Boole vs Hegel vs Wittgenstein. Triviality of Logic and Contingency of the World.
Quid est veritas?
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.
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.
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
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.
