my tape.

Weber, Work, Energy

Einstein’s \(E=mc^2\) is the most famous formula in history, but what does it mean? Here we emphasize that Einstein derived the formula from mathematics in 1905, but Wilhelm Weber derived the…

Modified Fizeau Sansbury Spinning Wheel Experiment

We propose a modified Fizeau-Sansbury spinning sawtooth experiment to answer the outstanding question: is light even something that travels in vacuum at all?