Anıl Zenginoğlu
Anıl Zenginoğlu
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How to solve wave equations on unbounded domains
I demonstrate the hyperboloidal compactification method for numerically solving wave equations on unbounded domains. Animations and code included!
Anıl Zenginoğlu
Dec 14, 2023
12 min read
Excising the universe over the rainbow
The last three papers by Charles W. Misner were about the hyperboloidal approach. This post is a short review of these papers motivated by the Misner Memorial Symposium on November 11, 2023.
Anıl Zenginoğlu
Nov 27, 2023
14 min read
Splitting Spacetime
Hyperboloidal hypersurfaces split spacetime into space and time. Their mathematical definition connects to a physical principle that may be useful as a mental image for the quantum foam.
Anıl Zenginoğlu
Sep 20, 2023
11 min read
Cross-entropy
Cross-entropy is a measure of the difference between two probability distributions. It also plays a role in the information-theoretic formulation of the Second Law of Thermodynamics, thereby providing a bridge between physics and machine learning.
Anıl Zenginoğlu
Apr 2, 2023
13 min read
Learning Machine Learning
This is a short tutorial on machine learning. We implement a single-layer neural network to recognize images of handwritten digits from the MNIST dataset using only NumPy as a simple starting point for further experimentation. A
Colab
notebook is available.
Anıl Zenginoğlu
Dec 8, 2022
12 min read
Tutorial
How to draw Penrose diagrams
This is the first installment of a three-piece series on Penrose diagrams and the associated conformal compactification procedure. This post is a technical how-to describing how I draw quantitatively accurate Penrose diagrams to illustrate the causal structure of time surfaces using free and open-source software.
Anıl Zenginoğlu
Sep 1, 2022
10 min read
Tutorial
Jealous of hyperbolic fish
If you are a physicist jealous of hyperbolic fish living in
Escher
’s
Circle Limit III
, I have good news for you! The asymptotic geometry of space is hyperbolic if you want it to be.
Anıl Zenginoğlu
Jan 23, 2022
9 min read
Research
Special relativity as hyperbolic geometry
Hyperbolic geometry provides a natural setting for special relativity. This viewpoint simplifies calculations, provides insights into the theory, and has applications beyond special relativity in machine learning and general relativity.
Anıl Zenginoğlu
Nov 6, 2021
10 min read
Research
Hyperboloidal Holography
Minkowski spacetime in hyperboloidal coordinates takes the form of a stack of hyperbolic manifolds with the same spatial geometry as anti-de Sitter spacetime. Is there a hyperboloidal realization of holography for isolated systems?
Oct 7, 2021
11 min read
Research
How far is infinity?
Infinity may be closer than you think.
Anıl Zenginoğlu
Sep 8, 2021
6 min read
Research
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