Xah Talk Show 2026-03-07 Ep777. Wolfram language coding. Geometry. Light ray reflection on curve. caustics.

• https://youtu.be/-17CSHzEUSs

• me coding on wolfram language, geometry, writing code that draw caustics of a curve.
• meaning, light ray reflections and refractions.
• come just watch me code, or ask questions.

highlights

• python coders, javascript coders, java, c++ coders, must watch.
• real-time formatting of code and 2d typeset math.
• https://youtu.be/-17CSHzEUSs?t=73m28s
• Wolfram language.

Video Summary (Generated by AI, Edited by Human.)

In this video (0:05), Xah Lee live-codes in the Wolfram Language to draw geometrical caustics, which are the envelopes of light rays reflected off or refracted through curves (0:19). The goal is to visualize complex mathematical curves that were previously documented in his visual dictionary 30 years ago (0:48).

Video Highlights:

• Demonstration: Xah shows images of caustic curves generated by parabolas (0:52) and discusses the properties of a nephroid curve (17:16).
• Mathematical Explanation: The video explains how to find the tangent line to a curve, calculate the normal line, and use these to compute the reflection of light rays (13:15, 30:07).
• Practical Example: Xah attempts to demonstrate the cardioid effect inside a coffee cup, explaining that the liquid level and light strength are crucial for visibility (7:29-9:54).
• Coding in Wolfram Language: Xah writes code to generate these visuals using parametric equations for circles and other shapes (22:10). He also highlights unique features of the Wolfram Notebook editor, such as expanding selection based on syntactical units (1:15:30).
• Comparison: Xah discusses the similarities between Wolfram Language and Lisp (1:20:00).

• Visual Dictionary of Special Plane Curves

• Wolfram: Download Wolfram Engine
• Wolfram Language in Depth (tutorial)
• Wolfram language packages by Xah Lee
• Wolfram: Plane Curve Generator Package 📦

• Emacs: Xah Fly Keys 📦

• Ultimate Hacking Keyboard 80 (UHK 80)
• Nulea M505 Trackball
• Huion H640P Drawing Tablet

• Nephroid
• Cardioid
• Tangent
• Deltoid

• https://blogs.ams.org/visualinsight/2013/11/15/astroid-as-catacaustic-of-deltoid/

• show proof that caustics of parallel rays on deltoid is an astroid
• https://x.com/i/grok/share/60edb71fd0844fa59680cd618b420f04

• Syntax: Wolfram Language vs Lisp (2013)

• Wolfram Language Design, LISP / APL History
• Wolfram language vs LISP
• Concepts and Confusions of Prefix, Infix, Postfix and Lisp Notations (2006)
• LISP Infix Syntax Survey (2013)
• Fundamental Problems of Lisp, Syntax Irregularity (2008)
• Xah Talk Show 2024-06-11 Ep558, Which is Best Lisp? Common Lisp, Scheme, Elisp, Clojure, Wolfram Language