#Introduction

Hi!

I’m a researcher and administrator at the University of Maryland. I live in Washington, DC, with my wife and three kids. I lived in many different places following a scientific career but then left active duty to focus on my family. I’m slowly getting back to research these days, with the intention to share what I learn more broadly.

My main contribution to science is a family of coordinate transformations:
\[ t = \tau - h(\rho), \]
\[ r = g(\rho), \]
where \(g(.)\) is a compactification that maps an infinite domain in \(r\) to a finite domain in \(\rho\) and \(h(.)\) is a height function that suitably transforms time so that the spatial surfaces with constant $\tau$ have asymptotically hyperbolic geometry.

That’s it? A coordinate transformation?

Well, sure, I did other things, too. But yes, that’s the main thing. These are called #hyperboloidal coordinates. It took me years of exploration to understand the implications of this family of coordinates. Still working on it.

These transformations are particularly relevant for wave equations. God is a wave function, so studying wave equations is clearly the most important thing 😉

I’ll share stuff about relativity, black holes, gravitational waves, and other wave equations, but maybe even more about #HyperbolicGeometry. I recently became convinced that hyperbolic geometry is the geometry of Nature. I’d like to understand what I mean a little bit better. I’ll seek people who know more about hyperbolic geometry than I do and share what I encounter along the way.

Hyperbolic Ball packings from Coxeter groups!

These two packings are the same, generated from the same Coxeter group:
\[ \begin{pmatrix}1&3&3&4&3\\3&1&3&4&4\\3&3&1&2&3\\4&4&2&1&3\\3&4&3&3&1\end{pmatrix} \]

The first image is 2D: it draws a plane slice of the 3D ball packing in the second image.

Check for more images at

https://github.com/neozhaoliang/Hyperbolic-Honeycombs

#HyperbolicHoneycombs #HyperbolicGeometry

"Who Pioneers the Concept of 4-Dimensional Spacetime" by Areeba Merriam 🔗 https://www.cantorsparadise.com/who-pioneers-the-concept-of-4-dimensional-spacetime-ae705369c1b0

#Spacetime #Time #Space #FourDimensionalSpacetime #RelativisticMechanics #NewtonianMechanics #EuclideanGeometry #HyperbolicGeometry #AlbertEinstein #Einstein #DavidHilbert #Hilbert #Lobachevsky #Riemann #Bolyai #HermannMinkowski #Minkowski #Poincaré #Framework #Relativity #GeneralRelativity #SpecialRelativity #Geometry #Mathematics #RelativisticPhysics

People liked the #HyperbolicGeometry bit, so let's dive into it a bit more.

We cannot represent faithfully hyperbolic geometry in this Euclidean(ish) world. So, we need models!

#SciComm #Maths

#introduction

I've joined up to better explore this place - mostly the mathy bits so I can share things with my students!

Always looking for new things about #stellation, #statistics, #logic, #intuitionisticlogic, #geometry, and #hyperbolicgeometry. Oh, and that magical thing call #sleep that seems to happen to other people!

For discoverability, here are some topics I like, as hashtags:

#ArtificialChemistry
#ArtificialLife
#CellularAutomata
#ComputerVision
#Fractals
#HyperbolicGeometry
#ReactionDiffusion